Molecular simulation study of the potentials of mean force for the interactions between models of like-charged and between charged and nonpolar amino acid side chains in water

The purpose of this study was to determine the potentials of mean force (PMF) of the interactions between models of like-charged and between models of charged and nonpolar amino acid side chains in water to design improved side chain-side chain interaction potentials for our united residue UNRES force field for protein-structure prediction. Restrained molecular dynamics with the AMBER force field, the TIP3P model of water, and the Ewald summation were used to carry out simulations, and the weighted histogram analysis method (WHAM) was used to calculate the PMFs as functions of solute-solute distances. The following types of systems were considered to model the interactions between like-charged side chains and the interactions between charged and nonpolar side chains: (i) a pair of positively charged ions (potassium, ammonium, and guanidine, respectively); (ii) a pair of negatively charged ions (chloride and acetate, respectively), and (iii) pairs of methane with potassium, ammonium, and chloride ions, respectively. Additionally, a pair of potassium and chloride ions was included for comparison with the work of other authors. Except for the pair of acetate ions, where the PMF curve exhibited all-repulsive behavior, a minimum or two coalescing minima with positive PMF values appeared for pairs of like-charged ions. In the potassium-chloride ion pair, a contact and a solvent-separated minimum was observed. Comparison of our results with those obtained by other authors showed that including Ewald summation in computing electrostatic interactions has substantial influence on the PMFs of like-charged ions; for oppositely charged ions including Ewald summation only causes deepening of the contact minimum. It was found that the appearance of the minimum in the PMFs of like-charged ion pairs is caused by a high degree of ordering of water molecules and counterions between the solutes at this distance. The solvent contribution to the PMFs of pairs of charged and nonpolar solutes is positive in all cases; the most unfavorable contribution was observed for the methane-chloride ion pair. The results demonstrate that the use of all-repulsive potentials for the interactions between like-charged and between charged and nonpolar side chains in the UNRES force field is essentially correct, but the distance dependence should be more long range in the like-charged side chain interaction potential, because the PMF curves of like-charged ion pairs are reasonably fitted with a combination of r(-1), r(-2), and r(-3) terms (r being the distance between the centers of the mass), while they are not reproduced well with combinations of r(-6) and r(-12) terms of the present version of UNRES.