Reply to “Comment on ‘Molecular Origin of Anticooperativity in Hydrophobic Association'”

Hydrophobic interactions in model enclosures from small to large length scales: non-additivity in explicit and implicit solvent models

The binding affinities between a united-atom methane and various model hydrophobic enclosures were studied through high accuracy free energy perturbation methods (FEP). We investigated the non-additivity of the hydrophobic interaction in these systems, measured by the deviation of its binding affinity from that predicted by the pairwise additivity approximation. While only small non-additivity effects were previously reported in the interactions in methane trimers, we found large cooperative effects (as large as -1.14 kcal mol(-1) or approximately a 25% increase in the binding affinity) and anti-cooperative effects (as large as 0.45 kcal mol(-1)) for these model enclosed systems. Decomposition of the total potential of mean force (PMF) into increasing orders of multi-body interactions indicates that the contributions of the higher order multi-body interactions can be either positive or negative in different systems, and increasing the order of multi-body interactions considered did not necessarily improve the accuracy. A general correlation between the sign of the non-additivity effect and the curvature of the solute molecular surface was observed. We found that implicit solvent models based on the molecular surface area (MSA) performed much better, not only in predicting binding affinities, but also in predicting the non-additivity effects, compared with models based on the solvent accessible surface area (SASA), suggesting that MSA is a better descriptor of the curvature of the solutes. We also show how the non-additivity contribution changes as the hydrophobicity of the plate is decreased from the dewetting regime to the wetting regime.

Pressure and temperature dependence of hydrophobic hydration: Volumetric, compressibility, and thermodynamic signatures

The combined effect of pressure and temperature on hydrophobic hydration of a nonpolar methanelike solute is investigated by extensive simulations in the TIP4P model of water. Using test-particle insertion techniques, free energies of hydration under a range of pressures from 1 to 3000 atm are computed at eight temperatures ranging from 278.15 to 368.15 K. Corresponding enthalpy, entropy, and heat capacity accompanying the hydration process are estimated from the temperature dependence of the free energies. Partial molar and excess volumes calculated using pressure derivatives of the simulated free energies are consistent with those determined by direct volume simulations; but direct volume determination offers more reliable estimates for compressibility. At 298.15 K, partial molar and excess isothermal compressibilities of methane are negative at 1 atm. Partial molar and excess adiabatic (isentropic) compressibilities are estimated to be also negative under the same conditions. But partial molar and excess isothermal compressibilities are positive at high pressures, with a crossover from negative to positive compressibility at approximately 100-1000 atm. This trend is consistent with experiments on aliphatic amino acids and pressure-unfolded states of proteins. For the range of pressures simulated, hydration heat capacity exhibits little pressure dependence, also in apparent agreement with experiment. When pressure is raised at constant room temperature, hydration free energy increases while its entropic component remains essentially constant. Thus, the increasing unfavorability of hydration under raised pressure is seen as largely an enthalpic effect. Ramifications of the findings of the authors for biopolymer conformational transitions are discussed.