PNP Equations with Steric Effects: A Model of Ion Flow through Channels

Department of Applied Mathematics, Feng Chia University, 100 Wen-Hwa Road, Taichung, Taiwan 40724
Department of Mathematics, Taida Institute for Mathematical Sciences (TIMS), No. 1, Sec. 4, National Taiwan University, Roosevelt Road, Taipei 106, Taiwan
Department of Mathematics, Pennsylvania State University University Park, Pennsylvania 16802, United States
Department of Molecular Biophysics and Physiology, Rush University, 1653 West Congress Parkway, Chicago, Illinois 60612, United States
J. Phys. Chem. B, 2012, 116 (37), pp 11422–11441
DOI: 10.1021/jp305273n
Publication Date (Web): August 17, 2012
Copyright © 2012 American Chemical Society
Thermodynamics, Thermochemistry, and Thermal Properties

Abstract

Abstract Image

The flow of current through an ionic channel is studied using the energetic variational approach of Liu applied to the primitive (implicit solvent) model of ionic solutions. This approach allows the derivation of self-consistent (Euler–Lagrange) equations to describe the flow of spheres through channels. The partial differential equations derived involve the global interactions of the spheres and are replaced here with a local approximation that we call steric PNP (Poisson–Nernst–Planck) (Lin, T. C.; Eisenberg, B. To be submitted for publication, 2012). Kong combining rules are used and a range of values of steric interaction parameters are studied. These parameters change the energetics of steric interaction but have no effect on diffusion coefficients in models and simulations. Calculations are made for the calcium (EEEE, EEEA) and sodium channels (DEKA) previously studied in Monte Carlo simulations with comparable results. The biological function is quite sensitive to the steric interaction parameters, and we speculate that a wide range of the function of channels and transporters, even enzymes, might depend on such terms. We point out that classical theories of channels, transporters, and enzymes depend on ideal representations of ionic solutions in which nothing interacts with nothing, even in the enormous concentrations found near and in these proteins or near electrodes in electrochemical cells for that matter. We suggest that a theory designed to handle interactions might be more appropriate. We show that one such theory is feasible and computable: steric PNP allows a direct comparison with experiments measuring flows as well as equilibrium properties. Steric PNP combines atomic and macroscales in a computable formulation that allows the calculation of the macroscopic effects of changes in atomic scale structures (size 10–10 meters) studied very extensively in channology and molecular biology.

Introduction

Ion channels are protein molecules that conduct ions (such as Na+, K+, Ca2+, and Cl– that might be named bioions because of their universal importance in biology) through a narrow pore of fixed charge formed by the amino acids of the channel protein.(-2) Membranes are otherwise quite impermeable to natural substances, so channels are gatekeepers for cells. Channels are natural nanovalves that control a wide range of biological function.(3) Channels open and close stochastically, allowing ionic current to flow and forming a path for solute movement when they are open.(4-6) Only electrodiffusion moves ions through channels, so this biological system is like a hole in a wall that we should be able to understand physically.(7-9)
Ion channels are responsible for signaling in the nervous system. Ion channels are responsible for the coordination of muscle contraction and the transport of dissolved substances and water in all tissues. Each of these functions has been so important for so long that evolution has probably produced a nearly optimal adaptation within physical constraints and conserved it using the same design principle again and again.
Investigation of the physical mechanisms of current flow has just begun, although there is no shortage of descriptive metaphors in the literature of structural and molecular biology and biophysics.(2) The fundamental problem in a physical analysis is one of scale.(10) Mutations in single amino acids, which sometimes change only a handful of atoms involving perhaps just one permanent charge (radius of 0.1 nm), have dramatic biological effects. Such sensitivity comes as no surprise to the biologically oriented chemist or physicist.
Theories and simulations must account for the sensitivity of macroscopic function to atomic detail. Ion channels are nanovalves designed so that a few atoms, coded by the genetic blueprint of the protein, can control macroscopic function: that is what nanovalves (and channels) are all about. Theories and simulations must deal with 0.1 nm structural changes in charged groups that produce changes on the macroscopic scale of function. Structures as small as 0.1 nm move, and cannot be stopped from moving, via thermal (nearly Brownian) motion in 10–16 s. Their trajectories reverse direction infinitely often, whereas biology moves on time scales of 10–3 s or so in much simpler trajectories. The central physical issue is how to preserve this sensitivity to tiny structures while averaging over trajectories with such complex behavior over a 1013 range of time. Other scales also pose problems. Physics and biology and simulations of physics and biology must cope with a wide range of time scales and concentrations(10) as well as the immense range and strength of the electric field.(11-15)
The extremes of length, time, and concentration scales are all involved in the natural function of ion channels (or any nanovalve), so theory and simulations must deal with all of these extremes together. It is not likely that atomic-scale simulations by themselves will be able to deal with these, all together in finite time. Rather, reduced models of the type used widely in the physical sciences are more likely to be helpful in the foreseeable future.
A useful reduced model will include atomic-scale structural variables that determine macroscopic function. Sensitivity functions, determined by the theory of inverse problems, can help evaluate and construct reduced models. Biological function will be sensitive to important parameters and insensitive to others. The utility of these models can be evaluated by solving the relevant inverse problem for channels(16-18) using general methods.(19, 20)
So far, the most studied reduced model for ion flow in the bulk and in channels is the Poisson–Nernst–Planck (PNP) equation.(11, 12, 21-26) Although this model has had some success in dealing with experimental data,(22, 27-51) it does not include correlations introduced by the finite diameter of ions,(52) and these are of great importance in determining the selectivity of channels(9, 53, 54) and the properties of ionic solutions in general.(55-69) Crudely speaking, PNP is to nonequilibrium systems (such as channels) what Poisson–Boltzmann is to static systems: both are first approximations, useful in showing the crucial role of the electric field,(11, 12, 14, 70) the ionic atmosphere, and screening.(71) Neither are adequate models for ionic solutions such as seawater or the related solutions inside and outside biological cells.(52, 72-74)
Recently, work by Eisenberg, et al.,(75-78) built on the energetic variational theory of complex fluids,(77, 79-86) has developed a new set of PNP equations to implement and generalize an approach to selectivity started by Nonner and Eisenberg.(87-92) Nonner and Eisenberg considered a simplified model with ions (and side chains of the channel protein) represented as spheres of different finite sizes. They have shown in a long series of papers that important (static) selectivity properties of some significant types of ion channels can be explained with this model (reviewed in refs 9, 53, and 93). They have in fact constructed a single model with two adjustable parameters (diameter of channel, dielectric coefficient of protein, both set only once to unchanging values) using a single set of (crystal) radii of ions that fits the detailed and complex selectivity properties of two quite different types of channels, the heart CaV calcium channel(90, 94-98) and the nerve NaV sodium channel.(9, 91, 99) The theory accounts for the properties observed in solutions of different composition, with concentrations ranging from 10–7 to 0.5 M. When the side chains in the model are amino acid residues Asp-Glu-Lys-Ala, the channel has net charge of −1 although it is very salty (the magnitude of net charge is 3). The channel then is a DEKA sodium channel. When the side chains are Asp-Glu-Glu-Ala, then the channel is even saltier (the channel has net charge of −3). It is a DEEA calcium channel with quite different properties, although no parameters in the model are changed whatsoever, except the side chains that determine selectivity.
Most importantly, channels have been built according to the prescription of this theory, and they behave as predicted.(100-102) In studying another channel, the ryanodine receptor (of enormous biological importance as the final regulator of Ca2+ concentration in muscle and thus of contractions), Gillespie successfully predicted subtle and complex properties of selectivity and permeation before experiments were done and also the properties of drastic mutants in a wide range of solutions before the experiments were performed,(103-112) extending work on an earlier unsuccessful reduced model of the receptor that did not deal with the finite diameter of ions.(30, 32, 113, 114) One of the Meissner–Gillespie mutants reduces the permanent charge from 13 M to zero, yet Gillespie’s theory fits current voltage relations in several solutions with nearly the same approximately eight parameters as for wild type.
The calculations reported here extend the pioneering calculations of Hyon(75, 76, 78) by applying the energy variational approach to ion channels.(115) The bath and boundary condition treatments are somewhat different. A full 3D treatment is needed before the appropriate 1D approximation (particularly boundary conditions) can be determined without ambiguity.(25, 43, 88, 116-121)
Here, we simulate the properties of the family of calcium channels CaV (reviewed in refs 9 and 98) and sodium channels NaV(91, 99) using parameters already shown to fit a wide range of stationary (time-independent) experimental data in a variety of “symmetrical” solutions, which are designed so that current does not flow. Our results agree with previous equilibrium binding results and extend them to the world of current–voltage relations using a model and numerical methods that can be easily implemented on inexpensive computers. Current–voltage relations can be computed in a few hours on a notebook system.

Mathematical Model

Poisson–Nernst–Planck (PNP) Equations with Size Effects
The energy functional and the procedures for handling it with variational calculus are central to the energetic variational approach (EnVarA) formulated by Liu, more than anyone else. Liu’s approach is described in refs 75, 79–82, 84, 115, and 122–126. The “energy” of EnVarA is shown to correspond to the Helmholtz free energy of classical thermodynamics (in applicable equilibrium systems) in a recent article.(127) The application of EnVarA to membranes,(128) biological cells and tissues,(77) and ions, in channels and bulk solution, is described in detail in refs 1 and 75−78 in a way that is accessible to physicists and chemists without extensive experience with variational methods.
The energy functional for the ion channel is defined by(1)where ci and zi are concentration and valence for the ith ion (i = 1,···, N – 1); cN = cO–1/2 is the concentration for side chain O–1/2 (as in the glutamate side chain) with valence zN = zO–1/2 = −1/2 located in the filter only; is the electrostatic potential; kB is the Boltzmann constant; T is the absolute temperature; N is the number of ions; e is the unit charge; ρ0 is the permanent charge density; cO–1/2 is the concentration of the spherical “side chain” with valence zO–1/2 = −1/2 located in the filter only; V is the restraining potential that keeps the side chain inside the filter at all times; ai and aj are the radii of ions i and j; and εij is the energy coupling constant between ion i (including side chain O–1/2) and j (including side chain O–1/2). The last term is the repulsive part of the hard sphere potential that keeps ions apart.
The hard sphere repulsion characterizes the finite-size effect of ions and side chains inside the filter. These repulsive terms obviously depend on the chemical species and are called combining rules when they describe the interactions of different species. We discuss the combining rules later.
The basic reasoning is that the ion filter is so narrow that extra energy is needed to crowd ions into its tiny volume.(-9, 53, 54, 87, 89, 95-97, 99, 101, 102, 104, 129-131) Without finite size effects, the total energy will yield the traditional PNP equations.
The Euler–Lagrange equation (eq 1) will introduce PNP equations with size effects that depend on the global properties of the problem in the following way(2)(3)where flux Ji is(4)There is extra flux from the restraining potential that keeps side chains within the selectivity filter:(5)These equations are very similar to the drift-diffusion equations of semiconductors,(11, 12, 23, 24, 116, 121, 132-149) with the first term in the flux being the diffusion term and the second one being the drift term driven by the electrostatic potential of the field.
The third term involves a mutual repulsive force and interparticle hard sphere potential that is not typically found in semiconductor equations (although the semiconductor literature is so large that the volume exclusion of finite-sized holes and electrons is probably found somewhere that we do not know). This term includes forces usually called Lennard-Jones and depends globally on the properties of the solution everywhere because of the range of the integral on the right-hand side of eqs 4 and 5.
We call attention to the important role that the coefficients of these steric terms will have in determining biological function. The role of these steric terms will be somewhat different in our calculations from those in classical equilibrium analysis of ionic solutions using Monte Carlo simulations, for example. The cross terms in our expression appear as part of partial differential equations. These terms will then have effects on all terms in the solution of those partial differential equations. The integration process spreads out the effects of the cross terms. They propagate into everything as the partial differential equations are solved. The usual classical equilibrium treatment of Monte Carlo simulations is likely to produce different radial distribution functions from those produced by our differential equations, but a detailed comparison of MC and EnVarA calculations of absolutely identical models is necessary to determine the significance (or even existence) of this effect.
The steric cross terms, often called combining rules, turn out to have significant effects on the properties of ion channels. As mentioned, we use the Kong combining rules(150) to describe the repulsion between ionic spheres because they seem to be more accurate and justified(151, 152) than the more common Lorentz–Berthelot rules. It will turn out that the biological properties of ion channels are quite sensitive to these terms, but the choice of parameters seems to require detailed fitting to the properties of specific biological channels and transporters. We do not know what the effects of attractive terms (known to be present in bulk solutions) will be when we include them. We reiterate that these terms do not change the diffusion coefficients in our model.
One might think that simulations in full atomic detail (of molecular dynamics) would give good estimates of the combining rules, but sadly that is not the case. These simulations of molecular dynamics use combining rules (similar or identical to what we use in our reduced models) in the force fields of their own calculations.(150-152) We cannot use molecular dynamics to justify our combining rules because molecular dynamics itself uses those rules. It is possible that no one knows what cross terms to use in bulk solution. It seems likely that no one knows what cross terms should be used inside a channel or between side chains and ions. Indeed, it is difficult to conceive of experiments that might measure these inside channels with reasonable reliability.
Returning to the mathematical issues, we note that the singular convolution integral term can be regularized by a cutoff in the integration domain or simply by letting the integrand be 0 when |x – y| ≤ ai + aj. However, the regularized term still produces numerical difficulty and is very time-consuming to compute, particularly at high dimensions, even if fast Fourier transform methods are used. We have tried. In addition, computing the convolution term generates an artificial boundary layer with a length of several grid spacings that needs to be filtered out and may have troublesome qualitative effects that are not so easy to remove by any local filtering because it has some of the properties of aliasing. Aliasing has devastating effects if not handled properly in both temporal and spatial systems that are treated as periodic when they are not.
We turn now to a simplified steric model that is much easier to compute because it uses only a local representation of interatomic forces. As we shall see, this steric model allows the computation of a large range of interesting phenomena, despite this simplification.
Local PNP Equations with Steric Effects (PNP–Steric Equations)
(6)and (7)where δ is a small number for the cutoff length, cδ is a dimensionless integration factor associated with δ, and d is the dimension. Here, the symmetry εij = εji has been assumed for notational convenience. To obtain this model, we have two important considerations: (1) the localization of the nonlocal size effects and (2) the finite truncations, which make the term local. Compared to the standard PNP equations, the PNP–steric equations have extra nonlinear differential terms (in the spatial variables) called steric effects. These represent the effective averaging/coarse graining of microscopic size effects for the macroscopic/continuum scales.
It should be clearly understood that coarsening terms of this sort are used throughout the chemistry literature, including within the simulations of molecular dynamics. The potentials of molecular dynamics simulations of proteins are not transferrable from quantum mechanical simulations of interatomic forces. The force fields that are used in every time step of an atomic-scale simulation include terms such as our εij justified only in the way that we have. Thus, molecular dynamics simulations depend on effective parameters, as do ours. Molecular dynamics simulations are no more derivable from quantum mechanics than are our models.
The main difficulty with eqs 2–5 comes from the convolution integral of the energy functional E with the following form(8)Usually, one would approximate the above integral by truncating the kernel 1/|x – y|12 with the cutoff length δ, which causes kernel 1/|x – y|12 to have a flat top when |x – y| ≤ δ. To approach kernel 1/|x – y|12, the length δ must be set as a small number tending to zero. One may expect that the smaller the cutoff length δ, the better the approximation. However, because of the effect of high-frequency Fourier modes, the approximation may lose the accuracy of numerical computations and makes numerical simulations difficult and inefficient.(153)
To deal with the effect of high-frequency Fourier modes, band-limited functions are used to cut off high-frequency Fourier modes. The functions act as optical filters by selectively transmitting light in a particular range of wavelengths. Band-limited functions play important roles in the design of signal transmission systems with many applications in engineering, physics, and statistics.(154) See also any textbook on digital signal or image processing. In ref 1, a class of band-limited functions depending on the length δ is found to approximate the kernel 1/|x – y|12 and allow the derivation of the PNP–steric equations. The same approach can be used to modify the Poisson–Boltzmann equations used widely in physical chemistry, applied mathematics, and molecular biology.(70, 155) Once modified, these new steric Poisson–Boltzmann equations are particularly useful for the study of crowded boundary layers near charged walls, including the special behavior usually attributed to Stern layers. As the length δ goes to zero, the singular integral (eq 8) can be approximated by the integral Sδ ∫ ci(x) cj(x)dx with Sδ ≈ δ–12+d. Hence, the energy functional (eq 1) can also be approximated bywhich gives eqs 2, 3, 6, and 7, where gij = εij(ai+aj)12Sδ for i = 1,···, N–1 and gNj = εNj(ai + aj)12cδSδ.
The PNP–steric equations (eqs 2, 3, 6, and 7) are convection–diffusion equations following the energy dissipation lawwhere μi = ∑j = 1N gijcj is the chemical potential.
Note that eqs 6 and 7 contain no singular integrals such as in eqs 4 and 5 but have extra nonlinear differential terms. These extra nonlinear terms are crucial to simulating the selectivity of ion channels that cannot be found by simulating the standard PNP equations. Hence, the (local) PNP–steric equations are more useful than the standard PNP equations and are significantly more efficient and easy to work with than the global equations of the EnVarA treatment (eqs 2–5) discussed in the Introduction and Discussion sections of this article. These extra local terms in differential equations 6 and 7 have global effects when the differential equations are solved. Thus, pair correlation functions described by the solutions to differential equations 4 and 5 may have properties not present in classical equilibrium analyses containing local steric forces. (Classical analyses often deal only with positions and correlations and not with solutions of differential equations containing the forces.) Detailed fitting to specific experimental data is needed to compare the solutions of the local steric differential equations (eqs 6 and 7), the solutions of the more general differential equations (eqs 4 and 5), and the actual nonlocal phenomena of experiments.
We Adopt the PNP–Steric Equations
We replace eqs 4 and 5 with more approximate eqs 6 and 7 from now on. The real 3D geometry of an ion channel shown in Figure 1 is replaced with the simple axisymmetric geometry shown in Figure 2, with eqs 2, 3, and 6 valid in Ω and eq 7 valid only in Ωf, where Ωf is the filter part of the channel and Ωf  Ω. The associated boundary conditions are also shown in Figure 2, with the Dirichlet boundary conditions specified for both the ionic concentration and potential at the channel inlet (left end) and outlet (right end); no-flux boundary conditions are set for both the ionic concentration and potential at the side wall of the channel. Extra no-flux boundary conditions are set for side chains JO–1/2 = 0 at the interfaces (z = α and β) between the filter and the other part of the channel because side-chain molecules are free to move inside the filter only.
figure

Figure 1. Typical geometry configuration of an ion channel. The usual time scale for an ion passing through the channel is 200 ns. Specifically, a channel passing 1 pA of current with an occupancy of 1 ion has a mean passage time of 160 ns.

figure

Figure 2. Cartoon of the configuration of an ion channel with specified boundary conditions. Ω denotes the domain of the whole channel; Ωf denotes the filter part of the channel bounded by α ≤ z ≤ β and a side wall; n̂ is the unit outward vector normal to the side wall.

This model is meant to be nearly identical to that used in the many papers using Monte Carlo methods reviewed in ref 9, particularly the key papers.(54, 90, 93-96, 99, 156) The treatment of the region outside the channel and thus buildup phenomena are different from those in refs 75, 76, and 78.
Because no-flux boundary conditions are implemented for both the ionic concentration and potential at the side walls (orthogonal to the direction of current flow), this 2D problem (eqs 2, 3, 6, and 7) can be well approximated by a reduced 1D problem along the axial direction z, with a cross-sectional area factor A(z) included as in refs 25, 43, 88, and 116−121, described succinctly in ref 119, and perhaps included most carefully in the 3D spectral element calculations of Hollerbach.(-34, 43) Of course, some phenomena cannot be reproduced well in one dimension. See Figure 7 in ref 99.
The resulting 1D equations are(9)(10)(11)and(12)with boundary and interface conditions(13)and(14)The no-flux interface conditions for the side chains guarantee that side chains are not allowed to leave the filter. Mass conservation is preserved inside the filter:Also, in eqs 11 and 12, the Einstein relation is used for both the drift current and hard-sphere-potential flux, which is μe,i = Di/kBT, μLJ,i = Di/kBT(i = 1,···, N – 1), and μV,N = DN/kBT, where μe,i and μL J,i are the electrical mobility and the mobility associated with the hard sphere potential for ionic species i and μV,N is the mobility associated with the restraining potential for glutamate. Note that Di and i do not have to be homogeneous in space, nor do the dielectric coefficients of the solution and channel protein. We have not yet studied the effects of variation in these parameters, however. Usually, Di and i are set to 1/20th of their bulk solution values inside the channel filter but are set to bulk solution values in the rest of the channel as discussed at length in the Supporting Information and body of ref 109.
Dimensionless Equations
Nondimensionalization of the governing equations is especially important in discovering the structure, such as the boundary or internal layer, of the solution of PNP-type equations in advance, and so perturbation methods,(21, 24, 25, 135, 157) including some using the powerful and rigorous methods of geometrical perturbation theory,(24, 147, 148) have been used. We follow this work and scale the dimensional variables by physically meaningful quantitieswhere s denotes all length scales and L = rmin (the narrowest radius in the channel shown in Figure 2) unless otherwise specified. Note the scaling with respect to the physical dimension and not the Debye length. The Debye length varies with concentration and concentration varies with location and conditions. Equation 8 becomes(15)where Γ = λ2/L2 and the Debye length is λ = (εkBT/cmaxe2)1/2. Γ is the reciprocal of the length of the channel in units of Debye lengths. Note that Γ can vary dramatically with location and conditions if the contents of the channel vary with location or conditions. In the channels dealt with here, the contents of the channel are “buffered” by the charge of the side chains of the protein, most clearly in calcium channels EEEE and EEEA but also for the salty DEKA channel. Such buffering is not expected in all channels (e.g., potassium channels).
Equations 9–11 then become(16)(17)(18)We remove all of the tilde decorations () and rewrite the dimensionless governing equations (eqs 15–18) for the mixture of Na+, Ca2+, Cl–, and O–1/2 as follows:(19)(20)(21)(22)Note that ε̃ijcδδ̃–9(ãi + ãj)12 in eq 17 is lumped into g̃ij along with cδδ̃–9 and is assumed to be the same for all species. Lennard-Jones parameters ε̃ij are obtained from the literature for alike species (i = j) and computed by Kong’s rule for unlike species (i ≠ j). They do not change diffusion coefficients in our model or calculations.
Channel Wall Shape Function
The wall shape function g(z) in Figure 2 can be arbitrarily specified, for example, g(z) = ((rmaz – rmin)/((a/2)2p))(z – a/2)2p + rmin, or nondimensionalized asWe remove all of the tilde accents () and write(23)In our calculation, we choose p = 4. The geometrical parameters are typically a = 50 Å, rmin = 3.5 Å, rmax = 40 Å, and D = DNa,bulk = 1.334 × 10–5 cm2/s . We set ε = 30ε0 inside the filter; in the rest of the channel, ε = εwater = 80ε0. For a typical cmax = 100 mM, we have Debye length λ = 8.48 Å and Γ=5.87 inside the filter and λ = 13.8 Å and Γ = 15.65 outside the filter. The above Γ values are based on L = rmin = 3.5Å.
The fact that Γ is not small implies that no internal or boundary layer is expected in the radial (transverse) direction. However, we sometimes choose L = a = 50 Å and Γ = 0.0288 inside the filter and Γ = 0.07668 outside the filter. Though Γ is not as small as in semiconductor devices, an internal/boundary layer is still expected in the lateral (axial) direction. We must not forget that the nonlocal hard sphere potential term (present in ionic solutions but not in semiconductors) may produce internal layers as well. See Figure 7 in ref 99.
A noticeable problem in all PNP (and Poisson–Boltzmann) theories without finite size are internal boundary layers near all boundaries with charge (permanent or induced). Such layers are customarily removed by introducing a single distance of closest approach for all ions, however ill-defined. Of course, no single distance of closest approach can deal with ions of different diameters, a problem that Debye, Hückel, and Bjerrum were evidently quite aware of. The need for multiple distances of closest approach (different for each ion and very nonideal, depending on each other and everything else in the system) means that the complex layering phenomena seen near walls of charge can have counterparts in channels. Indeed, complex layering is expected when ionic solutions are mixtures, such as the salt water in oceans or biology, and spatial inhomogeneities are present. Reference 158 is a gateway into the enormous chemical literature on layering phenomena near walls of charge. Reference 78 is a mathematical approach. Layering in ionic solutions might be able to produce nonlinear phenomena as important as pn junctions or even pnp junctions in semiconductors.
One might argue the validity of choosing rmin = 3.5 Å and wonder if an exclusion zone adjacent to the channel side wall for an ion sphere center with the thickness of an ion radius should be given extra consideration. In 3D models, this may be necessary and requires extra care in computation because the radial exclusion zone is different for ions of different sizes and charge: see Figure 7 in ref 99. However, in the 1D continuum model studied here, which ignores such ion-specific radial effects, our single radial zone would change only the value of rmin. Because all of the governing equations are scaled to be dimensionless, the effect of changing rmin would change only the value of Γ in eq 19. That in turn would only change the distribution of the electric potential. Γ is proportional to 1/rmin2. The permanent charge concentration ρ0 in eq 19 is also proportional to 1/rmin2. The net effect is simply reduced to the amplification or shrinking of the influence of the contribution of the electric potential exerted by ion distributions. The permanent charge concentration ρ0 is generally much larger than all ion concentrations and dominates the distribution of electric potential, we imagine. We then reason that a minor change in rmin would not affect our results significantly.
Numerical Methods
Now we apply the multiblock Chebyshev pseudospectral method(153) together with the method of lines (MOL) to solve eqs 19–22 with the associated boundary/interface conditions (eqs 13 and 14). These governing equations are semidiscretized in space together with boundary/interface conditions.
The resulting PNP delta representation is a set of coupled ordinary differential algebraic equations (ODAE’s). The algebraic equations come from the boundary/interface conditions that are time-independent. The resulting ODAE’s have an index of 1, which can be solved by many well-developed ODAE solvers. For example, ode15s in MATLAB is a variable-order, variable-step index-1 ODAE solver that can adjust the time step to meet the specified error tolerance and integrate with time efficiently. The numerical stability in time is automatically assured at the same time. The spatial discretization here is performed by the highly accurate Chebyshev pseudospectral method with the Chebyshev Gauss–Lobatto grid and its associated collocation derivative matrix. To cope with the computational domain of side chains being strictly within the [α, β] region and the conformation of grids, we need to use domain decomposition. We decompose the whole domain into [0, α], [α, β], and [β, a].
The extra interface conditions from this domain decomposition for ions are implemented simply by continuity of ion concentration and the associated flux. Finally, the Poisson equation for the electric potential is solved by the direct inverse at every time step, which is easy because it is only 1D.

Results

Here we consider a calcium channel (EEEE) with four glutamate side chains and eight O–1/2 particles that are free to move inside the filter, which is essentially the model introduced by Nonner and Eisenberg(53, 87-89) and used by them and their collaborators since then (reviewed in refs 9 and 72). Our goal is to demonstrate the feasibility of a PNP–steric model and the range of phenomena that can be calculated despite its local approximation. Note that the effects of a local approximation on the right-hand side of partial differential equations are not the same as the effects of a local approximation in a classical analysis of the BBGKY hierarchy. The much-needed detailed comparison with experimental results lies in the future. We are particularly interested in the effects of the steric parameters that we call εij in eq 1 and then the effects of gij as well, so we concentrate on steady-state results. Transients of the type previously reported(75) have been computed and will be reported separately.
The channel geometry used for the current 1D simulations is shown in Figure 3, and the parameters used are shown below. These parameters are not changed in the calculations (e.g., the diffusion coefficients are always the same and are not changed as the interaction (Kong) parameters are changed).
figure

Figure 3. Channel geometry. A precise specification of the geometry of our model.

Parameters

Filter radius, 3.5 Å; filter length, 10 Å; diffusion coefficients (cm2/s) in the nonfilter region, DNa+ = 1.334 × 10–5, DCa+2 = 0.792 × 10–5, DCl– = 2.032 × 10–5, and DO–1/2 = 0.76 × 10–5; diffusion coefficients in the filter region, 1/20 of the above values (see Gillespie,(109) particularly the Supporting Information); ion radii, aNa+ = 0.95 Å, aCa+2 = 0.99 Å, aCl– = 1.81 Å, and aO–1/2 = 1.4 Å; relative dielectric constant, 30 in the filter region and 80 in the nonfilter region.
Dimensionless restraining potential for O–1/2 inside the filter required by eq 22(24)where γ is a scaling constant that makes V reach Vmax at z = α and β.

Boundary Conditions

Voltage in both reservoirs, 100 mV; Na+ concentration in both reservoirs, 100 mM; Ca2+ concentration in both reservoirs, 0.001–10 mM. The Cl– concentration in both reservoirs is chosen to keep the whole solution electrically neutral.
To measure the selectivity, as reported in the biological literature of calcium channels, we need to compute the Ca binding ratio(25)Turning to the precise description of the spherical ions, we need to specify many Lennard-Jones-style parameters. There are 10 parameters of the gij’s that must be chosen, without specific experimental data relevant to the interior of a channel. (We note that this problem is not ours alone. The same situation is faced for any atomic-scale model. No one knows how to choose force fields of molecular dynamics that are suitable for the special conditions inside an ion channel. If one follows the convention of molecular dynamics and uses force fields that depend only on the distance between two atoms, this problem is particularly serious. Note that dielectric boundary forces are almost always of great importance in confined systems such as ion channels.(159, 160) It is not likely that dielectric boundary forces acting on two ions can be well approximated as a function of only the distance between two ions.)
We use the energy well εij data from the traditional Lennard-Jones (12–6 rule) potential as a reference. From the work in refs 151 and 152. we choose εNa,Na/εCl,Cl/εCa,Ca/εO,O = 1:1:1:1.56. Kong’s combining rule(150) seems to be the best for ionic solutions,(151, 152) with σij = (ai + aj). This gives us the εij values for the rest of the cross hard-sphere potential terms.and similarlyWe can see that gCl,j (especially gCl,Cl) is much larger than the other gij terms because the size is increased so dramatically by the exponent in (ai + aj)12. These large values would make the governing equations very stiff in numerical properties and hard to integrate in time. To resolve this numerical difficulty, we remove all of the hard sphere forces involving Cl–, which means that gCl,j = 0, j. This approach can be rigorously justified because Cl– is usually very dilute inside the filter, as are all co-ions in ion exchangers,(161) because of the electrostatic repulsion from the highly concentrated permanent charge of eight O–1/2.
Choosing Self-Coupling Coefficients gNa,Na
The above coupling terms gij are derived as ratios, and we still need to determine actual gij values by choosing self-quantities gNa,Na. The self-coupling gNa,Na is known only from its relationship to its effective ion radius: it is proportional to (aNa + aNa)12. Larger gNa,Na values imply a stronger hard sphere potential and more pushing among particles. Smaller gNa,Na implies less interaction and pushing among particles. If we choose gNa,Na to be too small, then the finite-size effect will be trivial and (judging from previous work cited above) the correct selectivity of calcium ions will not be found. If we choose gNa,Na to be too large, then repulsion will be too strong and the profile of concentration of all species (inside the filter) will be flat. Selectivity, as biology knows it, will not be present.
A numerical experiment (Figure 4 and Table 1) shows how gNa,Na changes the Ca binding ratio. The conditions of each case are stated in the figure captions. Note that many of the cases considered below correspond to different physiological states that may have profound implications on function. Cycling between such states has been the explanation of most behavior of channels and transporters for some 60 years, since Hodgkin and Huxley (who, one notes, did not use such explanations themselves). But the states in those explanations are ad hoc, arising as inputs of models from wisdom and experimentation on macroscopic systems, not from a direct physical knowledge of channels. The states shown here in our calculations arise without human intervention or wisdom. Rather, they arise as outputs of direct self-consistent calculations. Sometimes it is better to be wise, and sometimes it is not. The choice between handcrafted traditional models of states and direct calculations of ions that are sometimes in definite states should be made, in our view, by success or failure in explaining and predicting experimental results with models. The models should be parsimonious and specific, of course, so they can be falsified, at least in principle. Otherwise, they are more poetry than science.
figure

Figure 4. Species concentration distributions with various gNa,Na values. For Vmax = 200: (a) gNa,Na = 0 and Ca2+ binding ratio = 0.60214; (b) gNa,Na = 10–4 and Ca2+ binding ratio = 0.59418; (c) gNa,Na = 10–3 and Ca2+ binding ratio = 0.75433; (d) gNa,Na = 10–2 and Ca2+ binding ratio = 0.86109; (e) gNa,Na = 10–1 and Ca2+ binding ratio = 0.82580; (f) gNa,Na = 1, Ca2+ binding ratio = 0.71644, and the symmetrical symmetric boundary conditions are [Ca2+]L = [Ca2+]R = 1 mM, [Na+]L = [Na+]R = 100 mM, L = R = 100 mV. Note the 4-fold scaling of the [O–1/2] concentration.

Table 1. Effect of Increasing εglobal on the Ca Binding Ratio with [Ca2+]L = [Ca2+]R = 1 mM [Na+]L = [Na+]R = 100 mM, L = R = 100 mM, and Vmax = 200
gNa,Na010–410–310–210–11
gNa,Cl000000
gCl,Cl000000
gNa,Ca06.41 × 10–56.41 × 10–46.41 × 10–36.42 × 10–26.42 × 10–1
gCl,Ca000000
gCa,Ca01.64 × 10–41.64 × 10–31.64 × 10–21.64 × 10–11.64
gNa,O–1/208.19 × 10–48.19 × 10–38.19 × 10–28.20 × 10–18.20
gCl,O–1/2000000
gCa,O–1/201.00 × 10–31.00 × 10–21.00 × 10–11.00341.00 × 101
gO–1/2,O–1/201.63 × 10–21.64 × 10–11.641.65 × 101.64 × 102
Ca binding ratio0.6020.5940.7540.8610.8250.72
We can summarize the observations in the following text.
(1) From eqs 21 and 22, the flux of ion species consists of diffusion, migration (i.e., electrostatic drift driven by electric potential), and particle-to-particle steric-effect interaction. The typical steric-effect flux of −D̃ic̃ig̃ij(∂c̃j/∂z̃) can be seen as a chemical potential drift exerted on ion species i by species j, in which i = j is also allowed. The steric-effect flux generally includes a flux coupling between species i and j, and this coupling is not captured in plain PNP and DFT–PNP theory, where fluxes of one species are driven only by gradients of the chemical potential of that one species. Here, everything interacts with everything else: the flux of one species is driven by gradients of the chemical potential of another species, even though we use (nearly) the same constitutive (NP) relation for transport as in classical PNP or DFT–PNP. Our chemical-potential drift term is not like electrostatic drift. The electrostatic drift can flow uphill or downhill along the electric potential, depending on the sign of the valence zi being negative or positive. The chemical potential drift, however, always flows downhill along the chemical potential unless D̃ig̃ij is negative, which is impossible if the particle-to-particle steric-effect interaction is always repulsive (not attractive). If particles push each other away, then peaks of ion concentration (for different species) tend to separate from each other as best they can, unless frustrated or overcome by additional electrostatic force. Here, in the present case, Na+ and Ca2+ chiefly feel a strong push from O–1/2 as gNa,Na gets larger (because aO–1/2 is large and O–1/2 is kept inside the filter) as well as the electrostatic attractive force from O–1/2. This can be clearly seen in Figure 4. Note the 4-fold scaling of O–1/2 concentration. In Figure 4a, for gNa,Na = 0, the concentration profiles of O–1/2, Na+, and Ca2+ reach equilibrium (at the minimum of total energy) simply by diffusion and the electrostatic force because the extra restraining force is felt by glutamate O–1/2 only. O–1/2, Na+, and Ca2+ all form single-peak concentration profiles in the same region of the channel for the same range of z. Physically, Na+ and Ca2+ are attracted to focused O–1/2 by the electrostatic force. The attraction for Ca2+ has a larger effect than the attraction for Na+ because Ca2+ is divalent. Also, Na+ and Ca2+ at the same time repel each other by electrostatic (and steric) forces.
This complex balance of forces can produce a wide range of behavior that varies a great deal as concentrations and conditions are changed. The biological function of channels and transporters has been defined experimentally for many decades by their behavior in complex ionic mixtures of variable composition as different voltages are applied across the cell membrane. We have not yet investigated the properties of our model as the concentrations of ions are made unequal on either side of the channel, as the electrical potential is varied, or, most importantly, as different species of ions are included in ionic mixtures on both sides of the channel.
The interaction forces (without the attractive component) may be responsible for many of the single-file properties of channels. More complete descriptions of Lennard-Jones forces include an attractive component. The interaction forces with the attractive component might (conceivably) produce the phenomena that define transporters, whether they are co-transporters or counter-transporters.
(2) As gNa,Na becomes larger in Figure 4b–f, the primary force is still the electrostatic attraction of Na+ and Ca2+ by O–1/2 but is modified by the finite-size effect (hard-sphere force). This electrostatic force will make peaks of Na+ and Ca2+ occur in the selectivity filter (i.e., in the same region of the channel that contains the O–1/2 side chains). For Na+, Ca2+, and O–1/2, the hard-sphere forces between ions of the same species will make the concentration profiles flatter as gNa,Na gets larger, when particles feel the push from similar particles. Flattening is clearly seen in Figure 4b–f.
(3) As gNa,Na gets larger in Figure 4b–f, Ca2+ pushes Na+ away from the middle part of the filter and forms a depletion zone and double-peak profile for Na+ in Figure 4c–e. Depletion zones of this sort have profound effects on the selectivity of ion channels in Monte Carlo simulations. See Figure 6 in refs 99 and 54. Depletion zones have profound effects on the behavior of transistors(132-135, 162) and the selectivity of channels.(9, 54, 99) A single transistor can have qualitatively distinct properties (e.g., gain, switch, logarithm, and exponential) for different boundary electrical potentials (bias for one transistor; power supply more generally) because the different boundary potentials produce different arrangements (layering) of depletion zones. Each arrangement of layers or depletion zones makes the same transistor a different device with a different device equation, corresponding to a different reduced model for the transistor. Different reduced models are appropriate for different conditions and have different functions. The function of the depletion zones found here is not yet known nor is the pattern or effect of cycling through structures known, but the complex properties of the Ca/Na exchanger, wonderfully characterized by Hilgemann,(163-166) immediately come to mind.
The major mechanism in Figure 4c–e is still that Ca2+ is more attracted to O–1/2 than to Na+. However, with extra help from the interspecies hard sphere force between Na+ and Ca2+ (in addition to the electrical repulsive force between Na+ and Ca2+), Ca2+ is able to push Na+ out of the filter. Note that again Figure 4f is an exception because all concentration profiles in it are very flat. In Figure 4f, the interspecies repulsive forces are greatly reduced and Na+ resides in the middle of the filter along with Ca2+. Note that Ca2+ forms a single-peak concentration profile in all of these cases without splitting into two peaks. Na+, however, can form a double peak when gNa,Na increases. The splitting occurs when the electrostatic attraction by O–1/2 is large enough to survive the push of different species from O–1/2 and Na+ in addition to the repulsive electrostatic force from Na+.
The singular behavior in Figure 4f may have direct functional significance. The splitting of a single peak into a double peak can create a depletion zone that can dominate the channel behavior (even though it is very small) because it is in series with the rest of the channel. A depletion zone can block flow and create switching behavior, as it does in transistors.
The depletion zones could help create the many states of a channel, identified as activated, inactivated, slowly inactivated, blocked, and so forth.(2) The depletion zones could be responsible for many of the similar (but correlated) states identified in classical experiments on transporters. In our calculations, of course, states arise as outputs of a self-consistent calculation and as a result of theory and computation, not as handcrafted metaphors summarizing the experimental experience and wisdom of structural biology and classical channology.(2)
Despite our enthusiasm and focus on our work, it must be clearly understood that our treatment of correlations is incomplete. We leave out many of the correlation effects of more complete variational treatments(1, 75, 76) and the more subtle correlations in the BBGKY hierarchy, derived for nonequilibrium systems(67) such as PNP (without finite-sized ions) from a Langevin description of trajectories in refs 278, 167, and 168. Our treatment is mathematically fully self-consistent but physically incomplete in its treatment of correlations and of course chemical interactions as well. The classical discussion of the BBGKY hierarchy and its treatment of correlations is not directly applicable to our analysis, however. The correlation forces of the hierarchy appear as driving forces in our partial differential equations, so the results of those forces are spread through all the terms of the solution of our partial differential equations. Thus, the effects of the correlations are likely to be more widespread than the effects of classical equilibrium analysis. Only detailed fitting of theory to data will show which correlations must be included in our model to explain the experimental data. Conclusions from equilibrium analysis may not apply.
(4) From Table 1, the Ca2+ binding ratio starts from 0.60214 when the finite size effect is zero (i.e., gNa,Na = 0). Affinity for Ca2+ in the filter region shows itself, even without the finite-size effect. This is obviously because Ca2+ feels a stronger electrostatic force than Na+ because of the larger valence. The valence effect dominates even though the concentration of Ca2+ is much lower than that of Na+ in reservoirs. The fact that valence effects overwhelm concentration effects when studying divalents has been known for at least 100 years. The binding ratio of Ca2+ decreases, increases, and then decreases again as gNa,Na increases, which shows the influence of the finite-size effect. The Ca2+ binding ratio roughly reaches its maximum at gNa,Na = 0.01 with a value of 0.861. This is far larger than the 0.602 that occurs when the finite size effect is zero and helps generate the affinity of Ca (selectivity). These effects can be further seen from the computational results shown later, when gNa,Na = 0.01.
We have not yet studied the effects of concentration gradients. Note that in biological systems, gradients of Ca2+ are large and have profound effects in experiments. Calcium concentrations outside cells are typically 2 × 10–3 M, whereas those inside cells (cytoplasm) are <10–7 M. There are many compartments within cells (vesicles, mitochondria, endoplasmic reticulum, and sarcoplasmic reticulum) essential to living function that maintain distinctive concentrations of Ca2+ without which they cannot function. We anticipate complex behavior of concentration profiles of ions within the selectivity filter when our model is studied in realistic ionic mixtures. It seems unlikely that these are uninvolved in biological function, however obscure that involvement seems today and however difficult it is to discover. It seems wise to do calculations under conditions in which the systems can actually perform their natural function, and it is unwise to simulate conditions in which biological systems are known not to function properly.
Ca Binding Curve
In these calculations, we first studied how finite size effects change the Ca binding curve, and the results are shown in Table 2 and its associated Figure 5. We choose gNa,Na = 0 and an appropriate finite size effect by choosing gNa,Na = 0.01 to calculate the binding curves of Na+ and Ca2+ respectively. Vmax = 200 mV as above, boundary conditions L = R = 100 mV, and concentration of Na+ inside and outside = 100 mM.
figure

Figure 5. Binding curves corresponding to Table 2.

