Nonpolar Solvation Free Energy from Proximal Distribution Functions

Abstract

Using precomputed near neighbor or proximal distribution functions (pDFs) that approximate solvent density about atoms in a chemically bonded context one can estimate the solvation structures around complex solutes and the corresponding solute–solvent energetics. In this contribution, we extend this technique to calculate the solvation free energies (ΔG) of a variety of solutes. In particular we use pDFs computed for small peptide molecules to estimate ΔG for larger peptide systems. We separately compute the non polar (ΔGvdW) and electrostatic (ΔGelec) components of the underlying potential model. Here we show how the former can be estimated by thermodynamic integration using pDF-reconstructed solute–solvent interaction energy. The electrostatic component can be approximated with Linear Response theory as half of the electrostatic solute–solvent interaction energy. We test the method by calculating the solvation free energies of butane, propanol, polyalanine, and polyglycine and by comparing with traditional free energy simulations. Results indicate that the pDF-reconstruction algorithm approximately reproduces ΔGvdW calculated by benchmark free energy simulations to within ~ kcal/mol accuracy. The use of transferable pDFs for each solute atom allows for a rapid estimation of ΔG for arbitrary molecular systems.

Molecular Interpretation of Preferential Interactions in Protein Solvation: A Solvent-Shell Perspective by Means of Minimum-Distance Distribution Functions

“…[18][19][20][21] In particular, the use of the distance of one solvent site (an atom or the center of mass) of the solvent molecule to the surface of the solute, or to the nearest solute atom, was proposed independently by different authors as an alternative to overcome the complexity of the solute shape. [18][19][20][22][23][24][25][26][27] This choice defines what has been called the "solvation-shell" distribution functions, g ss (r), 23,24 or proximal distribution functions, g ⊥ (r), 18,22,26,27 which appeal directly to the concept of Voronoi tesselation. 21,28 In all cases, the counting of nearest distances is straightforward from a simulation, but the normalization procedure leading to the distribution functions can be cumbersome.…”

Free Energy Calculations Based on Coupling Proximal Distribution Functions and Thermodynamic Cycles

“…Details are addressed in Supporting Information and the references. 55,56 2.3. Thermodynamic Integration for Solvation Free Energetics.…”

“…43,44 When coupled with the van der Waals components of the excess chemical potentials from pDF-reconstructions the total solvation free energy difference for small molecules is reasonably approximated (within kcal/mol accuracy). 43,44,55,56 In this contribution, we extend the method to challenging thermodynamic chemical processes, including the length dependence of a polypeptide, 57 mutating a residue on a polypeptide, and finally, association between two alanine peptides.…”

Energetics of cosolvent effect on peptide aggregation

“…It is a density-functional method for solutions and evaluates the solvation free energy with a functional of a set of distribution functions for the pair-interaction energy between the solute and solvent. A variety of approximate methods have been proposed for freeenergy computation [57][58][59][60][61][62][63][64][65][66][67][68][69][70][71][72][73][74][75], and the energy-representation method is unique in compromising the accuracy, efficiency, and range of applicability [30,53,55,56,. In the method of energy representation, the molecular simulation is to be performed only at the endpoints of solute insertion (solution and reference-solvent systems of interest), leading to the reduction of the computational load.…”