Erratum: “Free-energy analysis of water affinity in polymer studied by atomistic molecular simulation combined with the theory of solutions in the energy representation” [J. Chem. Phys. 137, 234903 (2012)]

Solvation energetics of proteins and their aggregates analyzed by all-atom molecular dynamics simulations and the energy-representation theory of solvation

Solvation is a controlling factor for the structure and function of proteins. This article addresses the effects of solvation from an energetic perspective for the fluctuations and cosolvent-induced changes in protein structures and the equilibrium of aggregate formation for a peptide. A theoretical framework to analyze the solvation effects with an explicit solvent is introduced by adopting the energy-representation theory of solvation, and the connection of the solvation free energy to the protein structure and the aggregation tendency is quantitatively described in combination with all-atom molecular dynamics simulations. The interaction components that govern the solvation effects on the structural variations of proteins are further identified through correlation analysis, and a computational scheme to assess the shift of an aggregation equilibrium due to the addition of a cosolvent is provided.

Water Dissolved in a Variety of Polymers Studied by Molecular Dynamics Simulation and a Theory of Solutions

The performance of a polymer medium as a separation membrane is determined by the dissolution free energy ΔG and diffusion coefficient D of the permeant. In this work, ΔG and D of water are investigated with all-atom molecular dynamics simulation in a wide variety of polymer species in the amorphous state. The computed ΔG is shown to agree well with the experimental value for linear homopolymers, and the degrees of polymerization of the homopolymers do not affect ΔG when they are beyond ∼10. The copolymers of ethylene-vinylidene difluoride, ethylene-vinyl acetate, and ethylene-acrylamide are then examined by changing the repeating patterns of the constituent monomers in both the periodic and graft forms. It is found that ΔG is determined primarily by the overall compositions of the monomers and is not affected by the copolymerization topology (periodic or graft). The hydrophobicity of the copolymer is enhanced, furthermore, when the hydrophobicity and hydrophilicity of the ethylene and non-ethylene parts are well contrasted and those parts are fragmented along the polymer chain. According to the computed D, the diffusivity of water tends to be larger when the (co)polymer is more hydrophobic and ΔG is more positive. D is actually seen to vary by orders of magnitude with the polymer structures, while the effect of the polymer species on the water permeation is stronger for ΔG than for D.

Free-energy analysis of physisorption on solid-liquid interface with the solution theory in the energy representation

Physisorption of urea on its crystal in contact with water was subject to energetics analysis with all-atom molecular dynamics simulation. The transfer free energy of urea to an adsorption site was treated in the framework of the energy-representation theory of solutions, which allows a fast computation of the free energy in an inhomogeneous environment with solid-liquid interface. The preference of adsorption was then compared between the (001) and (110) faces, and it was found that the physisorption is more favorable on (001) than on (110) in correspondence to the hydrogen bonding between the adsorbed urea and the crystal urea. Among the terrace configurations of adsorption, the attractive interaction governs the preferable site with a minor role of the repulsive interaction. The effect of an edge was also treated by examining the terrace and step and was shown to be strongly operative on the (110) face when the CO group of the adsorbed urea points toward the edge. The present work demonstrates that the solution theory can be a framework for analyzing the energetics of physisorption and addressing the roles of the crystal and liquid at the interface through the systematic decomposition of free energy.

Probabilistic analysis for identifying the driving force of protein folding

Toward identifying the driving force of protein folding, energetics was analyzed in water for Trp-cage (20 residues), protein G (56 residues), and ubiquitin (76 residues) at their native (folded) and heat-denatured (unfolded) states. All-atom molecular dynamics simulation was conducted, and the hydration effect was quantified by the solvation free energy. The free-energy calculation was done by employing the solution theory in the energy representation, and it was seen that the sum of the protein intramolecular (structural) energy and the solvation free energy is more favorable for a folded structure than for an unfolded one generated by heat. Probabilistic arguments were then developed to determine which of the electrostatic, van der Waals, and excluded-volume components of the interactions in the protein-water system governs the relative stabilities between the folded and unfolded structures. It was found that the electrostatic interaction does not correspond to the preference order of the two structures. The van der Waals and excluded-volume components were shown, on the other hand, to provide the right order of preference at probabilities of almost unity, and it is argued that a useful modeling of protein folding is possible on the basis of the excluded-volume effect.