Table 2. Ca Binding Ratio vs [Ca2+]L = [Ca2+]R with gNa,Na = 0 (No Finite-Size Effect) and gNa,Na= 0.01 (Having a Finite-Size Effect)a
[Ca2+], mMCa binding ratio gNa,Na = 0Ca binding ratio gNa,Na = 0.01
10–69.2286 × 10–64.4525 × 10–3
10–59.2257 × 10–53.1819 × 10–2
10–49.1970 × 10–40.12233
10–38.9241 × 10–30.28671
10–27.0641 × 10–20.49926
10–10.291710.70778
10.602140.86109
100.828160.94502
1000.936610.98080
a

Vmax = 200, L = R = 100 mV, and [Na+]L = [Na+]R = 100 mM.

The results are shown in Table 2 and its associated Figure 5. The finite-size effect greatly enhances the selectivity, as observed previously in Monte Carlo simulations. The concentration profiles for different species are shown for both cases in Figures 6 and 7, respectively. Note the 2-fold scaling of the O–1/2 concentration in both figures. Figure 6 shows the increase in Ca2+ and the decrease in Na+ as the Ca2+ concentration increases (in the baths on both sides of the channel). Increases are due to the interplay of diffusion and electrostatic forces. There are no special chemical forces in our calculations. Binding forces are the output of our calculation, not the input as in so many treatments of selectivity.
figure

Figure 6. Species concentration distributions under various [Ca2+]L = [Ca2+]R with gNa,Na = 0 (no finite-size effect). Vmax = 200, L = R = 100 mV, and [Na+]L = [Na+]R = 100mM: (a) [Ca2+]L = [Ca2+]R = 10–7 M; (b) [Ca2+]L = [Ca2+]R = 10–6 M; (c) [Ca2+]L = [Ca2+]R = 10–5M; (d) [Ca2+]L = [Ca2+]R = 10–4 M; (e) [Ca2+]L = [Ca2+]R = 1 mM; (f) [Ca2+]L = [Ca2+]R = 10mM. Note the 2-fold scaling of the O–1/2 concentration.

figure

Figure 7. Species concentration distributions under various [Ca2+]L = [Ca2+]R with gNa,Na = 0.01 (with finite-size effect). Vmax 200, L = R = 100 mV, and [Na+]L = [Na+]R = 100 mM: (a) [Ca2+]L = [Ca2+]R = 10–7M, (b) [Ca2+]L = [Ca2+]R = 10–6 M, (c) [Ca2+]L = [Ca2+]R = 10–5 M, (d) [Ca2+]L = [Ca2+]R = 10–4 M, (e) [Ca2+]L = [Ca2+]R = 1 mM, (f) [Ca2+]L = [Ca2+]R = 10 mM. Note the 2-fold scaling of the O–1/2 concentration.

In our model, Na+ and Ca2+ are both attracted to confined O–1/2. They repel each other at the same time. Na+ and Ca2+ both form only single-peak concentration profiles; therefore, the depletion of Na+ in the middle of the filter occurs only at the largest peak as the Ca2+ concentration increases (on both sides).
Figure 7 shows the extra influence of the finite-size effect compared to Figure 6. The single-peak profile of Ca2+ found in all cases means the pull from O–1/2 by electrostatics survives the electrostatic repulsive force from Na+ as well as the hard-sphere pushes from both O–1/2 and Na+. The pull is so strong that there is no splitting and no double-peak profile.
However, the electrostatic pull for Na+ from O–1/2 is much smaller than its counterpart for Ca2+. The combination of the hard-sphere pushes from both O–1/2 and Ca2+ and also the electrostatic repulsive force from Ca2+ have qualitative effects. The concentration profile of Na+ changes from a single-peak to a double-peak profile as the Ca2+ concentration increases (on both sides of the channel). Also, a depletion zone of Na+ inside the filter is observed as the Ca2+ concentration increases (on both sides of the channel). A depletion zone, which arises when a peak splits in two, can have profound functional consequences because it is in series with the entire channel. A series barrier can entirely block the current flow.
DEEA Ca2+ Binding Curve
We have also computed the Ca2+ binding curve of a mutant sodium channel (DEEA) with three glutamate side chains. These are represented as six O–1/2 particles freely moving inside the filter as in previous work, consisting mostly of Monte Carlo simulations previously cited. Figure 8 shows the effect of a −4e side chain in EEEE and a −3e side chain in DEEA on the Ca2+ binding curve. Obviously, EEEE with a −4e side chain has a slightly larger affinity for Ca2+ than does DEEA with a −3e side chain. This DEEA binding curve, employing the PNP–steric model, agrees well with its counterpart in ref 75 using the PNP–LJ model and its counterpart in ref 99 using Monte Carlo simulations.
figure

Figure 8. Binding curves of EEEE (−4e) and DEEA (−3e).

DEKA Ca2+ Binding Curve
Here we compute the Ca2+ binding curve of the sodium channel (DEKA) with two glutamate side chains (four O–1/2 particles) and one lysine side chain (one NH4+ particle) free to move inside the filter. The Ca2+ binding curve is shown in Figure 9, and the associated species concentration profiles are shown in Figure 10. Note that the scaling of [O–1/2] is the same as the scaling of other concentrations in Figure 10, unlike those in Figures 4, 6, and 7. The loss of affinity for Ca2+ is obviously due to the existence of a lysine side chain with a +1e charge, though the net charge on glutamate and lysine side chains taken together is still −1e. We also computed an artificial EAAA channel with only one glutamate side chain (two O–1/2 particles) in which the net permanent charge on the filter is −1e, to correspond precisely to the experimental situation as discussed in ref 99 and references cited therein. EAAA still has a much higher affinity for Ca2+ than for Na+ (data not shown). The DEKA binding curve, employing the PNP–steric model, agrees well with its counterpart in ref 75 computed using the PNP–LJ model and also with its counterpart in ref 99 computed using Monte Carlo simulation. The concentration profiles of individual species shown in Figure 10 also resemble those in ref 99. We have not yet performed the calculations with multiple ion species needed to evaluate the selectivity of the DEKA model for K+ ions.
figure

Figure 9. Binding curves of DEKA (−1e).

figure

Figure 10. Species concentration distributions under various [Ca+2]L = [Ca+2]R with gNa,Na = 0.01 (having a finite-size effect). Vmax = −200 for glutamate side chain, Vmax = 200 for lysine side chain, L = R = 100 mV, and [Na+]L = [Na+]R = 100 mN: (a) [Ca2+]L = [Ca2+]R = 10–7M, (b) [Ca2+]L = [Ca2+]R = 10–6M, (c) [Ca2+]L = [Ca2+]R = 10–5M, (d) [Ca2+]L = [Ca2+]R = 10–4M, (e) [Ca2+]L = [Ca2+]R = 1 mM, and (f) [Ca2+]L = [Ca2+]R = 10 mM. Note that the scaling of [O–1/2] is the same as the scaling of other concentrations in this figure, unlike that in Figures 4, 6, and 7.

Discussion

Ion channel function depends on the properties of ionic solutions and ions in channels, along with the properties of the channel protein itself, so it is necessary to relate our work to previous work in each field, emphasizing the properties of ions in bulk solutions, ions in proteins, and proteins that determine the biological function in our model of channels, if not in the real world.
Relation to Classical Work on Ionic Solutions, Poisson–Boltzmann, and PNP
The limitations of Poisson–Boltzmann and PNP models of ionic solutions have been known a very long time to the physical chemistry community but seem not to be so well known to either applied mathematicians or biophysicists. Exhaustive references to the literature are in refs 52, 59, 65, and 169−171. Applied mathematicians understandably are attracted to the simplicity of the Poisson–Boltzmann–PNP equations and view them as a starting point for more realistic treatments.(70) Biophysicists(2) use the independence principle that worked so well(-172, 173) when applied to membranes in which ions flow through separated, independent protein channels.(174-177) When channels are not selective(178, 179) or two types of ions flow through one channel, as in classical ligand-gated acetylcholine channels nAChRs,(180) the independence does not apply.
The independence principle is a restatement of Kohlraush’s law of a century ago, which does not apply to bulk ionic solutions of the type found in biology (eq 3.27a,b on p 125 of ref 67). References to the physical chemistry literature include refs 21, 57−63, 66−69, 74, 129, 158, 169, 171, and 181−230. Many of these papers are strictly experimental, presenting compilations of physical chemistry data. These papers also show that ionic solutions are not well described by Poisson–Boltzmann or PNP, if they contain divalents, multivalents, or mixtures of monovalents. (Biological solutions are mixtures usually containing divalents.) Interactions are strong in all ionic solutions because they all satisfy global electroneutrality. Thus, ionic solutions are nothing like ideal, so the law of mass action, for example, does not apply as usually used with rate constants independent of concentration. Note that rate constants in complex models will depend on each other as well as on concentration because the electric field in one part of a channel (described by one rate constant) will interact with charges in another part of the channel (described by another rate constant). It is that variation of the electric field that allows Kirchoff’s current law (and its generalization to the Maxwell equations(-232-234)) to be true. The electric field is long-range and cannot be broken into independent spatial components as it is in most classical treatments.(2)
Classical Work on Channel Proteins: Permeation
Currents permeate biological membranes by flowing through channel proteins that are either open or closed. A single ionic channel controls the current by opening and closing (spontaneous gating),(5, 6, 235-237) thereby making a random telegraph signal(238) that has been studied in enormous detail for many (hundreds or thousands of) channel types(178, 179, 239, 240) using the wonderful techniques of single-channel recording, patch clamp,(6, 241-245) and bilayer reconstitution.(246)
Sadly, the structures and mechanisms that produce this gating are still mostly unknown. However, progress is at hand.(247-251) Special structures modulate spontaneous stochastic gating in most channels to produce the macroscopic gating properties of classical electrophysiology.(2, 4, 5, 252, 253) The properties of macroscopically modulated gating are complex, as is clear from the variety and number of complex schemes in the classic text(2) (chapters 18 and 19 and Figure 19.11). Some of these schemes involve nearly 100 ill-determined rate constants (Figures 18-11 and 18-12 in ref 2) and have attracted the attention of literally hundreds of investigators over many decades.(239, 240) So far, no theoretical model can explain gating and selectivity using the fundamental physics that is described (crudely) in the PNP equations, but this situation may change.
Despite our ignorance of the mechanism of gating, the phenomena of spontaneous gating is remarkably clear, one might even say crystal clear, despite the amorphous structures involved. Once the single channel is open, the current through the single channel is remarkably stable. Single-channel (mean) currents are independent of time from say 10 μs to 10 s or longer, strongly suggesting that the channel protein has only one structure over a range of (at least) 106. A glance at an MD simulation of channels or the numerical values of energies computed from Coulomb’s law or Lennard-Jones potentials suggests that the structure of the channel pores and the pore walls must be very constant indeed over these time scales. A change in radius of 3% would produce a change in current of at least (and probably much more than) 9%. Single-channel currents are routinely resolved to within 2% (and can be resolved much better(5, 242, 243, 254-256) if necessary because the stability is nearly perfect and signal-to-noise ratios are often larger than 50). The complexity and ignorance of the gating mechanism reappear when we consider the time course of the opening and closing processes themselves (e.g., on a much faster time scale(244) or in cooled systems(245)). The opening and closing processes do not in fact have well-defined time courses, and nothing seems to be known about their physical origin in either case.
Classical Work on Channel Proteins: Permeation and Selectivity
Once open, channels select between ions of different chemical types. Channels allow only some types of ions to flow, even though the different chemical types are quite similar. For example, Na+ and K+ ions differ only in diameter; Na+ and Ca2+ ions differ only in charge. Simple models do surprisingly well in dealing with the selectivity of some types of channels. This work was reviewed in the Introduction of this article and elsewhere.(7, 9, 72)
Dealing with Biological Reality
It is important that the study of permeation and selectivity be carried out in the context of specific channels using parameters known to fit a wide range of experimental data properly.(9, 16-18, 90, 94-97, 99-112)
It is a surprise, particularly to structural biologists and traditional channologists, who customarily deal with metaphors(257-259) and not quantitative fits to data that powerful results, with quantitative fits to data in important cases, can arise from the Nonner and Eisenberg models with their very simple structures. We do not know why these models work, but one reason may be that the structures are the computed consequences of the forces in the model so the structures of the channel protein and of the ionic solutions are always exactly self-consistent. Even tiny deviations in the location of side chains from their free-energy minima produce large energy and functional effects.(54, 93) Exact self-consistency between channel protein and ionic solution seems to be necessary to make reasonable models. We suspect that exact self-consistency is why some simulations fit some data so well.
If exact self-consistency is necessary to make reasonable models, then classical models in much of molecular biology(260-264) will need to be reconsidered, even in much of chemistry,(73, 74) because classical chemical and biochemical models are almost never self-consistent. They almost never calculate the electric field from the charges present, let alone deal self-consistently with boundary conditions, steric forces, or the resulting interactions of everything with everything else. Our approach in this article represents the ionic atmosphere around an ion consistently in a simplified way using the approximated LJ potential instead of the original LJ potential. Surely, we have not included all of the correlations among ions. Only detailed fitting to large amounts of data will show whether we have captured enough correlations, and captured them well enough.
It is also possible that the Nonner and Eisenberg models work well because the community of scientists working on them has recapitulated evolutionary history. Perhaps those scientists have stumbled on the adaptation that biological organisms found eons ago, as evolution selected mutations that allowed cells to live and reproduce. It is even possible (for the same reason) that simple, nearly 1D models will capture most of what we need to understand time-dependent nonequilibrium properties of channels.
Nonequilibrium Treatments
An important advantage of the methods considered here is their extension to nonequilibrium in a mathematically precise and defined way, always fully self-consistent. Other approaches depend on physical approximations that are not self-consistent. They were the best that could be done at the time but cannot substitute for self-consistent treatments, in our view. For example, the DFT–PNP method(18, 105, 107, 108, 110-112) is not self-consistent (i.e., it does not precisely satisfy sum rules of statistical mechanics(265, 266) or Poisson’s equation and boundary conditions) and apparently leaves out relaxation and dielectrophoresis terms of the (more or less) self-consistent Debye–Hückel–Onsager equation. See the classical work(267-278) and the textbook(207) (p 282, Figure 7.7). DFT–PNP indeed assumes local equilibrium, as do other approaches using combinations of simulation and PNP equations,(279-281) although it computes global flux.
It must be clearly understood that any assumption of local equilibrium is also an assumption of local zero flux. It is not clear how a system can have zero local flux and long-range substantial flux as does DFT–PNP, particularly when the system is a nanovalve connected in series to a high-impedance entry process and macroscopic baths. DFT–PNP is inconsistent in its treatment of both flux and electrostatics. Adopting models that are inherently inconsistent is dangerous because the results of calculations can depend on how the inconsistency is resolved, and that resolution may be presented sotto voce, or chosen without conscious thought.
It is striking that very successful PNP calculations in a closely related field such as computational electronics do not use inconsistent assumptions (such as local equilibrium and global nonequilibrium) and always satisfy Poisson and boundary conditions with great accuracy. Simulations in computational electronics directly solve the relevant equations and so are fully self-consistent. Otherwise, they have difficulty accounting for the function of semiconductor devices that arises from small differences in large forces. Calculations of computational electronics account for the macroscopic function using atomic-scale models.(8, 9, 11, 12, 134, 136, 149, 282-284) Most treatments of ions in water and channels have been much less successful, perhaps because they are inconsistent.
Resolving inconsistencies can be a difficult task. It took a detailed stochastic analysis (lasting many years) of a second-order Langevin equation with doubly conditioned nondifferentiable Brownian trajectories(285, 286) to resolve a similar inconsistency in an analysis of noninteracting particles. And the results of that analysis were not at all what had been anticipated, although they were pleasingly simple when interpreted correctly with the classical theory of mass action.(74) The stochastic analysis allowed one to derive the law of mass action, but with variable rate constants that were specific functions of everything in the system, as given by the analysis. It is not clear how one can evaluate or resolve the paradox of local equilibrium and global flow in DFT–PNP. One attempt is in refs 76 and Appendix C of ref 75.
Flows in Complex Mixtures
An important advantage of the methods presented here is their indifference to flow. The methods work at thermodynamic equilibrium and when flows are vigorous. Thus, calculations can be made in the nonequilibrium situations and mixed ionic solutions used nearly always in experimental work. Such calculations require some further numerical work because they involve many species of ions and ionic tracers (radioactive ions with properties identical to nonradioactive isotopes but present in trace amounts) that must be included appropriately in our Euler–Lagrange equations. Such calculations will allow the direct simulation of the experiments used historically to define single filing by ratios of unidirectional fluxes (e.g., which are estimated by the net fluxes of tracers) and most importantly to define the properties of transporters of every type, whether they transport species in the same direction or in opposite directions or in both. It is likely that some of the properties attributed to the interactions of ions with the channel protein actually occur between ions themselves.(73, 74) After all, interactions between ions had been ignored almost entirely in classical theories because ions were treated as ideal solutions(264, 287, 288) even when present in enormous concentrations.(9, 260) The effect of nonideality on the very definition of transporters remains to be investigated. This investigation can be done abstractly in general but much better if it can be done by realistic simulations of actual experimental setups using the PNP–steric model and other models that deal even more realistically with interactions.
Future Work: Inverse Problems
The distribution of permanent charge within the channel can be determined reliably from measurements of current voltage relations. Surprisingly, the inverse problem of determining the charge within the channel of the Nonner and Eisenberg model has been solved.(16-18) The sensitivity to noise and errors is small when the problem is solved by standard methods of inverse problems. The inverse problem of interest to biologists has a well-posed solution and can be used to determine the internal structure of the model channel from the kind of experimental information recorded in hundreds if not thousands of laboratories every day. The inverse problem for the PNP–steric model needs to be studied so that experiments can be designed to reveal properties of interest.
Future Work: One-Dimensional Models
The forward PNP problem has in some ways been more difficult to compute than the inverse problem because it has had to deal with the complex geometry of the channel protein. The inverse problem hides much of this geometrical complexity in effective 1D parameters. In fact, most numerical work assumes simple geometry for the ion channel and reduces the problem to one dimension. These papers all assumed that the pore diameter had some simple dependence on location, either parabolic or some kind of funnel shape that is easier to deal with analytically.(24, 25, 47, 48, 51, 88, 116, 143, 147, 148, 167, 289, 290) Although some 2D and 3D work has been reported in the past,(24, 35-40, 43-45, 49, 50, 281, 291-295) many results have not been as well converged as one might wish, and others simply were not checked as carefully as refs 26, 43, and 230 showed was necessary, as the semiconductor community had learned earlier (reviewed in ref 136; see ref 149). Very few computations have been reported using the real shape of channels, and even then the accuracy of the electrostatic treatment was not sufficient to be sure that important details were resolved (Claudio Berti, personal communication(139, 296)). Obviously, the difficulty is expected to be much greater when extending the traditional PNP equations to the modified ones of Eisenberg et al. and others.(26, 75-77, 230)
The difficulties in dealing with the full structural complexity of an ion channel should not be underestimated. The spatial resolution needed can put severe burdens on the memory bandwidth of even modern day computers. The relation of structures determined by the X-ray analysis of crystals to the spatial distribution of the mass density of each species, the spatial distribution of the (effective) diffusion coefficient (of each species), and the spatial distribution of polarization (i.e., induced dielectric) charge cannot be determined by presently available methods, but these distributions must be specified with precision in 3D calculations. The issues of temporal properties are hardly ever discussed, yet the polarization properties of electrolyte solutions change tremendously in the time range from biological function to atomic motion. It is not clear how these effects are involved in protein function or how to include them in models. It may be that these issues are less important in 1D models than in 3D models because the lower-dimensional models smooth over them in an appropriate way.
Time Dependence: Future Work
Future work needs to address each of the time-dependent phenomena to see what part of the classical properties of ion channels, studied in innumerable experimental papers, might arise from a model as simple as that used here. Obviously, many of those classical properties will involve conformational changes of the channel protein not described by our simple model. But just as obviously, those conformational changes will be coupled to ions in the channel by the electric field and probably by steric interactions as well, so everything must be analyzed together—ions, channel conformation, bathing solutions, ion flux, and current flow—as is usually the case in complex fluids flowing through complex spatial domains. Theory and simulations must allow everything to interact with everything else. They must not assume nothing interacts with nothing, as in ideal solutions.

Conclusions

Traditional PNP equations do not include the finite-size effect that is known to be significant in ionic solutions containing divalents and containing mixtures and even in pure monovalent solutions more concentrated than 50 mM. The concentration of ions in seawater, in and around cells, and inside channels is much higher than that. Therefore, classical PNP cannot describe the specific ion properties of bulk solutions such as seawater and the solutions in living systems, the plasmas of life. It cannot predict the ion-selectivity behavior of ion channels correctly. Here, we introduce the finite-size effect by treating ions and side chains as solid spheres and using hard sphere potentials to characterize this effect. Our work shows that selectivity is found in a simple 1D analysis and simulations.
Complex effects of changes in the repulsion parameters show a variety of states and depletion zones that are likely to be important in the functioning of channels and transporters. For example, the sudden appearance of a depletion zone, because of instability or a stochastic fluctuation, would surely gate a channel closed. If that gating happened on one side of a channel, then the properties on the other side would surely be affected. Everything interacts with everything else in these systems profoundly coupled by Coulomb and steric exclusion forces. If an exclusion zone moved from one side of a channel to another and then back and forth, then the channel protein could easily produce a reciprocating ping pong effect and mimic the alternating access states of transporters discovered with such wisdom and work by experimentalists who did not have the help of self-consistent models. The everything interacts with everything nature of the crowded charge environment inside a channel, or active sites,(2, 260, 297) makes such nonlinear interactions possible. It is not clear if the correlations included in our model are sufficient to produce ping pong effects or not: our model leaves out many forms of correlation, we are sad to say. It also remains to be seen whether biology actually uses such interactions at all. Alternating access could be produced in quite different ways, as most assume.
It is very important for the reader in the physical sciences to understand that complex systems of states and rates have been used by experimental biologists to characterize the function of hundreds of channels(178, 179, 239, 240) and transporters(298) studied by thousands of laboratories daily because of their medical and biological importance.
It is very important for the reader in the biological sciences to understand that an enormous wealth of living behavior could be controlled by the physical phenomena described here, as outputs of a self-consistent model and as solutions of a set of partial differential equations and boundary conditions, without invoking classical, vaguely defined effects. Those classical effects are more vitalistic than vital in many cases, in our view.
Early workers of some reputation in molecular biology, including Nobel Prize winners,(299-301) attributed the secret of life to allosteric interactions of chemical signals acting on proteins and then channels.(2) It is striking to the biologists among us that a self-consistent model of ions and side chains in channels produces strong interactions over long distances (i.e., more than 1 nm) without invoking the metaphors of vitalistic allostery. The calculations of a self-consistent variational theory of the energetics of complex fluids seem ready to replace the poetry of our ancestors.
Self-consistent theory is useful only because it can be evaluated with computers. Those computers in turn are possible only because of the successful treatment of complex physical interactions by self-consistent mathematics. It is amusing that physicists learned to use self-consistent mathematics to analyze (control and build) complex interacting systems of holes and electrons(302-304) during the same years that biologists used poetry to describe complex interacting systems of cations and anions.
Channels are nearly enzymes,(9, 297) and it is possible that the interactions described by models of the sort described here for channels underlie the complex interactions of a wide range of proteins that produce the special properties of life. Certainly, a theoretical and computational approach to biology and its molecules must allow everything to interact with everything else, instead of assuming that everything is ideal and nothing interacts with nothing.

The authors declare no competing financial interest.

Acknowledgment

The Taida Institute for Mathematical Sciences (TIMS) and National Center for Theoretical Sciences at Taipei (NCTS/Taipei) funded two meetings at which we met and developed these ideas. This paper is a result of their generous support, for which we are grateful. This work would not have been possible without the previous investigations of Dr. YunKyong Hyon. We are most grateful for his generosity in sharing all the details with us in innumerable communications and discussions. We thank Wolfgang Nonner and the referees for helpful suggestions that materially improved the article.

This research was sponsored in part by the National Science Council of Taiwan under grant no. NSC-100-2115-M-035-001 (T.L.H.). B.E. is supported by the Bard Endowed Chair of Rush University. He is particularly grateful for the administrative work he was not asked to do.

References

This article references 304 other publications.

  1. 1.
    Lin, T. C.; Eisenberg, B. To be submitted for publication, 2012.
    There is no corresponding record for this reference.
  2. 2.
    Hille, B. Ionic Channels of Excitable Membranes, 3rd ed.; Sinauer Associates Inc.: Sunderland, England, 2001.
    There is no corresponding record for this reference.
  3. 3.
    Ashcroft, F. M. Ion Channels and Disease; Academic Press: New York, 1999.
    There is no corresponding record for this reference.
  4. 4.
    Neher, E.Ion Channels for Communication between and within Cells. In Nobel Lectures, Physiology or Medicine 1991–1995; Ringertz, N., Ed.; World Scientific: Singapore, 1997; p 10,

    Nobel Lecture, December 9, 1991.

