Quasi-Chemical Theory and Implicit Solvent Models for Simulations

A statistical thermodynamic development is given of a new implicit solvent model that avoids the traditional system size limitations of computer simulation of macromolecular solutions with periodic boundary conditions. This implicit solvent model is based upon the quasi-chemical approach, distinct from the common integral equation trunk of the theory of liquid solutions. The physical content of this theory is the hypothesis that a small set of solvent molecules are decisive for these solvation problems. A detailed derivation of the quasi-chemical theory escorts the development of this proposal. The numerical application of the quasi-chemical treatment to Li$^+$ ion hydration in liquid water is used to motivate and exemplify the quasi-chemical theory. Those results underscore the fact that the quasi-chemical approach refines the path for utilization of ion-water cluster results for the statistical thermodynamics of solutions.Comment: 30 pages, contribution to Santa Fe Workshop on Treatment of Electrostatic Interactions in Computer Simulation of Condensed Medi

Ion Sizes and Finite-Size Corrections for Ionic-Solvation Free Energies

Free energies of ionic solvation calculated from computer simulations exhibit a strong system size dependence. We perform a finite-size analysis based on a dielectric-continuum model with periodic boundary conditions. That analysis results in an estimate of the Born ion size. Remarkably, the finite-size correction applies to systems with only eight water molecules hydrating a sodium ion and results in an estimate of the Born radius of sodium that agrees with the experimental value.Comment: 2 EPS figure

Role of fluctuations in a snug-fit mechanism of KcsA channel selectivity

The KcsA potassium channel belongs to a class of K+ channels that is selective for K+ over Na+ at rates of K+ transport approaching the diffusion limit. This selectivity is explained thermodynamically in terms of favorable partitioning of K+ relative to Na+ in a narrow selectivity filter in the channel. One mechanism for selectivity based on the atomic structure of the KcsA channel invokes the size difference between K+ and Na+, and the molecular complementarity of the selectivity filter with the larger K+ ion. An alternative view holds that size-based selectivity is precluded because atomic structural fluctuations are greater than the size difference between these two ions. We examine these hypotheses by calculating the distribution of binding energies for Na+ and K+ in a simplified model of the selectivity filter of the KcsA channel. We find that Na+ binds strongly to the selectivity filter with a mean binding energy substantially lower than that for K+. The difference is comparable to the difference in hydration free energies of Na+ and K+ in bulk aqueous solution. Thus, the average filter binding energies do not discriminate Na+ from K+ when measured from the baseline of the difference in bulk hydration free energies. Instead, Na+/K+ discrimination can be attributed to scarcity of good binding configurations for Na+ compared to K+. That relative scarcity is quantified as enhanced binding energy fluctuations, and is consistent with predicted relative constriction of the filter by Na+.Comment: 8 pages, 6 figure