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\section*{Responses to Reviewers}

We wish to thank the reviewers for both their favorable evaluation of this manuscript and for letting us have so many detailed notes from their readings. We have carefully considered all comments and believe that we have been able to improve the manuscript in many respects. 

\section*{Reviewer \#1}

\noindent \textbf{General Comments:}

\begin{itemize}

\item A sentence pointing out the usefulness of a reduced model in evaluating future more detailed models has been added in Introduction. We also quote a study of Noskov and Roux that presents a reduced model of the K channel.

\item Regarding the problem of verifying buffered `free' Ca$^{2+}$ concentrations, there seems to be no simple solution. For one, the notion of a `free' Ca$^{2+}$ concentration entirely rests on a heuristic theory. The quantity that might be actually measured (e.g., by a Ca$^{2+}$-specific electrode with sub-micromolar resolution in the relevant background of 1:1 salts) is Ca$^{2+}$ activity (or chemical potential). Unfortunately, a method for resolving Ca$^{2+}$ activities in such conditions seems to be an open problem. Perhaps, the best an experimenter could do is to remove as much Ca$^{2+}$ impurity as possible from the solutions using a `Ca$^{2+}$ sponge' and then adding back known amounts of calcium salt, confining solutions in plasticware rather than glassware. A technical discussion of this or perhaps other possibilities would be beyond the scope of our paper. We have presented buffered Ca$^{2+}$ solutions as a potential experimental problem, and we have shown that a reduced model of a Ca$^{2+}$ selective pore has substantial alkali metal ion dependence. Indeed, constructing a model that has strong alkali metal selectivity under some conditions, and no such selectivity in others, is virtually impossible in our experience with modeling such systems. We have reworked the discussion of the Ca$^{2+}$ buffering problem.
\end{itemize}

\noindent \textbf{Minor points:}

\begin{enumerate}

\item Indeed, if we were to set ionic charges in our system to zero, the excess chemical potential of particles would be entirely entropic because our particles (and confining walls) are incompressible. The excess entropy is configurational and reflects the likelihood that a particle finds a niche. This entropy is independent of temperature. With charge introduced, there is also an excess entropy contributed by formation of screening configurations. We have discussed these aspects in earlier theoretical treatments of such systems and have pointed out consequences for the temperature dependence of selectivity. These references are included. We have removed statements regarding `entropy' from the text, so that we do not confuse readers by a remark that may be too brief for many.

\item This part of the Abstract has been trimmed.

\item We describe transport using a constitutive relation whose place within more comprehensive descriptions (based on conservation laws) is well understood (Bearman and Kirkwood (1958). J. Chem. Phys. 28:136-145). It was important for this paper that we give a clean account of the averaging and approximations involved in taking the theory from 3D to 1D. The chemical potential of eq. 1 is the total chemical potential including the ideal concentration term. The components of this total potential are now mentioned explicitly. The Boltzmann relation that you write for the concentration involves the `excess` (non-ideal) part of $\mu$.
\end{enumerate}

\section*{Reviewer \#2}

\noindent \textbf{Major Comments}

\begin{enumerate}
\item The experimental work that we use in fig. 4B did not determine reversal potentials, only current at a fixed voltage (0 mV). We thus were left with the options of either converting current to conductance using guessed reversal potentials, or of scaling our computed conductances by a factor (driving force) that matches theoretical and experimental currents at some end of the plot. We chose to do the latter, having to accept the risk that the actual reversal potential varied with the amount of Ca added and thus biased the comparison.

\item We do not wish to ignore the Ca channel work of Chung's group. Indeed, we have made a careful, step by step, comparison of our two kinds of model (using the Corry et al. geometry but placing the oxygen ions either in the wall (like Corry et al. did) or in the pore lumen (like we do)) and of the two methods to compute the models. A detailed paper about this work has been published (Boda et al. (2008). Biophys. J. 94:3486-3498). Shin-Ho Chung was a reviewer of this paper, and we have been discussing our results among our groups. In short, when we actually simulate micromolar Ca concentrations (which were extrapolated in Corry et al.), the Corry et al. model does not give the micromolar binding selectivity that their BD simulations of flux seemed to suggest. Placement of the oxygen ions in the lumen gives stronger selectivity than the placement in the wall. We now mention these two papers in Introduction.
\end{enumerate}

\noindent \textbf{Minor comments}

Minor comments \#1, \#4, \#5 suggest that we discuss existing chemical-kinetics models in the light of our simulation results. Our approach has been to directly compare experimental results and computed consequences of the physical model that we present. We also describe computed ion distributions in our model as a phenomenon that is of interest in itself. We have touched upon chemical-kinetics models only in discussing Li$^+$ action on Ca$^{2+}$ permeation rate because we point out a new mechanistic aspect not envisaged in these models. This way we have avoided speculating about phenomena that have not been measured or are not actually computed in our work (such as ion trajectories or `energy landscapes' for ions in the channel).  We give specific responses to the reviewer's comments below. We have kept changes made to the discussion within the bounds just described.

\begin{enumerate}  

\item We find on average no more than one Ca$^{2+}$ in the `high-affinity' region located in the central 5 {\AA} of the model pore. Additional Ca$^{2+}$ is found in the `low-affinity' regions near the pore mouths. Thus the ion distribution in our model is more like that in the DM model than like that in the HTAM model. We have pointed out the single occupancy and included DM as the sole reference when describing the ion distribution (section 'Ca$^{2+}$ entry/exit rates ...').

\item We have removed terms like `chemical sources of selectivity' and simply state what we do include into the model.

\item We are embarrassed. Thanks for catching this lapse of perspective.

\item The low-affinity region of the model pore picks up substantial amounts of Ca$^{2+}$ only if the bath Ca$^{2+}$ levels are increased into the millimolar range. Computations with simulated concentration profiles and eq. 3 show that Ca$^{2+}$ conductance increases in this range of bath concentration, but the increase reflects mostly an increase of Ca$^{2+}$ concentration in the `depletion' zones between the high- and low-affinity regions of the pore. Such computations have been presented in a previous paper from our group, which we cite (Gillespie and Boda (2008), Biophys. J. 95:2658-2672). 

\item The statements that we make about the excess chemical potential of Ca$^{2+}$ in the depletion regions are verifiable from the simulation results by inspecting the electrostatic and volume-exclusion parts of the excess chemical potential (not discussed in this paper). We probably have stretched our own discussion limits a bit when mentioning the ``making and breaking'' of the chelate, and have reworded that part in a more conservative way. Our simulation results show that variation of the bath concentration of Li$^+$ modulates the Ca$^{2+}$ concentration in the depletion regions but we cannot reason that interactions among two particular ions underly this outcome. This is because in our physical model (involving mobile ions, `flexible' structural ions, and dielectrics) an ion interacts with any other ion and thus will affect the position of the other ion (via its electric field or excluded volume). This way any two ions are coupled through smaller or larger adjustments in the positions of other ions. If we were to fix the positions of ions in the simulation, we would not simulate a system at equilibrium (minimal thermodynamic potential) but a system subject to arbitrary external forces. 

\item Done

\item Reference mentioned and included. We have not used these data for comparison with simulation because we have used only single-channel data or results complemented by single-channel data.

\item Yes -- we trimmed this from Abstract.

\item The terms `grand canonical' and `self-consistent' are now defined (in section 'Method of Simulation'). `PNP' is now explained. 

\item We have tried to make these sentences more clear.

\item Corrected. The total concentrations are given in the legend of fig. 2.

\item Done

\item Done (but `soaked' was so descriptive!)

\item Done

\item Thanks again!
\end{enumerate}


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