    There is no corresponding record for this reference.
  5. 5.
    Neher, E.; Sakmann, B. Nature 1976, 260, 799
    [CrossRef], [PubMed], [CAS]
    5.
    Single-channel currents recorded from membrane of denervated frog muscle fibres
    Neher E; Sakmann B
    Nature (1976), 260 (5554), 799-802 ISSN:0028-0836.
    There is no expanded citation for this reference.
    >> More from SciFinder ®
    https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A280%3ADyaE287nsVGhtA%253D%253D&md5=f88eb7e304314635339f9ede4f7a4827
  6. 6.
    Sakmann, B.; Neher, E. Single Channel Recording, 2nd ed.; Plenum: New York, 1995.
    [CrossRef]
    There is no corresponding record for this reference.
  7. 7.
    Eisenberg, B. ( 2012, available on arXiv as http://arxiv.org/abs/1206.6490.
    There is no corresponding record for this reference.
  8. 8.
    Eisenberg, B. Fluctuations Noise Lett. 2012, 11, 76
    There is no corresponding record for this reference.
  9. 9.
    Eisenberg, B.Crowded Charges in Ion Channels. Advances in Chemical Physics; John Wiley & Sons: New York, 2011; p 77.
    [CrossRef]
    There is no corresponding record for this reference.
  10. 10.
    Eisenberg, B. J. Phys. Chem. C 2010, 114, 20719
    [ACS Full Text ACS Full Text], [CAS]
    10.
    Multiple Scales in the Simulation of Ion Channels and Proteins
    Eisenberg, Bob
    Journal of Physical Chemistry C (2010), 114 (48), 20719-20733 CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)
    Computation of living processes creates great promise for the everyday life of mankind and great challenges for phys. scientists. Simulations of mol. dynamics have great appeal to biologists as a natural extension of structural biol. Once a biologist sees a structure, she/he wants to see it move. Mol. biol. has shown that a small no. of atoms, sometimes even one messenger ion, like Ca2+, can control biol. function on the scale of cells, organs, tissues, and organisms. Enormously concd. ions, at no. densities of 20 M, in protein channels and enzymes are responsible for many of the characteristics of living systems, just as highly concd. ions near electrodes are responsible for many of the characteristics of electrochem. systems. Here the authors confront the reality of the scale differences of ions. The authors show that the scale differences needed to simulate all the atoms of biol. cells are 107 in linear dimension, 1021 in 3 dimensions, 109 in resoln., 1011 in time, and 1013 in particle no. (to deal with concns. of Ca2+). These scales must be dealt with simultaneously if the simulation is to deal with most biol. functions. Biol. function extends across all of them, all at once in most cases. The authors suggest a computational approach using explicit multiscale anal. instead of implicit simulation of all scales. The approach is based on an energy variational principle EnVarA introduced by Chun Liu to deal with complex fluids. Variational methods deal automatically with multiple interacting components and scales. When an addnl. component is added to the system, the resulting Euler-Lagrange field equations change form automatically, by algebra alone, without addnl. unknown parameters. Multifaceted interactions are solns. of the resulting equations. The authors suggest that ionic solns. should be viewed as complex fluids with simple components. Highly concd. solns., dominated by interactions of components, are easily computed by EnVarA. Successful computation of ions concd. in special places may be a significant step to understanding the defining characteristics of biol. and electrochem. systems. Indeed, computing ions near proteins and nucleic acids may prove as important to mol. biol. and chem. technol. as computing holes and electrons was to the authors' semiconductor and digital technol.
    >> More from SciFinder ®
    https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3cXhtlaitb%252FI&md5=569ecd57de41c6117388cf6188045488
  11. 11.
    Eisenberg, R. S.Atomic Biology, Electrostatics and Ionic Channels. In New Developments and Theoretical Studies of Proteins; Elber, R., Ed.; World Scientific: Philadelphia, 1996; Vol. 7, p 269.
    [CrossRef]
    There is no corresponding record for this reference.
  12. 12.
    Eisenberg, R. S. J. Membr. Biol. 1996, 150, 1
    [CrossRef], [PubMed], [CAS]
    12.
    Computing the fields in protein and channels
    Eisenberg, R. S.
    Journal of Membrane Biology (1996), 150 (1), 1-25 CODEN: JMBBBO; ISSN:0022-2631. (Springer)
    A review, with 270 refs.
    >> More from SciFinder ®
    https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK28XhslCmtbw%253D&md5=4f1779d64ff9dbd5ea8f017bc386965c
  13. 13.
    Warshel, A. Proc. Natl. Acad. Sci. U.S.A. 1978, 75, 5250
    [CrossRef], [PubMed], [CAS]
    13.
    Energetics of enzyme catalysis
    Warshel, Arieh
    Proceedings of the National Academy of Sciences of the United States of America (1978), 75 (11), 5250-4 CODEN: PNASA6; ISSN:0027-8424.
    Quant. studies of the energetics of enzymic reactions and the corresponding reactions in aq. solns. indicated that charge stabilization is the most important energy contribution in enzyme catalysis. Low electrostatic stabilization in aq. solns. is consistent with large electrostatic stabilization effects in active sites of enzymes. This was established quant. by comparing the relative stabilization of the transition states of the reaction of lysozyme and the corresponding reaction in aq. soln.
    >> More from SciFinder ®
    https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaE1MXltVGnsw%253D%253D&md5=2158ad6d08173983cdac8fda277c325c
  14. 14.
    Warshel, A.; Russell, S. T. Q. Rev. Biophys. 1984, 17, 283
    [CrossRef], [PubMed], [CAS]
    14.
    Calculations of electrostatic interactions in biological systems and in solutions
    Warshel, Arieh; Russell, Stephen T.
    Quarterly Reviews of Biophysics (1984), 17 (3), 283-422 CODEN: QURBAW; ISSN:0033-5835.
    A review with many refs. about methods for calcg. electrostatic energies in solns., proteins, and membranes.
    >> More from SciFinder ®
    https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaL2MXitFOlsrc%253D&md5=3942a7d8401d57133bc4af9cf7226bdc
  15. 15.
    Warshel, A.; Sharma, P. K.; Chu, Z. T.; Aqvist, J. Biochemistry 2007, 46, 1466
    [ACS Full Text ACS Full Text], [PubMed], [CAS]
    15.
    Electrostatic Contributions to Binding of Transition State Analogues Can Be Very Different from the Corresponding Contributions to Catalysis: Phenolates Binding to the Oxyanion Hole of Ketosteroid Isomerase
    Warshel, Arieh; Sharma, Pankaz K.; Chu, Zhen T.; Aqvist, Johan
    Biochemistry (2007), 46 (6), 1466-1476 CODEN: BICHAW; ISSN:0006-2960. (American Chemical Society)
    The relationship between binding of transition state analogs (TSAs) and catalysis is an open problem. A recent study of the binding of phenolate TSAs to ketosteroid isomerase (KSI) found a small change in the binding energy with a change in charge delocalization of the TSAs. This has been taken as proof that electrostatic effects do not contribute in a major way to catalysis. Here we reanalyze the relationship between the binding of the TSAs and the chem. catalysis by KSI as well as the binding of the transition state (TS), by computer simulation approaches. Since the simulations reproduce the relevant exptl. results, they can be used to quantify the different contributions to the obsd. effects. It is found that the binding of the TSA and the chem. catalysis represent different thermodn. cycles with very different electrostatic contributions. While the binding of the TSA involves a small electrostatic contribution, the chem. catalysis involves a charge transfer process and a major electrostatic contribution due to the preorganization of the active site. Furthermore, it is found that the electrostatic preorganization contributions to the binding of the enolate intermediate of KSI and the TS are much larger than the corresponding effect for the binding of the TSAs. This reflects the dependence of the preorganization on the orientation of the nonpolar form of the TSAs relative to the oxyanion hole. It seems to us that this work provides an excellent example of the need for computational studies in analyzing key exptl. findings about enzyme catalysis.
    >> More from SciFinder ®
    https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2sXltVegsQ%253D%253D&md5=01de45b90befdb449b9337f799baaf3f
  16. 16.
    Arning, K. Mathematical Modelling and Simulation of Ion Channels; Johannes Kepler University Linz, 2009.
    There is no corresponding record for this reference.
  17. 17.
    Arning, K.; Burger, M.; Eisenberg, R. S.; Engl, H. W.; He, L. PAMM 2007, 7, 1120801
    [CrossRef]
    There is no corresponding record for this reference.
  18. 18.
    Burger, M.; Eisenberg, R. S.; Engl, H. SIAM J. Appl. Math. 2007, 67, 960
    [CrossRef], [CAS]
    18.
    Inverse problems related to ion channel selectivity
    Burger, Martin; Elsenberg, Robert S.; Engl, Heinz W.
    SIAM Journal on Applied Mathematics (2007), 67 (4), 960-989 CODEN: SMJMAP; ISSN:0036-1399. (Society for Industrial and Applied Mathematics)
    Ion channels control many biol. processes in cells, and, consequently, a large amt. of research is devoted to this topic. Great progress in the understanding of channel function has been made recently using advanced math. modeling and simulation. This paper investigates another interesting math. topic, namely inverse problems, in connection with ion channels. We conc. on problems that arise when we try to det. ("identify") one of the structural features of a channel-its permanent charge-from measurements of its function, namely current-voltage curves in many solns. We also try to design channels with desirable properties-for example with particular selectivity properties-using the methods of inverse problems. The use of math. methods of identification will help in the design of efficient expts. to det. the properties of ion channels. Closely related math. methods will allow the rational design of ion channels useful in many applications, technol. and medical. We also discuss certain math. issues arising in these inverse problems, such as their ill-posedness and the choice of regularization techniques, as well as challenges in their numerical soln. The L-type Ca channel is studied with the methods of inverse problems to see how mathematics can aid in the anal. of existing ion channels and the design of new ones.
    >> More from SciFinder ®
    https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2sXpsFais7g%253D&md5=1dd7abc313b7054ba13b66e36c97518f
  19. 19.
    Engl, H. W.; Hanke, M.; Neubauer, A. Regularization of Inverse Problems: Kluwer: Dordrecht, The Netherlands, 2000.
    There is no corresponding record for this reference.
  20. 20.
    Kaipio, J.; Somersalo, E. Statistical and Computational Inverse Problems: Springer: New York, 2005.
    There is no corresponding record for this reference.
  21. 21.
    Bazant, M. Z.; Thornton, K.; Ajdari, A. Phys. Rev. E 2004, 70, 021506
    [CrossRef], [CAS]
    21.
    Diffuse-charge dynamics in electrochemical systems
    Bazant, Martin Z.; Thornton, Katsuyo; Ajdari, Armand
    Physical Review E: Statistical, Nonlinear, and Soft Matter Physics (2004), 70 (2-1), 021506/1-021506/24 CODEN: PRESCM; ISSN:1539-3755. (American Physical Society)
    A review. The response of a model microelectrochem. system to a time-dependent applied voltage is analyzed. The article begins with a fresh historical review including electrochem., colloidal science, and microfluidics. The model problem consists of a sym. binary electrolyte between parallel-plate blocking electrodes, which suddenly apply a voltage. Compact Stern layers on the electrodes are also taken into account. The Nernst-Planck-Poisson equations are 1st linearized and solved by Laplace transforms for small voltages, and numerical solns. are obtained for large voltages. The weakly nonlinear limit of thin double layers is then analyzed by matched asymptotic expansions in the small parameter ε=λD/L, where λD is the screening length and L the electrode sepn. At leading order, the system initially behaves like an RC circuit with a response time of λDL/D (not λD2/D), where D is the ionic diffusivity, but nonlinearity violates this common picture and introduces multiple time scales. The charging process slows down, and neutral-salt adsorption by the diffuse part of the double layer couples to bulk diffusion at the time scale, L2/D. In the strongly nonlinear regime (controlled by a dimensionless parameter resembling the Dukhin no.), this effect produces bulk concn. gradients, and, at very large voltages, transient space charge. The article concludes with an overview of more general situations involving surface conduction, multicomponent electrolytes, and faradaic processes.
    >> More from SciFinder ®
    https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2cXnsVCms7c%253D&md5=caac9495c0ab385350b64e48cee3b980
  22. 22.
    Coalson, R. D.; Kurnikova, M. G. IEEE Trans. Nanobiosci. 2005, 4, 81
    [CrossRef], [PubMed], [CAS]
    22.
    Poisson-Nernst-Planck theory approach to the calculation of current through biological ion channels
    Coalson Rob D; Kurnikova Maria G
    IEEE transactions on nanobioscience (2005), 4 (1), 81-93 ISSN:1536-1241.
    The Poisson-Nernst-Planck (PNP) theory of electro-diffusion is reviewed. Techniques for numerical solution of the three-dimensional PNP equations are summarized, and several illustrative applications to ion transport through protein channels are presented. Strengths and weaknesses of the theory are discussed, as well as attempts to improve it via increasingly realistic evaluation of the force acting on each ion due to the protein/membrane environment.
    >> More from SciFinder ®
    https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A280%3ADC%252BD2M7otlGjtA%253D%253D&md5=0a759dc965a54ceb61503e8a14fdbfa3
  23. 23.
    Eisenberg, R.; Chen, D. Biophys. J. 1993, 64, A22
    There is no corresponding record for this reference.
  24. 24.
    Liu, W.; Wang, B. J. Dynam. Differ. Equations 2010, 22, 413
    [CrossRef]
    There is no corresponding record for this reference.
  25. 25.
    Singer, A.; Norbury, J. SIAM J. Appl. Math. 2009, 70, 949
    [CrossRef]
    There is no corresponding record for this reference.
  26. 26.
    Zheng, Q.; Wei, G.-W. J. Chem. Phys. 2011, 134, 194101
    [CrossRef], [CAS]
    26.
    Poisson-Boltzmann-Nernst-Planck model
    Zheng, Qiong; Wei, Guo-Wei
    Journal of Chemical Physics (2011), 134 (19), 194101/1-194101/17 CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    The Poisson-Nernst-Planck (PNP) model is based on a mean-field approxn. of ion interactions and continuum descriptions of concn. and electrostatic potential. It provides qual. explanation and increasingly quant. predictions of exptl. measurements for the ion transport problems in many areas such as semiconductor devices, nanofluidic systems, and biol. systems, despite many limitations. While the PNP model gives a good prediction of the ion transport phenomenon for chem., phys., and biol. systems, the no. of equations to be solved and the no. of diffusion coeff. profiles to be detd. for the calcn. directly depend on the no. of ion species in the system, since each ion species corresponds to one Nernst-Planck equation and one position-dependent diffusion coeff. profile. In a complex system with multiple ion species, the PNP can be computationally expensive and parameter demanding, as exptl. measurements of diffusion coeff. profiles are generally quite limited for most confined regions such as ion channels, nanostructures and nanopores. We propose an alternative model to reduce no. of Nernst-Planck equations to be solved in complex chem. and biol. systems with multiple ion species by substituting Nernst-Planck equations with Boltzmann distributions of ion concns. As such, we solve the coupled Poisson-Boltzmann and Nernst-Planck (PBNP) equations, instead of the PNP equations. The proposed PBNP equations are derived from a total energy functional by using the variational principle. We design a no. of computational techniques, including the Dirichlet to Neumann mapping, the matched interface and boundary, and relaxation based iterative procedure, to ensure efficient soln. of the proposed PBNP equations. Two protein mols., cytochrome c551 and Gramicidin A, are employed to validate the proposed model under a wide range of bulk ion concns. and external voltages. Extensive numerical expts. show that there is an excellent consistency between the results predicted from the present PBNP model and those obtained from the PNP model in terms of the electrostatic potentials, ion concn. profiles, and current-voltage (I-V) curves. The present PBNP model is further validated by a comparison with exptl. measurements of I-V curves under various ion bulk concns. Numerical expts. indicate that the proposed PBNP model is more efficient than the original PNP model in terms of simulation time. (c) 2011 American Institute of Physics.
    >> More from SciFinder ®
    https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3MXmtl2qu7g%253D&md5=25bbe5e842be751b1c54e740bc9bbaa2
  27. 27.
    Chen, D. P.; Lear, J.; Eisenberg, R. S. Biophys. J. 1997, 72, 97
    [CrossRef], [PubMed], [CAS]
    27.
    Permeation through an open channel: Poisson-Nernst-Planck theory of a synthetic ionic channel
    Chen, Duan; Lear, James; Eisenberg, Bob
    Biophysical Journal (1997), 72 (1), 97-116 CODEN: BIOJAU; ISSN:0006-3495. (Biophysical Society)
    The synthetic channel [acetyl-(LeuSerSerLeuLeuSerLeu)3-CONH2]6 (pore diam. 8 Å, length 30 Å) is a bundle of six α-helixes with blocked termini. This simple channel has complex properties, which are difficult to explain, even qual., by traditional theories: its single-channel currents rectify in sym. solns. and its selectivity (defined by reversal potential) is a sensitive function of bathing soln. These complex properties can be fit quant. if the channel has fixed charge at its ends, forming a kind of macrodipole, bracketing a central charged region, and the shielding of the fixed charges is described by the Poisson-Nernst-Planck (PNP) equations. PNP fits current voltage relations measured in 15 solns. with an r.m.s. error of 3.6% using four adjustable parameters: the diffusion coeffs. in the channel's pore DK = 2.1×10-6 and DCl = 2.6×10-7 cm2/s; and the fixed charge at the ends of the channel of ±0.12e (with unequal densities 0.71 M = 0.021e/Å on the N-side and -1.9 M = -0.058e/Å on the C-side). The fixed charge in the central region is 0.31e (with d. P2 = 0.47 M = 0.014e/Å). In contrast to traditional theories, PNP computes the elec. field in the open channel from all of the charges in the system, by a rapid and accurate numerical procedure. In essence, PNP is a theory of the shielding of fixed (i.e., permanent) charge of the channel by mobile charge and by the ionic atm. in and near the channel's pore. The theory fits a wide range of data because the ionic contents and potential profile in the channel change significantly with exptl. conditions, as they must, if the channel simultaneously satisfies the Poisson and Nernst-Planck equations and boundary conditions. Qual. speaking, the theory shows that small changes in the ionic atm. of the channel (i.e., shielding) make big changes in the potential profile and even bigger changes in flux, because potential is a sensitive function of charge and shielding, and flux is an exponential function of potential.
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  28. 28.
    Dieckmann, G. R.; Lear, J. D.; Zhong, Q.; Klein, M. L.; DeGrado, W. F.; Sharp, K. A. Biophys. J. 1999, 76, 618
    [CrossRef], [PubMed], [CAS]
    28.
    Exploration of the structural features defining the conduction properties of a synthetic ion channel
    Dieckmann, Gregg R.; Lear, James D.; Zhong, Qingfeng; Klein, Michael L.; DeGrado, William F.; Sharp, Kim A.
    Biophysical Journal (1999), 76 (2), 618-630 CODEN: BIOJAU; ISSN:0006-3495. (Biophysical Society)
    The finite-difference Poisson-Boltzmann methodol. was applied to a series of parallel, α-helical bundle models of the designed ion channel peptide Ac-(LSSLLSL)3-CONH2. This method is able to fully describe the current-voltage curves for this channel and quant. explains their cation selectivity and rectification. We examd. a series of energy-minimized models representing different aggregation states, side-chain rotamers, and helical rotations, as well as an ensemble of structures from a mol. dynamics trajectory. Potential energies were computed for single, permeating K+ and Cl- ions at a series of positions along a central pathway through the models. A variable-elec.-field Nernst-Planck electrodiffusion model was used, with two adjustable parameters representing the diffusion coeffs. of K+ and Cl- to scale the individual ion current magnitudes. The ability of a given DelPhi potential profile to fit the exptl. data depended strongly on the magnitude of the desolvation of the permeating ion. Below a pore radius of 3.8 Å, the predicted profiles showed large energy barriers, and the exptl. data could be fit only with unrealistically high values for the K+ and Cl- diffusion coeffs. For pore radii above 3.8 Å, the desolvation energies were 2kT or less. The electrostatic calcns. were sensitive to positioning of the Ser side chains, with the best fits assocd. with max. exposure of the Ser side-chain hydroxyls to the pore. The backbone component was shown to be the major source of asymmetry in the DelPhi potential profiles. Only two of the energy-minimized structures were able to explain the exptl. data, whereas an av. of the dynamics structures gave excellent agreement with exptl. results. Thus this method provides a promising approach to prediction of current-voltage curves from three-dimensional structures of ion channel proteins.
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  29. 29.
    Chen, D. P.; Nonner, W.; Eisenberg, R. S. Biophys. J. 1995, 68, A370
    [CrossRef]
    There is no corresponding record for this reference.
  30. 30.
    Chen, D.; Xu, L.; Tripathy, A.; Meissner, G.; Eisenberg, R. Biophys. J. 1997, 73, 1337
    [CrossRef], [PubMed], [CAS]
    30.
    Permeation through the calcium release channel of cardiac muscle
    Chen, Duan; Xu, Le; Tripathy, Ashutosh; Meissner, Gerhard; Eisenberg, Bob
    Biophysical Journal (1997), 73 (3), 1337-1354 CODEN: BIOJAU; ISSN:0006-3495. (Biophysical Society)
    Current voltage (I-V) relations were measured from the calcium release channel (CRC) of the sarcoplasmic reticulum of cardiac muscle in 12 KCl solns., sym. and asym., from 25 mM to 2 M. I-V curves are nearly linear, in the voltage range ±150 mV ≈ 12kT/e, even in asym. solns., e.g., 2 M ‖ 100 mM. It is awkward to describe straight lines as sums of exponentials in a wide range of solns. and potentials, and so traditional barrier models have difficulty fitting this data. Diffusion theories with const. fields predict curvilinear I-V regions, and so they are also unsatisfactory. The Poisson and Nernst-Planck equations (PNP) form a diffusion theory with variable fields. They fit the data by using adjustable parameters for the diffusion const. of each ion and for the effective d. of fixed (i.e., permanent) charge P(x) along the channel's "filter" (7-Å diam., 10 Å long). If P(x) is described by just one parameter, independent of x (i.e., P(x) = Po = -4.2 M), the fits are satisfactory (RMS error/RMS current = 6.4/67), and the ests. of diffusion coeffs. are reasonable DK = 1.3 × 10-6 cm2/s, DCl = 3.9 × 10-6 cm2/s. The CRC seems to have a small selectivity filter with a very high d. of permanent charge. This may be a design principle of channels specialized for large flux. The Appendix derives barrier models, and their prefactor, from diffusion theories (with variable fields) and argues that barrier models are poor descriptions of CRCs in particular and open channels in general.
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  31. 31.
    Allen, T. W.; Kuyucak, S.; Chung, S. H. Biophys. J. 1999, 77, 2502
    [CrossRef], [PubMed], [CAS]
    31.
    Molecular dynamics study of the KcsA potassium channel
    Allen, Toby W.; Kuyucak, Serdar; Chung, Shin-Ho
    Biophysical Journal (1999), 77 (5), 2502-2516 CODEN: BIOJAU; ISSN:0006-3495. (Biophysical Society)
    The structural, dynamic, and thermodn. properties of a model K channel were studied using mol. dynamics simulations. The authors used the recently unveiled protein structure for the KcsA K channel from Streptomyces lividans. Total and free energy profiles of K+ and Na+ revealed a considerable preference for the larger K+ ions. The selectivity of the channel arose from its ability to completely solvate the K+ ions, but not the smaller Na+ ions. Self-diffusion of water within the narrow selectivity filter was found to be reduced by an order of magnitude from bulk levels, whereas the wider hydrophobic section of the pore maintained near-bulk self-diffusion. Simulations examg. multiple ion configurations suggested a 2-ion channel. Ion diffusion was found to be reduced to 1/3 of bulk diffusion within the selectivity filter. The reduced ion mobility did not hinder the passage of ions, as permeation appeared to be driven by Coulomb repulsion within this multiple ion channel.
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  32. 32.
    Chen, D.; Xu, L.; Tripathy, A.; Meissner, G.; Eisenberg, B. Biophys. J. 1999, 76, 1346
    [CrossRef], [PubMed], [CAS]
    32.
    Selectivity and permeation in calcium release channel of cardiac muscle: alkali metal ions
    Chen, Duan P.; Xu, Le; Tripathy, Ashutosh; Meissner, Gerhard; Eisenberg, Bob
    Biophysical Journal (1999), 76 (3), 1346-1366 CODEN: BIOJAU; ISSN:0006-3495. (Biophysical Society)
    Current was measured from single open channels of the calcium release channel (CRC) of cardiac sarcoplasmic reticulum (over the range ± 180 mV) in pure and mixed solns. (e.g., biionic conditions) of the alkali metal ions Li+, K+, Na+, Rb+, Cs+, ranging in concn. from 25 mM to 2 M. The current-voltage (I-V) relations were analyzed by an extension of the Poisson-Nernst-Planck (PNP) formulation of electrodiffusion, which includes local chem. interaction described by an offset in chem. potential, which likely reflects the difference in dehydration/solvation/rehydration energies in the entry/exit steps of permeation. The theory fits all of the data with few adjustable parameters: the diffusion coeff. of each ion species, the av. effective charge distribution on the wall of the pore, and an offset in chem. potential for lithium and sodium ions. In particular, the theory explains the discrepancy between "selectivities" defined by conductance sequence and "selectivities" detd. by the permeability ratios (i.e., reversal potentials) in biionic conditions. The extended PNP formulation seems to offer a successful combined treatment of selectivity and permeation. Conductance selectivity in this channel arises mostly from friction: different species of ions have different diffusion coeffs. in the channel. Permeability selectivity of an ion is detd. by its electrochem. potential gradient and local chem. interaction with the channel. Neither selectivity (in CRC) seems to involve different electrostatic interaction of different ions with the channel protein, even though the ions have widely varying diams.
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  33. 33.
    Corry, B.; Kuyucak, S.; Chung, S. H. J. Gen. Physiol. 1999, 114, 597
    [CrossRef], [PubMed], [CAS]
    33.
    Test of Poisson-Nernst-Planck theory in ion channels
    Corry B; Kuyucak S; Chung S H
    The Journal of general physiology (1999), 114 (4), 597-9 ISSN:0022-1295.
    There is no expanded citation for this reference.
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  34. 34.
    Eisenberg, R. S. J. Membr. Biol. 1999, 171, 1
    [CrossRef], [PubMed], [CAS]
    34.
    From structure to function in open ionic channels
    Eisenberg, R. S.
    Journal of Membrane Biology (1999), 171 (1), 1-24 CODEN: JMBBBO; ISSN:0022-2631. (Springer-Verlag New York Inc.)
    A review with many refs. on the protein structure of ionic channels and their function.
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  35. 35.
    Hollerbach, U.; Chen, D.; Nonner, W.; Eisenberg, B. Biophys. J. 1999, 76, A205
    There is no corresponding record for this reference.
  36. 36.
    Kurnikova, M. G.; Coalson, R. D.; Graf, P.; Nitzan, A. Biophys. J. 1999, 76, 642
    [CrossRef], [PubMed], [CAS]
    36.
    A lattice relaxation algorithm for three-dimensional Poisson-Nernst-Planck theory with application to ion transport through the gramicidin A channel
    Kurnikova, Maria G.; Coalson, Rob D.; Graf, Peter; Nitzan, Abraham
    Biophysical Journal (1999), 76 (2), 642-656 CODEN: BIOJAU; ISSN:0006-3495. (Biophysical Society)
    A lattice relaxation algorithm is developed to solve the Poisson-Nernst-Planck (PNP) equations for ion transport through arbitrary three-dimensional vols. Calcns. of systems characterized by simple parallel plate and cylindrical pore geometries are presented in order to calibrate the accuracy of the method. A study of ion transport through gramicidin A dimer is carried out within this PNP framework. Good agreement with exptl. measurements is obtained. Strengths and weaknesses of the PNP approach are discussed.
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  37. 37.
    Corry, B.; Kuyucak, S.; Chung, S. H. Biophys. J. 2000, 78, 2364
    [CrossRef], [PubMed], [CAS]
    37.
    Tests of continuum theories as models of ion channels. II. Poisson-Nernst-Planck theory versus Brownian dynamics
    Corry, Ben; Kuyucak, Serdar; Chung, Shin-Ho
    Biophysical Journal (2000), 78 (5), 2364-2381 CODEN: BIOJAU; ISSN:0006-3495. (Biophysical Society)
    A review, with 40 refs. We test the validity of the mean-field approxn. in Poisson-Nernst-Planck theory by contrasting its predictions with those of Brownian dynamics simulations in schematic cylindrical channels and in a realistic potassium channel. Equivalence of the two theories in bulk situations is demonstrated in a control study. In simple cylindrical channels, considerable differences are found between the two theories with regard to the concn. profiles in the channel and its conductance properties. These differences are at a max. in narrow channels with a radius smaller than the Debye length and diminish with increasing radius. Convergence occurs when the channel radius is over 2 Debye lengths. These tests unequivocally demonstrate that the mean-field approxn. in the Poisson-Nernst-Planck theory breaks down in narrow ion channels that have radii smaller than the Debye length.
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  38. 38.
    Graf, P.; Nitzan, A.; Kurnikova, M. G.; Coalson, R. D. J. Phys. Chem. B 2000, 104, 12324
    [ACS Full Text ACS Full Text], [CAS]
    38.
    A Dynamic Lattice Monte Carlo Model of Ion Transport in Inhomogeneous Dielectric Environments: Method and Implementation
    Graf, Peter; Nitzan, Abraham; Kurnikova, Maria G.; Coalson, Rob D.
    Journal of Physical Chemistry B (2000), 104 (51), 12324-12338 CODEN: JPCBFK; ISSN:1089-5647. (American Chemical Society)
    A dynamic lattice Monte Carlo (DLMC) simulation approach to the description of ion transport in dielec. environments is presented. Conventional approaches using periodic boundary conditions are inefficient for nonequil. situations in inhomogeneous systems; instead, the simulated system is embedded in a bigger system that dets. the av. electrostatic potential and the ionic concns. at its boundaries. Two issues are of special importance: implementing the given boundary conditions in the treatment of dynamical processes at and near the boundaries, and efficient evaluation of ion-ion interaction in the heterogeneous dielec. medium during the Monte Carlo simulation. The performance of the method is checked by comparing numerical results to exact solns. for simple geometries, and to mean field (Poisson-Nernst-Planck, PNP) theory in a system where the latter should provide a reasonable description. Other examples in which the PNP theory fails in various degrees are shown and discussed. In particular, PNP results deviate considerably from the DLMC dynamics for ion transport through rigid narrow membrane channels with large disparity between the dielec. consts. of the protein and the water environments.
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  39. 39.
    Hollerbach, U.; Chen, D. P.; Busath, D. D.; Eisenberg, B. Langmuir 2000, 16, 5509
    [ACS Full Text ACS Full Text], [CAS]
    39.
    Predicting Function from Structure Using the Poisson-Nernst-Planck Equations: Sodium Current in the Gramicidin A Channel
    Hollerbach, Uwe; Chen, Duan P.; Busath, David D.; Eisenberg, Bob
    Langmuir (2000), 16 (13), 5509-5514 CODEN: LANGD5; ISSN:0743-7463. (American Chemical Society)
    We predict the sodium current through an ion channel of known structure-gramicidin A (gA)-using an electrostatic model of the ion channel and an electrodiffusion model of ion movement. We use three-dimensional (3D) spectral elements to represent the channel and macroscopic surrounding baths in a 3D Poisson-Nernst-Planck (PNP) calcn. that uses fine resoln. only where needed in the channel pore region. Diffusion coeff. and dielec. consts. are estd. from a 1D PNP representation of the exptl. data. The 3D at. structure and std. empirical partial charges of gA are used, along with the diffusion coeffs. estd. from 1D PNP. No adjustable parameters were used in the 3D PNP calcn. No attempts were made to improve fit by adjusting parameters. Our results show that 3D PNP is an accurate description of charge transport in this channel system and thus a good place to start investigation of other channels. We predict unreported expts. as a further test of the theory.
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  40. 40.
    Moy, G.; Corry, B.; Kuyucak, S.; Chung, S. H. Biophys. J. 2000, 78, 2349
    [CrossRef], [PubMed], [CAS]
    40.
    Tests of continuum theories as models of ion channels. I. Poisson-Boltzmann theory versus Brownian dynamics
    Moy, Glenn; Corry, Ben; Kuyucak, Serdar; Chung, Shin-Ho
    Biophysical Journal (2000), 78 (5), 2349-2363 CODEN: BIOJAU; ISSN:0006-3495. (Biophysical Society)
    Continuum theories of electrolytes are widely used to describe phys. processes in various biol. systems. Although these are well-established theories in macroscopic situations, it is not clear from the outset that they should work in small systems whose dimensions are comparable to or smaller than the Debye length. Here, we test the validity of the mean-field approxn. in Poisson-Boltzmann theory by comparing its predictions with those of Brownian dynamics simulations. For this purpose we use spherical and cylindrical boundaries and a catenary shape similar to that of the acetylcholine receptor channel. The interior region filled with electrolyte is assumed to have a high dielec. const., and the exterior region representing protein a low one. Comparisons of the force on a test ion obtained with the two methods show that the shielding effect due to counterions is overestimated in Poisson-Boltzmann theory when the ion is within a Debye length of the boundary. As the ion gets closer to the boundary, the discrepancy in force grows rapidly. The implication for membrane channels, whose radii are typically smaller than the Debye length, is that Poisson-Boltzmann theory cannot be used to obtain reliable ests. of the electrostatic potential energy and force on an ion in the channel environment.
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  41. 41.
    Im, W.; Roux, B. Biophys. J. 2001, 115, 4850
    There is no corresponding record for this reference.
  42. 42.
    Edwards, S.; Corry, B.; Kuyucak, S.; Chung, S. H. Biophys. J. 2002, 83, 1348
    [CrossRef], [PubMed], [CAS]
    42.
    Continuum electrostatics fails to describe ion permeation in the gramicidin channel
    Edwards, Scott; Corry, Ben; Kuyucak, Serdar; Chung, Shin-Ho
    Biophysical Journal (2002), 83 (3), 1348-1360 CODEN: BIOJAU; ISSN:0006-3495. (Biophysical Society)
    We investigate the validity of continuum electrostatics in the gramicidin A channel using a recently detd. high-resoln. structure. The potential and elec. field acting on ions in and around the channel are computed by solving Poisson's equation. These are then used in Brownian dynamics simulations to obtain concn. profiles and the current passing through the channel. We show that regardless of the effective dielec. const. used for water in the channel or the channel protein, it is not possible to reproduce all the exptl. data on gramicidin A; thus, continuum electrostatics cannot provide a valid framework for the description of ion dynamics in gramicidin channels. Using exptl. data and mol. dynamics simulations as guides, we have constructed potential energy profiles that can satisfactorily describe the available physiol. data. These profiles provide useful benchmarks for future potential of mean force calcns. of permeating ions from mol. dynamics simulations of gramicidin A. They also offer a convenient starting point for studying structure-function relationships in modified gramicidin channels.
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  43. 43.
    Hollerbach, U.; Chen, D.-P.; Eisenberg, R. S. J. Comput. Sci. 2002, 16, 373
    There is no corresponding record for this reference.
  44. 44.
    Hollerbach, U.; Eisenberg, R. Langmuir 2002, 18, 3262
    [ACS Full Text ACS Full Text]
    There is no corresponding record for this reference.
  45. 45.
    Im, W.; Roux, B. J. Mol. Biol. 2002, 322, 851
    [CrossRef], [PubMed], [CAS]
    45.
    Ion Permeation and Selectivity of OmpF Porin: A Theoretical Study Based on Molecular Dynamics, Brownian Dynamics, and Continuum Electrodiffusion Theory
    Im, Wonpil; Roux, Benoit
    Journal of Molecular Biology (2002), 322 (4), 851-869 CODEN: JMOBAK; ISSN:0022-2836. (Elsevier Science Ltd.)
    Three different theor. approaches are used and compared to refine our understanding of ion permeation through the channel formed by OmpF porin from Escherichia coli. Those approaches are all-atom mol. dynamics (MD) in which ions, solvent, and lipids are represented explicitly, Brownian dynamics (BD) in which ions are represented explicitly, while solvent and lipids are represented as featureless dielecs., and Poisson-Nernst-Planck (PNP) electrodiffusion theory in which both solvent and local ion concns. are represented as a continuum. First, the ability of the different theor. approaches in reproducing the equil. av. ion d. distribution in OmpF porin bathed by a 1 M KCl sym. salt soln. is examd. Under those conditions the PNP theory is equiv. to the non-linear Poisson-Boltzmann (PB) theory. Anal. shows that all the three approaches are able to capture the important electrostatic interactions between ions and the charge distribution of the channel that govern ion permeation and selectivity in OmpF. The K+ and Cl- d. distributions obtained from the three approaches are very consistent with one another, which suggests that a treatment on the basis of a rigid protein and continuum dielec. solvent is valid in the case of OmpF. Interestingly, both BD and continuum electrostatics reproduce the distinct left-handed twisted ion pathways for K+ and Cl- extending over the length of the pore which were obsd. previously in MD. Equil. BD simulations in the grand canonical ensemble indicate that the channel is very attractive for cations, particularly at low salt concn. On an av. there is 1.55 K+ inside the pore in 10 mM KCl. Remarkably, there is still 0.17 K+ on av. inside the pore even at a concn. as low as 1 μM KCl. Secondly, non-equil. ion flow through OmpF is calcd. using BD and PNP and compared with exptl. data. The channel conductance in 0.2 M and 1 M KCl calcd. using BD is in excellent accord with the exptl. data. The calcns. reproduce the exptl. well-known conductance-concn. relation and also reveal an asymmetry in the channel conductance (a larger conductance is obsd. under a pos. transmembrane potential). Calcns. of the channel conductance for three mutants (R168A, R132A, and K16A) in 1 M KCl suggest that the asymmetry in the channel conductance arises mostly from the permanent charge distribution of the channel rather than the shape of the pore itself. Lastly, the calcd. reversal potential in a tenfold salt gradient (0.1:1 M KCl) is 27.4(±1.3) mV (BD) and 22.1(±0.6) mV (PNP), in excellent accord with the exptl. value of 24.3 mV. Although most of the results from PNP are qual. reasonable, the calcd. channel conductance is about 50% higher than that calcd. from BD probably because of a lack of some dynamical ion-ion correlations.
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  46. 46.
    Im, W.; Roux, B. J. Mol. Biol. 2002, 319, 1177
    [CrossRef], [PubMed], [CAS]
    46.
    Ions and Counterions in a Biological Channel: A Molecular Dynamics Simulation of OmpF Porin from Escherichia coli in an Explicit Membrane with 1 M KCl Aqueous Salt Solution
    Im, Wonpil; Roux, Benot
    Journal of Molecular Biology (2002), 319 (5), 1177-1197 CODEN: JMOBAK; ISSN:0022-2836. (Elsevier Science Ltd.)
    A 5 ns all-atom mol. dynamics trajectory of Escherichia coli OmpF porin embedded in an explicit dimyristoyl-phosphatidylcholine (DMPC) bilayer bathed by a 1 M [KCl] aq. salt soln. is generated to explore the microscopic details of the mechanism of ion permeation. The at. model includes the OmpF trimer, 124 DMPC, 13470 water mols. as well as 231 K+ and 201 Cl-, for a total of 70,693 atoms. The structural and dynamical results are in excellent agreement with the x-ray data. The global root-mean-square deviation of the backbone atoms relative to the x-ray structure is 1.4. A cluster of three fully charged arginine (Arg42, Arg82, and Arg132) facing two acidic residues (Asp113 and Glu117) on L3 in the narrowest part of the aq. pore is obsd. to be very stable in the crystallog. conformation. In this region of the pore, the water mols. are markedly oriented perpendicular to the channel axis due to the strong transversal electrostatic field arising from those residues. On av. the size of the pore is smaller during the simulation than in the x-ray structure, undergoing small fluctuations. No large movements of loop L3 leading to a gating of the pore are obsd. Remarkably, it is obsd. that K+ and Cl- follow two well-sepd. av. pathways spanning over nearly 40 along the axis of the pore. In the center of the monomer, the two screw-like pathways have a left-handed twist, undergoing a counter-clockwise rotation of 180° from the extracellular vestibule to the pore periplasmic side. In the pore, the dynamical diffusion consts. of the ions are reduced by about 50% relative to their value in bulk solvent. Anal. of ion solvation across the channel reveals that the contributions from the water and the protein are complementary, keeping the total solvation no. of both ions nearly const. Unsurprisingly, K+ have a higher propensity to occupy the aq. pore than Cl-, consistent with the cation selectivity of the channel. However, further anal. suggests that ion-ion pairs play an important role. In particular, it is obsd. that the passage of Cl- occurs only in the presence of K+ counterions, and isolated K+ can move through the channel and permeate on their own. The presence of K+ in the pore screens the neg. electrostatic potential arising from OmpF to help the translocation of Cl- by formation of ion pairs.
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  47. 47.
    van der Straaten, T. A.; Tang, J.; Eisenberg, R. S.; Ravaioli, U.; Aluru, N. R. J. Comput. Electron. 2002, 1, 335
    [CrossRef], [CAS]
    47.
    Three-dimensional continuum simulations of ion transport through biological ion channels: effect of charge distribution in the constriction region of porin
    Van Der Straaten, T. A.; Tang, J.; Eisenberg, R. S.; Ravaioli, U.; Aluru, N. R.
    Journal of Computational Electronics (2002), 1 (3), 335-340 CODEN: JCEOA7; ISSN:1569-8025. (Kluwer Academic Publishers)
    Drift-diffusion models are useful for studying ion transport in open protein channel systems over time scales that cannot be resolved practically by detailed mol. dynamics or quantum approaches. Water is treated as a uniform background medium with a specific dielec. const. and macroscopic current flow is resolved by assigning an appropriate mobility and diffusivity to each ionic species. The soln. of Poisson's equation over the entire domain provides a simple way to include external boundary conditions and image force effects at dielec. discontinuities. Here we present a 3-D drift-diffusion model of ion (K+ and Cl-) permeation through the porin channel ompF, and its mutant G119D, implemented using the computational platform PROPHET.
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  48. 48.
    van der Straaten, T. A.; Tang, J. M.; Eisenberg, R. S.; Ravaioli, U.; Aluru, N.; Varma, S.; E., J. Biophys. J. 2002, 82, 207a
    There is no corresponding record for this reference.
  49. 49.
    Corry, B.; Kuyucak, S.; Chung, S. H. Biophys. J. 2003, 84, 3594
    [CrossRef], [PubMed], [CAS]
    49.
    Dielectric self-energy in Poisson-Boltzmann and Poisson-Nernst-Planck models of ion channels
    Corry, Ben; Kuyucak, Serdar; Chung, Shin-Ho
    Biophysical Journal (2003), 84 (6), 3594-3606 CODEN: BIOJAU; ISSN:0006-3495. (Biophysical Society)
    We demonstrated previously that the two continuum theories widely used in modeling biol. ion channels give unreliable results when the radius of the conduit is less than two Debye lengths. The reason for this failure is the neglect of surface charges on the protein wall induced by permeating ions. Here we attempt to improve the accuracy of the Poisson-Boltzmann and Poisson-Nernst-Planck theories, when applied to channel-like environments, by including a specific dielec. self-energy term to overcome spurious shielding effects inherent in these theories. By comparing results with Brownian dynamics simulations, we show that the inclusion of an addnl. term in the equations yields significant qual. improvements. The modified theories perform well in very wide and very narrow channels, but are less successful at intermediate sizes. The situation is worse in multi-ion channels because of the inability of the continuum theories to handle the ion-to-ion interactions correctly. Thus, further work is required if these continuum theories are to be reliably salvaged for quant. studies of biol. ion channels in all situations.
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  50. 50.
    Mamonov, A. B.; Coalson, R. D.; Nitzan, A.; Kurnikova, M. G. Biophys. J. 2003, 84, 3646
    [CrossRef], [PubMed], [CAS]
    50.
    The role of the dielectric barrier in narrow biological channels: A novel composite approach to modeling single-channel currents
    Mamonov, Artem B.; Coalson, Rob D.; Nitzan, Abraham; Kurnikova, Maria G.
    Biophysical Journal (2003), 84 (6), 3646-3661 CODEN: BIOJAU; ISSN:0006-3495. (Biophysical Society)
    A composite continuum theory for calcg. ion current through a protein channel of known structure is proposed, which incorporates information about the channel dynamics. The approach is utilized to predict current through the Gramicidin A ion channel, a narrow pore in which the applicability of conventional continuum theories is questionable. The proposed approach utilizes a modified version of Poisson-Nernst-Planck (PNP) theory, termed Potential-of-Mean-Force-Poisson-Nernst-Planck theory (PMFPNP), to compute ion currents. As in std. PNP, ion permeation is modeled as a continuum drift-diffusion process in a self-consistent electrostatic potential. In PMFPNP, however, information about the dynamic relaxation of the protein and the surrounding medium is incorporated into the model of ion permeation by including the free energy of inserting a single ion into the channel, i.e., the potential of mean force along the permeation pathway. In this way the dynamic flexibility of the channel environment is approx. accounted for. The PMF profile of the ion along the Gramicidin A channel is obtained by combining an equil. mol. dynamics (MD) simulation that samples dynamic protein configurations when an ion resides at a particular location in the channel with a continuum electrostatics calcn. of the free energy. The diffusion coeff. of a potassium ion within the channel is also calcd. using the MD trajectory. Therefore, except for a reasonable choice of dielec. consts., no direct fitting parameters enter into this model. The results of our study reveal that the channel response to the permeating ion produces significant electrostatic stabilization of the ion inside the channel. The dielec. self-energy of the ion remains essentially unchanged in the course of the MD simulation, indicating that no substantial changes in the protein geometry occur as the ion passes through it. Also, the model accounts for the exptl. obsd. satn. of ion current with increase of the electrolyte concn., in contrast to the predictions of std. PNP theory.
