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.

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.

The potentials of mean force of 21 heterodimers 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), methyl propyl sulfide (for methionine), and indole (for tryptophane) 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 proposed in our earlier work 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, are well represented by the analytical expressions for all systems; large deviations between the MD-determined PMF and the analytical approximations are observed for pairs involving the least spheroidal solutes: ethylbenzene, indole, and methyl propyl sulfide at short distances at which the PMF is high and, consequently, these regions are rarely visited. When data from the PMF within only 10 kcal/mol above the global minimum are considered, the standard deviation between the MD-determined and the fitted PMF is from 0.25 to 0.55 kcal/mol (the relative standard deviation being from 4% to 8%); it is larger for pairs involving nonspherical solute molecules. The free energies of contact computed from the PMF surfaces are well correlated with those determined from proteincrystal data with a slope close to that relating the free energies of transfer of amino acids (from water to n-octanol) to the average contact free energies determined from protein-crystal data. These observations justify future use of the determined potentials in coarse-grained protein-folding simulations.

Human cystatin C (HCC) is one of the amyloidogenic proteins to be shown to oligomerize via a three-dimensional domain swapping mechanism. This process precedes the formation of a stable dimer and proceeds particularly easily in the case of the L68Q mutant. According to the proposed mechanism, dimerization of the HCC precedes conformational changes within the beta2 and beta3 strands. In this article, we present conformational studies, using circular dichroism and MD methods, of the beta2-L1-beta3 (His43-Thr72) fragment of the HCC involved in HCC dimer formation. We also carried out studies of the beta2-L1-beta3 peptide, in which the Val57 residue was replaced by residues promoting beta-turn structure formation (Asp, Asn, or Pro). The present study established that point mutation could modify the structure of the L1 loop in the beta-hairpin peptide. Our results showed that the L1 loop in the peptide excised from human cystatin C is broader than that in cystatin C. In the HCC protein, broadening of the L1 loop together with the unfavorable L68Q mutation in the hydrophobic pocket could be a force sufficient to cause the partial unfolding and then the opening of HCC or its L68Q mutant structure for further dimerization. We presume further that the Asp57 and Asn57 mutations in the L1 loop of HCC could stabilize the closed form of HCC, whereas the Pro57 mutation could lead to the opening of the HCC structure and then to dimer/oligomer formation.

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.

Phosphorylation is a common post-translational modification of the amino-acid side chains (serine, tyrosine, and threonine) that contain hydroxyl groups. The transfer of the negatively charged phosphate group from an ATP molecule to such amino-acid side chains leads to changes in the local conformations of proteins and the pattern of interactions with other amino-acid side-chains. A convenient characteristic of the side chain–side chain interactions in the context of an aqueous environment is the potential of mean force (PMF) in water. A series of umbrella-sampling molecular dynamic (MD) simulations with the AMBER force field were carried out for pairs of O-phosphorylated serine (pSer), threonine (pThr), and tyrosine, (pTyr) with natural amino acids in a TIP3P water model as a solvent at 298 K. The weighted-histogram analysis method was used to calculate the four-dimensional potentials of mean force. The results demonstrate that the positions and depths of the contact minima and the positions and heights of the desolvation maxima, including their dependence on the relative orientation depend on the character of the interacting pairs. More distinct minima are observed for oppositely charged pairs such as, e.g., O-phosphorylated side-chains and positively charged ones, such as the side-chains of lysine and arginine.

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 K, 323 K and 373 K, respectively. The systems were found to fall into the following four categories as far as the temperature dependence of the potential of mean force 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.