Simple Physics-Based Analytical Formulas for the Potentials of Mean Force for the Interaction of Amino Acid Side Chains in Water. 2. Tests with Simple Spherical Systems

Abstract

Simple analytical functions consisting of electrostatic, polarization, Lennard-Jones or modified Lennard-Jones, and cavity terms are proposed to express the potentials of mean force analytically for spherical particles interacting in water. The cavity term was expressed either through the molecular-surface area of the solute or by using the Gaussian-overlap model of hydrophobic hydration developed in paper 1 of this series. The analytical expressions were fitted to the potentials of mean force of a methane homodimer, heterodimers composed of a methane molecule, and an ammonium cation or a chloride anion, respectively, and dimers consisting of two chloride anions, two ammonium cations, or a chloride ion and an ammonium cation. The potentials of mean force for these dimers were determined by umbrella-sampling molecular dynamics simulations with the AMBER 7.0 force field with TIP3P water either in our earlier work or in this work. For all systems, the analytical formulas fitted the potentials of mean force very well. However, using the molecular-surface area to express the cavity term provided a good fit only when the nonbonded interactions were expressed by an all-repulsive modified Lennard-Jones potential but also resulted in non-physical values of some of the parameters. Conversely, the use of our new Gaussian-overlap-based expression for the cavity term provided a good fit to the potentials of mean force (PMFs) with Lennard-Jones nonbonded potential, and the values of all parameters were physically reasonable.

Simple Physics-Based Analytical Formulas for the Potentials of Mean Force of the Interaction of Amino-Acid Side Chains in Water. V. Like-Charged Side Chains

“…The model reproduces the desolvation maxima. 14,15 The Gaussian overlap model of the solvent and counter-ion density in the first solvation sphere is supported by the spatial distribution of water molecules and counter-ions obtained from simulation of model systems, where counter-ions and water density around a solute have clear maxima in the center of the first solvation sphere (Figures 9 and 10 in ref 38). …”

Simple Physics-Based Analytical Formulas for the Potentials of Mean Force for the Interaction of Amino Acid Side Chains in Water. IV. Pairs of Different Hydrophobic Side Chains

“…In one of these papers,2 we showed that the derived expression for the cavity creation term reproduces the features of the cavity part of the potentials of mean forces of homo- and heterodimers of simple spherical solutes in water very well. In the third paper3 of the series, we considered models of pairs of identical nonpolar amino acid side-chain models.…”

Simple Physics-Based Analytical Formulas for the Potentials of Mean Force of the Interaction of Amino Acid Side Chains in Water. VII. Charged–Hydrophobic/Polar and Polar–Hydrophobic/Polar Side Chains

“…In this work, the parameters mentioned above were determined by least-squares fitting of the analytical expression for the free energy of two side chains interacting in water (eqs 1–4) to the PMFs determined from MD simulations, as in our earlier work. 3,4,6,7 …”

“…The expression for Δ F cav of spheroidal particles was derived in ref 3 on the basis of the Gaussian-overlap model of hydrophobic association introduced in that work and is given by eq 14. This term accounts for the free-energy contribution due to restructuring water molecules around a hydrophobic dimer and has been derived and discussed in detail in ref 2.…”