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  51. 51.
    Nadler, B.; Hollerbach, U.; Eisenberg, R. S. Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys. 2003, 68, 021905
    [CrossRef], [CAS]
    51.
    Dielectric boundary force and its crucial role in gramicidin
    Nadler, Boaz; Hollerbach, Uwe; Eisenberg, R. S.
    Physical Review E: Statistical, Nonlinear, and Soft Matter Physics (2003), 68 (2-1), 021905/1-021905/9 CODEN: PRESCM ISSN:. (American Physical Society)
    In an electrostatic problem with nonuniform geometry, a charge Q in one region induces surface charges [called dielec. boundary charges (DBC)] at boundaries between different dielecs. These induced surface charges, in return, exert a force [called dielec. boundary force (DBF)] on the charge Q that induced them. The DBF is often overlooked. It is not present in std. continuum theories of (point) ions in or near membranes and proteins, such as Gouy-Chapman, Debye-Huckel, Poisson-Boltzmann or Poisson-Nernst- Planck. The DBF is important when a charge Q is near dielec. interfaces, for example, when ions permeate through protein channels embedded in biol. membranes. In this paper, we define the DBF and calc. it explicitly for a planar dielec. wall and for a tunnel geometry resembling the ionic channel gramicidin. In general, we formulate the DBF in a form useful for continuum theories, namely, as a soln. of a partial differential equation with boundary conditions. The DBF plays a crucial role in the permeation of ions through the gramicidin channel. A pos. ion in the channel produces a DBF of opposite sign to that of the fixed charge force (FCF) produced by the permanent charge of the gramicidin polypeptide, and so the net force on the pos. ion is reduced. A neg. ion creates a DBF of the same sign as the FCF and so the net (repulsive) force on the neg. ion is increased. Thus, a pos. ion can permeate the channel, while a neg. ion is excluded from it. In gramicidin, it is this balance between the FCF and DBF that allows only singly charged pos. ions to move into and through the channel. The DBF is not directly responsible, however, for selectivity between the alkali metal ions (e.g., Li+, Na+, K+): we prove that the DBF on a mobile spherical ion is independent of the ion's radius.
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  52. 52.
    Eisenberg, B., available on arXiv as http://arxiv.org/abs/1207.4737 , 2012.
    There is no corresponding record for this reference.
  53. 53.
    Eisenberg, B. Biophys. Chem. 2003, 100, 507
    [CrossRef], [PubMed], [CAS]
    53.
    Proteins, channels and crowded ions
    Eisenberg, Bob
    Biophysical Chemistry (2003), 100 (), 507-517 CODEN: BICIAZ; ISSN:0301-4622. (Elsevier Science B.V.)
    A review. Ion channels are proteins with a hole down their middle that control a vast range of biol. function in health and disease. Selectivity is an important biol. function detd. by the open channel, which does not change conformation on the biol. time scale. The challenge is to predict the function-the current of ions of different types and concns. through a variety of channels-from structure, given fundamental phys. laws. Walls of ion channels, like active sites of enzymes, often contain several fixed charges. Those fixed charges demand counter ions nearby, and the d. of those counter ions is very high, greater than 5 M, because of the tiny vols. of the channel's pore. Phys. chemists can now calc. the free energy per mol of salt solns. (e.g. the activity coeff.) from infinite diln. to satn., even in ionic melts. Such calcns. of a model of the L-type calcium channel show that the large energies needed to crowd charges into the channel can account for the substantial selectivity and complex properties found exptl. The properties of such crowded charge are likely to be an important determinant of the properties of proteins in general because channels are nearly enzymes.
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  54. 54.
    Giri, J.; Fonseca, J. E.; Boda, D.; Henderson, D.; Eisenberg, B. Phys. Biol. 2011, 8, 026004
    [CrossRef], [CAS]
    54.
    Self-organized models of selectivity in calcium channels
    Giri, Janhavi; Fonseca, James E.; Boda, Dezso; Henderson, Douglas; Eisenberg, Bob
    Physical Biology (2011), 8 (2), 026004/1-026004/14 CODEN: PBHIAT; ISSN:1478-3975. (Institute of Physics Publishing)
    The role of flexibility in the selectivity of calcium channels is studied using a simple model with two parameters that accounts for the selectivity of calcium (and sodium) channels in many ionic solns. of different compns. and concns. using two parameters with unchanging values. We compare the distribution of side chains (oxygens) and cations (Na+ and Ca2+) and integrated quantities. We compare the occupancies of cations Ca2+/Na+ and linearized conductance of Na+. The distributions show a strong dependence on the locations of fixed side chains and the flexibility of the side chains. Holding the side chains fixed at certain predetd. locations in the selectivity filter distorts the distribution of Ca2+ and Na+ in the selectivity filter. However, integrated quantities-occupancy and normalized conductance-are much less sensitive. Our results show that some flexibility of side chains is necessary to avoid obstruction of the ionic pathway by oxygen ions in "unfortunate" fixed positions. When oxygen ions are mobile, they adjust "automatically" and move "out of the way", so they can accommodate the permeable cations in the selectivity filter. Structure is the computed consequence of the forces in this model. The structures are self-organized, at their free energy min. The relationship of ions and side chains varies with an ionic soln. Monte Carlo simulations are particularly well suited to compute induced-fit, self-organized structures because the simulations yield an ensemble of structures near their free energy min. The exact location and mobility of oxygen ions has little effect on the selectivity behavior of calcium channels. Seemingly, nature has chosen a robust mechanism to control selectivity in calcium channels: the first-order determinant of selectivity is the d. of charge in the selectivity filter. The d. is detd. by filter vol. along with the charge and excluded vol. of structural ions confined within it. Flexibility seems a second-order determinant. These results justify our original assumption that the important factor in Ca2+ vs. Na+ selectivity is the d. of oxygen ions in the selectivity filter along with (charge) polarization (i.e. dielec. properties). The assumption of max. mobility of oxygens seems to be an excellent approx. working hypothesis in the absence of exact structural information. These conclusions, of course, apply to what we study here. Flexibility and fine structural details may have an important role in other properties of calcium channels that are not studied in this paper. They surely have important roles in other channels, enzymes, and proteins.
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  55. 55.
    Ganguly, P.; Mukherji, D.; Junghans, C.; van der Vegt, N. F. A. J. Chem. Theory Comput. 2012, 8, 1802
    [ACS Full Text ACS Full Text], [CAS]
    55.
    Kirkwood-Buff Coarse-Grained Force Fields for Aqueous Solutions
    Ganguly, Pritam; Mukherji, Debashish; Junghans, Christoph; van der Vegt, Nico F. A.
    Journal of Chemical Theory and Computation (2012), 8 (5), 1802-1807 CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
    We present an approach to systematically coarse-grain liq. mixts. using the fluctuation soln. theory of Kirkwood and Buff in conjunction with the iterative Boltzmann inversion method. The approach preserves both the liq. structure at pair level and the dependence of solvation free energies on solvent compn. within a unified coarse-graining framework. To test the robustness of our approach, we simulated urea-water and benzene-water systems at different concns. For urea-water, three different coarse-grained potentials were developed at different urea concns., in order to extend the simulations of urea-water mixts. up to 8 M urea concn. In spite of their inherent state point dependence, we find that the single-site models for urea and water are transferable in concn. windows of approx. 2 M. We discuss the development and application of these solvent models in coarse-grained biomol. simulations.
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  56. 56.
    Molina, J. J.; Dufreche, J.-F.; Salanne, M.; Bernard, O.; Turq, P. J. Chem. Phys. 2011, 135, 234509
    [CrossRef], [CAS]
    56.
    Primitive models of ions in solution from molecular descriptions: A perturbation approach
    Molina, John J.; Dufreche, Jean-Francois; Salanne, Mathieu; Bernard, Olivier; Turq, Pierre
    Journal of Chemical Physics (2011), 135 (23), 234509/1-234509/20 CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    The development of simple, primitive model descriptions for electrolyte solns. is usually carried out by fitting the system parameters to reproduce some exptl. data. We propose an alternative method, that allows one to derive implicit solvent models of electrolyte solns. from all-atom descriptions. We obtain analytic expressions for the thermodn. and structural properties of the ions, which are in good agreement with the underlying explicit solvent representation, provided that ion assocn. is taken into account. Effective ion-ion potentials are derived from mol. dynamics simulations and are used within a first-order perturbation theory to derive the best possible description in terms of charged hard-spheres. We show that our model provides a valid description for a series of 1-1 electrolytes. (c) 2011 American Institute of Physics.
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  57. 57.
    Fraenkel, D. J. Phys. Chem. B 2010, 115, 557
    [ACS Full Text ACS Full Text]
    There is no corresponding record for this reference.
  58. 58.
    Kunz, W.; Neueder, R.An Attempt at an Overview. In Specific Ion Effects; Kunz, W., Ed.; World Scientific: Singapore, 2009; p 11.
    There is no corresponding record for this reference.
  59. 59.
    Kunz, W. Specific Ion Effects; World Scientific: Singapore, 2009.
    [CrossRef]
    There is no corresponding record for this reference.
  60. 60.
    Kontogeorgis, G. M.; Folas, G. K. Thermodynamic Models for Industrial Applications: From Classical and Advanced Mixing Rules to Association Theories; Wiley: Chichester, U.K., 2009.
    There is no corresponding record for this reference.
  61. 61.
    Abbas, Z.; Ahlberg, E.; Nordholm, S. J. Phys. Chem. B 2009, 113, 5905
    [ACS Full Text ACS Full Text], [PubMed], [CAS]
    61.
    Monte Carlo Simulations of Salt Solutions: Exploring the Validity of Primitive Models
    Abbas, Zareen; Ahlberg, Elisabet; Nordholm, Sture
    Journal of Physical Chemistry B (2009), 113 (17), 5905-5916 CODEN: JPCBFK; ISSN:1520-6106. (American Chemical Society)
    An extensive series of Monte Carlo (MC) simulations were performed in order to explore the validity of simple primitive models of electrolyte solns. and in particular the effect of ion size asymmetry on the bulk thermodn. properties of real salt solns. Ionic activity and osmotic coeffs. were calcd. for 1:1, 2:1, and 3:1 electrolytes by using the unrestricted primitive model (UPM); i.e., ions are considered as charged hard spheres of different sizes dissolved in a dielec. continuum. Mean ionic activity and osmotic coeffs. calcd. by the MC simulations were fitted simultaneously to the exptl. data by adjusting only the cation radius while keeping the anion radius fixed at its crystallog. value. Ionic radii were further optimized by systematically varying the cation and anion radii at a fixed sum of ionic radii. The success of this approach is found to be highly salt specific. For example, exptl. data (mean ionic activity and osmotic coeffs.) of salts which are usually considered as dissocd. such as HCl, HBr, LiCl, LiBr, LiClO4, and KOH were successfully fitted up to 1.9, 2.5, 1.9, 3, 2.5, and 4.5 M concns., resp. In the case of partially dissocd. salts such as NaCl, the successful fits were only obtained in a more restricted concn. range. Consistent sets of the best fitted cation radii were obtained for acids, alkali and alk. earth halides. A list of recommended ionic radii is also provided. The reliability of the optimized ionic radii was further tested in simulations of the osmotic coeffs. of LiCl-NaCl-KCl salt mixts. A very good agreement between the simulated and exptl. data was obtained up to ionic strength of 4.5 M.
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  62. 62.
    Lee, L. L. Molecular Thermodynamics of Electrolyte Solutions; World Scientific: Singapore, 2008.
    [CrossRef]
    There is no corresponding record for this reference.
  63. 63.
    Jungwirth, P.; Winter, B. Annu. Rev. Phys. Chem. 2008, 59, 343
    [CrossRef], [PubMed], [CAS]
    63.
    Ions at aqueous interfaces: from water surface to hydrated proteins
    Jungwirth, Pavel; Winter, Bernd
    Annual Review of Physical Chemistry (2008), 59 (), 343-366 CODEN: ARPLAP; ISSN:0066-426X. (Annual Reviews Inc.)
    A review. The surfaces of aq. solns. are traditionally viewed as devoid of inorg. ions. Mol. simulations and surface-selective spectroscopic techniques show, however, that large polarizable anions and hydronium cations can be found (and even enhanced) at the surface and are involved in chem. at the air/water interface. Here, recent studies of ions at the air/water interface are reviewed and are compared from this perspective water with other polar solvents. For water, it is focussed in particular on the surface behavior of its ionic product (i.e., hydronium and hydroxide ions). Also the feasibility of dielec. models for the description of the protein/water interface, in analogy to the air/water interface was investigated. Little correlation was found between these two interfaces in terms of ion segregation. Therefore, a local model of pairing of ions from the soln. with charged and polar groups at the protein surface is suggested. Also corresponding results of exptl. studies on aq. model systems are described.
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  64. 64.
    Jungwirth, P.; Finlayson-Pitts, B. J.; Tobias, D. J. Chem. Rev. 2006, 106, 1137
    [ACS Full Text ACS Full Text], [CAS]
    64.
    Introduction: Structure and Chemistry at Aqueous Interfaces
    Jungwirth, Pavel; Finlayson-Pitts, Barbara J.; Tobias, Douglas J.
    Chemical Reviews (Washington, DC, United States) (2006), 106 (4), 1137-1139 CODEN: CHREAY; ISSN:0009-2665. (American Chemical Society)
    A review. The topics include nonlinear vibrational spectroscopy and photoemission measurements tailored for aq. interfaces, atmospherically relevant processes at air/water and air/ice interfaces, nanoscale aq. interfaces of small particles and thin films, and computational results for biol. active water/membrane interfaces.
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  65. 65.
    Ben-Naim, A. Molecular Theory of Solutions; Oxford University Press: New York, 2006.
    There is no corresponding record for this reference.
  66. 66.
    Fawcett, W. R. Liquids, Solutions, and Interfaces: From Classical Macroscopic Descriptions to Modern Microscopic Details; Oxford University Press: New York, 2004.
    There is no corresponding record for this reference.
  67. 67.
    Barthel, J.; Krienke, H.; Kunz, W. Physical Chemistry of Electrolyte Solutions: Modern Aspects; Springer: New York, 1998.
    There is no corresponding record for this reference.
  68. 68.
    Durand-Vidal, S.; Turq, P.; Bernard, O.; Treiner, C.; Blum, L. Physica A 1996, 231, 123
    [CrossRef], [CAS]
    68.
    New perspectives in transport phenomena in electrolytes
    Durand-Vidal, Serge; Turq, Pierre; Bernard, Olivier; Treiner, Claude; Blum, Lesser
    Physica A: Statistical and Theoretical Physics (Amsterdam) (1996), 231 (1-3), 123-143 CODEN: PHYADX; ISSN:0378-4371. (Elsevier)
    A review with 45 refs. Using the Fuoss-Onsager theory the authors recently obtained simple expressions for the variation with concn. of the transport coeffs. of electrolytes in aq. soln. Self-diffusion, conductance of binary and ternary ionic mixts., and micellar systems were studied. The authors used in the formulation of the mean spherical approxn. (MSA) pair correlation functions which yield explicit formulas in terms of the MSA inverse screening length Γ and the dynamical Debye-Falkenhagen lengths. It was found that the use of more accurate correlation functions, such as HNC, did not produce a significant improvement in the results. Assocd. electrolytes are also well described by a natural extension of this theory. The simple expressions derived by the authors yield good agreement with the expts. for both unassocd. and assocd. electrolytes.
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  69. 69.
    Pitzer, K. S. Thermodynamics, 3rd ed.; McGraw Hill: New York, 1995.
    There is no corresponding record for this reference.
  70. 70.
    Xu, Z.; Cai, W. SIAM Rev. 2011, 53, 683
    [CrossRef]
    There is no corresponding record for this reference.
  71. 71.
    Chazalviel, J.-N. Coulomb Screening by Mobile Charges; Birkhäuser: New York, 1999.
    There is no corresponding record for this reference.
  72. 72.
    Eisenberg, B. Trans. Faraday Soc. 2012, doi: 10.1039/C2FD20066J.
    [CrossRef]
    There is no corresponding record for this reference.
  73. 73.
    Eisenberg, B., posted on arXiv.org under paper ID arXiv:1105.0184v1, 2011.
    There is no corresponding record for this reference.
  74. 74.
    Eisenberg, B. Chem. Phys. Lett. 2011, 511, 1
    [CrossRef], [CAS]
    74.
    Mass action in ionic solutions
    Eisenberg, Bob
    Chemical Physics Letters (2011), 511 (1-3), 1-6 CODEN: CHPLBC; ISSN:0009-2614. (Elsevier B.V.)
    A review. The law of mass action describes reactants as simple ideal fluids of concns. of uncharged noninteracting particles. Ionic solns. contain interacting charged particles and are not ideal. Interactions of reactants can then be mistaken for complexities in chem. reactions or enzymic catalysts. The variational theory of complex fluids describes flowing mixts. like biol. solns. When a component is added, the theory derives-by mathematics alone-a new set of differential equations that automatically captures all interactions. A variational theory of ionic solns. (as complex fluids) provides computable description of ions in solns. and proteins. Numerical inefficiencies have delayed exptl. verification.
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  75. 75.
    Eisenberg, B.; Hyon, Y.; Liu, C. J. Chem. Phys. 2010, 133, 104104
    [CrossRef], [PubMed], [CAS]
    75.
    Energy variational analysis of ions in water and channels: Field theory for primitive models of complex ionic fluids
    Eisenberg, Bob; Hyon, Yun Kyong; Liu, Chun
    Journal of Chemical Physics (2010), 133 (10), 104104/1-104104/23 CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    Ionic solns. are mixts. of interacting anions and cations. They hardly resemble dil. gases of uncharged noninteracting point particles described in elementary textbooks. Biol. and electrochem. solns. have many components that interact strongly as they flow in concd. environments near electrodes, ion channels, or active sites of enzymes. Interactions in concd. environments help det. the characteristic properties of electrodes, enzymes, and ion channels. Flows are driven by a combination of elec. and chem. potentials that depend on the charges, concns., and sizes of all ions, not just the same type of ion. A variational method EnVarA (energy variational anal.) is used that combines Hamilton's least action and Rayleigh's dissipation principles to create a variational field theory that includes flow, friction, and complex structure with phys. boundary conditions. EnVarA optimizes both the action integral functional of classical mechanics and the dissipation functional. These functionals can include entropy and dissipation as well as potential energy. The stationary point of the action is detd. with respect to the trajectory of particles. The stationary point of the dissipation is detd. with respect to rate functions (such as velocity). Both variations are written in one Eulerian (lab.) framework. In variational anal., an "extra layer" of mathematics is used to derive partial differential equations. Energies and dissipations of different components are combined in EnVarA and Euler-Lagrange equations are then derived. These partial differential equations are the unique consequence of the contributions of individual components. The form and parameters of the partial differential equations are detd. by algebra without addnl. phys. content or assumptions. The partial differential equations of mixts. automatically combine phys. properties of individual (unmixed) components. If a new component is added to the energy or dissipation, the Euler-Lagrange equations change form and interaction terms appear without addnl. adjustable parameters. EnVarA has previously been used to compute properties of liq. crystals, polymer fluids, and electrorheol. fluids contg. solid balls and charged oil droplets that fission and fuse. Here EnVarA is applied to the primitive model of electrolytes in which ions are spheres in a frictional dielec. The resulting Euler-Lagrange equations include electrostatics and diffusion and friction. They are a time dependent generalization of the Poisson-Nernst-Planck equations of semiconductors, electrochem., and mol. biophysics. They include the finite diam. of ions. The EnVarA treatment is applied to ions next to a charged wall, where layering is obsd. Applied to an ion channel, EnVarA calcs. a quick transient pile-up of elec. charge, transient and steady flow through the channel, stationary "binding" in the channel, and the eventual accumulation of salts in "unstirred layers" near channels. EnVarA treats electrolytes in a unified way as complex rather than simple fluids. Ad hoc descriptions of interactions and flow were used in many areas of science to deal with the nonideal properties of electrolytes. It seems likely that the variational treatment can simplify, unify, and perhaps derive and improve those descriptions. (c) 2010 American Institute of Physics.
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  76. 76.
    Hyon, Y.; Eisenberg, B.; Liu, C. Commun. Math. Sci. 2011, 9, 459
    There is no corresponding record for this reference.
  77. 77.
    Mori, Y.; Liu, C.; Eisenberg, R. S. Physica D 2011, 240, 1835
    [CrossRef]
    There is no corresponding record for this reference.
  78. 78.
    Hyon, Y.; Fonseca, J. E.; Eisenberg, B.; Liu, C. Discrete Continuous Dynamical Syst., Ser. B 2012, 17, 2725
    [CrossRef]
    There is no corresponding record for this reference.
  79. 79.
    Zhang, J.; Gong, X.; Liu, C.; Wen, W.; Sheng, P. Phys. Rev. Lett. 2008, 101, 194503
    [CrossRef], [PubMed], [CAS]
    79.
    Electrorheological Fluid Dynamics
    Zhang, Jianwei; Gong, Xiuqing; Liu, Chun; Wen, Weijia; Sheng, Ping
    Physical Review Letters (2008), 101 (19), 194503/1-194503/4 CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
    We use the Onsager principle to derive a two-phase continuum formulation for the hydrodynamics of the electrorheol. (ER) fluid, consisting of dielec. microspheres dispersed in an insulating liq. Predictions of the theory are in excellent agreement with the expts. In particular, it is shown that whereas the usual configuration of applied elec. field being perpendicular to the shearing direction can lead to shear thinning at high shear rates and thus the loss of ER effect, the interdigitated, alternating electrodes configuration can eliminate the shear-thinning effect.
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  80. 80.
    Doi, M. J. Phys. Soc. Jpn. 2009, 78, 052001
    [CrossRef], [CAS]
    80.
    Gel dynamics
    Doi, Masao
    Journal of the Physical Society of Japan (2009), 78 (5), 052001/1-052001/19 CODEN: JUPSAU; ISSN:0031-9015. (Physical Society of Japan)
    A review. Continuum mech. model is proposed for dynamical processes in gels that involve coupling between the elastic deformation and solvent permeation. Basic equations are derived by two methods, by a phys. argument, and by a variational principle. The model is then applied to discuss the swelling of gels, in which solvent permeation causes deformation, and the squeezing of gels, in which mech. force induce solvent permeation. The model is also applied to the dynamics of the vol. transition of gels. It is shown that the elasticity of gels creates various unusual features in the phase transition dynamics.
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  81. 81.
    Liu, C.An Introduction of Elastic Complex Fluids: An Energetic Variational Approach. In Multi-scale Phenomena in Complex Fluids: Modeling, Analysis and Numerical Simulations; Hou, T. Y.; Liu, C.; Liu, J.-G, Eds.; World Scientific: Singapore, 2009.
    There is no corresponding record for this reference.
  82. 82.
    Lin, F.-H.; Liu, C.; Zhang, P. Commun. Pure Appl. Math. 2007, 60, 838
    [CrossRef]
    There is no corresponding record for this reference.
  83. 83.
    Lin, F.-H.; Liu, C.; Zhang, P. Commun. Pure Appl. Math. 2005, 58, 1437
    [CrossRef]
    There is no corresponding record for this reference.
  84. 84.
    Sheng, P.; Zhang, J.; Liu, C. Prog. Theor. Phys. 2008, 131, Suppl. 175 .
    There is no corresponding record for this reference.
  85. 85.
    Larson, R. G. The Structure and Rheology of Complex Fluids; Oxford University Press: New York, 1995.
    There is no corresponding record for this reference.
  86. 86.
    Buyukdagli, S.; Manghi, M.; Palmeri, J. Phys. Rev. E 2010, 81, 041601
    [CrossRef], [CAS]
    86.
    Variational approach for electrolyte solutions: From dielectric interfaces to charged nanopores
    Buyukdagli, Sahin; Manghi, Manoel; Palmeri, John
    Physical Review E: Statistical, Nonlinear, and Soft Matter Physics (2010), 81 (4-1), 041601/1-041601/20 CODEN: PRESCM; ISSN:1539-3755. (American Physical Society)
    A variational theory is developed to study electrolyte solns., composed of interacting pointlike ions in a solvent, in the presence of dielec. discontinuities and charges at the boundaries. Three important and nonlinear electrostatic effects induced by these interfaces are taken into account: surface charge induced electrostatic field, solvation energies due to the ionic cloud, and image-charge repulsion. Our variational equations thus go beyond the mean-field theory, or weak coupling limit, where thermal fluctuations overcome electrostatic correlations, and allows one to reach the opposite strong coupling limit, where electrostatic interactions induced by interfaces dominate. The influence of salt concn., ion valency, dielec. jumps, and surface charge is studied in two geometries. (i) A single neutral dielec. interface (e.g., air-water or electrolyte-membrane) with an asym. electrolyte. A charge sepn. and thus an electrostatic field get established due to the different image-charge repulsions for coions and counterions. Both charge distributions and surface tension are computed and compared to previous approx. calcns. For sym. electrolyte solns. close to a charged surface, two zones are characterized. In the first one, in contact with the surface and with size proportional to the logarithm of the coupling parameter, strong image forces and strong coupling impose a total ion exclusion, while in the second zone the mean-field approach applies. (ii) A sym. electrolyte confined between two dielec. interfaces as a simple model of ion rejection from nanopores in membranes. The competition between image-charge repulsion and attraction of counterions by the membrane charge is studied. For small surface charge, the counterion partition coeff. decreases with increasing pore size up to a crit. pore size, contrary to neutral membranes. For larger pore sizes, the whole system behaves like a neutral pore. For strong coupling and small pore size, coion exclusion is total and the counterion partition coeff. is solely detd. by global electroneutrality. A quant. comparison is made with a previous approach, where image and surface charge effects were smeared out in the pore. It is shown that the variational method allows one to go beyond the const. Donnan potential approxn., with deviations stronger at high ion concns. or small pore sizes. The prediction of the variational method is also compared with MC simulations and good agreement is obsd.
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  87. 87.
    Nonner, W.; Chen, D. P.; Eisenberg, B. Biophys. J. 1998, 74, 2327
    [CrossRef], [PubMed], [CAS]
    87.
    Anomalous mole fraction effect, electrostatics, and binding in ionic channels
    Nonner, Wolfgang; Chen, Duan P.; Eisenberg, Bob
    Biophysical Journal (1998), 74 (5), 2327-2334 CODEN: BIOJAU; ISSN:0006-3495. (Biophysical Society)
    Ionic channels bathed in mixed solns. of two permeant electrolytes often conduct less current than channels bathed in pure solns. of either. For many years, this anomalous mole fraction effect (AMFE) has been thought to occur only in single-file pores contg. two or more ions at a time. Most thinking about channels incorporates this view. We show here that the AMFE arises naturally, as an electrostatic consequence of localized ion specific binding, if the av. current through a channel is described by a theory (Poisson-Nernst-Planck, PNP) that computes the av. elec. field from the av. concn. of charges in and near the channel. The theory contains only those ion-ion interactions mediated by the mean field, and it does not enforce single filing. The AMFE is predicted by PNP over a wide range of mean concns. of ions in the channel; for example, it is predicted when (on the av.) less, or much less, than one ion is found in the channel's pore. In this treatment, the AMFE arises, in large measure, from a depletion layer produced near a region of ion-specific binding. The small excess concn. of ions in the binding region repels all nearby ions of like charge, thereby creating a depletion layer. The overall conductance of the channel arises in effect from resistors in series, one from the binding region, one from the depletion zone, and one from the unbinding region. The highest value resistor (which occurs in the depletion zone) limits the overall series conductance. Here the AMFE is not the result of single filing or multiple occupancy, and so previous views of permeation need to be revised: the presence of an AMFE does not imply that ions permeate single file through a multiply occupied pore.
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  88. 88.
    Nonner, W.; Eisenberg, B. Biophys. J. 1998, 75, 1287
    [CrossRef], [PubMed], [CAS]
    88.
    Ion permeation and glutamate residues linked by Poisson-Nernst-Planck theory in L-type calcium channels
    Nonner, Wolfgang; Eisenberg, Bob
    Biophysical Journal (1998), 75 (3), 1287-1305 CODEN: BIOJAU; ISSN:0006-3495. (Biophysical Society)
    L-type Ca channels contain a cluster of four charged glutamate residues (EEEE locus), which seem essential for high Ca specificity. To understand how this highly charged structure might produce the currents and selectivity obsd. in this channel, a theory is needed that relates charge to current. We use an extended Poisson-Nernst-Planck (PNP2) theory to compute (mean) Coulombic interactions and thus to examine the role of the mean field electrostatic interactions in producing current and selectivity. The pore was modeled as a central cylinder with tapered atria; the cylinder (i.e., "pore proper") contained a uniform vol. d. of fixed charge equiv. to that of one to four carboxyl groups. The pore proper was assigned ion-specific, but spatially uniform, diffusion coeffs. and excess chem. potentials. Thus electrostatic selection by valency was computed self-consistently, and selection by other features was also allowed. The five external parameters needed for a system of four ionic species (Na, Ca, Cl, and H) were detd. anal. from published measurements of three limiting conductances and two crit. ion concns., while treating the pore as a macroscopic ion-exchange system in equil. with a uniform bath soln. The extended PNP equations were solved with these parameters, and the predictions were compared to currents measured in a variety of solns. over a range of transmembrane voltages. The extended PNP theory accurately predicted current-voltage relations, anomalous mole fraction effects in the obsd. current, satn. effects of varied Ca and Na concns., and block by protons. Pore geometry, dielec. permittivity, and the no. of carboxyl groups had only weak effects. The successful prediction of Ca fluxes in this paper demonstrates that ad hoc electrostatic parameters, multiple discrete binding sites, and logistic assumptions of single-file movement are all unnecessary for the prediction of permeation in Ca channels over a wide range of conditions. Further work is needed, however, to understand the at. origin of the fixed charge, excess chem. potentials, and diffusion coeffs. of the channel. The Appendix uses PNP2 theory to predict ionic currents for published "barrier-and-well" energy profiles of this channel.
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  89. 89.
    Nonner, W.; Catacuzzeno, L.; Eisenberg, B. Biophys. J. 2000, 79, 1976
    [CrossRef], [PubMed], [CAS]
    89.
    Binding and selectivity in L-type calcium channels: a mean spherical approximation
    Nonner, Wolfgang; Catacuzzeno, Luigi; Eisenberg, Bob
    Biophysical Journal (2000), 79 (4), 1976-1992 CODEN: BIOJAU; ISSN:0006-3495. (Biophysical Society)
    L-type calcium channels are Ca2+ binding proteins of great biol. importance. They generate an essential intracellular signal of living cells by allowing Ca2+ ions to move across the lipid membrane into the cell, thereby selecting an ion that is in low extracellular abundance. Their mechanism of selection involves four carboxylate groups, contg. eight oxygen ions, that belong to the side chains of the "EEEE" locus of the channel protein, a setting similar to that found in many Ca2+-chelating mols. This study examines the hypothesis that selectivity in this locus is detd. by mutual electrostatic screening and vol. exclusion between ions and carboxylate oxygens of finite diams. In this model, the eight half-charged oxygens of the tethered carboxylate groups of the protein are confined to a subvolume of the pore (the "filter"), but interact spontaneously with their mobile counterions as ions interact in concd. bulk solns. The mean spherical approxn. (MSA) is used to predict ion-specific excess chem. potentials in the filter and baths. The theory is calibrated using a single exptl. observation, concerning the apparent dissocn. const. of Ca2+ in the presence of a physiol. concn. of NaCl. When ions are assigned their independently known crystal diams. and the carboxylate oxygens are constrained, e.g., to a vol. of 0.375 nm3 in an environment with an effective dielec. coeff. of 63.5, the hypothesized selectivity filter produces the shape of the calcium binding curves obsd. in expt., and it predicts Ba2+/Ca2+ and Na+/Li+ competition, and Cl- exclusion as obsd. The selectivities for Na+, Ca2+, Ba2+, other alkali metal ions, and Cl- thus can be predicted by vol. exclusion and electrostatic screening alone. Spontaneous coordination of ions and carboxylates can produce a wide range of Ca2+ selectivities, depending on the vol. d. of carboxylate groups and the permittivity in the locus. A specific three-dimensional structure of atoms at the binding site is not needed to explain Ca2+ selectivity.
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  90. 90.
    Boda, D.; Gillespie, D.; Nonner, W.; Henderson, D.; Eisenberg, B. Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys. 2004, 69, 046702
    [CrossRef], [CAS]
    90.
    Computing induced charges in inhomogeneous dielectric media: application in a Monte Carlo simulation of complex ionic systems
    Boda, Dezso; Gillespie, Dirk; Nonner, Wolfgang; Henderson, Douglas; Eisenberg, Bob
    Physical Review E: Statistical, Nonlinear, and Soft Matter Physics (2004), 69 (4-2), 046702/1-046702/10 CODEN: PRESCM ISSN:. (American Physical Society)
    The efficient calcn. of induced charges in an inhomogeneous dielec. is important in simulations and coarse-grained models in mol. biol., chem. physics, and electrochem. The authors present the induced charge computation (ICC) method for the calcn. of the polarization charges based on the variational formulation of Allen et al [Phys. Chem. Chem. Phys. 3, 4177(2001)]. The authors give a different soln. for their extremum condition that produces a matrix formulation. The induced charges are directly calcd. by solving the linear matrix equation Ah = c, where h contains the discretized induced charge d., c depends only on the source charges-the ions moved in the simulation-and the matrix A depends on the geometry of dielecs., which is assumed to be unchanged during the simulation. Thus, the matrix need be inverted only once at the beginning of the simulation. The authors verify the efficiency and accuracy of the method by Monte Carlo simulations for two special cases. In the simplest case, a single sharp planar dielec. boundary is present, which allows comparison with exact results calcd. using the method of electrostatic images. The other special case is a particularly simple case where the matrix A is not diagonal: a slab with two parallel flat boundaries. The results for electrolyte solns. in these special cases show that the ICC method is both accurate and efficient.
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  91. 91.
    Boda, D.; Busath, D.; Eisenberg, B.; Henderson, D.; Nonner, W. Phys. Chem. Chem. Phys. 2002, 4, 5154
    [CrossRef], [CAS]
    91.
    Monte Carlo simulations of ion selectivity in a biological Na channel: Charge-space competition
    Boda, Dezso; Busath, David D.; Eisenberg, Bob; Henderson, Douglas; Nonner, Wolfgang
    Physical Chemistry Chemical Physics (2002), 4 (20), 5154-5160 CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
    Na channels that produce the action potentials of nerve and muscle include a selectivity filter formed by both pos. and neg. charged amino acid residues in a mol. pore. Here we present Monte Carlo simulations of equil. ion absorption in such a system. Ions are treated as charged hard spheres in a uniform dielec. Tethered carboxylate and amino groups known to line the selectivity filter of the Na channel are represented as charged hard spheres and restricted to the filter region of the channel. Consistent with expts., we find (1) that absorption of Ca2+ into the filter exceeds absorption of Na+ only when the concn. of Ca2+ is some tenfold larger than physiol.; (2) the model channel absorbs smaller alkali metal ions preferentially compared to larger ones. The alkali metal selectivity involves vol. exclusion of larger ions from the center of the filter region.
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  92. 92.
    Boda, D.; Henderson, D.; Busath, D. Mol. Phys. 2002, 100, 2361
    [CrossRef], [CAS]
    92.
    Monte Carlo study of the selectivity of calcium channels: improved geometrical model
    Boda, Dezso; Henderson, Douglas; Busath, David D.
    Molecular Physics (2002), 100 (14), 2361-2368 CODEN: MOPHAM; ISSN:0026-8976. (Taylor & Francis Ltd.)
    An extended model of a calcium channel is described involving a channel with a finite length. With this new geometry the channel is still selective but less so than in an infinite cylinder geometry. The selectivity of the channel depends on the width and length of the channel filter but is not significantly affected by changes in the size of the entry vestibules. Interestingly, changes in the size of the entry vestibules do affect the details of the concn. profiles of some of the ions.
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  93. 93.
    Eisenberg, B.Institute for Mathematics and its Applications; University of Minnesota; http://www.ima.umn.edu/, 2009.
    There is no corresponding record for this reference.
  94. 94.
    Boda, D.; Giri, J.; Henderson, D.; Eisenberg, B.; Gillespie, D. J. Chem. Phys. 2011, 134, 055102
    [CrossRef], [CAS]
    94.
    Analyzing the components of the free-energy landscape in a calcium selective ion channel by Widom's particle insertion method
    Boda, Dezso; Giri, Janhavi; Henderson, Douglas; Eisenberg, Bob; Gillespie, Dirk
    Journal of Chemical Physics (2011), 134 (5), 055102/1-055102/14 CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    The selectivity filter of the L-type calcium channel works as a Ca2+ binding site with a very large affinity for Ca2+ vs. Na+. Ca2+ replaces half of the Na+ ions in the filter even when these ions are present in 1 μM and 30 mM concns. in the bath, resp. The energetics of this strong selectivity is analyzed in this paper. We use Widom's particle insertion method to compute the space-dependent profiles of excess chem. potential in our grand canonical Monte Carlo simulations. These profiles define the free-energy landscape for the various ions. Following Gillespie, the difference of the excess chem. potentials for the two competing ions defines the advantage that one of the ions has over the other in the competition for space in the crowded selectivity filter. These advantages depend on ionic bath concns.: the ion that is present in the bath in larger quantity (Na+) has the "no." advantage which is balanced by the free-energy advantage of the other ion (Ca2+). The excess chem. potentials are decompd. into hard sphere exclusion and electrostatic components. The electrostatic terms correspond to interactions with the mean elec. field produced by ions and induced charges as well to ionic correlations beyond the mean field description. Dielecs. are needed to produce micromolar Ca2+ vs. Na+ selectivity in the L-type channel. We study the behavior of these terms with changes in bath concns. of ions, charges, and diams. of ions, as well as geometrical parameters such as radius of the pore and the dielec. const. of the protein. Ion selectivity in calcium binding proteins probably has a similar mechanism. (c) 2011 American Institute of Physics.
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  95. 95.
    Boda, D.; Valisko, M.; Henderson, D.; Eisenberg, B.; Gillespie, D.; Nonner, W. J. Gen. Physiol. 2009, 133, 497
    [CrossRef], [PubMed], [CAS]
    95.
    Ionic selectivity in L-type calcium channels by electrostatics and hard-core repulsion
    Boda, Dezso; Valisko, Monika; Henderson, Douglas; Eisenberg, Bob; Gillespie, Dirk; Nonner, Wolfgang
    Journal of General Physiology (2009), 133 (5), 497-509 CODEN: JGPLAD; ISSN:0022-1295. (Rockefeller University Press)
    A phys. model of selective "ion binding" in the L-type calcium channel is constructed, and consequences of the model are compared with exptl. data. This reduced model treats only ions and the carboxylate oxygens of the EEEE locus explicitly and restricts interactions to hard-core repulsion and ion-ion and ion-dielec. electrostatic forces. The structural atoms provide a flexible environment for passing cations, thus resulting in a self-organized induced-fit model of the selectivity filter. Exptl. conditions involving binary mixts. of alkali and/or alk. earth metal ions are computed using equil. Monte Carlo simulations in the grand canonical ensemble. The model pore rejects alkali metal ions in the presence of biol. concns. of Ca2+ and predicts the blockade of alkali metal ion currents by micromolar Ca2+. Conductance patterns obsd. in varied mixts. contg. Na+ and Li+, or Ba2+ and Ca2+, are predicted. Ca2+ is substantially more potent in blocking Na+ current than Ba2+. In apparent contrast to expts. using buffered Ca2+ solns., the predicted potency of Ca2+ in blocking alkali metal ion currents depends on the species and concn. of the alkali metal ion, as is expected if these ions compete with Ca2+ for the pore. These expts. depend on the problematic estn. of Ca2+ activity in solns. buffered for Ca2+ and pH in a varying background of bulk salt. Simulations of Ca2+ distribution with the model pore bathed in solns. contg. a varied amt. of Li+ reveal a "barrier and well" pattern. The entry/exit barrier for Ca2+ is strongly modulated by the Li+ concn. of the bath, suggesting a phys. explanation for obsd. kinetic phenomena. Our simulations show that the selectivity of L-type calcium channels can arise from an interplay of electrostatic and hard-core repulsion forces among ions and a few crucial channel atoms. The reduced system selects for the cation that delivers the largest charge in the smallest ion vol.
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  96. 96.
    Boda, D.; Nonner, W.; Henderson, D.; Eisenberg, B.; Gillespie, D. Biophys. J. 2008, 94, 3486
    [CrossRef], [PubMed], [CAS]
    96.
    Volume exclusion in calcium selective channels
    Boda, Dezso; Nonner, Wolfgang; Henderson, Douglas; Eisenberg, Bob; Gillespie, Dirk
    Biophysical Journal (2008), 94 (9), 3486-3496 CODEN: BIOJAU; ISSN:0006-3495. (Biophysical Society)
    A polemic in response to Chung , S. et al (ibid, 2001 80, pg. 195-214; Proc. IEEE., 2007, 95, pg. 853-880; Cell. Mol. Life Sci., 2006, 63, pg. 301-315; and Biochim. Biophys. Acta., 2006, 1711, pg. 72-86) is presented. Chung's research group has proposed an interesting model for calcium channel selectivity. However, on the basis of their reported results, we find it impossible to assess the merits of their model because their results and claims concerning selectivity are based on an extrapolation over four orders of magnitude to low Ca2+ concn. Their results and claims have been presented in several articles and reviews in several journals and, thus, need attention. In this article, we first establish that we obtain results on electrostatics and channel occupancies similar to the high-concn. simulations they present. We then perform grand canonical ensemble simulations that enable us to study micromolar Ca2+ concns. We find that their model channel is only weakly Ca2+ selective. A crucial problem with their model appears to be the placement of the neg. charged glutamate structural elements in fixed positions inside the protein rather than as flexible units inside the filter.
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  97. 97.
    Krauss, D.; Eisenberg, B.; Gillespie, D. Eur. Biophys. J. 2011, 40, 775
    [CrossRef], [CAS]
    97.
    Selectivity sequences in a model calcium channel: role of electrostatic field strength
    Krauss, Daniel; Eisenberg, Bob; Gillespie, Dirk
    European Biophysics Journal (2011), 40 (6), 775-782 CODEN: EBJOE8; ISSN:0175-7571. (Springer)
    The energetics that give rise to selectivity sequences of ionic binding selectivity of Li+, Na+, K+, Rb+, and Cs+ in a model of a calcium channel are considered. This work generalizes Eisenman's classic treatment (Biophys J 2(Suppl. 2):259, 1962) by including multiple, mobile binding site oxygens that coordinate many permeating ions (all modeled as charged, hard spheres). The selectivity filter of the model calcium channel allows the carboxyl terminal groups of glutamate and aspartate side chains to directly interact with and coordinate the permeating ions. Ion dehydration effects are represented with a Born energy between the dielec. coeffs. of the selectivity filter and the bath. High oxygen concn. creates a high field strength site that prefers small ions, as in Eisenman's model. On the other hand, a low filter dielec. const. also creates a high field strength site, but this site prefers large ions, contrary to Eisenman's model. These results indicate that field strength does not have a unique effect on ionic binding selectivity sequences once entropic, electrostatic, and dehydration forces are included in the model. Thus, Eisenman's classic relationship between field strength and selectivity sequences must be supplemented with addnl. information about selectivity filters such as the calcium channel that has amino acid side chains mixing with ions to make a crowded permeation pathway.
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  98. 98.
    Dolphin, A. C. Br. J. Pharmacol. 2006, 147, S56
    [CrossRef], [CAS]
    98.
    A short history of voltage-gated calcium channels
    Dolphin, Annette C.
    British Journal of Pharmacology (2006), 147 (Suppl. 1), S56-S62 CODEN: BJPCBM; ISSN:0007-1188. (Nature Publishing Group)
    A review. Topics discussed include pharmacol. and identification of calcium channel subtypes, auxiliary subunits, and modulation of calcium channels by G-proteins and second messenger pathways.
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  99. 99.
