Molecular dynamics study on binding free energy of Azurin–Cytochrome c551 complex

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.

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.

Computing conformational free energy differences in explicit solvent: An efficient thermodynamic cycle using an auxiliary potential and a free energy functional constructed from the end points

Many biomolecules undergo conformational changes associated with allostery or ligand binding. Observing these changes in computer simulations is difficult if their timescales are long. These calculations can be accelerated by observing the transition on an auxiliary free energy surface with a simpler Hamiltonian and connecting this free energy surface to the target free energy surface with free energy calculations. Here, we show that the free energy legs of the cycle can be replaced with energy representation (ER) density functional approximations. We compute: (1) The conformational free energy changes for alanine dipeptide transitioning from the right-handed free energy basin to the left-handed basin and (2) the free energy difference between the open and closed conformations of β-cyclodextrin, a "host" molecule that serves as a model for molecular recognition in host-guest binding. β-cyclodextrin contains 147 atoms compared to 22 atoms for alanine dipeptide, making β-cyclodextrin a large molecule for which to compute solvation free energies by free energy perturbation or integration methods and the largest system for which the ER method has been compared to exact free energy methods. The ER method replaced the 28 simulations to compute each coupling free energy with two endpoint simulations, reducing the computational time for the alanine dipeptide calculation by about 70% and for the β-cyclodextrin by > 95%. The method works even when the distribution of conformations on the auxiliary free energy surface differs substantially from that on the target free energy surface, although some degree of overlap between the two surfaces is required. © 2016 Wiley Periodicals, Inc.

Free-energy analysis of protein solvation with all-atom molecular dynamics simulation combined with a theory of solutions

The structure of a protein is strongly influenced by solvation. In the present review, the solvation effect is treated within the framework of statistical thermodynamics. The key quantity is the solvation free energy of protein and a fast method for its computation with explicit solvent is introduced. The applications of the method to the structural fluctuation of protein in water, structure determination of protein-protein complex, and urea effect on protein structure are then described, and the roles of solvent water and cosolvent are discussed from the standpoint of energetics.

Correlation analysis for heat denaturation of Trp-cage miniprotein with explicit solvent

Energetics was analyzed for Trp-cage miniprotein in water to elucidate the solvation effect in heat denaturation. The solvation free energy was computed for a set of protein structures at room and high temperatures with all-atom molecular dynamics simulation combined with the solution theory in the energy representation, and its correlations were investigated against the intramolecular (structural) energy of the protein and the average interaction energy of the protein with the solvent water. It was observed both at room and high temperatures that the solvation free energy is anticorrelated to the structural energy and varies in parallel to the electrostatic component of the protein-water interaction energy without correlations to the van der Waals and excluded-volume components. When the set of folded structures sampled at room temperature was compared with the set of unfolded ones at high temperature, it was found that the preference order of the two sets is in correspondence to the van der Waals and excluded-volume components in the sum of the protein intramolecular and protein-water intermolecular interactions and is not distinguished by the electrostatic component.