referee response X Inbox X Reply from Bob Eisenberg beisenbe@rush.edu sender-time Sent at 4:53 PM (GMT-05:00). Current time there: 9:23 PM. ? reply-to beisenbe@rush.edu to Yoichiro Mori , Chun Liu , Bob Eisenberg date Sun, May 15, 2011 at 4:53 PM subject referee response mailed-by gmail.com Important mainly because of the people in the conversation. hide details May 15 (5 days ago) Dear Yoichiro I think you did an admirable job of responding to the referees and rewriting and improving the paper. Attached is a Word version of the paper with some minor corrections and one minor suggesiton (concerning identification of the time scale with the "time constant" of the linear membrane). Concerning the importance of a variational structure, I have a great deal to say. 1) It is very easy for mathematicians, who work so hard to solve equations, to forget where the equations come from. One equation is not as good as another. In particular, equations solved by physicists and mathematicians describing solutions have not been anywhere near as useful as one might expect. As a leading experimentalist on ionic solutions says, “It is still a fact that over the last decades, it was easier to fly to the moon than to describe the free energy of even the simplest salt solutions beyond a concentration of 0.1M or so.” Kunz, W.; Neueder, R. An Attempt at an Overview. In "Specific Ion Effects" Kunz, W., Ed.; World Scientific Singapore, 2009; pp 11. Salt solutions containing divalent ions, or mixtures, are much LESS successfully described by classical equations than the simplest salt solutions mentioned in the quotation. One of the main reasons (indeed a sufficient reason) for these difficulties is that multiple components and force fields are involved whenever ions are dissolved in water AND THESE COMPONENTS AND FORCE FIELDS ALL INTERACT. They all interact because the electric field is created by all charge and is very long range. The usually interact as well because ions have finite diameter and are often spheres. Spheres differ from points just where the electric field is the strongest, so it is rarely possible to assume that the electric field of finite sized ions is approximated by the electric field of point ions. A variational approach avoids these difficulties. A variational approach automatically produces pde's (by the Euler Lagrange process) that are self consistent. If an additional electrolyte is added to the solution, or an additional force field is considered (e.g., temperature), or an additional structural component is added to a model, and one tries to derive pde's one will probably have as hard a time as Kunz reports. Indeed, no one has even tried to do this in electrochemistry for systems with flow, as far as I know, or more to the point as far as my friends and colleagues Jean-Pierre Hansen, Doug Henderson, and Stuart Rice know. (We are actually writing a paper on these issues.) e) The issue of mixing dimensions by dealing cavalierly with spatial variation is very very serious. In classical physiology, such an approach produced total confusion in the interpretation of electrical properties measured with single electrodes until three dimensional cable theory was analyzed and approximated BY MATHEMATICS with a series of problems of reduced dimensionality. Those approximations had not been guessed by several geneations of accomplished biophysicists and mathematicians. In the case of chemistry the issue is even more serious. The history of chemistry is the history of the well stirred approximation in which the law of mass action was applied to solutions of bulk concentration. This neglect of spatial gradients led to the neglect of a universe of self organizing phenomena. Just as importantly is the idea just now emerging: in most (but not every) case reactants have large concentrations WHEN THEY REACT. Certainly when catalysts or enzymes are present, or when conditions ensure a large "reaction cross section", reactants are at concentrations very different indeed from bulk WHEN REACTIONS OCCUR. The law of mass action does not apply when reactants are at high concentration because the law of mass action assumes ideality. Concetrated solutions are never ideal. Excess free energy is alway present when concentrations are high. Thus, the fundamental law used to interpret chemical reactions is grossly misleading when dimensionality is cavlierly ignored. A variational treatment cannot commit this kind of error. If a reduced dimensionality is introduced into part of the problem, in the variational principle, the resulting pde's from the Euler Lagrange process will still be consistent. Thus, in my view a variational approach is the only one that has any hope of working in salt solutions. Biological systems have a separate need for variational principles. Models of biological systems usually consist of several components (pumps and channels, cell volume and extracellular clefts, etc etc). The physics of each component is reasonably well known in favorable cases, and thanks to structural and molecular biology these favorable cases are numerous and rapidly increasing. BUT THESE COMPONENTS ALL INTERACT. Current through a calcium channel changes calcium concentration, which changes permeation and gating of the channel itself, and which interacts with pumps, signalling proteins and all sorts of nearby cellular components. There is no hope of writing selfconsistent equations for such system by cobbling together sets of pde's. It is just too easy to leave out improtant interactions. It is just too hard to avoid adding arbitrary parameters. Variational methods avoid these difficulties if models are made at the energy/dissipation level and pdes's are then derived from those variational models. Indeed, it is for similar reasons that high energy (and many other) physicists have used variational methods for many decades: they must combine different fields and components and only variational methods do that self consistently. As ever Bob PS I have not tried to polish either the above remarks or the few sentences I suggest in the paper since I think it important that they be in your voice not mine! ======================= Return Address for email: beisenbe@rush.edu