    Boda, D.; Nonner, W.; Valisko, M.; Henderson, D.; Eisenberg, B.; Gillespie, D. Biophys. J. 2007, 93, 1960
    [CrossRef], [PubMed], [CAS]
    99.
    Steric selectivity in Na channels arising from protein polarization and mobile side chains
    Boda, Dezso; Nonner, Wolfgang; Valisko, Monika; Henderson, Douglas; Eisenberg, Bob; Gillespie, Dirk
    Biophysical Journal (2007), 93 (6), 1960-1980 CODEN: BIOJAU; ISSN:0006-3495. (Biophysical Society)
    Monte Carlo (MC) simulations of equil. selectivity of Na channels with a DEKA locus are performed over a range of radius R and protein dielec. coeff. εp. Selectivity arises from the balance of electrostatic forces and steric repulsion by excluded vol. of ions and side chains of the channel protein in the highly concd. and charged (30 M) selectivity filter resembling an ionic liq. Ions and structural side chains are described as mobile charged hard spheres that assume positions of minimal free energy. Water is a dielec. continuum. Size selectivity (ratio of Na+ occupancy to K+ occupancy) and charge selectivity (Na+ to Ca2+) are computed in concns. as low as 10-5 M Ca2+. In general, small R reduces ion occupancy and favors Na+ over K+ because of steric repulsion. Small εp increases occupancy and favors Na+ over Ca2+ because protein polarization amplifies the pore's net charge. Size selectivity depends on R and is independent of εp; charge selectivity depends on both R and εp. Thus, small R and εp make an efficient Na channel that excludes K+ and Ca2+ while maximizing Na+ occupancy. Selectivity properties depend on interactions that cannot be described by qual. or verbal models or by quant. models with a fixed free energy landscape.
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  100. 100.
    Miedema, H.; Meter-Arkema, A.; Wierenga, J.; Tang, J.; Eisenberg, B.; Nonner, W.; Hektor, H.; Gillespie, D.; Meijberg, W. Biophys. J. 2004, 87, 3137
    [CrossRef], [PubMed], [CAS]
    100.
    Permeation properties of an engineered bacterial OmpF porin containing the EEEE-locus of Ca2+ channels
    Miedema, Henk; Meter-Arkema, Anita; Wierenga, Jenny; Tang, John; Eisenberg, Bob; Nonner, Wolfgang; Hektor, Hans; Gillespie, Dirk; Meijberg, Wim
    Biophysical Journal (2004), 87 (5), 3137-3147 CODEN: BIOJAU; ISSN:0006-3495. (Biophysical Society)
    The selectivity filter of the bacterial porin OmpF carries a small net charge close to -1 e and is therefore only slightly cation-selective. Calcium channels, on the other hand, contain four neg. charged glutamates, the EEEE-locus, and are among the most selective cation channels known. We aimed to turn the essentially nonselective OmpF into a Ca2+-selective channel. To that end, two addnl. glutamates (R42E and R132E) were introduced in the OmpF constriction zone that already contains D113 and E117. Mutant OmpF contg. this DEEE-locus has a high Ca2+ over Cl- selectivity and a Na+ current with a strongly increased sensitivity to 1 mM Ca2+. The charge/space competition model, initially applied to the L-type Ca2+ channel, identifies the fixed charge and filter vol. as key determinants of ion selectivity, with the precise at. arrangement having only second-order effects. By implication, the reprodn. of fixed charge and filter vol. should transform two channels into channels of similar selectivity, even if the two belong to entirely different ion channel families, as is the case for OmpF and the L-type Ca2+ channel. The results presented here fit quite well in the framework of charge/space competition theory.
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  101. 101.
    Miedema, H.; Vrouenraets, M.; Wierenga, J.; Gillespie, D.; Eisenberg, B.; Meijberg, W.; Nonner, W. Biophys. J. 2006, 91, 4392
    [CrossRef], [PubMed], [CAS]
    101.
    Ca2+ selectivity of a chemically modified OmpF with reduced pore volume
    Miedema, Henk; Vrouenraets, Maarten; Wierenga, Jenny; Gillespie, Dirk; Eisenberg, Bob; Meijberg, Wim; Nonner, Wolfgang
    Biophysical Journal (2006), 91 (12), 4392-4400 CODEN: BIOJAU; ISSN:0006-3495. (Biophysical Society)
    We studied an E. coli OmpF mutant (LECE) contg. both an EEEE-like locus, typical of Ca2+ channels, and an accessible and reactive cysteine. After chem. modification with the cysteine-specific, neg. charged (-1e) reagents MTSES or glutathione, this LECE mutant was tested for Ca2+ vs. alkali metal selectivity. Selectivity was measured by conductance and zero-current potential. Conductance measurements showed that glutathione-modified LECE had reduced conductance at Ca2+ mole fractions <10-3. MTSES-modified LECE did not. Apparently, the LECE protein is (somehow) a better Ca2+ chelator after modification with the larger glutathione. Zero-current potential measurements revealed a Ca2+ vs. monovalent cation selectivity that was highest in the presence of Li+ and lowest in the presence of Cs+. Our data clearly show that after the binding of Ca2+ the LECE pore (even with the bulky glutathione present) is spacious enough to allow monovalent cations to pass. Theor. computations based on d. functional theory combined with Poisson-Nernst-Planck theory and a reduced pore model suggest a functional sepn. of ionic pathways in the pore, one that is specific for small and highly charged ions, and one that accepts preferentially large ions, such as Cs+.
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  102. 102.
    Vrouenraets, M.; Wierenga, J.; Meijberg, W.; Miedema, H. Biophys. J. 2006, 90, 1202
    [CrossRef], [PubMed], [CAS]
    102.
    Chemical modification of the bacterial porin OmpF: gain of selectivity by volume reduction
    Vrouenraets, Maarten; Wierenga, Jenny; Meijberg, Wim; Miedema, Henk
    Biophysical Journal (2006), 90 (4), 1202-1211 CODEN: BIOJAU; ISSN:0006-3495. (Biophysical Society)
    OmpF is an essentially nonselective porin isolated from the outer membrane of Escherichia coli. Here we report on the manipulation of the ion selectivity of OmpF by chem. modification with MTS reagents (MTSET, MTSEA, and MTSES) and the (rather bulky) tripeptide glutathione, all cysteine-specific. When recorded in a gradient of 0.1//1 M CaCl2 or 0.1//1 M NaCl, pH 7.4 solns., measured reversal potentials of the most cation-selective modified mutants were (virtually) identical to the Nernst potential of Ca2+ or Na+. Compared to this full cation selectivity, the anion-selective modified mutants performed somewhat less but nevertheless showed high anion selectivity. We conclude that a low permanent charge in combination with a narrow pore can render the same selectivity as a highly charged but wider pore. These results favor the view that both the electrostatic potential arising from the fixed charge in the pore and the space available at the selectivity filter contribute to the charge selection (i.e., cation vs. anion selectivity) of a biol. ion channel.
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  103. 103.
    Malasics, A.; Boda, D.; Valisko, M.; Henderson, D.; Gillespie, D. Biochim. Biophys. Acta 2010, 1798, 2013
    [CrossRef], [CAS]
    103.
    Simulations of calcium channel block by trivalent cations: Gd3+ competes with permeant ions for the selectivity filter
    Malasics, Attila; Boda, Dezso; Valisko, Monika; Henderson, Douglas; Gillespie, Dirk
    Biochimica et Biophysica Acta, Biomembranes (2010), 1798 (11), 2013-2021 CODEN: BBBMBS; ISSN:0005-2736. (Elsevier B.V.)
    Current through L-type calcium channels (CaV1.2 or dihydropyridine receptor) can be blocked by micromolar concns. of trivalent cations like the lanthanide gadolinium (Gd3+). It has been proposed that trivalent block is due to ions competing for a binding site in both the open and closed configuration, but possibly with different trivalent affinities. Here, we corroborate this general view of trivalent block by computing conductance of a model L-type calcium channel. The model qual. reproduces the Gd3+ concn. dependence and the effect that substantially more Gd3+ is required to produce similar block in the presence of Sr2+ (compared to Ba2+) and even more in the presence of Ca2+. Trivalent block is explained in this model by cations binding in the selectivity filter with the charge/space competition mechanism. This is the same mechanism that in the model channel governs other selectivity properties. Specifically, selectivity is detd. by the combination of ions that most effectively screen the neg. glutamates of the protein while finding space in the midst of the closely packed carboxylate groups of the glutamate residues.
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  104. 104.
    Krauss, D.; Gillespie, D. Eur. Biophys. J. 2010, 39, 1513
    [CrossRef], [CAS]
    104.
    Sieving experiments and pore diameter: it's not a simple relationship
    Krauss, Daniel; Gillespie, Dirk
    European Biophysics Journal (2010), 39 (11), 1513-1521 CODEN: EBJOE8; ISSN:0175-7571. (Springer)
    The classic sieving expt. for estg. an ion channel's diam. with successively larger ions is re-examd. Using a very reduced model of a calcium channel, it is shown that sieving expts. measure a combination of three mechanisms: the cross-sectional area available to the sieving ions (the classic interpretation), the exclusion of the sieving ions from a pore crowded with amino acid side chains that protrude into the permeation pathway, and competitive selectivity of the sieving ions with other ions in the bath (even if those are present only at trace concns.). The latter two can be called sieving-by-crowding because they stem from the excluded vol. of the amino acids in the permeation pathway. The model shows that-to a first-order approxn.-sieving expts. measure the available vol. inside a selectivity filter, rather than the available cross-sectional area. The two are only the same if the narrow part of the pore does not have flexible amino acid side chains interacting directly with the permeant ions; this may be true of potassium channels, but not calcium, sodium, and other channels with "crowded" selectivity filters.
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  105. 105.
    Gillespie, D.; Giri, J.; Fill, M. Biophyis. J. 2009, 97, 2212
    [CrossRef]
    There is no corresponding record for this reference.
  106. 106.
    Gillespie, D.; Fill, M. Biophys. J. 2008, 95, 3706
    [CrossRef], [PubMed], [CAS]
    106.
    Intracellular calcium release channels mediate their own countercurrent: The ryanodine receptor case study
    Gillespie, Dirk; Fill, Michael
    Biophysical Journal (2008), 95 (8), 3706-3714 CODEN: BIOJAU; ISSN:0006-3495. (Biophysical Society)
    Intracellular calcium release channels like ryanodine receptors (RyRs) and inositol trisphosphate receptors (IP3Rs) mediate large Ca2+ release events from Ca2+ storage organelles lasting >5 ms. To have such long-lasting Ca2+ efflux, a countercurrent of other ions is necessary to prevent the membrane potential from becoming the Ca2+ Nernst potential in <1 ms. A recent model of ion permeation through a single, open RyR channel is used here to show that the vast majority of this countercurrent is conducted by the RyR itself. Consequently, changes in membrane potential are minimized locally and instantly, assuring maintenance of a Ca2+-driving force. This RyR autocountercurrent is possible because of the poor Ca2+ selectivity and high conductance for both monovalent and divalent cations of these channels. The model shows that, under physiol. conditions, the autocountercurrent clamps the membrane potential near 0 mV within 150 μs. Consistent with expts., the model shows how RyR unit Ca2+ current is defined by luminal [Ca2+], permeable ion compn. and concn., and pore selectivity and conductance. This very likely is true of the highly homologous pore of the IP3R channel.
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  107. 107.
    Gillespie, D.; Boda, D.; He, Y.; Apel, P.; Siwy, Z. S. Biophys. J. 2008, 95, 609
    [CrossRef], [PubMed], [CAS]
    107.
    Synthetic nanopores as a test case for ion channel theories: the anomalous mole fraction effect without single filing
    Gillespie, Dirk; Boda, Dezso; He, Yan; Apel, Pavel; Siwy, Zuzanna S.
    Biophysical Journal (2008), 95 (2), 609-619 CODEN: BIOJAU; ISSN:0006-3495. (Biophysical Society)
    The predictions of a theory for the anomalous mole fraction effect (AMFE) are tested exptl. with synthetic nanopores in plastic. The neg. charged synthetic nanopores under consideration are highly cation selective and 50 Å in diam. at their smallest point. These pores exhibit an AMFE in mixts. of Ca2+ and monovalent cations. An AMFE occurs when the conductance through a pore is lower in a mixt. of salts than in the pure salts at the same concn. For ion channels, the textbook interpretation of the AMFE is that multiple ions move through the pore in coordinated, single-file motion. However, because the synthetic nanopores are so wide, their AMFE shows that single filing is not necessary for the AMFE. It is shown that the AMFE in the synthetic nanopores is explained by a theory of preferential ion selectivity. The unique properties of the synthetic nanopores allow us to exptl. confirm several predictions of this theory. These same properties make synthetic nanopores an interesting new platform to test theories of ion channel permeation and selectivity in general.
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  108. 108.
    Gillespie, D.; Boda, D. Biophys. J. 2008, 95, 2658
    [CrossRef], [PubMed], [CAS]
    108.
    The anomalous mole fraction effect in calcium channels: a measure of preferential selectivity
    Gillespie, Dirk; Boda, Dezso
    Biophysical Journal (2008), 95 (6), 2658-2672 CODEN: BIOJAU; ISSN:0006-3495. (Biophysical Society)
    The cause of the anomalous mole fraction effect (AMFE) in calcium-selective ion channels is studied. An AMFE occurs when the conductance through a channel is lower in a mixt. of salts than in the pure salts at the same concn. The textbook interpretation of the AMFE is that multiple ions move through the pore in coordinated, single-file motion. Instead of this, we find that at its most basic level an AMFE reflects a channel's preferential binding selectivity for one ion species over another. The AMFE is explained by considering the charged and uncharged regions of the pore as elec. resistors in series: the AMFE is produced by these regions of high and low ion concn. changing differently with mole fraction due to the preferential ion selectivity. This is demonstrated with simulations of a model L-type calcium channel and a math. anal. of a simplistic point-charge model. The particle simulations reproduce the exptl. data of two L-type channel AMFEs. Conditions under which an AMFE may be found exptl. are discussed. The resistors-in-series model provides a fundamentally different explanation of the AMFE than the traditional theory and does not require single filing, multiple occupancy, or momentum-correlated ion motion.
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  109. 109.
    Gillespie, D. Biophys. J. 2008, 94, 1169
    [CrossRef], [PubMed], [CAS]
    109.
    Energetics of divalent selectivity in a calcium channel: the ryanodine receptor case study
    Gillespie, Dirk
    Biophysical Journal (2008), 94 (4), 1169-1184 CODEN: BIOJAU; ISSN:0006-3495. (Biophysical Society)
    A model of the ryanodine receptor (RyR) calcium channel is used to study the energetics of binding selectivity of Ca2+ vs. monovalent cations. RyR is a calcium-selective channel with a DDDD locus in the selectivity filter, similar to the EEEE locus of the L-type calcium channel. While the affinity of RyR for Ca2+ is in the millimolar range (as opposed to the micromolar range of the L-type channel), the ease of single-channel measurements compared to L-type and its similar selectivity filter make RyR an excellent candidate for studying calcium selectivity. A Poisson-Nernst-Planck/d. functional theory model of RyR is used to calc. the energetics of selectivity. Ca2+ vs. monovalent selectivity is driven by the charge/space competition mechanism in which selectivity arises from a balance of electrostatics and the excluded vol. of ions in the crowded selectivity filter. While electrostatic terms dominate the selectivity, the much smaller excluded-vol. term also plays a substantial role. In the D4899N and D4938N mutations of RyR that are analyzed, substantial changes in specific components of the chem. potential profiles are found far from the mutation site. These changes result in the significant redn. of Ca2+ selectivity found in both theory and expts.
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  110. 110.
    Gillespie, D.; Valisko, M.; Boda, D. J. Phys.: Condens. Matter 2005, 17, 6609
    [CrossRef], [CAS]
    110.
    Density functional theory of the electrical double layer: The RFD functional
    Gillespie, Dirk; Valisko, Monika; Boda, Dezso
    Journal of Physics: Condensed Matter (2005), 17 (42), 6609-6626 CODEN: JCOMEL; ISSN:0953-8984. (Institute of Physics Publishing)
    D. functional theory (DFT) of electrolytes is applied to the elec. double layer under a wide range of conditions. The ions are charged, hard spheres of different size and valence, and the wall creating the double layer is uncharged, weakly charged, and strongly charged. Under all conditions, the d. and electrostatic potential profiles calcd. using the recently proposed RFD electrostatic functional compare well to Monte Carlo simulations. When the wall is strongly charged, the RFD functional results agree with the results of a simpler perturbative electrostatic DFT, but the two functionals' results qual. disagree when the wall is uncharged or weakly charged. The RFD functional reproduces these phenomena of weakly charged double layers. It also reproduces bulk thermodn. quantities calcd. from pair correlation functions.
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  111. 111.
    Gillespie, D.; Nonner, W.; Eisenberg, R. S. Phys. Rev. E 2003, 68, 0313503
    [CrossRef]
    There is no corresponding record for this reference.
  112. 112.
    Gillespie, D.; Nonner, W.; Eisenberg, R. S. J. Phys.: Condens. Matter 2002, 14, 12129
    [CrossRef], [CAS]
    112.
    Coupling Poisson-Nernst-Planck and density functional theory to calculate ion flux
    Gillespie, Dirk; Nonner, Wolfgang; Eisenberg, Robert S.
    Journal of Physics: Condensed Matter (2002), 14 (46), 12129-12145 CODEN: JCOMEL; ISSN:0953-8984. (Institute of Physics Publishing)
    Ion transport between two baths of fixed ionic concns. and applied electrostatic (ES) potential is analyzed using a one-dimensional drift-diffusion (Poisson-Nernst-Planck, PNP) transport system designed to model biol. ion channels. The ions are described as charged, hard spheres with excess chem. potentials computed from equil. d. functional theory (DFT). The method of Rosenfeld (Rosenfeld Y 1993 J. Chem. Phys. 98 8126) is generalized to calc. the ES excess chem. potential in channels. A numerical algorithm for solving the set of integral-differential PNP/DFT equations is described and used to calc. flux through a calcium-selective ion channel.
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  113. 113.
    Chen, D. P.Nonequilibrium Thermodynamics of Transports in Ion Channels. In Progress of Cell Research: Towards Molecular Biophysics of Ion Channels; Sokabe, M.; Auerbach, A.; Sigworth, F., Eds.; Elsevier: Amsterdam, 1997; p 269.
    There is no corresponding record for this reference.
  114. 114.
    Chen, D.; Xu, L.; Tripathy, A.; Meissner, G.; Eisenberg, R. Biophys. J. 1997, 72, A108
    [CrossRef]
    There is no corresponding record for this reference.
  115. 115.
    Hyon, Y.; Kwak, D. Y.; Liu, C. Discrete Continuous Dynamical Syst., Ser. A 2010, 26, 1291
    [CrossRef]
    There is no corresponding record for this reference.
  116. 116.
    Barcilon, V.; Chen, D. P.; Eisenberg, R. S. SIAM J. Appl. Math. 1992, 52, 1405
    [CrossRef]
    There is no corresponding record for this reference.
  117. 117.
    Gillespie, D.; Eisenberg, R. S. Eur. Biophys. J. 2002, 31, 454
    [CrossRef], [PubMed], [CAS]
    117.
    Physical descriptions of experimental selectivity measurements in ion channels
    Gillespie, Dirk; Eisenberg, Robert S.
    European Biophysics Journal (2002), 31 (6), 454-466 CODEN: EBJOE8; ISSN:0175-7571. (Springer-Verlag)
    Three expts. that quantify the amt. of selectivity exhibited by a biol. ion channel are examd. with Poisson-Nernst-Planck (PNP) theory. Conductance ratios and the conductance mole fraction expts. are examd. by considering a simple model ion channel for which an approx. soln. to the PNP equations with Donnan boundary conditions is derived. A more general result is derived for the Goldman-Hodgkin-Katz permeability ratio. The results show that (1) the conductance ratio measures the ratio of the diffusion coeffs. of the ions inside the channel, (2) the mole fraction expt. measures the difference of the excess chem. potentials of the ions inside the channel, and (3) the permeability ratio measures both diffusion coeffs. and excess chem. potentials. The results are used to divide selectivity into two components: partitioning, an equil. measure of how well the ions enter the channel, and diffusion, a nonequil. measure of how well the ions move through the channel.
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  118. 118.
    Gillespie, D.; Nonner, W.; Eisenberg, R. S. Biophys. J. Abstr. 2002, 84, 67a
    There is no corresponding record for this reference.
  119. 119.
    Gardner, C. L.; Nonner, W.; Eisenberg, R. S. J. Comput. Electron. 2004, 3, 25
    [CrossRef], [CAS]
    119.
    Electrodiffusion model simulation of ionic channels: 1D simulations
    Gardner, Carl L.; Nonner, Wolfgang; Eisenberg, Robert S.
    Journal of Computational Electronics (2004), 3 (1), 25-31 CODEN: JCEOA7; ISSN:1569-8025. (Kluwer Academic Publishers)
    The drift-diffusion (Poisson-Nernst-Planck) model is applied to ionic channels in biol. membranes plus surrounding soln. baths. Simulations of the K channel in KCl solns. using the TRBDF2 method are presented which show significant boundary layers at the ends of the channel. The computed current-voltage curve for the K channel shows excellent agreement with exptl. measurements.
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  120. 120.
    Aguilella-Arzo, M.; Aguilella, V.; Eisenberg, R. S. Eur. Biophys. J. 2005, 34, 314
    [CrossRef], [PubMed], [CAS]
    120.
    Computing numerically the access resistance of a pore
    Aguilella-Arzo Marcel; Aguilella Vicente M; Eisenberg R S
    European biophysics journal : EBJ (2005), 34 (4), 314-22 ISSN:0175-7571.
    The access resistance (AR) of a channel is an important component of the conductance of ion channels, particularly in wide and short channels, where it accounts for a substantial fraction of the total resistance to the movement of ions. The AR is usually calculated by using a classical and simple expression derived by Hall from electrostatics (J.E. Hall 1975 J. Gen. Phys. 66:531-532), though other expressions, both analytical and numerical, have been proposed. Here we report some numerical results for the AR of a channel obtained by solving the Poisson-Nernst-Planck equations at the entrance of a circular pore. Agreement is found between numerical calculations and analytical results from Hall's equation for uncharged pores in neutral membranes. However, for channels embedded in charged membranes, Hall's expression overestimates the AR, which is much lower and can even be neglected in some cases. The weak dependence of AR on the pore radius for charged membranes at low salt concentration can be exploited to separate the channel and the access contributions to the measured conductance.
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  121. 121.
    Luchinsky, D. G.; Tindjong, R.; Kaufman, I.; McClintock, P. V. E.; Eisenberg, R. S. Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys. 2009, 80, 021925
    [CrossRef], [CAS]
    121.
    Self-consistent analytic solution for the current and the access resistance in open ion channels
    Luchinsky, D. G.; Tindjong, R.; Kaufman, I.; McClintock, P. V. E.; Eisenberg, R. S.
    Physical Review E: Statistical, Nonlinear, and Soft Matter Physics (2009), 80 (2-1), 021925/1-021925/12 CODEN: PRESCM; ISSN:1539-3755. (American Physical Society)
    A self-consistent analytic approach is introduced for the estn. of the access resistance and the current through an open ion channel for an arbitrary no. of species. For an ion current flowing radially inward from infinity to the channel mouth, the Poisson-Boltzmann-Nernst-Planck equations are solved anal. in the bulk with spherical symmetry in three dimensions, by linearization. Within the channel, the Poisson-Nernst-Planck equation is solved anal. in a one-dimensional approxn. An iterative procedure is used to match the two solns. together at the channel mouth in a self-consistent way. It is shown that the current-voltage characteristics obtained are in good quant. agreement with exptl. measurements.
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  122. 122.
    Doi, M. J. Phys.: Condens. Matter 2011, 23, 284118
    [CrossRef], [CAS]
    122.
    Onsager's variational principle in soft matter
    Doi, Masao
    Journal of Physics: Condensed Matter (2011), 23 (28), 284118/1-284118/8 CODEN: JCOMEL; ISSN:0953-8984. (Institute of Physics Publishing)
    In the celebrated paper on the reciprocal relation for the kinetic coeffs. in irreversible processes, Onsager extended Rayleigh's principle of the least energy dissipation to general irreversible processes. In this paper, I shall show that this variational principle gives us a very convenient framework for deriving many established equations which describe the nonlinear and non-equil. phenomena in soft matter, such as phase sepn. kinetics in solns., gel dynamics, mol. modeling for viscoelasticity nemato-hydrodynamics, etc. Onsager's variational principle can therefore be regarded as a solid general basis for soft matter physics.
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  123. 123.
    Hou, T. Y.; Liu, C.; Liu, J.-G. Multi-scale Phenomena in Complex Fluids: Modeling, Analysis and Numerical Simulations; World Scientific: Singapore, 2009.
    There is no corresponding record for this reference.
  124. 124.
    Hyon, Y.; Carrillo, J. A.; Du, Q.; Liu, C. Kinetic Relat. Models 2008, 1, 171
    [CrossRef]
    There is no corresponding record for this reference.
  125. 125.
    Hyon, Y.; Du, Q.; Liu, C. J. Comput. Theor. Nanosci. 2010, 7, 756
    [CrossRef], [CAS]
    125.
    On some probability density function based moment closure approximations of micro-macro models for viscoelastic polymeric fluids
    Hyon, YunKyong; Du, Qiang; Liu, Chun
    Journal of Computational and Theoretical Nanoscience (2010), 7 (4), 756-765 CODEN: JCTNAB; ISSN:1546-1955. (American Scientific Publishers)
    In this paper we will discuss several issues related to the moment-closure approxn. of multiscale models for viscoelastic polymeric fluids. These moment-closure approaches are based on special ansatz for the probability d. function (PDF) in the finite extensible nonlinear elastic (FENE) dumbbell micro-macro models which consist of the coupled incompressible Navier-Stokes equations and the Fokker-Planck equations. We present the exact energy law of the resulting closure systems and introduce a post-modification scheme to preserve the positivity of PDF. The scheme not only reduces the region of neg. PDF values but also preserves the structure of the induced stress tensor resulting from the mol. behaviors such as stretching and rotation. Numerical verifications are provided for the moment-closure system with some std. external flows. We also explore the relation of the max. entropy principle (MEP) and the moment-closure approach.
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  126. 126.
    Ryham, R. J.An Energetic Variational Approach to Mathematical Moldeling of Charged Fluids, Charge Phases, Simulation and Well Posedness. Ph.D. Thesis, The Pennsylvania State University, 2006.
    There is no corresponding record for this reference.
  127. 127.
    Xu, X.; Liu, C.; Qian, T. Commun. Math. Sci. 2012, 10, 1027
    There is no corresponding record for this reference.
  128. 128.
    Ryham, R.; Cohen, F.; Eisenberg, R. S. Commun. Math. Sci. 2012, not supplied.
    There is no corresponding record for this reference.
  129. 129.
    Dan, B.-Y.; Andelman, D.; Harries, D.; Podgornik, R. J. Phys.: Condens. Matter 2009, 21, 424106
    [CrossRef]
    There is no corresponding record for this reference.
  130. 130.
    Malasics, A.; Gillespie, D.; Boda, D. J. Chem. Phys. 2008, 128, 124102
    [CrossRef], [PubMed], [CAS]
    130.
    Simulating prescribed particle densities in the grand canonical ensemble using iterative algorithms
    Malasics, Attila; Gillespie, Dirk; Boda, Dezso
    Journal of Chemical Physics (2008), 128 (12), 124102/1-124102/6 CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    We present two efficient iterative Monte Carlo algorithms in the grand canonical ensemble with which the chem. potentials corresponding to prescribed (targeted) partial densities can be detd. The first algorithm works by always using the targeted densities in the kTlog(ρi) (ideal gas) terms and updating the excess chem. potentials from the previous iteration. The second algorithm extrapolates the chem. potentials in the next iteration from the results of the previous iteration using a first order series expansion of the densities. The coeffs. of the series, the derivs. of the densities with respect to the chem. potentials, are obtained from the simulations by fluctuation formulas. The convergence of this procedure is shown for the examples of a homogeneous Lennard-Jones mixt. and a NaCl-CaCl2 electrolyte mixt. in the primitive model. The methods are quite robust under the conditions investigated. The first algorithm is less sensitive to initial conditions. (c) 2008 American Institute of Physics.
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  131. 131.
    Bruna, M.; Chapman, S. J. Phys. Rev. E 2012, 85, 011103
    [CrossRef], [CAS]
    131.
    Excluded-volume effects in the diffusion of hard spheres
    Bruna, Maria; Chapman, S. Jonathan
    Physical Review E: Statistical, Nonlinear, and Soft Matter Physics (2012), 85 (1-1), 011103/1-011103/6 CODEN: PRESCM; ISSN:1539-3755. (American Physical Society)
    Excluded-vol. effects can play an important role in detg. transport properties in diffusion of particles. Here, the diffusion of finite-sized hard-core interacting particles in two or three dimensions is considered systematically using the method of matched asymptotic expansions. The result is a nonlinear diffusion equation for the one-particle distribution function, with excluded-vol. effects enhancing the overall collective diffusion rate. An expression for the effective (collective) diffusion coeff. is obtained. Stochastic simulations of the full particle system are shown to compare well with the soln. of this equation for two examples.
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  132. 132.
    Streetman, B. G. Solid State Electronic Devices, 4th ed.; Prentice Hall: Englewood Cliffs, NJ, 1972.
    There is no corresponding record for this reference.
  133. 133.
    Sze, S. M. Physics of Semiconductor Devices; John Wiley & Sons: New York, 1981.
    There is no corresponding record for this reference.
  134. 134.
    Selberherr, S. Analysis and Simulation of Semiconductor Devices; Springer-Verlag: New York, 1984.
    [CrossRef]
    There is no corresponding record for this reference.
  135. 135.
    Markowich, P. A.; Ringhofer, C. A.; Schmeiser, C. Semiconductor Equations; Springer-Verlag: New York, 1990.
    [CrossRef]
    There is no corresponding record for this reference.
  136. 136.
    Jerome, J. W. Analysis of Charge Transport: Mathematical Theory and Approximation of Semiconductor Models; Springer-Verlag: New York, 1995.
    There is no corresponding record for this reference.
  137. 137.
    Howe, R. T.; Sodini, C. G. Microelectronics: An Integrated Approach; Prentice Hall: Upper Saddle River, NJ, 1997.
    There is no corresponding record for this reference.
  138. 138.
    Hess, K. Advanced Theory of Semiconductor Devices; IEEE Press: New York, 2000.
    There is no corresponding record for this reference.
  139. 139.
    Berti, C.; Gillespie, D.; Eisenberg, R. S.; Fiegna, C. Nanoscale Res. Lett. 2012, not supplied.
    There is no corresponding record for this reference.
  140. 140.
    Eisenberg, B. Pro. Natl. Acad. Sci. U.S.A. 2008, 105, 6211
    [CrossRef], [PubMed], [CAS]
    140.
    Engineering channels: atomic biology
    Eisenberg, Bob
    Proceedings of the National Academy of Sciences of the United States of America (2008), 105 (17), 6211-6212 CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)
    A review. Mutations that change flexibility of parts of the protein can greatly reduce natural gating.
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  141. 141.
    Eisenberg, B. available on http://arxiv.org/ as q-bio/0506016v2, 2005.
    There is no corresponding record for this reference.
  142. 142.
    Eisenberg, B. J. Comput. Electron. 2003, 2, 245
    [CrossRef], [CAS]
    142.
    Ion channels as devices
    Eisenberg, Bob
    Journal of Computational Electronics (2003), 2 (2/3/4), 245-249 CODEN: JCEOA7; ISSN:1569-8025. (Kluwer Academic Publishers)
    A review. Ion channels are proteins with a hole down their middle that control an enormous range of biol. function. Channels are devices in the engineering sense of the word and engineering anal. helps understand their function. In particular, the current through channels is driven by the power supply of concn. gradient and elec. potential maintained by across membranes by cell metab. The current is controlled by the physics of ion permeation in a narrow charged tube. The wall of the tube contains a few fixed charges; the tube is less than 1 nm in diam. The d. of charge (mobile or fixed) in the tube is enormous, 10 M. (Liq. water is 55 M.). Movement of ions through this tube can be well described as the movement of charged spheres according to the Poisson-Drift-Diffusion equations of computational electronics. Selfconsistent computation of the elec. field is a necessity. The chem. specificity of channels seems to arise from the crowding of charge in their narrow tunnel. A purely phys. description of the energetics of crowded spheres is enough to explain the complex patterns of selectivity found in several types of channels.
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  143. 143.
    Barcilon, V.; Chen, D.-P.; Eisenberg, R. S.; Jerome, J. W. SIAM J. Appl. Math. 1997, 57, 631
    [CrossRef]
    There is no corresponding record for this reference.
  144. 144.
    Chen, D.; Eisenberg, R.; Jerome, J.; Shu, C. Biophys. J. 1995, 69, 2304
    [CrossRef], [PubMed], [CAS]
    144.
    Hydrodynamic model of temperature change in open ionic channels
    Chen, Duan P.; Eisenberg, Robert S.; Jerome, Joseph W.; Shu, Chi-Wang
    Biophysical Journal (1995), 69 (6), 2304-22 CODEN: BIOJAU; ISSN:0006-3495. (Biophysical Society)
    Most theories of open ion channels ignore heat generated by current flow, but that heat is known to be significant when analogous currents flow in semiconductors, so a generalization of the Poisson-Nernst-Planck theory of channels, called the hydrodynamic model, is needed. The hydrodynamic theory is a combination of the Poisson and Euler field equations of electrostatics and fluid dynamics, conservation laws that describe diffusive and convective flow of mass, heat, and charge (i.e., current), and their coupling. That is to say, it is a kinetic theory of solute and solvent flow, allowing heat and current flow as well, taking into account d. changes, temp. changes, and elec. potential gradients. The authors integrate the equations with an essentially non-oscillatory shock-capturing numerical scheme previously shown to be stable and accurate. The calcns. showed that (1) a significant amt. of elec. energy was exchanged with the permeating ions; (2) the local temp. of the ions rose some tens of degrees, and this temp. rise significantly altered the ion flux in a channel 25 Å long, such as gramicidin A; and (3) a crit. parameter, called the satn. velocity, detd. whether ionic motion was overdamped (Poisson-Nernst-Planck theory), was in an intermediate regime (called the adiabatic approxn. in semiconductor theory), or was altogether unrestricted (requiring the full hydrodynamic model). Apparently, significant temp. changes are likely to accompany current flow in the open ion channel.
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  145. 145.
    Chen, D. P.; Eisenberg, R. S. Biophys. J. 1993, 64, 1405
    [CrossRef], [PubMed], [CAS]
    145.
    Charges, currents, and potentials in ionic channels of one conformation
    Chen, Duanpin; Eisenberg, Robert
    Biophysical Journal (1993), 64 (5), 1405-21 CODEN: BIOJAU; ISSN:0006-3495.
    Flux through an open ionic channel is analyzed with Poisson-Nernst-Planck (PNP) theory. The channel protein is described as an unchanging but nonuniform distribution of permanent charge, the charge distribution obsd. (in principle) in x-ray diffraction. Appropriate boundary conditions are derived and presented in some generality. Three kinds of charge are present: (a) permanent charge on the atoms of the protein, the charge independent of the elec. field; (b) free or mobile charge, carried by ions in the pore as they flux through the channel; and (c) induced (sometimes called polarization) charge, in the pore and protein, created by the elec. field, zero when the elec. field is zero. The permanent charge produces an offset in potential, a built-in Donnan potential at both ends of the channel pore. The system is completely solved for bathing solns. of two ions. Graphs describe the distribution of potential, concn., free (i.e., mobile) and induced charge, and the potential energy assocd. with the concn. of charge, as well as the unidirectional flux as a function of concn. of ions in the bath, for a distribution of permanent charge that is uniform. The model shows surprising complexity, exhibiting some (but not all) of the properties usually attributed to single filing and exchange diffusion. The complexity arises because the arrangement of free and induced charge, and thus of potential and potential energy, varies, sometimes substantially, as conditions change, even though the channel structure and conformation (of permanent charge) is strictly const. Energy barriers and wells, and the concomitant binding sites and binding phenomena, are outputs of the PNP theory; they are computed, not assumed. They vary in size and location as exptl. conditions change, while the conformation of permanent charge remains const., thus giving the model much of its interesting behavior.
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  146. 146.
    Chen, D. P.; Barcilon, V.; Eisenberg, R. S. Biophys. J. 1992, 61, 1372
    [CrossRef], [PubMed], [CAS]
    146.
    Constant fields and constant gradients in open ionic channels
    Chen D P; Barcilon V; Eisenberg R S
    Biophysical journal (1992), 61 (5), 1372-93 ISSN:0006-3495.
    Ions enter cells through pores in proteins that are holes in dielectrics. The energy of interaction between ion and charge induced on the dielectric is many kT, and so the dielectric properties of channel and pore are important. We describe ionic movement by (three-dimensional) Nemst-Planck equations (including flux and net charge). Potential is described by Poisson's equation in the pore and Laplace's equation in the channel wall, allowing induced but not permanent charge. Asymptotic expansions are constructed exploiting the long narrow shape of the pore and the relatively high dielectric constant of the pore's contents. The resulting one-dimensional equations can be integrated numerically; they can be analyzed when channels are short or long (compared with the Debye length). Traditional constant field equations are derived if the induced charge is small, e.g., if the channel is short or if the total concentration gradient is zero. A constant gradient of concentration is derived if the channel is long. Plots directly comparable to experiments are given of current vs voltage, reversal potential vs. concentration, and slope conductance vs. concentration. This dielectric theory can easily be tested: its parameters can be determined by traditional constant field measurements. The dielectric theory then predicts current-voltage relations quite different from constant field, usually more linear, when gradients of total concentration are imposed. Numerical analysis shows that the interaction of ion and channel can be described by a mean potential if, but only if, the induced charge is negligible, that is to say, the electric field is spatially constant.
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  147. 147.
    Abaid, N.; Eisenberg, R. S.; Liu, W. SIAM J. Appl. Dynam. Syst. 2008, 7, 1507
    [CrossRef]
    There is no corresponding record for this reference.
  148. 148.
    Eisenberg, B.; Liu, W. SIAM J. Math. Anal. 2007, 38, 1932
    [CrossRef]
    There is no corresponding record for this reference.
  149. 149.
    Vasileska, D.; Goodnick, S. M.; Klimeck, G. Computational Electronics: Semiclassical and Quantum Device Modeling and Simulation; CRC Press: New York, 2010.
    There is no corresponding record for this reference.
  150. 150.
    Kong, C. L. J. Chem. Phys. 1973, 59, 2464
    [CrossRef], [CAS]
    150.
    Combining rules for intermolecular potential parameters. II. Rules for the Lennard-Jones (12-6) potential and the Morse potential
    Kong, Chang Lyoul
    Journal of Chemical Physics (1973), 59 (5), 2464-7 CODEN: JCPSA6; ISSN:0021-9606.
    A new set of combining rules for intermol. pair potentials of simple mols. were formulated based on an at. distortion model for the repulsive interactions and a geometric mean relationship for the attractive interactions. The rules are satisfactory in correlating the pair interactions of noble gas atoms when the effective pair interactions are represented by simple anal. potential functions such as the Lennard-Jones (12-6) potential and the Morse potential.
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  151. 151.
    Cazade, P. A.; Dweik, J.; Coasne, B.; Henn, F.; Palmeri, J. J. Phys. Chem. C 2010, 114, 12245
    [ACS Full Text ACS Full Text], [CAS]
    151.
    Molecular Simulation of Ion-Specific Effects in Confined Electrolyte Solutions Using Polarizable Force Fields
    Cazade, P.-A.; Dweik, J.; Coasne, B.; Henn, F.; Palmeri, J.
    Journal of Physical Chemistry C (2010), 114 (28), 12245-12257 CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)
    This paper reports on a mol. dynamics study of aq. electrolyte solns. confined in hydrophobic nanopores. The authors examd. for the 1st time the effect of the size and polarizability of the ions on the structure and dynamics of the confined electrolyte soln. by considering sodium halides (NaX with X = F, Cl, Br, and I). The authors also address the effect of pore size by varying the diam. of the nanochannel. As far as structural properties are concerned, the behavior of the NaF electrolyte soln. significantly differs from that of the other sodium halide solns. Because of their small size, Na and F in NaF are significantly solvated by water. Due to steric and hydrophobic effects, Cl, Br, and I tend to be repelled from the regions where the d. of water is larger. Ion-specific effects on the dynamics of water and ions are minimized when the electrolyte soln. is confined at the nanoscale in comparison to bulk water and the water-air interface. For instance, both the data for water and the ionic species indicate that the ratio of the self-diffusivity for the confined soln. to that for the bulk is independent of the nature of the anion F, Cl, Br, and I. Also, while the av. solvation times for Na in NaF and Na in NaX (X = Cl, Br, I) significantly differ for bulk electrolyte solns., they turn out to be very similar for the confined solns. Such a leveling of the dynamical properties of the electrolyte solns. due to confinement is also obsd. on the pairing of the anions and cations.
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  152. 152.
    Lakatos, G.; Patey, G. N. J. Chem. Phys. 2007, 126, 024703
    [CrossRef], [CAS]
    152.
    Water adsorption in ion-bearing nanopores
    Lakatos G; Patey G N
    The Journal of chemical physics (2007), 126 (2), 024703 ISSN:0021-9606.
    Grand canonical Monte Carlo simulations are used to examine the adsorption of water into cylindrical nanopores containing single ions. The isotherms for water adsorbing into nanopores with radii of 0.44, 0.54, 0.64, and 0.74 nm and containing Na+, K+, Ca2+, Cl-, or F- at 298 K are computed. In all cases the nanopores are found to fill at reservoir chemical potentials below the chemical potential of saturated water vapor at 298 K. The threshold chemical potential is found to be sensitive to both the size of the channel and the ion species, with the anion-bearing pores filling at lower chemical potentials. Additionally, the filling threshold chemical potential is found to decrease as the radius of the pores is decreased. Pores with K+ and Cl- are compared, and the Cl- pores are found to exhibit higher water densities in the filled states and a more energetically favorable water structure while yielding lower per particle entropies. Sample simulation configurations are also examined and indicate that at low chemical potentials, the adsorbed water forms a cluster around the ion. Finally, the influence of the choice of water model on the adsorption isotherms is examined.
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  153. 153.
    Horng, T.-L.; Teng, C.-H. J. Comput. Phys. 2012, 231, 2498
    [CrossRef]
    There is no corresponding record for this reference.
  154. 154.
    Temes, G. C.; Barcilon, V.; Marshall, F. C. Proc. IEEE 1973, 61, 196
    [CrossRef]
    There is no corresponding record for this reference.
  155. 155.
    Lee, C. C.; Hyon, Y.; Lin, T. C.; Liu, C. To be submitted for publication, 2012.
    There is no corresponding record for this reference.
  156. 156.
    Boda, D.; Henderson, D.; Eisenberg, B.; Gillespie, D. J. Chem. Phys. 2011, 135, 064105
    [CrossRef], [CAS]
    156.
    A method for treating the passage of a charged hard sphere ion as it passes through a sharp dielectric boundary
    Boda, Dezso; Henderson, Douglas; Eisenberg, Bob; Gillespie, Dirk
    Journal of Chemical Physics (2011), 135 (6), 064105/1-064105/12 CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    In the implicit solvent models of electrolytes (such as the primitive model (PM)), the ions are modeled as point charges in the centers of spheres (hard spheres in the case of the PM). The surfaces of the spheres are not polarizable which makes these models appropriate to use in computer simulations of electrolyte systems where these ions do not leave their host dielecs. The same assumption makes them inappropriate in simulations where these ions cross dielec. boundaries because the interaction energy of the point charge with the polarization charge induced on the dielec. boundary diverges. In this paper, we propose a procedure to treat the passage of such ions through dielec. interfaces with an interpolation method. Inspired by the "bubble ion" model (in which the ion's surface is polarizable), we define a space-dependent effective dielec. coeff., εeff(r), for the ion that overlaps with the dielec. boundary. Then, we replace the "bubble ion" with a point charge that has an effective charge q/εeff(r) and remove the portion of the dielec. boundary where the ion overlaps with it. We implement the interpolation procedure using the induced charge computation method. We analyze the various energy terms using a spherical ion passing through an infinite flat dielec. boundary as an example. (c) 2011 American Institute of Physics.
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  157. 157.
    Singer, A.; Gillespie, D.; Norbury, J.; Eisenberg, R. S. Eur. J. Appl. Math. 2008, 19, 541
    [CrossRef], [CAS]
    157.
    Singular perturbation analysis of the steady-state Poisson-Nernst-Planck system: Applications to ion channels
    Singer, A.; Gillespie, D.; Norbury, J.; Eisenberg, R. S.
    European Journal of Applied Mathematics (2008), 19 (5), 541-560 CODEN: EJAMBA; ISSN:0956-7925. (Cambridge University Press)
