title: A Simple and Accurate Method To Calculate Free Energy Profiles and Reaction Rates from Restrained Molecular Simulations of Diffusive Processes.
abstract: A method is developed to obtain simultaneously free energy profiles and diffusion constants from restrained molecular simulations in diffusive systems. The method is based on low-order expansions of the free energy and diffusivity as functions of the reaction coordinate. These expansions lead to simple analytical relationships between simulation statistics and model parameters. The method is tested on 1D and 2D model systems; its accuracy is found to be comparable to or better than that of the existing alternatives, which are briefly discussed. An important aspect of the method is that the free energy is constructed by integrating its derivatives, which can be computed without need for overlapping sampling windows. The implementation of the method in any molecular simulation program that supports external umbrella potentials (e.g., CHARMM) requires modification of only a few lines of code. As a demonstration of its applicability to realistic biomolecular systems, the method is applied to model the α-helix ↔ β-sheet transition in a 16-residue peptide in implicit solvent, with the reaction coordinate provided by the string method. Possible modifications of the method are briefly discussed; they include generalization to multidimensional reaction coordinates [in the spirit of the model of Ermak and McCammon (Ermak, D. L.; McCammon, J. A. J. Chem. Phys. 1978, 69, 1352-1360)], a higher-order expansion of the free energy surface, applicability in nonequilibrium systems, and a simple test for Markovianity. In view of the small overhead of the method relative to standard umbrella sampling, we suggest its routine application in the cases where umbrella potential simulations are appropriate.
authors.affiliation: Department of Chemistry and Chemical Biology, Harvard University , Cambridge, Massachusetts 02138, United States.
authors.forename: Victor
authors.initials: V
authors.lastname: Ovchinnikov
authors.affiliation: Department of Chemistry, Umeå University , Umeå, Sweden , 901 87.
authors.forename: Kwangho
authors.initials: K
authors.lastname: Nam
authors.affiliation: Department of Chemistry and Chemical Biology, Harvard University , Cambridge, Massachusetts 02138, United States.|Laboratoire de Chimie Biophysique, ISIS, Université de Strasbourg , 67000 Strasbourg, France.
authors.forename: Martin
authors.initials: M
authors.lastname: Karplus
mesh_terms: D001426:Bacterial Proteins / Q000737:chemistry / Q000378:metabolism; D003198:Computer Simulation; D004058:Diffusion; D007700:Kinetics; D008956:Models, Chemical; D008958:Models, Molecular; D015233:Models, Statistical; D010455:Peptides / Q000737:chemistry / Q000378:metabolism; D011487:Protein Conformation; D012997:Solvents / Q000737:chemistry; D013289:Streptococcaceae
chemical_list: D001426:Bacterial Proteins; C034284:IgG Fc-binding protein, Streptococcus; D010455:Peptides; D012997:Solvents