title: Efficient Determination of Free Energy Landscapes in Multiple Dimensions from Biased Umbrella Sampling Simulations Using Linear Regression.
abstract: The weighted histogram analysis method (WHAM) is a standard protocol for postprocessing the information from biased umbrella sampling simulations to construct the potential of mean force with respect to a set of order parameters. By virtue of the WHAM equations, the unbiased density of state is determined by satisfying a self-consistent condition through an iterative procedure. While the method works very effectively when the number of order parameters is small, its computational cost grows rapidly in higher dimension. Here, we present a simple and efficient alternative strategy, which avoids solving the self-consistent WHAM equations iteratively. An efficient multivariate linear regression framework is utilized to link the biased probability densities of individual umbrella windows and yield an unbiased global free energy landscape in the space of order parameters. It is demonstrated with practical examples that free energy landscapes that are comparable in accuracy to WHAM can be generated at a small fraction of the cost.
authors.affiliation: Department of Biochemistry and Molecular Biology, The University of Chicago , 929 East 57th Street, Chicago, Illinois 60637, United States.
authors.forename: Yilin
authors.initials: Y
authors.lastname: Meng
authors.affiliation: Department of Biochemistry and Molecular Biology, The University of Chicago , 929 East 57th Street, Chicago, Illinois 60637, United States.
authors.forename: Benoît
authors.initials: B
authors.lastname: Roux
mesh_terms: D004745:Enkephalins / Q000737:chemistry / Q000378:metabolism; D016014:Linear Models; D056004:Molecular Dynamics Simulation; D017510:Protein Folding; D013816:Thermodynamics
chemical_list: D004745:Enkephalins