Statistical thermodynamics of solvophobic solvation in water and simpler liquids
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Temperature, pressure, and length scale dependence of the solvation of simple solvophobic solutes is investigated in the Jagla liquid, a simple liquid consisting of particles that interact via a spherically symmetric potential combining hard and soft core interactions. The results are compared with identical calculations for a model of a typical atomic liquid, the Lennard-Jones (LJ) potential, and with predictions for hydrophobic solvation in water using the recently developed cavity equation of state and the extended simple point charge model. We find that the Jagla liquid captures the qualitative thermodynamic behavior of hydrophobic hydration as a function of temperature and pressure for both small and large length scale solutes. In particular, for both the Jagla liquid and water, we observe temperature-dependent enthalpy and entropy of solvation for all solute sizes as well as a negative solvation entropy for sufficiently small solutes at low temperature. This feature of water-like solvation is distinct from the strictly positive and temperature independent enthalpy and entropy of cavity solvation observed in the Lennard-Jones fluid. The results suggest that a competition between two energy scales that favors low-density, open structures as temperature is decreased is an essential interaction of a liquid that models hydrophobic hydration. In addition the Jagla liquid dewets surfaces of large radii of curvature less readily than the Lennard-Jones liquid, and the so-called ``length scale crossover'' in solvation, whereby solvation free energies change from scaling with the solute volume to scaling with the solute surface area, occurs at length scales that are larger relative to the solvent size. Both features reflect a greater flexibility or elasticity in the Jagla liquid structure than that of a typical liquid, similar to water's ability to maintain its hydrogen bond network. The implications of the differences in crossover behavior between water-like and typical liquids are examined in the context of a simple thought experiment on the aggregation of solvophobic solutes that builds on ideas from Chandler and Rajamani et al. We find that water-like crossover behavior exposes a size range of solvophobic aggregates to destabilization upon cooling and pressurizing, which may thereby precipitate phenomena such as cold and pressure denaturation of proteins. Statistics of density fluctuations, void space, and pair distributions are analyzed for molecular-scale volumes. The pair distribution functions are used to provide an estimate of the size of the Jagla particle with a physical basis. The void distributions are observed to be distinct in the three liquids, with low temperature distributions in the LJ and Jagla liquids demonstrating a high degree of skewness. The void distributions observed in LJ liquid are hard sphere-like, while those of water and the Jagla liquid exhibit a higher degree of density inhomogeneity relative to a hard sphere system. The well-known Gaussian behavior of density fluctuations in molecular volumes in water is not generally observed in other liquids, as evidenced by the fact that this behavior is not consistently observed in either the LJ or the Jagla liquids. An exploratory study of the effects of explicit solvent on the sequence energy landscape of model heteropolymers has been performed. For a fixed set of configurations, the energy landscape of all possible sequences taken from a two letter alphabet consisting of only solvophilic and solvophobic monomers is characterized at different solvent temperatures. Non-trivial solvent and temperature effects are manifest in the distribution of sequences, confirming that the negation of these effects may have profound consequences on designability.