    Ion channels are proteins with a narrow hole down their middle that control a wide range of biol. function by controlling the flow of spherical ions from one macroscopic region to another. Ion channels do not change their conformation on the biol. time scale once they are open, so they can be described by a combination of Poisson and drift-diffusion (Nernst-Planck) equations called PNP in biophysics. Singular perturbation techniques are used to analyze the steady-state PNP system for a channel with a general geometry and a piecewise const. permanent charge profile. An outer soln. is constructed for the case of a const. permanent charge d. in three dimensions that is also a valid soln. of the one-dimensional system. The asymptotical current-voltage (I-V) characteristic curve of the device (obtained by the singular perturbation anal.) is shown to be a very good approxn. of the numerical I-V curve (obtained by solving the system numerically). The phys. constraint of non-neg. concns. implies a unique soln., i.e., for each given applied potential there corresponds a unique elec. current (relaxing this constraint yields non-phys. multiple solns. for sufficiently large voltages).
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  158. 158.
    Howard, J. J.; Perkyns, J. S.; Pettitt, B. M. J. Phys. Chem. B 2010, 114, 6074
    [ACS Full Text ACS Full Text], [PubMed], [CAS]
    158.
    The behavior of ions near a charged wall. Dependence on ion size, concentration, and surface charge
    Howard, Jesse J.; Perkyns, John S.; Pettitt, B. Montgomery
    Journal of Physical Chemistry B (2010), 114 (18), 6074-6083 CODEN: JPCBFK; ISSN:1520-6106. (American Chemical Society)
    A renormalization of the 3D-RISM-HNC integral equation is used to study the solvent and ion distributions at neutral and neg. charged planar atomistic surfaces. The charge d. of the surfaces ranged from 0.0 to 0.4116 C/m2, and the modeled electrolyte solns. consist of the salts NaCl, KCl, and CsCl at concns. of 0.1, 0.25, and 1.0 M in SPC/E water. The results are qual. compared to the results from other integral equation methods and simulations for similar models. The 3D-IEs predict an elec. multilayer screening behavior in the solvent and ion distributions in contrast to the double layer anticipated from Poisson-Boltzmann theory. The cation size has a significant effect on the distributions near the surface up to 3 solvation layers beyond which the behavior is the same among the different cations. The response of the distributions to the charged surface is described as an increase in ion and solvent d. near the wall. The higher concn. solns. screen the electrostatic source more strongly at the wall as expected. The importance of ion-solvent and ion-ion correlations near the surface is shown through 3-body correlation functions which are obtainable from the 3D-IEs in this study.
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  159. 159.
    Varsos, K.; Luntz, J.; Welsh, M.; Sarabandi, K. Proc. IEEE 2011, 99, 2112
    [CrossRef]
    There is no corresponding record for this reference.
  160. 160.
    Fiedziuszko, S. J.; Hunter, I. C.; Itoh, T.; Kobayashi, Y.; Nishikawa, T.; Stitzer, S.; Wakino, K. IEEE Trans. Microwave Theory Tech. 2002, 50, 706
    [CrossRef], [CAS]
    160.
    Dielectric materials, devices, and circuits
    Fiedziuszko, S. Jerry; Hunter, Ian C.; Itoh, Tatsuo; Kobayashi, Yoshio; Nishikawa, Toshio; Stitzer, Steven N.; Wakino, Kikuo
    IEEE Transactions on Microwave Theory and Techniques (2002), 50 (3), 706-720 CODEN: IETMAB; ISSN:0018-9480. (Institute of Electrical and Electronics Engineers)
    A review. In this paper, a sequential evolution of the dielec. materials applications in microwave devices will be reviewed. This includes dielec. waveguides, low-loss temp.-stable ceramic materials, dielec. resonators, and filters. The recent advances in the multilayer circuit modules, dielec. antennas, and ferroelecs. are also described.
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  161. 161.
    Helfferich, F. Ion Exchange; Dover: New York, 1995.
    There is no corresponding record for this reference.
  162. 162.
    Shur, M. Physics of Semiconductor Devices; Prentice Hall: New York, 1990.
    There is no corresponding record for this reference.
  163. 163.
    Collins, A.; Somlyo, A. V.; Hilgemann, D. W. J. Physiol. 1992, 454, 27
    [PubMed], [CAS]
    163.
    The giant cardiac membrane patch method: stimulation of outward sodium-calcium exchange current by magnesium-ATP
    Collins, Anthony; Somlyo, Avril V.; Hilgemann, Donald W.
    Journal of Physiology (Cambridge, United Kingdom) (1992), 454 (), 27-57 CODEN: JPHYA7; ISSN:0022-3751.
    A giant patch method was used to study the stimulatory effect of cytoplasmic MgATP on outward Na+ Ca2+ exchange current in inside-out cardiac membrane patches (1-10 GΩ seals with 14-24 μm pipet tip diams.) excised from guinea pig, rabbit, and mouse myocytes. To establish the validity of the method with respect to structure, bleb formation was examd. with electron microscopy and with confocal fluorescence light microscopy. The blebs, which form as the sarcolemma detaches, excluded intracellular organelles and transverse tubules. The blebbed cells contained normal sarcomeres, sarcoplasmic reticulum, triads and diads. To further establish the validity of the method for ion transport studies, measurements of Na+-K+ pump currents and charge movements are described briefly which demonstrate (i) free access to the cytoplasmic membrane side, (ii) MgATP dependence comparable to reconstituted pump (Kd, 94 μM), (iii) fast, rigorous concn. control, and (iv) Na+-K+ pump densities in the range of whole-cell densities. Stimulation of outward Na+-Ca2+ exchange current by MgATP attenuated exchange current decay during step increments of cytoplasmic sodium, shifted the secondary activation of outward exchange current by cytoplasmic calcium to lower free calcium concns. and, particularly in mouse cardiac sarcolemma, induced cytoplasmic calcium-independent current. Upon removal of MgATP the stimulatory effect usually decayed with a t50 (half-time) of 3 min. However, the reversal took place much more rapidly (t50, 5-20 s) in patches from individual guinea pig and rabbit myocyte batches. When decay was rapid, secondary activation by cytoplasmic calcium was shifted to higher free cytoplasmic calcium concns. (Kd, 10-65 μM-free calcium). With repeated applications of MgATP the rate and magnitude of the stimulatory effect progressively decreased. The Kd for MgATP of the initial rate of stimulation of outward exchange current was ≥3 mM. When decay was rapid, the steady-state dependence of exchange current on MgATP also had a Kd of ≥3 mM. The results indicated stimulation of Na+-Ca2+ exchange current in excised sarcolemmal patches by MgATP is not a calcium-dependent process and probably does not involve protein kinases.
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  164. 164.
    Hilgemann, D. W.; Collins, A.; Matsuoka, S. J. Gen. Physiol. 1992, 100, 933
    [CrossRef], [CAS]
    164.
    Steady-state and dynamic properties of cardiac sodium-calcium exchange: secondary modulation by cytoplasmic calcium and ATP
    Hilgemann, Donald W.; Collins, Anthony; Matsuoka, Satoshi
    Journal of General Physiology (1992), 100 (6), 933-61 CODEN: JGPLAD; ISSN:0022-1295.
    Dynamic responses of cardiac sodium-calcium exchange current to changes of cytoplasmic calcium and MgATP were monitored and analyzed in giant membrane patches excised from guinea pig myocytes. Secondary dependencies of exchange current on cytoplasmic calcium are accounted for in terms of two mechanisms: (a) the sodium-dependent inactivation process, termed I1 modulation, is itself strongly modulated by cytoplasmic calcium. Recovery from the I1 inactivated state is accelerated by increasing cytoplasmic calcium, and the calcd. rate of entrance into I1 inactivation is slowed. (B) a second modulation process, termed I2 modulation, is not sodium dependent. As with I1 modulation, the entrance into I2 inactivation takes place over seconds in the absence of cytoplasmic calcium. The recovery from I2 inactivation is a calcium-dependent transition and is rapid (<200 ms) in the presence of micromolar free calcium. I1 and I2 modulation can be treated as linear, independent processes to account for most exchange modulation patterns obsd.: (a) when cytoplasmic calcium is increased or decreased in the presence of high cytoplasmic sodium, outward exchange current turns on or off, resp., on a time scale of multiple seconds. (B) when sodium is applied in the absence of cytoplasmic calcium, no outward current is activated. However, the full outward current is activated within soln. switch time when cytoplasmic calcium is applied together with sodium. (C) the calcium dependent of peak outward current attained upon application of cytoplasmic sodium is shifted by 1 log unit to lower concns. from the calcium dependence of steady-state exchange current. (D) the time course of outward current decay upon decreasing cytoplasmic calcium becomes more rapid as calcium is reduced into the submicromolar range. (E) under nearly all conditions, the time courses of current decay during application of cytoplasmic sodium and/or removal of cytoplasmic calcium are well fit by single exponentials. Both of the modulation processes are evidently affected by MgATP. Similar to the effects of cytoplasmic calcium, MgATP slows the entrance into I1 inactivation and accelerates the recovery from inactivation. MgATP addnl. slows the decay of outward exchange current upon removal of cytoplasmic calcium by 2-10-fold, indicative of an effect on I2 inactivation. Finally, the effects of cytoplasmic calcium on sodium-calcium exchange current are reconstructed in simulations of the I1 and I2 modulation processes as independent reactions.
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  165. 165.
    Hilgemann, D. W.; Matsuoka, S.; Nagel, G. A.; Collins, A. J. Gen. Physiol. 1992, 100, 905
    [CrossRef], [PubMed], [CAS]
    165.
    Steady-state and dynamic properties of cardiac sodium-calcium exchange: sodium-dependent inactivation
    Hilgemann, Donald W.; Matsuoka, Satoshi; Nagel, Georg A.; Collins, Anthony
    Journal of General Physiology (1992), 100 (6), 905-32 CODEN: JGPLAD; ISSN:0022-1295.
    Sodium-calcium exchange current was isolated in inside-out patches excised from guinea pig ventricular cells using the giant patch method. The outward exchange current decayed exponentially upon activation by cytoplasmic sodium (sodium-dependent inactivation). The kinetics and mechanism of the inactivation were studied. (A) the rate of inactivation and the peak current amplitude were both strongly temp. dependent (Q10 = 2.2). (B) an increase in cytoplasmic pH from 6.8 to 7.8 attenuated the current decay and shifted the apparent dissocn. const. (Kd) of cytoplasmic calcium for secondary activation of the exchange current from 9.6 μM to <0.3 μM. (C) the amplitude of exchange current decreased synchronously over the membrane potential range from -120 to 60 mV during the inactivation, indicating that voltage dependence of the exchanger did not change during the inactivation process. The voltage dependence of exchange current also did not change during secondary modulation by cytoplasmic calcium and activation by chymotrypsin. (D) in the presence of 150 mM extracellular sodium and 2 mM extracellular calcium, outward exchange current decayed similarly upon application of cytoplasmic sodium. Upon removal of cytoplasmic sodium in the presence of 2-5 μM cytoplasmic free calcium, the inward exchange current developed in two phases, a fast phase within the time course of soln. changes, and a slow phase (τ ≈ 4 s) indicative of recovery from sodium-dependent inactivation. (E) under zero-trans conditions, the inward current was fully activated within soln. switch times upon application of cytoplasmic calcium and did not decay. (F) the slow recovery phase of inward current upon removal of cytoplasmic sodium was also present under the zero-trans condition. (G) sodium-dependent inactivation shows little or no dependence on membrane potential in guinea pig myocyte sarcolemma. (H) sodium-dependent inactivation of outward current is attenuated in rate and extent as extracellular calcium is decreased. (I) kinetics of the sodium-dependent inactivation and its dependence on major exptl. variables are well described by a simple two-state inactivation model assuming one fully active and one fully inactive exchanger state, whereby the transition to the inactive state takes place from a fully sodium-loaded exchanger conformation with cytoplasmic orientation of binding sites (E1·3Ni).
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  166. 166.
    Matsuoka, S.; Hilgemann, D. W. J. Gen. Physiol. 1992, 100, 963
    [CrossRef], [PubMed], [CAS]
    166.
    Steady-state and dynamic properties of cardiac sodium-calcium exchange. Ion and voltage dependencies of the transport cycle
    Matsuoka S; Hilgemann D W
    The Journal of general physiology (1992), 100 (6), 963-1001 ISSN:0022-1295.
    Ion and voltage dependencies of sodium-calcium exchange current were studied in giant membrane patches from guinea pig ventricular cells after deregulation of the exchanger with chymotrypsin. (a) Under zero-trans conditions, the half-maximum concentration (Kh) of cytoplasmic calcium (Cai) for activation of the isolated inward exchange current decreased as the extracellular sodium (Nao) concentration was decreased. The Kh of cytoplasmic sodium (Nai) for activation of the isolated outward exchange current decreased as the extracellular calcium (Cao) concentration was decreased. (b) The current-voltage (I-V) relation of the outward exchange current with saturating concentrations of Nai and Cao had a shallow slope (twofold change in approximately 100 mV) and a slight saturation tendency at very positive potentials. The outward current gained in steepness as the Nai concentration was decreased, such that the Kh for Nai decreased with depolarization. The decrease of Kh for Nai with depolarization was well described by a Boltzmann equation (e alpha.Em/26.6) with a slope (alpha) of -0.06. (c) Voltage dependence of the outward current was lost as the Cao concentration was decreased, and the Kh for Cao increased upon depolarization with a Boltzmann slope of 0.26. (d) The I-V relation of the inward exchange current, under zero-trans conditions, was also almost linear (twofold change in approximately 100 mV) and showed some saturation tendency with hyperpolarization as the Cai concentration was decreased. The Kh for Cai decreased with depolarization (Boltzmann slope, -0.10). Voltage dependence of the inward current was decreased in the presence of a high (300 mM) Nao concentration. (e) In the presence of both Na and Ca on both membrane sides, the I-V relations with saturating Nai show sigmoidal shape and clear saturation at positive potentials. Measured reversal potentials were close to the equilibrium potential expected for a 3 Na to 1 Ca exchange. (f) Nai and Cai interacted competitively with respect to the outward current, but in a mixed competitive-noncompetitive fashion with respect to the inward current. (g) Cai inhibited the outward exchange current in a voltage-dependent manner. The half-effective concentration for inhibition (Ki) by Cai increased upon depolarization with a Boltzmann slope of 0.32 in 25 mM Nai and 0.20 in 100 mM Nai. (h) Nai also inhibited the inward exchange current voltage dependently. The Ki decreased upon depolarization (Boltzmann slope, -0.11 at 3 microM Cai and -0.10 at 1.08 mM Cai).(ABSTRACT TRUNCATED AT 400 WORDS)
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  167. 167.
    Schuss, Z.; Nadler, B.; Eisenberg, R. S. Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys. 2001, 64, 036116
    [CrossRef], [CAS]
    167.
    Derivation of Poisson and Nernst-Planck equations in a bath and channel from a molecular model
    Schuss, Z.; Nadler, B.; Eisenberg, R. S.
    Physical Review E: Statistical, Nonlinear, and Soft Matter Physics (2001), 64 (3-2), 036116/1-036116/14 CODEN: PRESCM ISSN:. (American Physical Society)
    Permeation of ions from one electrolytic soln. to another, through a protein channel, is a biol. process of considerable importance. Permeation occurs on a time scale of micro- to milliseconds, far longer than the femtosecond time scales of at. motion. Direct simulations of at. dynamics are not yet possible for such long-time scales; thus, averaging is unavoidable. The question is what and how to av. In this paper, we av. a Langevin model of ionic motion in a bulk soln. and protein channel. The main result is a coupled system of averaged Poisson and Nernst-Planck equations (CPNP) involving conditional and unconditional charge densities and conditional potentials. The resulting NP equations contain the averaged force on a single ion, which is the sum of two components. The first component is the gradient of a conditional elec. potential that is the soln. of Poisson's equation with conditional and permanent charge densities and boundary conditions of the applied voltage. The second component is the self-induced force on an ion due to surface charges induced only by that ion at dielec. interfaces. The ion induces surface polarization charge that exerts a significant force on the ion itself, not present in earlier PNP equations. The proposed CPNP system is not complete, however, because the elec. potential satisfies Poisson's equation with conditional charge densities, conditioned on the location of an ion, while the NP equations contain unconditional densities. The conditional densities are closely related to the well-studied pair-correlation functions of equil. statistical mechanics. We examine a specific closure relation, which on the one hand replaces the conditional charge densities by the unconditional ones in the Poisson equation, and on the other hand replaces the self-induced force in the NP equation by an effective self-induced force. This effective self-induced force is nearly zero in the baths but is approx. equal to the self-induced force in and near the channel. The charge densities in the NP equations are interpreted as time avs. over long times of the motion of a quasiparticle that diffuses with the same diffusion coeff. as that of a real ion, but is driven by the averaged force. In this way, continuum equations with averaged charge densities and mean-fields can be used to describe permeation through a protein channel.
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  168. 168.
    Schuss, Z.; Nadler, B.; Singer, A.; Eisenberg, R.A PDE Formulation of Non-Equilibrium Statistical Mechanics for Ionic Permeation. In Unsolved problems of noise and fluctuations : UPoN 2002 : Third International Conference of Unsolved Problems of Noise and Fluctuations in Physics, Biology, and High Technology, AIP Conference Proceedings, Washington, DC, September 3–6, 2002; Bezrukov, S. M., Ed.; American Institute of Physics: Melville, NY, 2003; No. 665.
    There is no corresponding record for this reference.
  169. 169.
    Hünenberger, P. H.; Reif, M. Single-Ion Solvation; RSC Publishing: Cambridge U.K., 2011.
    There is no corresponding record for this reference.
  170. 170.
    Ben-Naim, A. Molecular Theory of Water and Aqueous Solutions Part II: The Role of Water in Protein Folding, Self-Assembly and Molecular Recognition; World Scientific: Singapore, 2011.
    There is no corresponding record for this reference.
  171. 171.
    Fraenkel, D. Mol. Phys. 2010, 108, 1435
    [CrossRef], [CAS]
    171.
    Simplified electrostatic model for the thermodynamic excess potentials of binary strong electrolyte solutions with size-dissimilar ions
    Fraenkel, Dan
    Molecular Physics (2010), 108 (11), 1435-1466 CODEN: MOPHAM; ISSN:0026-8976. (Taylor & Francis Ltd.)
    Modern theories of electrolyte solns. are phys. accurate but difficult to apply for real-life systems; a need therefore exists to theor. derive simplified and practically useful math. expressions for thermodn. excess functions. This can be done by incorporating ion-size dissimilarity into the classical Debye-Huckel model [Physik Z. 24, 185 (1923)], under conditions at which non-electrostatic contributions are negligible. If the contact distance between the central (β) ion and a cloud (α) ion is a for counter-ions and b for co-ions, two basic cases exist, b < a and b > a. In both, a 'smaller-ion shell' (SiS) at the edge of the ionic cloud, bordered by the spherical surfaces of radius b and a, admits only the smaller α ions [Thomlinson and Outhwaite, Mol. Phys. 47, 1113 (1982)]. In the b < a case, the SiS contributes an ionic repulsion effect and the overall extra-electrostatic potential energy, Ψb<a(κ) - κ, reciprocal screening length-exhibits a min. For b > a, the SiS contributes an 'extra ionic attraction' and the overall extra-electrostatic energy, Ψb>a(κ) declines monotonically with increasing κ. The entire Ψ contribution, Ψ±, is a linear combination of the Ψs of the two counter β ions. The effectiveness of Ψ± is demonstrated for real-life electrolyte systems, based on exptl. mean ionic activity coeffs. and their concn. dependencies. Fitting theory with expt. generates ion-size parameters that represent realistic interionic collision distances in soln., unlike parallel parameters based on other simplified theories.
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  172. 172.
    Hodgkin, A. L.; Huxley, A. F. J. Physiol. 1952, 116, 449
    [PubMed], [CAS]
    172.
    Currents carried by sodium and potassium ions through the membrane of the giant axon of Loligo
    HODGKIN A L; HUXLEY A F
    The Journal of physiology (1952), 116 (4), 449-72 ISSN:0022-3751.
    There is no expanded citation for this reference.
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  173. 173.
    Hodgkin, A. L.; Huxley, A. F. J. Physiol. 1952, 116, 473
    [PubMed], [CAS]
    173.
    The components of membrane conductance in the giant axon of Loligo
    HODGKIN A L; HUXLEY A F
    The Journal of physiology (1952), 116 (4), 473-96 ISSN:0022-3751.
    There is no expanded citation for this reference.
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  174. 174.
    Mullins, L. J. J. Gen. Physiol. 1968, 52, 555
    [CrossRef], [CAS]
    174.
    Single or dual channel mechanisms
    Mullins L J
    The Journal of general physiology (1968), 52 (3), 555-6 ISSN:0022-1295.
    There is no expanded citation for this reference.
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  175. 175.
    Mullins, L. J. J. Gen. Physiol. 1968, 52, 550
    [CrossRef], [CAS]
    175.
    A single channel or a dual channel mechanism for nerve excitation
    Mullins L J
    The Journal of general physiology (1968), 52 (3), 550-6 ISSN:0022-1295.
    There is no expanded citation for this reference.
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  176. 176.
    Moore, J. W.; Blaustein, M. P.; Anderson, N. C.; Narahashi, T. J. Gen. Physiol. 1967, 50, 1401
    [CrossRef], [PubMed], [CAS]
    176.
    Basis of tetrodotoxin's selectivity in blockage of squid axons
    Moore, John Wilson; Blaustein, Mordecai P.; Anderson, Nels C.; Narahashi, Toshio
    Journal of General Physiology (1967), 50 (5), 1401-11 CODEN: JGPLAD; ISSN:0022-1295.
    Li, Cs, K, and Rb were substituted for Na in seawater bathing an artificial node in a voltage-clamped squid axon. Tetrodotoxin (100-150 × 10-9M) added to the artificial seawaters always blocked the flow of cations through the early transient channel, both inward and outward, but it never blocked the flow of ions using the late steady pathway. The selectivity of tetrodotoxin seems to be based on some difference in these 2 channels. 19 references.
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  177. 177.
    Moore, J. W.; Narahashi, T.; Anderson, N. C.; Blaustein, M. P.; Watanabe, A.; Tasaki, I.; Singer, I.; Lerman, L. Science 1967, 157, 220
    [CrossRef], [CAS]
    177.
    Tetrodotoxin: comments on effects on squid axons
    Moore J W; Narahashi T; Anderson N C; Blaustein M P; Watanabe A; Tasaki I; Singer I; Lerman L
    Science (New York, N.Y.) (1967), 157 (3785), 220-1 ISSN:0036-8075.
    There is no expanded citation for this reference.
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  178. 178.
    Conley, E. C. The Ion Channel Facts Book. I. Extracellular Ligand-Gated Channels; Academic Press: New York, 1996; Vol. 1.
    There is no corresponding record for this reference.
  179. 179.
    Conley, E. C. The Ion Channel Facts Book. II. Intracellular Ligand-Gated Channels; Academic Press: New York, 1996; Vol. 2.
    There is no corresponding record for this reference.
  180. 180.
    Unwin, N. J. Mol. Biol. 2005, 346, 967
    [CrossRef], [PubMed], [CAS]
    180.
    Refined Structure of the Nicotinic Acetylcholine Receptor at 4Å Resolution
    Unwin, Nigel
    Journal of Molecular Biology (2005), 346 (4), 967-989 CODEN: JMOBAK; ISSN:0022-2836. (Elsevier B.V.)
    The authors present a refined model of the membrane-assocd. Torpedo acetylcholine (ACh) receptor at 4 Å resoln. An improved exptl. d. map was obtained from 342 electron images of helical tubes, and the refined structure was derived to an R-factor of 36.7% (R free 37.9%) by std. crystallog. methods, after placing the densities corresponding to a single mol. into an artificial unit cell. The agreement between exptl. and calcd. phases along the helical layer-lines was used to monitor progress in the refinement and to give an independent measure of the accuracy. The at. model allowed a detailed description of the whole receptor in the closed-channel form, including the ligand-binding and intracellular domains, which have not previously been interpreted at a chem. level. The authors confirm that the two ligand-binding α subunits have a different extended conformation from the three other subunits in the closed channel, and identify several interactions on both pairs of subunit interfaces, and within the α subunits, which may be responsible for their "distorted" structures. The ACh-coordinating amino acid side-chains of the α subunits are far apart in the closed channel, indicating that a localized rearrangement, involving closure of loops B and C around the bound ACh mol., occurs upon activation. A comparison of the structure of the α subunit with that of AChBP having ligand present, suggests how the localized rearrangement overcomes the distortions and initiates the rotational movements assocd. with opening of the channel. Both vestibules of the channel are strongly electroneg., providing a cation-stabilizing environment at either entrance of the membrane pore. Access to the pore on the intracellular side is further influenced by narrow lateral windows, which would be expected to screen out electrostatically ions of the wrong charge and size.
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  181. 181.
    Kraus, C. A. Bull. Am. Math. Soc. 1938, 44, 361
    [CrossRef]
    There is no corresponding record for this reference.
  182. 182.
    Harned, H. S.; Owen, B. B. The Physical Chemistry of Electrolytic Solutions, 3rd ed.; Reinhold Publishing Corporation: New York, 1958.
    There is no corresponding record for this reference.
  183. 183.
    Friedman, H. L. Ionic Solution Theory; Interscience Publishers: New York, 1962.
    There is no corresponding record for this reference.
  184. 184.
    Rice, S. A.; Gray, P. Statistical Mechanics of Simple Fluids; Wiley-Interscience: New York, 1965.
    There is no corresponding record for this reference.
  185. 185.
    Barlow, C. A., Jr.; Macdonald, J. R.Theory of Discreteness of Charge Effects in the Electrolyte Compact Double Layer. In Advances in Electrochemistry and Electrochemical Engineering; Delahay, P., Ed.; Interscience Publishers: New York, 1967; Vol. 6.
    There is no corresponding record for this reference.
  186. 186.
    Resibois, P. M. V. Electrolyte Theory; Harper & Row: New York, 1968.
    There is no corresponding record for this reference.
  187. 187.
    Conway, B. E. Electrochemical Data; Greenwood Press Publishers: Westport CT, 1969.
    There is no corresponding record for this reference.
  188. 188.
    Barker, J.; Henderson, D. Rev. Mod. Phys. 1976, 48, 587
    [CrossRef], [CAS]
    188.
    What is "liquid"? Understanding the states of matter
    Barker, J. A.; Henderson, D.
    Reviews of Modern Physics (1976), 48 (4), 587-671 CODEN: RMPHAT; ISSN:0034-6861.
    A review with many refs. of theories describing the liq. state.
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  189. 189.
    Ben-Naim, A. Inversion of the Kirkwood Buff Theory of Solutions: Application to the Water Ethanol System; American Institute of Physics: Melville, NY, 1977; Vol. 67.
    There is no corresponding record for this reference.
  190. 190.
    Pytkowicz, R. M. Activity Coefficients in Electrolyte Solutions; CRC: Boca Raton FL, 1979; Vol. 1.
    There is no corresponding record for this reference.
  191. 191.
    Torrie, G. M.; Valleau, A. J. Phys. Chem. 1982, 86, 3251
    [ACS Full Text ACS Full Text], [CAS]
    191.
    Electrical double layers. 4. Limitations of the Gouy-Chapman theory
    Torrie, G. M.; Valleau, J. P.
    Journal of Physical Chemistry (1982), 86 (16), 3251-7 CODEN: JPCHAX; ISSN:0022-3654.
    Monte Carlo (MC) calcns. were made of the charge distribution and mean potential of the diffuse double layer for the restricted primitive model of 2:1 and 2:2 aq. electrolytes next to a uniformly charged plane surface. In the latter case the parameters used in the primitive model correspond also to 1:1 electrolytes in nonaq. solvents. The MC results are compared with the modified Gouy-Chapman (MGC) and modified Poisson-Boltzmann (MPB) theories of these systems for surface charges ≤25 μC cm-2 and electrolyte concns. ≤0.5 M. When the counterions in the 2:1 system are single charged, the success of the MPB theory and the relatively mild shortcomings of the MGC theory are similar to those found previously for 1:1 electrolytes. For doubly charged counterions in both the 2:2 and 2:1 systems, however, the MC results show the MGC theory to be totally inadequate; the MGC greatly overests. the surface potential even at quite low surface charges and electrolyte concns. In fact, the MC diffuse-layer potential as a function of surface charge has an extremum, and oscillations occur in the ion densities at concns. as low as 0.05 M. The MPB theory is successful in predicting some of these qual. features but differs quant. from the MC results in several respects.
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  192. 192.
    Hovarth, A. L. Handbook of Aqueous Electrolyte Solutions: Physical Properties, Estimation, and Correlation Methods; Ellis Horwood: New York, 1985.
    There is no corresponding record for this reference.
  193. 193.
    Patwardhan, V. S.; Kumar, A. AIChE J. 1986, 32, 1429
    [CrossRef], [CAS]
    193.
    A unified approach for prediction of thermodynamic properties of aqueous mixed-electrolyte solutions. Part II: Volume, thermal, and other properties
    Patwardhan, V. S.; Kumar, Anil
    AIChE Journal (1986), 32 (9), 1429-38 CODEN: AICEAC; ISSN:0001-1541.
    The overall reduced ionic activity coeff. Γ* is useful in characterizing the overall nonideality of an aq. mixed-electrolyte soln. The Γ* can be simply related to Γ of single-electrolyte solns. contg. the component electrolytes without using empirical consts. (P. et. al., 1986). This basic relationship is used for deriving predictive equations for several properties in terms of corresponding properties of single-electrolyte solns. contg. the component electrolytes. The predictive equations need no empirical consts. The properties covered include vol. properties (d. and adiabatic compressibility) thermal properties (enthalpy, sp. heats, free energy, expansibility, and depression in f.p.). Comparison with exptl. data shows that the predictive equations have an accuracy varying from 0.03% for d. to 2% for f.p. depression, and are valid for the entire range of concns. encountered in practice.
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  194. 194.
    Stell, G.; Joslin, C. G. Biophys. J. 1986, 50, 855
    [CrossRef], [CAS]
    194.
    The Donnan equilibrium. A theoretical study of the effects of interionic forces
    Stell, G.; Joslin, C. G.
    Biophysical Journal (1986), 50 (5), 855-9 CODEN: BIOJAU; ISSN:0006-3495.
    The conditions under which nonideality in soln. influences the Donnan equil. were examd. Of the various parameters that characterize this equil., the osmotic pressure established across the Donnan membrane is found to be particularly sensitive to intermol. interactions between the diffusible and nondiffusible ionic species. Under physiol. appropriate conditions, it is almost never valid to use Debye-Hueckel theory to calc. ionic activities: it is important to take proper account of ion size. When the diffusible species is a 1-1 electrolyte, this can be done using the mean spherical approxn. (MSA) for a mixt. of ions of different diams. For 2-2, or high-valent, electrolytes one should also include the effects of the second ionic virial coeff., which the MSA omits.
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  195. 195.
    Zemaitis, J. F., Jr.; Clark, D. M.; Rafal, M.; Scrivner, N. C. Handbook of Aqueous Electrolyte Thermodynamics; Design Institute for Physical Property Data sponsored by the American Institute of Chemical Engineers: New York, 1986.
    [CrossRef]
    There is no corresponding record for this reference.
  196. 196.
    Lee, L. L. Molecular Thermodynamics of Nonideal Fluids: Butterworth-Heinemann: New York, 1988.
    There is no corresponding record for this reference.
  197. 197.
    Pitzer, K. S. Activity Coefficients in Electrolyte Solutions; CRC Press: Boca Raton, FL, 1991.
    There is no corresponding record for this reference.
  198. 198.
    Cabezas, H.; O’Connell, J. P. Ind. Eng. Chem. Res. 1993, 32, 2892
    [ACS Full Text ACS Full Text], [CAS]
    198.
    Some uses and misuses of thermodynamic models for dilute liquid solutions
    Cabezas, Heriberto, Jr.; O'Connell, John P.
    Industrial & Engineering Chemistry Research (1993), 32 (11), 2892-904 CODEN: IECRED; ISSN:0888-5885.
    Polymer soly., liq.-liq. solute partitioning, and electrolyte activities are examples of important thermodn. properties of liq. systems where components are found at low concns. in solvents. It is common to analyze soln. compn. data with expressions such as osmotic virial expansions and/or Debye-Hueckel electrostatic models without careful regard for the correct relation of the coeffs. to the mol. solute-solute interactions. The purpose of this work is to (1) note the different thermodn. variables of solns.; 2) briefly summarize the connections of the coeffs. to mol. interactions; (3) demonstrate how the differences are related to exptl. values; and (4) illustrate practical cases in phase equil. of polymeric and ionic solutes.
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  199. 199.
    Patwardhan, V. S.; Kumar, A. AIChE J. 1993, 39, 711
    [CrossRef], [CAS]
    199.
    Thermodynamic properties of aqueous solutions of mixed electrolytes: a new mixing rule
    Patwardhan, V. S.; Kumar, Anil
    AIChE Journal (1993), 39 (4), 711-14 CODEN: AICEAC; ISSN:0001-1541.
    A new mixing rule is presented which improves methods for the prediction of d., compressibility and expansibility of aq. systems with no common ions.
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  200. 200.
    Chhih, A.; Bernard, O.; Barthel, J. M. G.; Blum, L. Ber. Bunsen-Ges. Phys. Chem. 1994, 98, 1516
    [CrossRef], [CAS]
    200.
    Transport coefficients and apparent charges of concentrated electrolyte solutions - equations for practical use
    Chhih, Aziza; Turq, Pierre; Bernard, Olivier; Barthel, Josef M. G.; Blum, Lesser
    Berichte der Bunsen-Gesellschaft (1994), 98 (12), 1516-25 CODEN: BBPCAX; ISSN:0940-483X. (VCH)
    Simple expressions for the transport coeff. in the mean spherical approxn. (MSA) have been derived. The authors study the self-diffusion, conductance and apparent charge of simple electrolytes, where good agreement for the concn. dependence was found. Assocd. electrolytes are also well described by a natural extension of this theory. The MSA equations extend the concn. range of the chem. model (CM) calcns. which, in turn, are a reliable source for the input parameters of the MSA calcns.
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  201. 201.
    Hunenberger, P. H.; McCammon, J. A. J. Chem. Phys. 1999, 110, 1856
    [CrossRef], [CAS]
    201.
    Ewald artifacts in computer simulations of ionic solvation and ion-ion interaction: A continuum electrostatics study
    Hunenberger, Philippe H.; McCammon, J. Andrew
    Journal of Chemical Physics (1999), 110 (4), 1856-1872 CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    The use of Ewald and related methods to handle electrostatic interactions in explicit-solvent simulations of solns. imposes an artificial periodicity on systems which are inherently nonperiodic. The consequences of this approxn. should be assessed, since they may crucially affect the reliability of those computer simulations. In the present study, we propose a general method based on continuum electrostatics to investigate the nature and magnitude of periodicity-induced artifacts. As a first example, this scheme is applied to the solvation free energy of a spherical ion. It is found that artificial periodicity reduces the magnitude of the ionic solvation free energy, because the solvent in the periodic copies of the central unit cell is perturbed by the periodic copies of the ion, thus less available to solvate the central ion. In the limit of zero ionic radius and infinite solvent permittivity, this undersolvation can be cor. by adding the Wigner self-energy term to the solvation free energy. For ions of a finite size or a solvent of finite permittivity, a further correction is needed. An anal. expression for this correction is derived using continuum electrostatics. As a second example, the effect of artificial periodicity on the potential of mean force for the interaction between two spherical ions is investigated. It is found that artificial periodicity results in an attractive force between ions of like charges, and a repulsive force between ions of opposite charges. The anal. of these two simple test cases reveals that two individually large terms, the periodicity-induced perturbations of the Coulomb and solvation contributions, often cancel each other significantly, resulting in an overall small perturbation. Three factors may prevent this cancellation to occur and enhance the magnitude of periodicity-induced artifacts: (i) a solvent of low dielec. permittivity, (ii) a solute cavity of non-negligible size compared to the unit cell size, and (iii) a solute bearing a large overall charge.
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  202. 202.
    Baker, N. A.; Hunenberger, P. H.; McCammon, J. A. J. Chem. Phys. 2000, 113, 2510
    [CrossRef], [CAS]
    202.
    Polarization around an ion in a dielectric continuum with truncated electrostatic interactions. [Erratum to document cited in CA131:109660]
    Baker, Nathan A.; Hunenberger, Philippe H.; McCammon, J. Andrew
    Journal of Chemical Physics (2000), 113 (6), 2510-2511 CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    An error made in the derivation of Eq. (25) for the integrated elec. field which also affects Eq. (46). The right-hand sides of Eqs. (57) and (A1)-(A5) should be multiplied by (-1). The derivation of the optimum correction scheme presented in Sec. II G leads to a different soln. for Eq. (55). The reported results for the truncated Coulomb interaction (Sec. III A) are unchanged; modified graphs for the various other schemes are given. Using the cor. equations, the discussion of Sec. III B is pertinent to the function ∫s(r) = 1/4 - r2/Rss3 instead of the BW scheme. In the case of the generalized reaction field (GRF, Sec. III C), the new results show much less dependence on the cutoff distance; however, there is still significant underpolarization with respect to the Born model. For the shifting functions (Sec. III C), the agreement with the Born polarization is generally improved with respect to the original results; the polarization is overestd. for the CHARMm shifting function [Eq. (65)] and underestd. for the generalized force shift potential [Eq. (66)]. The numerically calcd. optimal effective potentials (Sec. III E) still show the best agreement with the Born polarization; the polarization is still consistently slightly underestd., but the difference between the optimal and Born values decreases with increasing polynomial order in the effective potential. The conclusions of the original paper remain largely unaffected; in fact, the demonstration that the optimal effective potential of order two in the limit of an infinitesimal ion (see Sec. II G) is the BW reaction field strengthens the conclusion that the BW scheme is the appropriate choice for ion solvation simulations with truncated electrostatic interactions.
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  203. 203.
    Durand-Vidal, S.; Simonin, J.-P.; Turq, P. Electrolytes at Interfaces; Kluwer: Boston, 2000.
    There is no corresponding record for this reference.
  204. 204.
    Kumar, P. V.; Maroncelli, M. J. Chem. Phys. 2000, 112, 5370
    [CrossRef], [CAS]
    204.
    The non-separability of "dielectric" and "mechanical" friction in molecular systems: A simulation study
    Kumar, P. V.; Maroncelli, M.
    Journal of Chemical Physics (2000), 112 (12), 5370-5381 CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    Simulations of the time-dependent friction controlling rotational, translational, and vibrational motions of dipolar diat. solutes in acetonitrile and methanol have been used to examine the nature of "dielec." friction. The way in which elec. interactions increase the friction beyond that present in nonpolar systems is found to be rather different than what is anticipated by most theories of dielec. friction. Long-range electrostatic forces do not simply add an independent contribution to the friction due to short-ranged or "mech." sources (modeled here in terms of Lennard-Jones forces). Rather, the elec. and Lennard-Jones contributions are found to be strongly anticorrelated and not separable in any useful way. For some purposes, the mechanism by which elec. interactions increase friction is better viewed as a static electrostriction effect: elec. forces cause a subtle increase in at. d. in the solute's first solvation shell, which increases the amplitude of the force fluctuations derived from the Lennard-Jones interactions, i.e., the mech. friction. However, elec. interactions also modify the dynamics of the friction, typically adding a long-time tail, which significantly increases the integral friction. Both of these effects must be included in a correct description of friction in the presence of polar interactions.
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  205. 205.
    Heinz, T. N.; van Gunsteren, W. F.; Hunenberger, P. H. J. Chem. Phys. 2001, 115, 1125
    [CrossRef], [CAS]
    205.
    Comparison of four methods to compute the dielectric permittivity of liquids from molecular dynamics simulations
    Heinz, Tim N.; van Gunsteren, Wilfred F.; Hunenberger, Philippe H.
    Journal of Chemical Physics (2001), 115 (3), 1125-1136 CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    Four methods to compute the dielec. permittivity ε of a liq. from mol. simulations are compared in the context of the simple point charge (SPC) water model. In the 1st method (unrestrained method), ε is evaluated from the fluctuations of the box dipole moment M, monitored during a single equil. simulation. In the three other methods, ε is evaluated from the probability distribution p(M) of the dipole moment norm. This distribution is itself evaluated in three different ways: (i) from multiple simulations involving a M-dependent biasing potential (umbrella-sampling method), (ii) from multiple simulations involving a constrained dipole moment norm (M-constraint method), or (iii) from fitting of incomplete p(M) ests. to a Maxwell distribution (fitting method). The four methods converge to an identical est. of ε=61 ± 1 for SPC water (256 mols., reaction-field electrostatics). The convergence properties, advantages, and drawbacks of the different methods are analyzed.
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  206. 206.
    Abbas, Z.; Gunnarsson, M.; Ahlberg, E.; Nordholm, S. J. Phys. Chem. B 2002, 106, 1403
    [ACS Full Text ACS Full Text], [CAS]
    206.
    Corrected Debye-Hueckel Theory of Salt Solutions: Size Asymmetry and Effective Diameters
    Abbas, Zareen; Gunnarsson, Magnus; Ahlberg, Elisabet; Nordholm, Sture
    Journal of Physical Chemistry B (2002), 106 (6), 1403-1420 CODEN: JPCBFK; ISSN:1089-5647. (American Chemical Society)
    A recently developed extension of the Debye-Hueckel theory, the cor. Debye-Hueckel theory, is applied to salt solns. as described in Monte Carlo (MC) simulations and expt. From modern d. functional anal., the theory accounts for both long-range electrostatic interactions in a linear response approxn. and short-range ion size effects by a generalized van der Waals anal. In its simplest implementation, the cor. Debye-Hueckel restricted primitive model (CDH-RPM) theory, all ions are taken to be of the same diam. d in which case the excluded vol. effects vanish in the linear response domain. Comparison with MC simulations verify the a priori application of the CDH theory to RPM electrolytes over a wide range of concns. Here, the authors study the relation between the appropriate effective diam. d and the real diams. d1 and d2 in simulated binary salt solns. also, in the exptl. studies of salt solns., the relation between d and the crystallog. or hydrated ionic diams. was studied. Calcns. were performed for 67 salts. The optimized diams. are in accord with current understanding of hydration effects. The range of concns. in which a good fit is obtained for mean ionic activity coeffs. and osmotic coeffs. is typically 0-1 M. Comparison is also made with the Specific Interaction theory and the Pitzer and Bromley models of salt solns.
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  207. 207.
    Laidler, K. J.; Meiser, J. H.; Sanctuary, B. C. Physical Chemistry, 4th ed.; BrooksCole: Belmont, CA, 2003.
    There is no corresponding record for this reference.
  208. 208.
    Kastenholz, M. A.; Hunenberger, P. H. J. Chem. Phys. 2006, 124, 124106
    [CrossRef], [PubMed], [CAS]
    208.
    Computation of methodology-independent ionic solvation free energies from molecular simulations. I. The electrostatic potential in molecular liquids
    Kastenholz M A; Hunenberger Philippe H
    The Journal of chemical physics (2006), 124 (12), 124106 ISSN:0021-9606.
    The computation of ionic solvation free energies from atomistic simulations is a surprisingly difficult problem that has found no satisfactory solution for more than 15 years. The reason is that the charging free energies evaluated from such simulations are affected by very large errors. One of these is related to the choice of a specific convention for summing up the contributions of solvent charges to the electrostatic potential in the ionic cavity, namely, on the basis of point charges within entire solvent molecules (M scheme) or on the basis of individual point charges (P scheme). The use of an inappropriate convention may lead to a charge-independent offset in the calculated potential, which depends on the details of the summation scheme, on the quadrupole-moment trace of the solvent molecule, and on the approximate form used to represent electrostatic interactions in the system. However, whether the M or P scheme (if any) represents the appropriate convention is still a matter of on-going debate. The goal of the present article is to settle this long-standing controversy by carefully analyzing (both analytically and numerically) the properties of the electrostatic potential in molecular liquids (and inside cavities within them). Restricting the discussion to real liquids of "spherical" solvent molecules (represented by a classical solvent model with a single van der Waals interaction site), it is concluded that (i) for Coulombic (or straight-cutoff truncated) electrostatic interactions, the M scheme is the appropriate way of calculating the electrostatic potential; (ii) for non-Coulombic interactions deriving from a continuously differentiable function, both M and P schemes generally deliver an incorrect result (for which an analytical correction must be applied); and (iii) finite-temperature effects, including intermolecular orientation correlations and a preferential orientational structure in the neighborhood of a liquid-vacuum interface, must be taken into account. Applications of these results to the computation methodology-independent ionic solvation free energies from molecular simulations will be the scope of a forthcoming article.
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  209. 209.
    Kornyshev, A. A. J. Phys. Chem. B 2007, 111, 5545
    [ACS Full Text ACS Full Text], [PubMed], [CAS]
    209.
    Double-Layer in Ionic Liquids: Paradigm Change?
    Kornyshev, Alexei A.
    Journal of Physical Chemistry B (2007), 111 (20), 5545-5557 CODEN: JPCBFK; ISSN:1520-6106. (American Chemical Society)
