Scaled-Particle Theory and the Length-scales Involved in Hydrophobic Hydration of Aqueous Biomolecular Assemblies

Hydrophobic hydration plays a crucial role in self-assembly processes over multiple length-scales, but the extrapolation of molecular-scale models to larger length-scale hydration phenomena is sometimes not warranted. Scaled-particle theories are based upon an interpolative view of that issue. We revisit the scaled-particle theory proposed thirty years ago by Stillinger, adopt a practical generalization, and consider the implications for hydrophobic hydration in light of our current understanding. The generalization is based upon identifying a molecular length, implicit in previous applications of scaled-particle models, that provides an effective radius for joining microscopic and macroscopic descriptions. We demonstrate that the generalized theory correctly reproduces many of the anomalous thermodynamic properties of hydrophobic hydration for molecularly sized solutes, including solubility minima and entropy convergence, successfully interpolates between the microscopic and macroscopic extremes, and provides new insights into the underlying molecular mechanisms. The results are discussed in terms of length-scales associated with component phenomena; in particular we first discuss the micro-macroscopic joining radius identified by the theory, then we discuss in turn the Tolman length that leads to an analogous length describing curvature corrections of a surface area model of hydrophobic hydration free energies, and the length-scales on which entropy convergence of hydration free energies are expected.Comment: 19 pages, 14 figures, one figure added, submitted to Rev. Mod. Phy

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