Comparison of two approaches to potential of mean force calculations of hydrophobic association: particle insertion and weighted histogram analysis methods

Hydrophobic hydration and pairwise hydrophobic interaction of Lennard-Jones and Mie particles in different water models

The study provides a deep computational analysis of the thermodynamic and structural features associated with the hydration of xenon, Xe, and its pairwise hydrophobic interaction (i.e., the potential of mean force, PMF), over a large temperature range. Xe is described both as a Lennard-Jones particle, LJ-Xe, and as a Mie particle, Mie-Xe (pseudo hard sphere). Three different water models are used: TIP3P-Ew, SPCE and TIP4P-2005. Mie-Xe is more hydrophobic than LJ-Xe due to the lack of the attractive energetic interactions with water molecules; its hydration, around room temperature, is opposed by a large and negative entropy change and a positive enthalpy change. The PMF of Mie-Xe is characterized by a deep minimum at contact distance whose depth increases with temperature, and whose magnitude is significantly larger than that obtained for LJ-Xe. The contact minimum configuration of Mie-Xe is favoured by a large positive entropy change and contrasted by a positive enthalpy change. These results are qualitatively the same regardless of the water model used. There is no clear connection between the values determined for the thermodynamic functions and the structural features of the hydration shells surrounding the single Mie-Xe and the couple of Mie-Xe particles in the contact minimum configuration. This confirms that the structural reorganization of water associated with such processes is characterized by an almost complete enthalpy-entropy compensation.

Toward temperature-dependent coarse-grained potentials of side-chain interactions for protein folding simulations. II. Molecular dynamics study of pairs of different types of interactions in water at various temperatures

By means of molecular dynamics simulations of 15 pairs of molecules selected to model the interactions of nonpolar, nonpolar and polar, nonpolar and charged, polar, and polar and charged side chains in water, we determined the potentials of mean force (PMFs) of pairs of interacting molecules in water as functions of distance between the interacting particles or their distance and orientations at three temperatures: 283, 323, and 373 K, respectively. The systems were found to fall into the following four categories as far as the temperature dependence of the PMF is concerned: (i) pairs for which association is entropy-driven, (ii) pairs for which association is energy-driven, (iii) pairs of positively charged solute molecules, for which association is energy-driven with unfavorable entropy change, and (iv) the remaining systems for which temperature dependence is weak. For each pair of PMFs, entropic and energetic contributions have been discussed.

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.

Towards temperature-dependent coarse-grained potentials of side-chain interactions for protein folding simulations. I: molecular dynamics study of a pair of methane molecules in water at various temperatures

By means of molecular dynamics simulations of a pair of methane molecules in a TIP3P periodic water box with the NVT scheme at six temperatures and, additionally, the NPT scheme at three temperatures ranging from T = 283 to 373 K, we determined the potential of mean force (PMF) of pairs of interacting methane molecules in water as functions of distance between the methane molecules. The PMFs converge to a single baseline only for r> 11 A at all temperatures. The curves of the dimensionless PMF obtained at different temperatures with the NVT scheme overlap almost perfectly in the region of the contact minimum and still very well in the regions of the desolvation maximum and the solvent-separated minimum, which suggests that the temperature-dependent hydrophobic interaction potentials at constant volume in united-residue force fields can be obtained by scaling the respective dimensionless potentials by RT, R being the universal gas constant. For the dimensionless potentials of mean force obtained with the NPT scheme, the depth of the contact minimum increases, whereas the height of the desolvation maximum and the depth of the solvent-separated minimum decrease with temperature, in agreement with results reported in the literature.

Potential of Mean Force of Hydrophobic Association: Dependence on Solute Size

The potentials of mean force (PMFs) were determined for systems involving formation of nonpolar dimers composed of methane, ethane, propane, isobutane, and neopentane, respectively, in water, using the TIP3P water model, and in vacuo. A series of umbrella-sampling molecular dynamics simulations with the AMBER force field was carried out for each pair in either water or in vacuo. The PMFs were calculated by using the weighted histogram analysis method (WHAM). The shape of the PMFs for dimers of all five nonpolar molecules is characteristic of hydrophobic interactions with contact and solvent-separated minima and desolvation maxima. The positions of all these minima and maxima change with the size of the nonpolar molecule, that is, for larger molecules they shift toward larger distances. The PMF of the neopentane dimer is similar to those of other small nonpolar molecules studied in this work, and hence the neopentane dimer is too small to be treated as a nanoscale hydrophobic object. The solvent contribution to the PMF was also computed by subtracting the PMF determined in vacuo from the PMF in explicit solvent. The molecular surface area model correctly describes the solvent contribution to the PMF together with the changes of the height and positions of the desolvation barrier for all dimers investigated. The water molecules in the first solvation sphere of the dimer are more ordered compared to bulk water, with their dipole moments pointing away from the surface of the dimer. The average number of hydrogen bonds per water molecule in this first hydration shell is smaller compared to that in bulk water, which can be explained by coordination of water molecules to the hydrocarbon surface. In the second hydration shell, the average number of hydrogen bonds is greater compared to bulk water, which can be explained by increased ordering of water from the first hydration shell; the net effect is more efficient hydrogen bonding between the water molecules in the first and second hydration shells.

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.

Simple physics-based analytical formulas for the potentials of mean force for the interaction of amino acid side chains in water. 3. Calculation and parameterization of the potentials of mean force of pairs of identical hydrophobic side chains

The potentials of mean force of homodimers of the molecules modeling hydrophobic amino acid side chains (ethane (for alanine), propane (for proline), isobutane (for valine), isopentane (for leucine and isoleucine), ethylbenzene (for phenylalanine), and methyl propyl sulfide (for methionine)) were determined by umbrella-sampling molecular dynamics simulations in explicit water as functions of distance and orientation. Analytical expressions consisting of the Gay-Berne term to represent effective van der Waals interactions and the cavity term derived in paper 1 of this series were fitted to the potentials of mean force. The positions and depths of the contact minima and the positions and heights of the desolvation maxima, including their dependence on the orientation of the molecules, were well represented by the analytical expressions for all systems, which justifies use of such potentials in coarse-grain protein-folding simulations.