    A review. Applications of ionic liqs. at electrified interfaces to energy-storage systems, electrowetting devices, or nanojunction gating media cannot proceed without a deep understanding of the structure and properties of the interfacial double layer. This article provides a detailed critique of the present work on this problem. It promotes the point of view that future considerations of ionic liqs. should be based on the modern statistical mechanics of dense Coulomb systems, or d.-functional theory, rather than classical electrochem. theories which hinge on a dil.-soln. approxn. The article will, however, contain more questions than answers. To trigger the discussion, it starts with a simplified original result. A new anal. formula is derived to rationalize the potential dependence of double-layer capacitance at a planar metal-ionic liq. interface. The theory behind it has a mean-field character, based on the Poisson-Boltzmann lattice-gas model, with a modification to account for the finite vol. occupied by ions. When the vol. of liq. excluded by the ions is taken to be zero (i.e., if ions are extremely sparsely packed in the liq.), the expression reduces to the nonlinear Gouy-Chapman law, the canonical result typically used to describe the potential dependence of capacitance in electrochem. double layers. If ionic vol. exclusion takes more realistic values, the formula shows that capacitance-potential curves for an ionic liq. may differ dramatically from the Gouy-Chapman law. Capacitance has a max. close to the potential of zero charge, rather than the familiar min. At large potentials, capacitance decreases with the square root of potential, rather than increases exponentially. The reported formula does not take into account the specific adsorption of ions, which, if present, can complicate the anal. of exptl. data. Since electrochemists use to think about the capacitance data in terms of the classical Gouy-Chapman theory, which, as we know, should be good only for electrolytes of moderate concn., the question of which result is "better" arises. Exptl. data are sparse, but a quick look at them suggests that the new formula seems to be closer to reality. Opinions here could, however, split. Indeed, a comparison with Monte Carlo simulations has shown that incorporation of restricted-vol. effects in the mean-field theory of electrolyte solns. may give results that are worse than the simple Gouy-Chapman theory. Generally, should the simple mean-field theory work for such highly concd. ionic systems, where the so-called ion-correlation effects must be strong It may not, as it does not incorporate a possibility of charge-d. oscillations. Somehow, to answer this question definitely, one should do further work. This could be based on d.-functional theory (and possibly not on what is referred to as local d. approxn. but rather "weighted d. approxn."), field theory methods for the account of fluctuations in the calcn. of partition function, heuristic integral equation theory extended to the nonlinear response, systematic force-field computer simulations, and, most importantly, expts. with independently detd. potentials of zero charge, as discussed in the paper.
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  210. 210.
    Che, J.; Dzubiella, J.; Li, B.; McCammon, J. A. J. Phys. Chem. B 2008, 112, 3058
    [ACS Full Text ACS Full Text], [PubMed], [CAS]
    210.
    Electrostatic Free Energy and Its Variations in Implicit Solvent Models
    Che, Jianwei; Dzubiella, Joachim; Li, Bo; McCammon, J. Andrew
    Journal of Physical Chemistry B (2008), 112 (10), 3058-3069 CODEN: JPCBFK; ISSN:1520-6106. (American Chemical Society)
    A mean-field approach to the electrostatics for solutes in electrolyte soln. is revisited and rigorously justified. In this approach, an electrostatic free energy functional is constructed that depends solely on the local ionic concns. The unique set of such concns. that minimize this free energy are given by the usual Boltzmann distributions through the electrostatic potential which is detd. by the Poisson-Boltzmann equation. This approach is then applied to the variational implicit solvent description of the solvation of mols. Care is taken for the singularities of the potential generated by the solute point charges. The variation of the electrostatic free energy with respect to the location change of solute-solvent interfaces, i.e., dielec. boundaries, is derived. Such a variation gives rise to the normal component of the effective surface force per unit surface area that is shown to be attractive to the fixed point charges in the solutes. Two examples of applications are given to validate the anal. results. The first one is a one-dimensional model system resembling, for example, a charged solute or cavity in a one-dimensional channel. The second one, which is of its own interest, is the electrostatic free energy of a charged spherical solute immersed in an ionic soln. An anal. formula is derived for the Debye-Huckel approxn. of the free energy, extending the classical Born's formula to one that includes ionic concns. Variations of the nonlinear Poisson-Boltzmann free energy are also obtained.
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  211. 211.
    Henderson, D.; Boda, D. Phys. Chem. Chem. Phys. 2009, 11, 3822
    [CrossRef], [PubMed], [CAS]
    211.
    Insights from theory and simulation on the electrical double layer
    Henderson, Douglas; Boda, Dezso
    Physical Chemistry Chemical Physics (2009), 11 (20), 3822-3830 CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
    A review. Despite the fact that our conceptual understanding of the elec. double layer has advanced during the past few decades, the interpretation of exptl. and applied work is still largely based on the venerable Poisson-Boltzmann theory of Gouy, Chapman and Stern. This is understandable since this theory is simple and analytic. However, it is not very accurate because the at./mol. nature of the ions/solvent and their correlations are ignored. Simulation and some theor. studies by ourselves and others that have advanced our understanding are discussed. These studies show that the GCS theory predicts a narrow double layer with monotonic profiles. This is not correct. The double layer is wider, and there can be substantial layering that would be even more pronounced if explicit solvent mols. are considered. For many years, exptl. studies of the double layer have been directed to the use of electrochem. as an anal. tool. This is acceptable for analytic chem. studies. However, the understanding of electrochem. reactions that typically occur at the electrode surface, where simulation and theory indicate that the GCS theory can have substantial errors, requires modern approaches. New, fundamental exptl. studies that would lead to deeper insights using more novel systems would be desirable. Further, biophysics is an interesting field. Recent studies of the selectivity of ion channels and of the adsorption of ions in a binding sites of a protein have shown that the linearized GCS theory has substantial errors.
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  212. 212.
    Horinek, D.; Mamatkulov, S.; Netz, R. J. Chem. Phys. 2009, 130, 124507
    [CrossRef], [PubMed], [CAS]
    212.
    Rational design of ion force fields based on thermodynamic solvation properties
    Horinek, Dominik; Mamatkulov, Shavkat I.; Netz, Roland R.
    Journal of Chemical Physics (2009), 130 (12), 124507/1-124507/21 CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    Most aq. biol. and technol. systems contain solvated ions. Atomistic explicit-water simulations of ionic solns. rely crucially on accurate ionic force fields, which contain most commonly two adjustable parameters: the Lennard-Jones diam. and the interaction strength. Assuming these parameters to be properly optimized, the plethora of parameters one finds in the literature for one and the same ion is surprising. In principle, the two parameters should be uniquely detd. by matching two ionic properties obtained for a particular water model and within a given simulation protocol with the corresponding exptl. observables. Traditionally, ion parameters were chosen in a somewhat unsystematic way to reproduce the solvation free energy and to give the correct ion size when compared with scattering results. Which exptl. observable one chooses to reproduce should in principle depend on the context within which the ionic force field is going to be used. In the present work we suggest to use the solvation free energy in conjunction with the solvation entropy to construct thermodynamically sound force fields for the alkali and halide ions for the simulation of ion-specific effects in aq. environment. To that end we det. the solvation free energy and entropy of both cations and anions in the entire relevant parameter space. As an independent check on the quality of the resulting force fields we also det. the effective ionic radius from the first peak of the radial ion-water distribution function. Several difficulties during parameter optimization are discussed in detail. (i) Single-ion solvation depends decisively on water-air surface properties, which exptl. becomes relevant when introducing extrathermodynamic assumptions on the hydronium (H3O+) solvation energy. Fitting ion pairs circumvents this problem but leaves the parameters of one ref. ion (here we choose chloride) undetd. (ii) For the halides the problem is almost underdetd., i.e., there is a whole set of degenerate parameters that equally well describe, e.g., chloride and bromide ions. (iii) For the heavy cations the problem is overdetd., i.e., no combination of Lennard-Jones parameters is able to reproduce simultaneously energy and entropy of solvation. We discuss various possibilities to deal with these problems and finally present an optimized force field for the halide anions that reproduces the free energy and the entropy of solvation. For the alkali metal cations there is no unambiguous choice of parameters. Therefore, we give three different parameter sets for every ion with a small, intermediate, or large Lennard-Jones interaction strength, where the Lennard-Jones diams. are optimized to reproduce the solvation free energy. The ionic radius is reproduced with acceptable accuracy by this optimization strategy, meaning that the proposed force fields are reliable beyond the target observables (i.e., free energy and entropy of solvation). (c) 2009 American Institute of Physics.
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  213. 213.
    Ibarra-Armenta, J. G.; Martin-Molina, A.; Quesada-Perez, M. Phys. Chem. Chem. Phys. 2009, 11, 309
    [CrossRef], [PubMed], [CAS]
    213.
    Testing a modified model of the Poisson-Boltzmann theory that includes ion size effects through Monte Carlo simulations
    Ibarra-Armenta, Jose Guadalupe; Martin-Molina, Alberto; Quesada-Perez, Manuel
    Physical Chemistry Chemical Physics (2009), 11 (2), 309-316 CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
    In this work we test the validity of a recent modified Poisson-Boltzmann (MPB) theory that includes ion size effects through a Langmuir-type correction. In particular, we will focus on an analytic charge-potential relationship accounting for such effects. Previous elec. double layer (EDL) surveys have demonstrated that the inclusion of ions size in classical EDL theories, based on the Poisson-Boltzmann (PB) equation, can yield considerable improvements. In this sense, the theory we analyze assumes that, as a result of the excluded vol., the ion concn. close to the charged surface cannot exceed a fixed value detd. by the close packing fraction. This leads to predictions of counterion concns. (in this region) smaller than the corresponding PB values. In our opinion, it is worthwhile to test the validity of this novel theory. To this end, computer simulations appear as a useful tool for this kind of task. Our results prove that the above-mentioned anal. expression works fairly well for 1 : 1 electrolytes and large ions, and its predictions can be considerably improved with certain corrections in the estn. of some key parameters. However, it fails for multivalent electrolytes.
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  214. 214.
    JaneCek, J.; Netz, R. R. J. Chem. Phys. 2009, 130, 074502
    [CrossRef], [CAS]
    214.
    Effective screening length and quasiuniversality for the restricted primitive model of an electrolyte solution
    Janecek, Jiri; Netz, Roland R.
    Journal of Chemical Physics (2009), 130 (7), 074502/1-074502/15 CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    Monte Carlo simulations for the restricted primitive model of an electrolyte soln. above the crit. temp. are performed at a wide range of concns. and temps. Thermodn. properties such as internal energy, osmotic coeff., activity coeff., as well as spatial correlation functions are detd. These observables are used to investigate whether quasiuniversality in terms of an effective screening length exists, similar to the role played by the effective electron mass in solid-state physics. To that end, an effective screening length is extd. from the asymptotic behavior of the Fourier-transformed charge-correlation function and plugged into the Debye-Hueckel limiting expressions for various thermodn. properties. Comparison with numerical results is favorable, suggesting that correlation and other effects not captured on the Debye-Hueckel limiting level can be successfully incorporated by a single effective parameter while keeping the functional form of Debye-Hueckel expressions. Different methods were also compared to det. mean ionic activity coeff. in mol. simulations and check the internal consistency of the numerical data. (c) 2009 American Institute of Physics.
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  215. 215.
    Kalcher, I.; Dzubiella, J. J. Chem. Phys. 2009, 130, 134507
    [CrossRef], [PubMed], [CAS]
    215.
    Structure-thermodynamics relation of electrolyte solutions
    Kalcher, Immanuel; Dzubiella, Joachim
    Journal of Chemical Physics (2009), 130 (13), 134507/1-134507/12 CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    The structure of aq. LiCl, NaCl, KCl, CsCl, KF, and NaI solns. is calcd. by mol. dynamics (MD) simulations of the frequently employed Dang force-field in SPC/E water. By using liq. state theory, we integrate the structure to obtain the electrolytes' osmotic coeff. .vphi. and systematically investigate force-field quality and structural consequences to ion-specific bulk thermodn. The osmotic coeffs. .vphi.χ calcd. from the exact compressibility route for the cation-Cl- force-fields match expts. for concns. ρ .ltorsim. 2M, while NaI and KF parameters fail. Comparison of .vphi.χ with .vphi.v from the virial route, which relies on the pair potential approxn., shows that many-body effects become important for all salts above ρ 0.5M. They can be efficiently cor., however, by employing a salt-type and ρ-dependent dielec. const. ε(ρ), generalizing previous observations on NaCl only. For physiol. concns., ρ .ltorsim. 0.5M, the specific osmotic behavior is found to be detd. by the short-ranged cation-anion pair potential only and is strongly related to the second virial coeff. of the latter. Presented methods and findings, based on simple integrations over the electrolyte structure, enable efficient MD force-field refinement by direct benchmarking to the sensitive electrolyte thermodn., instead to non-collective, single ion properties. (c) 2009 American Institute of Physics.
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  216. 216.
    Li, B. Nonlinearity 2009, 22, 811
    [CrossRef]
    There is no corresponding record for this reference.
  217. 217.
    Li, B. SIAM J. Math. Anal. 2009, 40, 2536
    [CrossRef]
    There is no corresponding record for this reference.
  218. 218.
    Luo, Y.; Roux, B. J. Phys. Chem. Lett. 2009, 1, 183
    [ACS Full Text ACS Full Text]
    There is no corresponding record for this reference.
  219. 219.
    Maginn, E. J. AIChE J. 2009, 55, 1304
    [CrossRef], [CAS]
    219.
    From discovery to data: What must happen for molecular simulation to become a mainstream chemical engineering tool
    Maginn, Edward J.
    AIChE Journal (2009), 55 (6), 1304-1310 CODEN: AICEAC; ISSN:0001-1541. (John Wiley & Sons, Inc.)
    The emergence of mol. simulation in research, making the mol. simulations a mainstream chem. engineering tool, narrowing the scope of the problems addressed, simplifying calcn. setup, providing integrated software and anal. tools, developing and archiving force fields, providing validation databases, and creation of a mol. simulation database are discussed.
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  220. 220.
    Kalcher, I.; Schulz, J. C. F.; Dzubiella, J. Phys. Rev. Lett. 2010, 104, 097802
    [CrossRef], [CAS]
    220.
    Ion-specific excluded-volume correlations and solvation forces
    Kalcher, Immanuel; Schulz, Julius C. F.; Dzubiella, Joachim
    Physical Review Letters (2010), 104 (9), 097802/1-097802/4 CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
    Realistic ion-ion and ion-surface potentials from explicit-water simulations are used in implicit-solvent Monte Carlo simulations to study the ionic structure and double-layer forces in a nanometer slab confinement. The highly salt-specific results can be reproduced and rationalized by a simple nonlocal Poisson-Boltzmann theory of a nonadditive primitive model, in which effective hard-sphere radii are obtained from the short-ranged part of the pair potentials. Steric corrections to solvation forces are mainly repulsive and strongly coupled to the ion-surface interactions.
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  221. 221.
    Kalyuzhnyi, Y. V.; Vlachy, V.; Dill, K. A. Phys. Chem. Chem. Phys. 2010, 12, 6260
    [CrossRef], [CAS]
    221.
    Aqueous alkali halide solutions: can osmotic coefficients be explained on the basis of the ionic sizes alone?
    Kalyuzhnyi, Yu V.; Vlachy, Vojko; Dill, Ken A.
    Physical Chemistry Chemical Physics (2010), 12 (23), 6260-6266 CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
    We use the AMSA, associative mean spherical theory of associative fluids, to study ion-ion interactions in explicit water. We model water mols. as hard spheres with four off-center square-well sites and ions as charged hard spheres with sticky sites that bind to water mols. or other ions. We consider alkali halide salts. The choice of model parameters is based on two premises: (i) The strength of the interaction between a monovalent ion and a water mol. is inversely proportional to the ionic (crystal) diam. σi. Smaller ions bind to water more strongly than larger ions do, taking into account the asymmetry of the cation-water and anion-water interactions. (ii) The no. of contacts an ion can make is proportional to σi2. In short, small ions bind waters strongly, but only a few of them. Large ions bind waters weakly, but many of them. When both a monovalent cation and anion are large, it yields a small osmotic coeff. of the salt, since the water mols. avoid the space in between large ions. On the other hand, salts formed from one small and one large ion remain hydrated and their osmotic coeff. is high. The osmotic coeffs., calcd. using this model in combination with the integral equation theory developed for associative fluids, follow the exptl. trends, including the unusual behavior of cesium salts.
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  222. 222.
    Lipparini, F.; Scalmani, G.; Mennucci, B.; Cances, E.; Caricato, M.; Frisch, M. J. J. Chem. Phys. 2010, 133, 014106
    [CrossRef], [CAS]
    222.
    A variational formulation of the polarizable continuum model
    Lipparini, Filippo; Scalmani, Giovanni; Mennucci, Benedetta; Cances, Eric; Caricato, Marco; Frisch, Michael J.
    Journal of Chemical Physics (2010), 133 (1), 014106/1-014106/11 CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    Continuum solvation models are widely used to accurately est. solvent effects on energy, structural and spectroscopic properties of complex mol. systems. The polarizable continuum model (PCM) is one of the most versatile among the continuum models because of the variety of properties that can be computed and the diversity of methods that can be used to describe the solute from mol. mechanics (MM) to sophisticated quantum mech. (QM) post-SCF methods or even hybrid QM/MM methods. In this contribution, we present a new formulation of PCM in terms of a free energy functional whose variational parameters include the continuum polarization (represented by the apparent surface charges), the solute's at. coordinates and-possibly-its electronic d. The problem of finding the optimized geometry of the (polarized) solute, with the corresponding self-consistent reaction field, is recast as the minimization of this free energy functional, simultaneously with respect to all its variables. The numerous potential applications of this variational formulation of PCM are discussed, including simultaneous optimization of solute's geometry and polarization charges and extended Lagrangian dynamics. In particular, we describe in details the simultaneous optimization procedure and we include several numerical examples. (c) 2010 American Institute of Physics.
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  223. 223.
    Sala, J.; Guardia, E.; Marti, J. J. Chem. Phys. 2010, 132, 214505
    [CrossRef], [PubMed], [CAS]
    223.
    Effects of concentration on structure, dielectric, and dynamic properties of aqueous NaCl solutions using a polarizable model
    Sala J; Guardia E; Marti J
    The Journal of chemical physics (2010), 132 (21), 214505 ISSN:.
    The study of NaCl solutions in water at finite concentration, explicitly including polarization in water molecules and ions, has been carried out by molecular dynamics simulations. A comparison of the RPOL polarizable model with the rigid SPC/E potential for water has been included. Structure obtained with the two models does not show significant differences, although some deviations in the NaNa radial distribution functions at all concentrations are observed. Dielectric properties such as total and molecular dipole moment correlation functions revealed decay times of the order of 10 ps, roughly independent of concentration. The analysis of electric conductivity by means of current-current correlation functions also included the calculation of cross terms corresponding to dipole moment-current correlations, which proved to be non-neglectable at short times and especially relevant at high concentrations (m=4 mol kg(-1)). Frequency dependent dielectric constants and conductivities have been computed and the role of cross correlations has been analyzed. In all cases both concentration and cross correlations have significant influence in the results.
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  224. 224.
    Vincze, J.; Valisko, M.; Boda, D. J. Chem. Phys. 2010, 133, 154507
    [CrossRef], [PubMed], [CAS]
    224.
    The nonmonotonic concentration dependence of the mean activity coefficient of electrolytes is a result of a balance between solvation and ion-ion correlations
    Vincze, Julianna; Valisko, Monika; Boda, Dezso
    Journal of Chemical Physics (2010), 133 (15), 154507/1-154507/6 CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    We propose a simple model to explain the nonmonotonic concn. dependence of the mean activity coeff. of simple electrolytes without using any adjustable parameters. The primitive model of electrolytes is used to describe the interaction between ions computed by the adaptive grand canonical Monte Carlo method. For the dielec. const. of the electrolyte, we use exptl. concn. dependent values. This is included through a solvation term in our treatment to describe the interaction between ions and water that changes as the dielec. const. changes with concn. This term is computed by a Born-treatment fitted to exptl. hydration energies. Our results for LiCl, NaCl, KCl, CsCl, NaBr, NaI, MgCl2, CaCl2, SrCl2, and BaCl2 demonstrate that the principal reason of the nonmonotonic behavior of the activity coeff. is a balance between the solvation and ion-ion correlation terms. This conclusion differs from previous studies that assumed that it is the balance of hard sphere repulsion and electrostatic attraction that produces the nonmonotonic behavior. Our results indicate that the earlier assumption that solvation can be taken into account by a larger, "solvated" ionic radius should be reconsidered. To explain second order effects (such as dependence on ionic size), we conclude that explicit water models are needed. (c) 2010 American Institute of Physics.
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  225. 225.
    Yu, H.; Whitfield, T. W.; Harder, E.; Lamoureux, G.; Vorobyov, I.; Anisimov, V. M.; MacKerell, A. D.; Roux, B. J. Chem. Theory Comput. 2010, 6, 774
    [ACS Full Text ACS Full Text], [PubMed], [CAS]
    225.
    Simulating Monovalent and Divalent Ions in Aqueous Solution Using a Drude Polarizable Force Field
    Yu, Haibo; Whitfield, Troy W.; Harder, Edward; Lamoureux, Guillaume; Vorobyov, Igor; Anisimov, Victor M.; MacKerell, Alexander D.; Roux, Benoit
    Journal of Chemical Theory and Computation (2010), 6 (3), 774-786 CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
    An accurate representation of ion solvation in aq. soln. is crit. for meaningful computer simulations of a broad range of phys. and biol. processes. Polarizable models based on classical Drude oscillators are introduced and parametrized for a large set of monat. ions including cations of the alkali metals (Li+, Na+, K+, Rb+, and Cs+) and alk. earth elements (Mg2+, Ca2+, Sr2+, and Ba2+) along with Zn2+ and halide anions (F-, Cl-, Br-, and I-). The models are parametrized, in conjunction with the polarizable SWM4-NDP water model [Lamoureux et al. Chem. Phys. Lett.2006, 418, 245], to be consistent with a wide assortment of exptl. measured aq. bulk thermodn. properties and the energetics of small ion-water clusters. Structural and dynamic properties of the resulting ion models in aq. solns. at infinite diln. are presented.
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  226. 226.
    Zhang, C.; Raugei, S.; Eisenberg, B.; Carloni, P. J. Chem. Theory Comput. 2010, 6, 2167
    [ACS Full Text ACS Full Text], [CAS]
    226.
    Molecular Dynamics in Physiological Solutions: Force Fields, Alkali Metal Ions, and Ionic Strength
    Zhang, Chao; Raugei, Simone; Eisenberg, Bob; Carloni, Paolo
    Journal of Chemical Theory and Computation (2010), 6 (7), 2167-2175 CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
    The monovalent ions Na+ and K+ and Cl- are present in any living organism. The fundamental thermodn. properties of solns. contg. such ions is given as the excess (electro-)chem. potential differences of single ions at finite ionic strength. This quantity is key for many biol. processes, including ion permeation in membrane ion channels and DNA-protein interaction. It is given by a chem. contribution, related to the ion activity, and an elec. contribution, related to the Galvani potential of the water/air interface. Here, l. dynamics based predictions of these quantities were investigated by using a variety of ion/water force fields commonly used in biol. simulation, namely the AMBER (the newly developed), CHARMM, OPLS, Dang95 with TIP3P, and SPC/E water. Comparison with expt. is made with the corresponding values for salts, for which data are available. The calcns. based on the newly developed AMBER force field with TIP3P water agrees well with expt. for both KCl and NaCl electrolytes in water solns., as previously reported. The simulations based on the CHARMM-TIP3P and Dang95-SPC/E force fields agree well for the KCl and NaCl solns., resp. The other models are not as accurate. Single cations excess (electro-)chem. potential differences turn out to be similar for all the force fields considered here. In the case of KCl, the calcd. elec. contribution is consistent with higher level calcns. Instead, such agreement is not found with NaCl. Finally, it was found that the calcd. activities for single Cl- ions turn out to depend clearly on the type of counterion used, with all the force fields investigated. The implications of these findings for biomol. systems are discussed.
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  227. 227.
    Bazant, M. Z.; Storey, B. D.; Kornyshev, A. A. Phys. Rev. Lett. 2011, 106, 046102
    [CrossRef], [CAS]
    227.
    Double layer in ionic liquids. Overscreening versus crowding
    Bazant, Martin Z.; Storey, Brian D.; Kornyshev, Alexei A.
    Physical Review Letters (2011), 106 (4), 046102/1-046102/4 CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
    We develop a simple Landau-Ginzburg-type continuum theory of solvent-free ionic liqs. and use it to predict the structure of the elec. double layer. The model captures overscreening from short-range correlations, dominant at small voltages, and steric constraints of finite ion sizes, which prevail at large voltages. Increasing the voltage gradually suppresses overscreening in favor of the crowding of counterions in a condensed inner layer near the electrode. This prediction, the ion profiles, and the capacitance-voltage dependence are consistent with recent computer simulations and expts. on room-temp. ionic liqs., using a correlation length of order the ion size.
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  228. 228.
    Gee, M. B.; Cox, N. R.; Jiao, Y.; Bentenitis, N.; Weerasinghe, S.; Smith, P. E. J. Chem. Theory Comput. 2011, not supplied.
    There is no corresponding record for this reference.
  229. 229.
    Xiao, T.; Song, X. J. Chem. Phys. 2011, 135, 104104
    [CrossRef], [CAS]
    229.
    A molecular Debye-Hueckel theory and its applications to electrolyte solutions
    Xiao, Tiejun; Song, Xueyu
    Journal of Chemical Physics (2011), 135 (10), 104104/1-104104/14 CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    A mol. Debye-Huckel theory for ionic fluids is developed. Starting from the macroscopic Maxwell equations for bulk systems, the dispersion relation leads to a generalized Debye-Huckel theory which is related to the dressed ion theory in the static case. Due to the multipole structure of dielec. function of ionic fluids, the elec. potential around a single ion has a multi-Yukawa form. Given the dielec. function, the multi-Yukawa potential can be detd. from our mol. Debye-Huckel theory, hence, the electrostatic contributions to thermodn. properties of ionic fluids can be obtained. Applications to binary as well as multi-component primitive models of electrolyte solns. demonstrated the accuracy of our approach. More importantly, for electrolyte soln. models with soft short-ranged interactions, it is shown that the traditional perturbation theory can be extended to ionic fluids successfully just as the perturbation theory has been successfully used for short-range systems. (c) 2011 American Institute of Physics.
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  230. 230.
    Zheng, Q.; Chen, D.; Wei, G.-W. J. Comput. Phys. 2011, 230, 5239
    [CrossRef], [CAS]
    230.
    Second-order Poisson-Nernst-Planck solver for ion transport
    Zheng, Qiong; Chen, Duan; Wei, Guo-Wei
    Journal of Computational Physics (2011), 230 (13), 5239-5262 CODEN: JCTPAH; ISSN:0021-9991. (Elsevier)
    The Poisson-Nernst-Planck (PNP) theory is a simplified continuum model for a wide variety of chem., phys. and biol. applications. Its ability of providing quant. explanation and increasingly qual. predictions of exptl. measurements has earned itself much recognition in the research community. Numerous computational algorithms have been constructed for the soln. of the PNP equations. However, in the realistic ion-channel context, no second-order convergent PNP algorithm has ever been reported in the literature, due to many numerical obstacles, including discontinuous coeffs., singular charges, geometric singularities, and nonlinear couplings. The present work introduces a no. of numerical algorithms to overcome the abovementioned numerical challenges and constructs the first second-order convergent PNP solver in the ion-channel context. First, a Dirichlet to Neumann mapping (DNM) algorithm is designed to alleviate the charge singularity due to the protein structure. Addnl., the matched interface and boundary (MIB) method is reformulated for solving the PNP equations. The MIB method systematically enforces the interface jump conditions and achieves the second order accuracy in the presence of complex geometry and geometric singularities of mol. surfaces. Moreover, two iterative schemes are utilized to deal with the coupled nonlinear equations. Furthermore, extensive and rigorous numerical validations are carried out over a no. of geometries, including a sphere, two proteins and an ion channel, to examine the numerical accuracy and convergence order of the present numerical algorithms. Finally, application is considered to a real transmembrane protein, the Gramicidin A channel protein. The performance of the proposed numerical techniques is tested against a no. of factors, including mesh sizes, diffusion coeff. profiles, iterative schemes, ion concns., and applied voltages. Numerical predictions are compared with exptl. measurements.
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  231. 231.
    Boron, W.; Boulpaep, E. Medical Physiology; Saunders: New York, 2008.
    There is no corresponding record for this reference.
  232. 232.
    Heras, J. A. Am. J. Phys. 2007, 75, 652
    [CrossRef]
    There is no corresponding record for this reference.
  233. 233.
    Heras, J. A. Am. J. Phys. 2008, 76, 101
    [CrossRef]
    There is no corresponding record for this reference.
  234. 234.
    Heras, J. A. Am. J. Phys. 2011, 79, 409
    [CrossRef]
    There is no corresponding record for this reference.
  235. 235.
    Hladky, S. B.; Haydon, D. A. Nature 1970, 225, 451
    [CrossRef], [PubMed], [CAS]
    235.
    Discreteness of conductance change in bimolecular lipid membranes in the presence of certain antibiotics
    Hladky, S. B.; Haydon, D. A.
    Nature (London, United Kingdom) (1970), 225 (5231), 451-3 CODEN: NATUAS; ISSN:0028-0836.
    The conductance of permeability-inducing substances such as nonactin, nystatin, and gramicidin A was studied in artificial bimol. lipid film formed from solns. of lecithin or glycerol mono-oleate in n-decane, in a hole on a Fluon support, by the injection manometer method. The conductance was measured by application of a known potential (100 mV) to 1 side of the film and by recording the current necessary to maintain the other side at zero. Transient increases in conductance of 5 × 10-13 ohms-1 could be obsd. provided they lasted for 100 msec; resolns. at higher conductances were 10 msec at 2 × 10-11 ohms-1 and 1 msec at 10-10 ohms-1. With nonactin, the conductance increased smoothly on formation of a black film; no step changes were obsd. down to a level of 5 × 10-13 ohms-1. For nystatin (reproducible) fluctuations in conductance were absent, the largest possible step being 2 × 10-13 ohms-1; there were no transient decreases in conductance. Gramicidin A in low concns. fluctuated conductance, with time, in a well defined step-like fashion, whereas at high concns. the steps overlapped to give a high conductance. In 1.0M NaCl the step heights had a peak at 2.4 × 10-11 ohms-1, the frequency of the step occurrence increased with applied potential. Gramicidin A is twice the size of either nonactin or nystatin, a fact which may explain the pronounced unit conductance changes it produced. In satd. NaCl and for 100 mV applied potential the net charge transfer per conducting channel corresponded to 2 × 107 ions/sec. This suggests that the effective ionic mobility across the membrane is less than that for the inorg. ion in water, and consequently a pore, rather than a carrier mechanism, is indicated.
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  236. 236.
    Sigworth, F. J.; Neher, E. Nature 1980, 287, 447
    [CrossRef], [PubMed], [CAS]
    236.
    Single sodium channel currents observed in cultured rat muscle cells
    Sigworth, Frederick J.; Neher, Erwin
    Nature (London, United Kingdom) (1980), 287 (5781), 447-9 CODEN: NATUAS; ISSN:0028-0836.
    Using an improvement of the extracellular patch-clamp technique on cultured rat cells under physiol. conditions, results were obtained which supported earlier inferences about channel gating and showed a single-channel Na+ conductance of 18 pS.
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  237. 237.
    Hamill, O. P.; Marty, A.; Neher, E.; Sakmann, B.; Sigworth, F. J. Pflugers Arch. 1981, 391, 85
    [CrossRef], [PubMed], [CAS]
    237.
    Improved patch-clamp techniques for high-resolution current recording from cells and cell-free membrane patches
    Hamill O P; Marty A; Neher E; Sakmann B; Sigworth F J
    Pflugers Archiv : European journal of physiology (1981), 391 (2), 85-100 ISSN:0031-6768.
    1. The extracellular patch clamp method, which first allowed the detection of single channel currents in biological membranes, has been further refined to enable higher current resolution, direct membrane patch potential control, and physical isolation of membrane patches. 2. A description of a convenient method for the fabrication of patch recording pipettes is given together with procedures followed to achieve giga-seals i.e. pipette-membrane seals with resistances of 10(9) - 10(11) omega. 3. The basic patch clamp recording circuit, and designs for improved frequency response are described along with the present limitations in recording the currents from single channels. 4. Procedures for preparation and recording from three representative cell types are given. Some properties of single acetylcholine-activated channels in muscle membrane are described to illustrate the improved current and time resolution achieved with giga-seals. 5. A description is given of the various ways that patches of membrane can be physically isolated from cells. This isolation enables the recording of single channel currents with well-defined solutions on both sides of the membrane. Two types of isolated cell-free patch configurations can be formed: an inside-out patch with its cytoplasmic membrane face exposed to the bath solution, and an outside-out patch with its extracellular membrane face exposed to the bath solution. 6. The application of the method for the recording of ionic currents and internal dialysis of small cells is considered. Single channel resolution can be achieved when recording from whole cells, if the cell diameter is small (less than 20 micrometer). 7. The wide range of cell types amenable to giga-seal formation is discussed.
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  238. 238.
    FitzHugh, R. Math. Biosci. 1983, 64, 75
    [CrossRef]
    There is no corresponding record for this reference.
  239. 239.
    Conley, E. C.; Brammar, W. J. The Ion Channel Facts Book IV: Voltage Gated Channels; Academic Press: New York, 1999.
    There is no corresponding record for this reference.
  240. 240.
    Conley, E. C.; Brammar, W. J. The Ion Channel Facts Book III: Inward Rectifier and Intercellular Channels: Academic Press: New York, 2000.
    There is no corresponding record for this reference.
  241. 241.
    Cherny, V. V.; Murphy, R.; Sokolov, V.; Levis, R. A.; DeCoursey, T. E. J. Gen. Physiol. 2003, 121, 615
    [CrossRef], [CAS]
    241.
    Properties of single voltage-gated proton channels in human eosinophils estimated by noise analysis and by direct measurement
    Cherny, Vladimir V.; Murphy, Ricardo; Sokolov, Valerij; Levis, Richard A.; DeCoursey, Thomas E.
    Journal of General Physiology (2003), 121 (6), 615-628 CODEN: JGPLAD; ISSN:0022-1295. (Rockefeller University Press)
    Voltage-gated proton channels were studied under voltage clamp in excised, inside-out patches of human eosinophils, at various pHi with pHo 7.5 or 6.5 pipet solns. H+ current fluctuations were obsd. consistently when the membrane was depolarized to voltages that activated H+ current. At pHi ≤ 5.5, the variance increased nonmonotonically with depolarization to a max. near the midpoint of the H+ conductance-voltage relationship, gH-V, and then decreased, supporting the idea that the noise is generated by H+ channel gating. Power spectral anal. indicated Lorentzian and 1/f components, both related to H+ currents. Unitary H+ current amplitude was estd. from stationary or quasi-stationary variance, σ2H. We analyze σ2H data obtained at various voltages on a linearized plot that provides ests. of both unitary conductance and the no. of channels in the patch, without requiring knowledge of open probability. The unitary conductance averaged 38 fS at pHi 6.5, and increased nearly fourfold to 140 fS at pHi 5.5, but was independent of pHo. In contrast, the macroscopic gH was only 1.8-fold larger at pHi 5.5 than at pHi 6.5. The max. H+ channel open probability during large depolarizations was 0.75 at pHi 6.5 and 0.95 at pHi 5.5. Because the unitary conductance increases at lower pHi more than the macroscopic gH, the no. of functional channels must decrease. Single H+ channel currents were too small to record directly at physiol. pH, but at pHi ≤ 5.5 near Vthreshold (the voltage at which gH turns on), single channel-like current events were obsd. with amplitudes 7-16 fA.
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  242. 242.
    Levis, R. A.; Rae, J. L.; Iverson, L.; Rudy, B. Methods Enzymol. 1992, 207, 66
    [CrossRef], [CAS]
    242.
    Glass technology for patch clamp electrodes
    Rae, James L.; Levis, Richard A.
    Methods in Enzymology (1992), 207 (Ion Channels), 66-92 CODEN: MENZAU; ISSN:0076-6879.
    The properties of various glasses and their applications in the construction of patch clamp electrodes are discussed.
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  243. 243.
    Levis, R. A.; Rae, J. L. Methods Enzymol. 1998, 293, 218
    [CrossRef], [PubMed], [CAS]
    243.
    Low-noise patch-clamp techniques
    Levis, Richard A.; Rae, James L.
    Methods in Enzymology (1998), 293 (Ion Channels, Part B), 218-266 CODEN: MENZAU; ISSN:0076-6879. (Academic Press)
    This article focuses on noise performance in patch and whole-cell voltage clamping. It attempts to describe both theor. and practical aspects of noise redn. for single-channel and whole-cell patch-clamp recordings. (c) 1998 Academic Press.
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  244. 244.
    Tang, J.; Levis, R.; Lynn, K.; Eisenberg, B. Biophys. J. 1995, 68, A145
    [CrossRef]
    There is no corresponding record for this reference.
  245. 245.
    Miodownik-Aisenberg, J. Gating Kinetics of a Calcium-Activated Potassium Channel Studied at Subzero Temperatures; University of Miami Medical School, 1995.
    There is no corresponding record for this reference.
  246. 246.
    Miller, C. Ion Channel Reconstitution; Plenum Press: New York, 1986.
    There is no corresponding record for this reference.
  247. 247.
    Miceli, F.; Vargas, E.; Bezanilla, F.; Taglialatela, M. Biophys. J. 2012, 102, 1372
    [CrossRef], [CAS]
    247.
    Gating Currents from Kv7 Channels Carrying Neuronal Hyperexcitability Mutations in the Voltage-Sensing Domain
    Miceli, Francesco; Vargas, Ernesto; Bezanilla, Francisco; Taglialatela, Maurizio
    Biophysical Journal (2012), 102 (6), 1372-1382 CODEN: BIOJAU; ISSN:0006-3495. (Cell Press)
    Changes in voltage-dependent gating represent a common pathogenetic mechanism for genetically inherited channelopathies, such as benign familial neonatal seizures or peripheral nerve hyperexcitability caused by mutations in neuronal Kv7.2 channels. Mutation-induced changes in channel voltage dependence are most often inferred from macroscopic current measurements, a technique unable to provide a detailed assessment of the structural rearrangements underlying channel gating behavior; by contrast, gating currents directly measure voltage-sensor displacement during voltage-dependent gating. In this work, we describe macroscopic and gating current measurements, together with mol. modeling and mol.-dynamics simulations, from channels carrying mutations responsible for benign familial neonatal seizures and/or peripheral nerve hyperexcitability; Kv7.4 channels, highly related to Kv7.2 channels both functionally and structurally, were used for these expts. The data obtained showed that mutations affecting charged residues located in the more distal portion of S4 decrease the stability of the open state and the active voltage-sensing domain configuration but do not directly participate in voltage sensing, whereas mutations affecting a residue (R4) located more proximally in S4 caused activation of gating-pore currents at depolarized potentials. These results reveal that distinct mol. mechanisms underlie the altered gating behavior of channels carrying disease-causing mutations at different voltage-sensing domain locations, thereby expanding our current view of the pathogenesis of neuronal hyperexcitability diseases.
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  248. 248.
    Dekel, N.; Priest, M. F.; Parnas, H.; Parnas, I.; Bezanilla, F. Proc. Natl. Acad. Sci. U.S.A. 2012, 109, 285
    [CrossRef], [CAS]
    248.
    Depolarization induces a conformational change in the binding site region of the M2 muscarinic receptor
    Dekel, Noa; Priest, Michael F.; Parnas, Hanna; Parnas, Itzchak; Bezanilla, Francisco
    Proceedings of the National Academy of Sciences of the United States of America (2012), 109 (1), 285-290, S285/1-S285/3 CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)
    G protein-coupled receptors play a central role in signal transduction and were only known to be activated by agonists. Recently it has been shown that membrane potential also affects the activity of G protein-coupled receptors. For the M2 muscarinic receptor, it was further shown that depolarization induces charge movement. A tight correlation was found between the voltage-dependence of the charge movement and the voltage-dependence of the agonist binding. Here we examine whether depolarization-induced charge movement causes a conformational change in the M2 receptor that may be responsible for the voltage-dependence of agonist binding. Using site-directed fluorescence labeling we show a voltage-dependent fluorescence signal, reflecting a conformational change, which correlates with the voltage-dependent charge movement. We further show that selected mutations in the orthosteric site abolish the fluorescence signal and concomitantly, the voltage-dependence of the agonist binding. Surprisingly, mutations in the allosteric site also abolished the voltage-dependence of agonist binding but did not reduce the fluorescence signal. Finally, we show that treatments, which reduced the charge movement or hindered the coupling between the charge movement and the volt- age-dependent binding, also reduced the fluorescence signal. Our results demonstrate that depolarization-induced conformational changes in the orthosteric binding site underlie the voltage-dependence of agonist binding. Our results are also unique in suggesting that the allosteric site is also involved in controlling the voltage-dependent agonist binding.
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  249. 249.
    Vargas, E.; Bezanilla, F.; Roux, B. Neuron 2011, 72, 713
    [CrossRef], [CAS]
    249.
    In Search of a Consensus Model of the Resting State of a Voltage-Sensing Domain
    Vargas, Ernesto; Bezanilla, Francisco; Roux, Benoit
    Neuron (2011), 72 (5), 713-720 CODEN: NERNET; ISSN:0896-6273. (Cell Press)
    Summary: Voltage-sensing domains (VSDs) undergo conformational changes in response to the membrane potential and are the crit. structural modules responsible for the activation of voltage-gated channels. Structural information about the key conformational states underlying voltage activation is currently incomplete. Through the use of exptl. detd. residue-residue interactions as structural constraints, we det. and refine a model of the Kv channel VSD in the resting conformation. The resulting structural model is in broad agreement with results that originate from various labs using different techniques, indicating the emergence of a consensus for the structural basis of voltage sensing.
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  250. 250.
    Lacroix, J. J.; Bezanilla, F. Proc. Natl. Acad. Sci. U.S.A. 2011, 108, 6444
    [CrossRef], [CAS]
    250.
    Control of a final gating charge transition by a hydrophobic residue in the S2 segment of a K+ channel voltage sensor
    Lacroix, Jerome J.; Bezanilla, Francisco
    Proceedings of the National Academy of Sciences of the United States of America (2011), 108 (16), 6444-6449, S6444/1-S6444/3 CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)
    It is now well established that the voltage-sensor domains present in voltage-gated ion channels and some phosphatases operate by transferring several charged residues (gating charges), mainly arginines located in the S4 segment, across the elec. field. The conserved phenylalanine F290 located in the S2 segment of the Shaker K channel is an arom. residue thought to interact with all the four gating arginines carried by the S4 segment and control their transfer. In this paper we study the possible interaction of the gating charges with this residue by directly detecting their movement with gating current measurements in 12 F290 mutants. Most mutations do not significantly alter the first approx. 80-90% of the gating charge transfer nor the kinetics of the gating currents during activation. The effects of the F290 mutants are (i) the modification of a final activation transition accounting for approx. 10-20% of the total charge, similar to the effect of the ILT mutant and (ii) the modification of the kinetics of the gating charge movement during deactivation. These effects are well correlated with the hydrophobicity of the substituted residue, showing that a hydrophobic residue at position 290 controls the energy barrier of the final gating transition. Our results suggest that F290 controls the transfer of R371, the fourth gating charge, during gating while not affecting the movement of the other three gating arginines.
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  251. 251.
    Lacroix, J.; Halaszovich, C. R.; Schreiber, D. N.; Leitner, M. G.; Bezanilla, F.; Oliver, D.; Villalba-Galea, C. A. J. Biol. Chem. 2011, 286, 17945
    [CrossRef], [CAS]
    251.
    Controlling the Activity of a Phosphatase and Tensin Homolog (PTEN) by Membrane Potential
    Lacroix, Jerome; Halaszovich, Christian R.; Schreiber, Daniela N.; Leitner, Michael G.; Bezanilla, Francisco; Oliver, Dominik; Villalba-Galea, Carlos A.
    Journal of Biological Chemistry (2011), 286 (20), 17945-17953 CODEN: JBCHA3; ISSN:0021-9258. (American Society for Biochemistry and Molecular Biology)
    The recently discovered voltage-sensitive phosphatases (VSPs) hydrolyze phosphoinositides upon depolarization of the membrane potential, thus representing a novel principle for the transduction of elec. activity into biochem. signals. Here, we examine the possibility of conferring voltage sensitivity to cytosolic enzymes. By fusing the tumor suppressor PTEN to the voltage sensor of the prototypic VSP from Ciona intestinalis, Ci-VSP, we generated chimeric proteins that are voltage-sensitive and display PTEN-like enzymic activity in a strictly depolarization-dependent manner in vivo. Functional coupling of the exogenous enzymic activity to the voltage sensor is mediated by a phospholipid-binding motif at the interface between voltage sensor and catalytic domains. Our findings reveal that the main domains of VSPs and related phosphoinositide phosphatases are intrinsically modular and define structural requirements for coupling of enzymic activity to a voltage sensor domain. A key feature of this prototype of novel engineered voltage-sensitive enzymes, termed Ci-VSPTEN, is the novel ability to switch enzymic activity of PTEN rapidly and reversibly. We demonstrate that exptl. control of Ci-VSPTEN can be obtained either by electrophysiol. techniques or more general techniques, using potassium-induced depolarization of intact cells. Thus, Ci-VSPTEN provides a novel approach for studying the complex mechanism of activation, cellular control, and pharmacol. of this important tumor suppressor. Moreover, by inducing temporally precise perturbation of phosphoinositide concns., Ci-VSPTEN will be useful for probing the role and specificity of these messengers in many cellular processes and to analyze the timing of phosphoinositide signaling.
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  252. 252.
    Vandenberg, C. A.; Bezanilla, F. Biophys. J. 1991, 60, 1511
    [CrossRef], [CAS]
    252.
    A sodium channel gating model based on single channel, macroscopic ionic, and gating currents in the squid giant axon
    Vandenberg, C. A.; Bezanilla, F.
    Biophysical Journal (1991), 60 (6), 1511-33 CODEN: BIOJAU; ISSN:0006-3495.
    Sodium channel gating behavior was modeled with Markovian models fitted to currents from the cut-open squid giant axon in the absence of divalent cations. Optimum models were selected with max. likelihood criteria using single-channel data, then models were refined and extended by simultaneous fitting of macroscopic ionic currents, ON and OFF currents, and single-channel first latency densities over a wide voltage range. Best models have 5 closed states before channel opening, with inactivation from at least 1 closed state as well as the open state. Forward activation rate consts. increase with depolarization, and deactivation rate consts. increase with hyperpolarization. Rates of inactivation from the open or closed states are generally slower than activation or deactivation rates and show little or no voltage dependence. Channels tend to reopen several times before inactivating. Macroscopic rates of activation and inactivation result from a combination of closed, open and inactivated state transitions. At neg. potentials the time to first opening dominates the macroscopic current due to slow activation rates compared with deactivation rates: channels tend to reopen rarely, and often inactivate from closed states before they reopen. At more pos. potentials, the time to first opening and burst duration together produce the macroscopic current.
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  253. 253.
    Vandenberg, C. A.; Bezanilla, F. Biophys. J. 1991, 60, 1499
    [CrossRef], [PubMed], [CAS]
    253.
    Single-channel, macroscopic, and gating currents from sodium channels in the squid giant axon
    Vandenberg, C. A.; Bezanilla, F.
    Biophysical Journal (1991), 60 (6), 1499-510 CODEN: BIOJAU; ISSN:0006-3495.
    Single-channel, macroscopic ionic, and macroscopic gating currents were recorded from the voltage-dependent sodium channel by use of patch-clamp techniques on the cut-open squid giant axon. To obtain a complete set of physiol. measurements of sodium channel gating under identical conditions, and to facilitate comparison with previous work, comparison was made between currents recorded in the absence of extracellular divalent cations and in the presence of physiol. concns. of extracellular Ca2+ (10 mM) and Mg2+ (50 mM). The single-channel currents were well resolved when divalent cations were not included in the extracellular soln., but were decreased in amplitude in the presence of Ca2+ and Mg2+. The instantaneous current-voltage relationship obtained from macroscopic tail current measurements similarly was depressed by divalents, and showed a neg. slope-conductance region for inward current at neg. potentials. Voltage dependent parameters of channel gating were shifted 9-13 mV towards depolarized potentials by external divalent cations, including the peak fraction of channels open vs. voltage, the time const. of tail current decline, the prepulse inactivation vs. voltage relationship, and the charge-voltage relationship for gating currents. The effects of divalent cations are consistent with open channel blocking by Ca2+ and Mg2+ together with divalent screening of membrane charges.
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  254. 254.
    Rae, J. L.; Levis, R. A. Pflugers Arch. 1992, 420, 618
    [CrossRef], [PubMed], [CAS]
    254.
    A method for exceptionally low noise single channel recordings
    Rae J L; Levis R A
    Pflugers Archiv : European journal of physiology (1992), 420 (5-6), 618-20 ISSN:0031-6768.
    We present a method whereby, with integrating electronics, quartz patch electrodes and a novel use of silicone oil, background noise levels as low as .083 pA RMS in a 5 kHz bandwidth (4-pole Butterworth filter) have been achieved in single channel patch clamp recordings. These approaches result in much higher signal to noise ratios for single channel recording than have previously been reported and should allow many investigators to significantly reduce noise at a constant bandwidth or to increase their recording bandwidths by several kHz.
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  255. 255.
    Levis, R. A.; Rae, J. L. Biophys. J. 1993, 65, 1666
    [CrossRef], [PubMed], [CAS]
    255.
    The use of quartz patch pipettes for low noise single channel recording
    Levis R A; Rae J L
    Biophysical journal (1993), 65 (4), 1666-77 ISSN:0006-3495.
    Quartz has a dissipation factor of approximately 10(-4), which is an order of magnitude less than that of the best glasses previously used to fabricate patch pipettes; it's dielectric constant of 3.8 is also lower than that of other glasses. On the basis of these electrical characteristics it is expected that patch pipettes pulled from quartz tubing will produce significantly less noise than pipettes made from other glasses. Our work confirms these expectations and we describe theoretical and practical aspects of the use of quartz pipettes for single channel patch voltage clamp measurements. Methods for pulling quartz pipettes with a laser-based puller and coating them with low-loss elastomers are discussed, as are precautions that are necessary to achieve low noise recordings. We have shown that quartz pipettes can be pulled from tubing with outer diameter to inner diameter ratios as large as 3 and a method of applying heavy elastomer coatings all the way to the tip of pipettes is presented. Noise sources arising from the pipette and its holder are described theoretically, and it is shown that measured noise is in good agreement with such predictions. With low noise capacitive feedback electronics, small geometry holders, and thick-walled quartz pipettes coated with low-loss elastomers we have been routinely able to achieve noise of 100 fA rms or less in a 5-kHz bandwidth with real cell patches and a pipette immersion depth of approximately 2 mm. On occasion we have achieved noise as low as 60 fA rms in this bandwidth.
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  256. 256.
    Levis, R. A.; Rae, J. L.Technology of Patch Clamp Recording Electrodes. In Patch-Clamp Applications and Protocols; Walz, W.; Boulton, A.; Baker, G., Eds.; Humana Press: Totowa, NJ, 1995.
    There is no corresponding record for this reference.
  257. 257.
    Doyle, D. A.; Cabral, J. M.; Pfuetzner, R. A.; Kuo, A.; Gulbis, J. M.; Cohen, S. L.; Chait, B. T.; MacKinnon, R. Science 1998, 280, 69
    [CrossRef], [PubMed], [CAS]
    257.
    The structure of the potassium channel: molecular basis of K+ conduction and selectivity
    Doyle, Declan A.; Cabral, Joao Morais; Pfuetzner, Richard A.; Kuo, Anling; Gulbis, Jacqueline M.; Cohen, Steven L.; Chait, Brian T.; MacKinnon, Roderick
    Science (Washington, D. C.) (1998), 280 (5360), 69-77 CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)
    A review with 34 refs. The K+ channel from Streptomyces lividans is an integral membrane protein with sequence similarity to all known K+ channels, particularly in the pore region. X-ray anal. with data to 3.2 Å reveals that 4 identical subunits create an inverted teepee, or cone, cradling the selectivity filter of the pore in its outer end. The narrow selectivity filter is only 12 Å long, whereas the remainder of the pore is wider and lined with hydrophobic amino acids. A large water-filled cavity and helix dipoles are positioned so as to overcome electrostatic destabilization of an ion in the pore at the center of the bilayer. The main-chain carbonyl O atoms from the K+ channel signature sequence line the selectivity filter, which is held open by structural constraints to coordinate K+ ions but not smaller Na+ ions. The selectivity filter contains 2 K+ ions 7.5 Å apart. This configuration promotes ion conduction by exploiting electrostatic repulsive forces to overcome attractive forces between K+ ions and the selectivity filter. The architecture of the pore establishes the phys. principles underlying selective K+ conduction.
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  258. 258.
    MacKinnon, R. Angew. Chem., Int. Ed. 2004, 43, 4265
    [CrossRef], [PubMed], [CAS]
    258.
    Ion channels: Potassium channels and the atomic basis of selective ion conduction (Nobel Lecture)
    MacKinnon, Roderick
    Angewandte Chemie, International Edition (2004), 43 (33), 4265-4277 CODEN: ACIEF5; ISSN:1433-7851. (Wiley-VCH Verlag GmbH & Co. KGaA)
    A review. The key to understanding the transport of K+ through the cell membrane is in the structural elucidation of a K+ channel. The studies of R. MacKinnon and coworkers have contributed significantly to the understanding of this research area. In his Nobel lecture, MacKinnon describes the structural characteristics of K+ channels as well as a possible mechanism for ion conduction.
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  259. 259.
    Schmidt, D.; Cross, S. R.; MacKinnon, R. J. Mol. Biol. 2009, 390, 902
    [CrossRef], [PubMed], [CAS]
    259.
    A Gating Model for the Archeal Voltage-Dependent K+ Channel KvAP in DPhPC and POPE:POPG Decane Lipid Bilayers
    Schmidt, Daniel; Cross, Samuel R.; MacKinnon, Roderick
    Journal of Molecular Biology (2009), 390 (5), 902-912 CODEN: JMOBAK; ISSN:0022-2836. (Elsevier Ltd.)
    Voltage-dependent K+ (Kv) channels form the basis of the excitability of nerves and muscles. KvAP is a well-characterized archeal Kv channel that has been widely used to investigate many aspects of Kv channel biochem., biophysics, and structure. In this study, a minimal kinetic gating model for KvAP function in two different phospholipid decane bilayers is developed. In most aspects, KvAP gating is similar to the well-studied eukaryotic Shaker Kv channel: conformational changes occur within four voltage sensors, followed by pore opening. Unlike the Shaker Kv channel, KvAP possesses an inactivated state that is accessible from the pre-open state of the channel. Changing the lipid compn. of the membrane influences multiple gating transitions in the model, but, most dramatically, the rate of recovery from inactivation. Inhibition by the voltage sensor toxin VSTx1 is most easily explained if VSTx1 binds only to the depolarized conformation of the voltage sensor. By delaying the voltage sensor's return to the hyperpolarized conformation, VSTx1 favors the inactivated state of KvAP.
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  260. 260.
    Jimenez-Morales, D.; Liang, J.; Eisenberg, B. Eur. Biophys. J. 2012, 41, 449
    [CrossRef], [CAS]
    260.
    Ionizable side chains at catalytic active sites of enzymes
    Jimenez-Morales, David; Liang, Jie; Eisenberg, Bob
    European Biophysics Journal (2012), 41 (5), 449-460 CODEN: EBJOE8; ISSN:0175-7571. (Springer)
    Catalytic active sites of enzymes of known structure can be well defined by a modern program of computational geometry. The CASTp program was used to define and measure the vol. of the catalytic active sites of 573 enzymes in the Catalytic Site Atlas database. The active sites are identified as catalytic because the amino acids they contain are known to participate in the chem. reaction catalyzed by the enzyme. Acid and base side chains are reliable markers of catalytic active sites. The catalytic active sites have 4 acid and 5 base side chains, in an av. vol. of 1,072 Å3. The no. d. of acid side chains is 8.3 M (in chem. units); the no. d. of basic side chains is 10.6 M. The catalytic active site of these enzymes is an unusual electrostatic and steric environment in which side chains and reactants are crowded together in a mixt. more like an ionic liq. than an ideal infinitely dil. soln. The electrostatics and crowding of reactants and side chains seems likely to be important for catalytic function. In three types of analogous ion channels, simulation of crowded charges accounts for the main properties of selectivity measured in a wide range of solns. and concns. It seems wise to use mathematics designed to study interacting complex fluids when making models of the catalytic active sites of enzymes.
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  261. 261.
    Lutz, S. Science 2010, 329, 285
    [CrossRef], [CAS]
    261.
    Reengineering enzymes
    Lutz, Stefan
    Science (Washington, DC, United States) (2010), 329 (5989), 285-287 CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)
    There is no expanded citation for this reference.
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  262. 262.
    Ringe, D.; Petsko, G. A. Science 2008, 1428
    [CrossRef], [CAS]
    262.
    How enzymes work
    Ringe, Dagmar; Petsko, Gregory A.
    Science (Washington, DC, United States) (2008), 320 (5882), 1428-1429 CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)
    A review. Fifty years of research since the induced-fit theory of D. E. Koshland, Jr. proposed that an enzyme surface is flexible, and that only a specific substrate can induce the proper actions that lead to catalysis, have led to a detailed understanding of the mechanism of enzymic catalysis.
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  263. 263.
    Warshel, A. J. Biol. Chem. 1998, 273, 27035
    [CrossRef], [PubMed], [CAS]
    263.
    Electrostatic origin of the catalytic power of enzymes and the role of preorganized active sites
    Warshel, Arieh
    Journal of Biological Chemistry (1998), 273 (42), 27035-27038 CODEN: JBCHA3; ISSN:0021-9258. (American Society for Biochemistry and Molecular Biology)
    A review with 66 refs., discussing the author's accounting for the origin of enzyme catalytic power in enzymes using their preoriented polar environment to stabilize the transition state. Energy considerations and computer simulations have been used to examine and evaluate various proposals put forward to account for enzyme catalytic power. The author concludes that although non-negligible contributions to enzyme catalytic power may be provided by entropy, tunneling, and some low-barrier H-bond character, large contributions are to be expected from electrostatic stabilization mechanisms due to small reorganization energies in forming transition state charges. Thus, the catalytic power of enzymes is stored in folding energy in the form of a preorganized polar environment, the catalytic energy being stored in the enzyme itself rather than in the enzyme-substrate interaction.
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  264. 264.
    Dixon, M.; Webb, E. C. Enzymes; Academic Press: New York, 1979.
    There is no corresponding record for this reference.
  265. 265.
    Martin, P. A. Rev. Mod. Phys. 1988, 60, 1075
    [CrossRef], [CAS]
    265.
    Sum rules in charged fluids
    Martin, P. A.
    Reviews of Modern Physics (1988), 60 (4), 1075-127 CODEN: RMPHAT; ISSN:0034-6861.
    A review with many refs. The screening effects in fluid phases of charged particles give rise to a variety of exact sum rules for thei correlation functions. Some of them have been known for a long time, while others have been derived more recently, in particular for nonuniform fluids. A presentation of these sum rules for static and time-displaced, classical or quantum-mech. correlations is given from a unifying viewpoint: they appear as consistency relations imposed by the long-range of the Coulomb force in the equil. or dynamical equations. The cluster properties and the fluctuations of elec. quantities are also discussed.
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  266. 266.
    Henderson, J. R.Statistical Mechanical Sum Rules. In Fundamentals of Inhomogeneous Fluids; Henderson, D., Ed.; Marcel Dekker: New York, 1992; p 23.
    There is no corresponding record for this reference.
  267. 267.
    Fuoss, R. M.; Kraus, C. A. J. Am. Chem. Soc. 1933, 55, 2387
    [ACS Full Text ACS Full Text], [CAS]
    267.
    Properties of electrolytic solutions. IV. The conductance minimum and the formation of triple ions due to the action of Coulomb forces
    Fuoss, Raymond M.; Kraus, Charles A.
    Journal of the American Chemical Society (1933), 55 (), 2387-99 CODEN: JACSAT; ISSN:0002-7863.
    cf. C. A. 27, 2083. The presence of triple ions, formed from a neutral mol. and a simple ion, largely account for the min. in cond. curves with solvents of low dielec. const. Dissocn. consts. calcd. theoretically agree with those obtained from cond. expts. The observed shift of the cond. min. toward higher concn. with increasing dielec. const. can also be explained.
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  268. 268.
    Fuoss, R. M. Chem. Rev. 1935, 17, 27
    [ACS Full Text ACS Full Text], [CAS]
    268.
    Properties of electrolytic solutions
    Fuoss, Raymond M.
    (1935), 17 (), 27-42 ISSN:.
    F. shows, after an investigation of the distribution of ions in soln., that it is possible to split interionic effects into long- and short-range interactions. The former may be treated by the time av. method of Debye and H.ovrddot.uckel, the latter by the formal methods of dissocn. theory. Based on these results equations are derived which quantitatively reproduce exptl. data on conductance for dil. solns. of ordinary electrolytes in all solvents so far investigated. Various limitations to the treatment are pointed out.
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  269. 269.
    Fuoss, R. M.; Onsager, L. Proc. Natl. Acad. Sci. U.S.A. 1955, 41, 274
    [CrossRef], [PubMed], [CAS]
    269.
    Conductance of strong electrolytes at finite dilutions
    Fuoss, Raymond M.; Onsager, Lars
    Proceedings of the National Academy of Sciences of the United States of America (1955), 41 (), 274-83 CODEN: PNASA6; ISSN:0027-8424.
    The following cond. equation was derived, which is valid for nonzero concns. up to about 0.1N for strong 1-1 electrolytes in H2O: Λ = Λ0 - α(1 - Δ1 + Δ2) Λ0 √c - β (1 + Δ3)√c, where Δ1 = {[(1 + q)κa]/[2p3(1 + κa)]}[1 + (1/b)], Δ2 = {[b(1 + q)κa]/[p2p3(1 + κa)2]}{[(11√2 + 3)/24] - (T0/2)(1 + κa + 2qκa) + (T1/8) (1 + κa + qκa) + (7T2/8) (1 + qκa)} - [(1 + q)κa]/[2p2(1 + κa)2], Δ3 = Δ'3 - [κa/(1 + κa)], Δ'3 = {- bκa/[p2(1 + κa)2]}{[(35 - 6 √2)/192] -(T0/8) (1 + κa + qκa) + (T1/32) (1 + κa) + (7T2/32)} + 11κa/[96p2(1 + κa)2], p1 = 1 + κa + (κ2a2/2), p2 = 1 + qκa + (κ2a2/4), p3 = 1 + qκa + (κ2a2/6), T0 = Tr(κa), T1 = Tr[(1 + q)κa], T2 = Tr[(2 + q)κa], Tr(x) = ex∫∞x(e-t/t)dt, κ2 = (4π/DkT)(n1e12 + n2e22), q2κ2 = (4π/DkT) [(n1e12ω1 + n2e22ω2)/(ω1 + ω2)], b = (-e1e2/aDkT) > 0, and a = ion size. The following a-values were found: LiCl 4.31 × 10-8, NaCl 4.20 × 10-8, KCl 4.23 × 10-8.
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  270. 270.
    Fuoss, R. M.; Onsager, L. J. Phys. Chem. B 1958, 62, 1339
    [ACS Full Text ACS Full Text]
    There is no corresponding record for this reference.
  271. 271.
    Fuoss, R. M. J. Phys. Chem. 1959, 63, 633
    [ACS Full Text ACS Full Text], [CAS]
    271.
    The velocity field in electrolytic solutions
    Fuoss, Raymond M.
    Journal of Physical Chemistry (1959), 63 (), 633-6 CODEN: JPCHAX; ISSN:0022-3654.
    The velocity field produced in an electrolytic soln. by an external elec. field was studied further (C.A. 51, 13526d). Both the hydrodynamic term in the relaxation field and the Onsager electrophoresis term can be derived from the Navier-Stokes equation, specialized to the conductance problem. The hydrodynamic radius that appears in the analysis must be identified with a, the center-to-center distance at contact between ions of opposite charge. If the ions are represented as spheres of diam. a, the hydrodynamic radius R is twice the electrostatic radius. This result follows from the facts that no charge except that of the reference ion can penetrate a sphere of radius a around the latter and that information concerning size can be detected only conductometrically from the consequences of interionic contacts.
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  272. 272.
    Fuoss, R. M.; Onsager, L. J. Phys. Chem. 1962, 66, 1722
    [ACS Full Text ACS Full Text], [CAS]
    272.
    The conductance of symmetrical electrolytes I. Potential of total force
    Fuoss, Raymond M.; Onsager, Lars
    Journal of Physical Chemistry (1962), 66 (), 1722-6 CODEN: JPCHAX; ISSN:0022-3654.
    By means of a multiplicative expansion of the distribution functions which describe local ionic concns., the 1932 Onsager-Fuoss equation of continuity can be integrated with explicit retention of the Boltzmann factor, instead of approximating the latter by a truncated power series. The result is expressed in terms of the potential μji of total force acting on a given ion; the present approxn. to .del.μji includes the external field, the forces due to neighboring ions and to the asymmetry of the ionic atm., and the virtual forces due to local concn. gradients. The differential equations which lead to the forces from the velocity field were also derived.
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  273. 273.
    Fuoss, R. M.; Onsager, L. J. Phys. Chem. 1962, 66, 1722
    [ACS Full Text ACS Full Text], [CAS]
    273.
    The conductance of symmetrical electrolytes I. Potential of total force
    Fuoss, Raymond M.; Onsager, Lars
    Journal of Physical Chemistry (1962), 66 (), 1722-6 CODEN: JPCHAX; ISSN:0022-3654.
    By means of a multiplicative expansion of the distribution functions which describe local ionic concns., the 1932 Onsager-Fuoss equation of continuity can be integrated with explicit retention of the Boltzmann factor, instead of approximating the latter by a truncated power series. The result is expressed in terms of the potential μji of total force acting on a given ion; the present approxn. to .del.μji includes the external field, the forces due to neighboring ions and to the asymmetry of the ionic atm., and the virtual forces due to local concn. gradients. The differential equations which lead to the forces from the velocity field were also derived.
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  274. 274.
    Fuoss, R. M.; Onsager, L. J. Phys. Chem. 1963, 67, 621
    [ACS Full Text ACS Full Text], [CAS]
    274.
    The conductance of symmetrical electrolytes. II. The relaxation field
    Fuoss, Raymond M.; Onsager, Lars
    Journal of Physical Chemistry (1963), 67 (), 621-8 CODEN: JPCHAX; ISSN:0022-3654.
    cf. CA 58, 69b. The Poisson equation for the asymmetry potentials of a sym. electrolyte in the conductance process was integrated by the use of the corresponding Green's function in order to obtain the purely electrostatic terms of the relaxation field. The Boltzmann factor in the distribution function was retained explicitly as an exponential throughout the calcn.., instead of approximating it as a truncated series as has been customary in previous derivations. The consequence of this refinement in math. methods is the appearance in the relaxation field of a term which will lead to a decrease in conductance with increasing concn. or decreasing dielec. const. The decrease is proportional to the product of concn. and the square of the mean activity coeff. It depends on dielec. const. through a function which has as its asymptotic limit e3/b3 (b = ε2/aDk T), which is the form of the theoretical assocn. constant for contact pairs. This result means that the ad hoe hypothesis of ion pairing controlled by a mass action equil. is no longer needed to obtain a satisfactory conductance function; the former mass action term is derivable from the Poisson equation. It was missed in earlier theoretical work by too drastic approxn. of the Boltzmann factor..
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  275. 275.
    Fuoss, R. M.; Onsager, L. J. Phys. Chem. 1963, 67, 628
    [ACS Full Text ACS Full Text], [CAS]
    275.
    The conductance of symmetrical electrolytes. III. Electrophoresis
    Fuoss, Raymond M.; Onsager, Lars
    Journal of Physical Chemistry (1963), 67 (), 628-32 CODEN: JPCHAX; ISSN:0022-3654.
    The electrophoretic velocity in a dil. solution of a sym. electrolyte was computed, with the following improvements over earlier treatments of the problem: (1) the vol. force is calcd. as the gradient of the potential of the total force acting on an ion instead of being approximated merely by the force due to the external field; (2) the Boltzmann factor is retained explicitly, instead of being approximated by a truncated series; and (3) the Oseen equations of motion (rather than the Stokes) are used. The result gives the Onsager 1926 limiting value (-jepsi;.vkappa.X/ 6πη) as the leading term; to next approximation, this is opposed by a term proportional to concn., which depends on b = ε2/ aDkT in a nonexponential fashion. For example, for b = 1.5(D equal or nearly equal to 100), F(b) = 2.31, and for b = 15(D equal or nearly equal to 10), F(b) = -0.77. The coeff. goes through-zero near b = 5.
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  276. 276.
    Fuoss, R. M.; Onsager, L. J. Phys. Chem. 1964, 68, 1
    [ACS Full Text ACS Full Text], [CAS]
    276.
    The conductance of symmetrical electrolytes. IV. Hydrodynamic and osmotic terms in the relaxation field
    Fuoss, Raymond M.; Onsager, Lars
    Journal of Physical Chemistry (1964), 68 (1), 1-8 CODEN: JPCHAX; ISSN:0022-3654.
    cf. CA 58, 8454h. Using (1) the differential equation which defines that part of the total potential which has hydrodynamic origin, (2) the corresponding Poisson equation, and (3) the appropriate boundary conditions, the term ΔXv in the relaxation field is calcd. up to terms of order c3/2 in concn. in the conductance function Λ(c). The Boltzmann factor eζ is kept explicit as exp(-βe-κγ/γ) throughout the computation, the principal approxns. made are to drop terms of order κ3 c3/2. The leading term contains the neg. exponential integrals En(2κa) and En(κa), and thus contributes c log c terms to Λ(c). The next term, linear in c, has a coeff. P2(b), b = ε2/aDkT, which contains most of the function K(b) which appeared in the electrostatic part ΔXe of the relaxation field. The kinetic term in Λ(c) is also computed to the same degree of approxn.; combined with ΔXv, it gives the complete function K(b), multiplied by a small coeff.
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  277. 277.
    Fuoss, R. M.; Onsager, L.; Skinner, J. F. J. Phys. Chem. 1965, 69, 2581
    [ACS Full Text ACS Full Text], [CAS]
    277.
    The conductance of symmetrical electrolytes. V. The conductance equation
    Fuoss, Raymond M.; Onsager, Lars; Skinner, James F.
    Journal of Physical Chemistry (1965), 69 (8), 2581-94 CODEN: JPCHAX; ISSN:0022-3654.
    cf. CA 60, 4872a. Using the potential of total directed force on charged spheres moving in a continuum under an external field and correcting for electrophoresis, the conductance Λ = Λ0 - Sc1/2 + E'c ln (6E1'c) + Lc - Acf2Λ0 is derived. Here S = αΛ0 + β0, α = 0.8204 + 106/(DT)3/2, β0 = 82.50/η(DT)1/2, E' = E1'Λ0 - E2', E1' = 2.942 × 1012/(DT)3, E2' = 0.4333 × 108/η(DT)2, L = L1 + L2(b), L1 = 3.202E1' Λ0 - 3.420E2' + αβ0, ab = 16.708 × 10-4/DT, L2(b) = 2E1'Λ0h(b) + 44E2'/3b - 2E' ln b, h(b) = (2b2 + 2b - 1)/b3, f2 = exp[-8.405 × 105c1/2γ1/3/(DT)3/2], and Λ = KA = (4πNa3/3000)ebb. This equation can be generalized to Λ = Λ0 Sc1/2γ1/2 + E'cγ ln (6E1'cγ) + Lcγ - KAcγf2Λ, where (1 - γ) = KAcγ2f2. The 1st equation reproduces conductance data for 1-1 electrolytes in solvents of higher dielec. const. The 2nd is required when the dielec. const. is small enough to stabilize ion pairs in contact. This result confirms the earlier (CA 51, 14382a) conductance function and establishes the functional form directly from the equation of continuity, the equations of motion, and Poisson's equation. Values of the contact distance calcd. from the parameter b for a given electrolyte in a series of mixed solvents usually increase with decreasing dielec. const. The source of this variation lies in inadequacy of the sphere-in-continuum model and not in math. approxns. made in solving the differential equations.
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  278. 278.
    Justice, J.-C.Conductance of Electrolyte Solutions. In Thermondynamic and Transport Properties of Aqueous and Molten Electrolytes; Conway, B. E.; Bockris, J. O. M.; Yaeger, E., Eds.; Comprehensive Treatise of Electrochemistry; Plenum: New York, 1983; Vol. 5, p 223.
    There is no corresponding record for this reference.
  279. 279.
    Csanyi, E.; Boda, D.; Gillespie, D.; Kristof, T. Biochim. Biophys. Acta 2012, 1818, 592
    [CrossRef], [CAS]
    279.
    Current and selectivity in a model sodium channel under physiological conditions: Dynamic Monte Carlo simulations
    Csanyi, Eva; Boda, Dezso; Gillespie, Dirk; Kristof, Tamas
    Biochimica et Biophysica Acta, Biomembranes (2012), 1818 (3), 592-600 CODEN: BBBMBS; ISSN:0005-2736. (Elsevier B.V.)
    A reduced model of a sodium channel is analyzed using Dynamic Monte Carlo (DMC) simulations. These include the first simulations of ionic current under approx. physiol. ionic conditions through a model sodium channel and an anal. of how mutations of the sodium channel's DEKA selectivity filter motif transform the channel from being Na+ selective to being Ca2+ selective. Even though the model of the pore, amino acids, and permeant ions is simplified, the model reproduces the fundamental properties of a sodium channel (e.g., 10 to 1 Na+ over K+ selectivity, Ca2+ exclusion, and Ca2+ selectivity after several point mutations). In this model pore, ions move through the pore one at a time by simple diffusion and Na+ vs. K+ selectivity is due to both the larger K+ not fitting well into the selectivity filter that contains amino acid terminal groups and K+ moving more slowly (compared to Na+) when it is in the selectivity filter.
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  280. 280.
    Boda, D.; Gillespie, D. J. Chem. Theory Comput. 2012, 8, 824
    [ACS Full Text ACS Full Text], [CAS]
    280.
    Steady-State Electrodiffusion from the Nernst-Planck Equation Coupled to Local Equilibrium Monte Carlo Simulations
    Boda, Dezso; Gillespie, Dirk
    Journal of Chemical Theory and Computation (2012), 8 (3), 824-829 CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
    A procedure is proposed to compute the steady-state transport of charged particles based on the Nernst-Planck (NP) equation of electrodiffusion. To close the NP equation and to establish a relation between the concn. and electrochem. potential profiles, the local equil. Monte Carlo (LEMC) method is introduced. In this method, grand canonical Monte Carlo simulations are performed using the electrochem. potential specified for the distinct vol. elements. An iteration procedure that self-consistently solves the NP and flux continuity equations with LEMC is shown to converge quickly. This NP + LEMC technique can be used in systems with diffusion of charged or uncharged particles in complex three-dimensional geometries, including systems with low concns. and small applied voltages that are difficult for other particle simulation techniques.
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  281. 281.
    Rutkai, G.; Boda, D.; Kristóf, T. J. Phys. Chem. Lett. 2010, 1, 2179
    [ACS Full Text ACS Full Text], [CAS]
    281.
    Relating Binding Affinity to Dynamical Selectivity from Dynamic Monte Carlo Simulations of a Model Calcium Channel
    Rutkai, Gabor; Boda, Dezso; Kristof, Tamas
    Journal of Physical Chemistry Letters (2010), 1 (14), 2179-2184 CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
    We have performed dynamic Monte Carlo simulations for a model calcium channel and present our results in terms of binding affinity (expressed as the occupancy of the selectivity filter by various ions) and dynamical selectivity (expressed as the flux carried by various ions). We show that the binding affinity of Ca2+ vs. Na+ is always larger than the dynamical selectivity because Ca2+ ions are tightly bound to the binding site of the selectivity filter of the channel and, at the same time, their mobility and drift velocity is smaller in this region. We present d. and drift velocity profiles of Ca2+ and Na+ in the channel for various mole fractions of Ca2+.
    >> More from SciFinder ®
    https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3cXot1amu7g%253D&md5=eeb22772242b3945aa0c77cc95892494
  282. 282.
    Damocles. Damocles Web Site, IBM Research. http://www.research.ibm.com/DAMOCLES/home.html, 2007.
    There is no corresponding record for this reference.
  283. 283.
    Lundstrom, M. Fundamentals of Carrier Transport, 2nd ed.; Addison-Wesley: New York, 2000.
    [CrossRef]
    There is no corresponding record for this reference.
  284. 284.
    Jacoboni, C.; Lugli, P. The Monte Carlo Method for Semiconductor Device Simulation; Springer-Verlag: New York, 1989.
    [CrossRef]
    There is no corresponding record for this reference.
  285. 285.
    Eisenberg, R. S.; Kłosek, M. M.; Schuss, Z. J. Chem. Phys. 1995, 102, 1767– 1780
    [CrossRef], [CAS]
    285.
    Diffusion as a chemical reaction: stochastic trajectories between fixed concentrations
    Eisenberg, R. S.; Klosek, M. M.; Schuss, Z.
    Journal of Chemical Physics (1995), 102 (4), 1767-80 CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    Stochastic trajectories are described that underly classical diffusion between known concns. The description of those exptl. boundary conditions requires a phase space using the full Langevin equation, with displacement and velocity as state variables, even if friction entirely dominates the dynamics of diffusion, because the incoming and outgoing trajectories have to be told apart. The conditional flux, probabilities, mean first-passage times, and contents (of the reaction region) of the four types of trajectories - the trans trajectories LR and RL and the cis trajectories LL and RR - are expressed in terms of solns. of the Fokker-Planck equation in phase space and are explicitly calcd. in the Smoluchowski limit of high friction. With these results, diffusion in a region between fixed concns. can be described exactly as a chem. reaction for any potential function in the region, made of any combination of high or low barriers or wells.
    >> More from SciFinder ®
    https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK2MXjtlemtrg%253D&md5=e006fc0d47b2c11390603f90c683624e
  286. 286.
    Kłosek, M. M. J. Stat. Phys. 1995, 79, 313
    [CrossRef]
    There is no corresponding record for this reference.
  287. 287.
    Segel, I. H. Enzyme Kinetics: Behavior and Analysis of Rapid Equilibrium and Steady State Enzyme Systems; Wiley: New York, 1993.
    There is no corresponding record for this reference.
  288. 288.
    Tosteson, D. Membrane Transport: People and Ideas; American Physiological Society: Bethesda, MD, 1989.
    There is no corresponding record for this reference.
  289. 289.
    van der Straaten, T. A.; Tang, J. M.; Ravaioli, U.; Eisenberg, R. S.; Aluru, N. R. J. Comput. Electron. 2003, 2, 29
    [CrossRef], [CAS]
    289.
    Simulating ion permeation through the ompF porin ion channel using three-dimensional drift-diffusion theory
    Van Der Straaten, T. A.; Tang, J. M.; Ravaioli, U.; Eisenberg, R. S.; Aluru, N. R.
    Journal of Computational Electronics (2003), 2 (1), 29-47 CODEN: JCEOA7; ISSN:1569-8025. (Kluwer Academic Publishers)
    Ionic channels, natural nanotubes found in biol. cells, are interesting to the electronics community because they display a range of device-like functions. The purpose of this paper is to illustrate how the soln. methodol., developed for 3-D drift-diffusion models of semiconductor devices, can be applied to ion permeation in ionic channels. For this study we select the ompF porin channel, found in the membrane of the E. coli bacterium. The self-consistent 3-D model is based on the simultaneous soln. of Poisson's equation, which captures Coulomb interactions, and a current continuity equation for each ion species, describing permeation down an electrochem. gradient. Water is treated as a uniform background medium with a specific dielec. const. For demonstration, a simple model is assumed for the mobility/diffusivity of each ionic species and we compute the current-voltage relations for ompF porin in a wide range of conditions. Agreement with exptl. measurements is surprisingly good given that the model uses the ion diffusivity as the only calibrated parameter.
    >> More from SciFinder ®
    https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2cXivFWnsg%253D%253D&md5=44806c3323b3c892bbde6857219a6d81
  290. 290.
    Eisenberg, B. Acc. Chem. Res. 1998, 31, 117
    [ACS Full Text ACS Full Text], [CAS]
    290.
    Ionic Channels in Biological Membranes: Natural Nanotubes
    Eisenberg, Bob
    Accounts of Chemical Research (1998), 31 (3), 117-123 CODEN: ACHRE4; ISSN:0001-4842. (American Chemical Society)
    A review with 41 refs. on modeling ionic channels with analogy to transistors.
    >> More from SciFinder ®
    https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK1cXht12ls7s%253D&md5=ff163daff26bd3d644c85ce87758f4c3
  291. 291.
    Lu, B.; McCammon, J. A. Chem. Phys. Lett. 2008, 451, 282
    [CrossRef], [CAS]
    291.
    Molecular surface-free continuum model for electrodiffusion processes
    Lu, Benzhuo; McCammon, J. Andrew
    Chemical Physics Letters (2008), 451 (4-6), 282-286 CODEN: CHPLBC; ISSN:0009-2614. (Elsevier B.V.)
    Incorporation of van der Waals interactions enables the continuum model of electrodiffusion in biomol. system to avoid the artifacts of introducing a mol. surface and the painful task of the surface mesh generation. Calcn. examples show that the electrostatics, diffusion-reaction kinetics, and mol. surface defined as an isosurface of a certain d. distribution can be extd. from the soln. of the Poisson-Nernst-Planck equations using this model. The mol. surface-free model enables a wider usage of some modern numerical methodologies such as finite element methods for biomol. modeling, and sheds light on a new paradigm of continuum modeling for biomol. systems.
    >> More from SciFinder ®
    https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD1cXlsVGnsQ%253D%253D&md5=76e02eaa138a08ee187f6f74f88aaec0
  292. 292.
    Vora, T.; Corry, B.; Chung, S. H. Biochim. Biophys. Acta 2006, 1758, 730
    [CrossRef], [PubMed], [CAS]
    292.
    Brownian dynamics investigation into the conductance state of the MscS channel crystal structure
    Vora, Taira; Corry, Ben; Chung, Shin-Ho
    Biochimica et Biophysica Acta, Biomembranes (2006), 1758 (6), 730-737 CODEN: BBBMBS; ISSN:0005-2736. (Elsevier B.V.)
    We suggest that the crystal structure of the mechanosensitive channel of small conductance is in a minimally conductive state rather than being fully activated. Performing Brownian dynamics simulations on the crystal structure show that no ions pass through it. When simulations are conducted on just the transmembrane domain (excluding the cytoplasmic residues 128 to 280) ions are seen to pass through the channel, but the conductance of 30 pS is well below exptl. measured values. The mutation L109S that replaces a pore lining hydrophobic residue with a polar one is found to have little effect on the conductance of the channel. Widening the hydrophobic region of the pore by 2.5 Å however, increases the channel conductance to over 200 pS suggesting that only a minimal conformational change is required to gate the pore.
    >> More from SciFinder ®
    https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD28Xnt1yktLs%253D&md5=79f16bf545aca9d100487cd5e2ec9dc9
  293. 293.
    Mamonov, A. B.; Kurnikova, M. G.; Coalson, R. D. Biophys. Chem. 2006, 124, 268
    [CrossRef], [PubMed], [CAS]
    293.
    Diffusion constant of K+ inside Gramicidin A: A comparative study of four computational methods
    Mamonov, Artem B.; Kurnikova, Maria G.; Coalson, Rob D.
    Biophysical Chemistry (2006), 124 (3), 268-278 CODEN: BICIAZ; ISSN:0301-4622. (Elsevier B.V.)
    The local diffusion const. of K+ inside the Gramicidin A (GA) channel has been calcd. using four computational methods based on mol. dynamics (MD) simulations, specifically: Mean Square Displacement (MSD), Velocity Autocorrelation Function (VACF), Second Fluctuation Dissipation Theorem (SFDT) and anal. of the Generalized Langevin Equation for a Harmonic Oscillator (GLE-HO). All methods were first tested and compared for K+ in bulk water-all predicted the correct diffusion const. Inside GA, MSD and VACF methods were found to be unreliable because they are biased by the systematic force exerted by the membrane-channel system on the ion. SFDT and GLE-HO techniques properly unbias the influence of the systematic force on the diffusion properties and predicted a similar diffusion const. of K+ inside GA, namely, ca. 10 times smaller than in the bulk. It was found that both SFDT and GLE-HO methods require extensive MD sampling on the order of tens of nanoseconds to predict a reliable diffusion const. of K+ inside GA.
    >> More from SciFinder ®
    https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD28Xht1Sgs7%252FJ&md5=ded85c19c0c16a99520034d5fcc6a8a3
  294. 294.
    Corry, B.; Vora, T.; Chung, S. H. Biochim. Biophys. Acta 2005, 1711, 72
    [CrossRef], [PubMed], [CAS]
    294.
    Electrostatic basis of valence selectivity in cationic channels
    Corry, Ben; Vora, Taira; Chung, Shin-Ho
    Biochimica et Biophysica Acta, Biomembranes (2005), 1711 (1), 72-86 CODEN: BBBMBS; ISSN:0005-2736. (Elsevier B.V.)
    We examine how a variety of cationic channels discriminate between ions of differing charge. We construct models of the KcsA potassium channel, voltage gated sodium channel and L-type calcium channel, and show that they all conduct monovalent cations, but that only the calcium channel conducts divalent cations. In the KcsA and sodium channels divalent ions block the channel and prevent any further conduction. We demonstrate that in each case, this discrimination and some of the more complex conductance properties of the channels is a consequence of the electrostatic interaction of the ions with the charges in the channel protein. The KcsA and sodium channels bind divalent ions strongly enough that they cannot be displaced by other ions and thereby block the channel. On the other hand, the calcium channel binds them less strongly such that they can be destabilized by the repulsion of another incoming divalent ion, but not by the lesser repulsion from monovalent ions.
    >> More from SciFinder ®
    https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2MXkt1Gjsb8%253D&md5=37ea199879b74747199e9036cf3d9469
  295. 295.
    Cardenas, A. E.; Coalson, R. D.; Kurnikova, M. G. Biophys. J. 2000, 79.
    [CrossRef]
    There is no corresponding record for this reference.
  296. 296.
    Berti, C.; Gillespie, D.; Eisenberg, B.; Furini, S.; Fiegna, C. Biophys. J. 2011, 100, 158a
    [CrossRef]
    There is no corresponding record for this reference.
  297. 297.
    Eisenberg, R. S. J. Membr. Biol. 1990, 115, 1
    [CrossRef], [PubMed], [CAS]
    297.
    Channels as enzymes
    Eisenberg, R. S.
    Journal of Membrane Biology (1990), 115 (1), 1-12 CODEN: JMBBBO; ISSN:0022-2631.
    A review, with 28 refs., on ion channels as catalysts for flow of elec. current and functional similarities channels have with enzymes. (1) Purifn., structure, and properties of proteins, (2) cofactors in enzymes and channels, and (3) channels and enzymes biosynthesis and mechanisms are discussed.
    >> More from SciFinder ®
    https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK3cXktF2msb8%253D&md5=0a86a8a1781be1625cceedd9faa06c09
  298. 298.
    Griffiths, J.; Sansom, C. The Transporter Facts Book; Academic Press: New York, 1997.
    There is no corresponding record for this reference.
  299. 299.
    Jacob, F. The Logic of Life: A History or Heredity; Princeton University Press: Princeton, NJ, 1993.
    There is no corresponding record for this reference.
  300. 300.
    Monod, J. Chance and Necessity: An Essay on the Natural Philosophy of Modern Biology; Vintage Books: New York, 1972.
    There is no corresponding record for this reference.
  301. 301.
    Schrödinger, E. What Is Life?; Cambridge University Press: New York, 1992.
    There is no corresponding record for this reference.
  302. 302.
    Shockley, W. Electrons and Holes in Semiconductors, with Applications to Transistor Electronics; Van Nostrand: New York, 1950.
    There is no corresponding record for this reference.
  303. 303.
    Van Roosbroeck, W. Bell Syst. Tech. J. 1950, 29, 560
    There is no corresponding record for this reference.
  304. 304.
    Gummel, H. K. IEEE Trans. Electron Devices 1964, ED-11, 445
    There is no corresponding record for this reference.

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History

  • Published In Issue September 20, 2012
  • Article ASAPSeptember 10, 2012
  • Just Accepted ManuscriptAugust 17, 2012
  • Received: May 30, 2012
    Revised: July 31, 2012

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