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Title: Using the method of weighted residuals to compute potentials of mean force

Abstract

We propose a general framework for approximating the potential of mean force (PMF) along a reaction coordinate in conformational space. This framework, based on the method of weighted residuals, can be viewed as a generalization of thermodynamic integration and direct histogram methods. Using weighted residuals allows for higher-order approximations to the PMF in the form of a global spectral method or a finite element method. In addition, the higher degree of continuity provided by spectral and higher-order elements makes weighted residual methods an attractive choice for use in tandem with biasing force methods. As an analysis tool, the weighted residuals framework provides a context for direct comparison of thermodynamic integration and histogram based methods. For validation of the new method, numerical experiments are performed on two systems: a simple double-well and alanine dipeptide in vacuum. Comparisons between the new weighted residual methods, thermodynamic integration, and WHAM are performed. When configuration space is perfectly sampled the high-order weighted residual methods are found to exhibit exponential convergence. For more realistic sampling, the weighted residual methods performed comparably to the other two. However, results suggest that spectral type methods are more robust with respect to parameter choices describing the solution space.

Authors:
 [1];  [1]
  1. University of Illinois at Urbana-Champaign, Department of Computer Science, Urbana, IL 61801 (United States)
Publication Date:
OSTI Identifier:
20991600
Resource Type:
Journal Article
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 225; Journal Issue: 1; Other Information: DOI: 10.1016/j.jcp.2006.12.015; PII: S0021-9991(06)00619-X; Copyright (c) 2007 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-9991
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALANINES; APPROXIMATIONS; CONVERGENCE; COORDINATES; FINITE ELEMENT METHOD; FREE ENERGY; MATHEMATICAL SPACE; POTENTIALS

Citation Formats

Cyr, Eric C, and Bond, Stephen D. Using the method of weighted residuals to compute potentials of mean force. United States: N. p., 2007. Web. doi:10.1016/j.jcp.2006.12.015.
Cyr, Eric C, & Bond, Stephen D. Using the method of weighted residuals to compute potentials of mean force. United States. https://doi.org/10.1016/j.jcp.2006.12.015
Cyr, Eric C, and Bond, Stephen D. 2007. "Using the method of weighted residuals to compute potentials of mean force". United States. https://doi.org/10.1016/j.jcp.2006.12.015.
@article{osti_20991600,
title = {Using the method of weighted residuals to compute potentials of mean force},
author = {Cyr, Eric C and Bond, Stephen D},
abstractNote = {We propose a general framework for approximating the potential of mean force (PMF) along a reaction coordinate in conformational space. This framework, based on the method of weighted residuals, can be viewed as a generalization of thermodynamic integration and direct histogram methods. Using weighted residuals allows for higher-order approximations to the PMF in the form of a global spectral method or a finite element method. In addition, the higher degree of continuity provided by spectral and higher-order elements makes weighted residual methods an attractive choice for use in tandem with biasing force methods. As an analysis tool, the weighted residuals framework provides a context for direct comparison of thermodynamic integration and histogram based methods. For validation of the new method, numerical experiments are performed on two systems: a simple double-well and alanine dipeptide in vacuum. Comparisons between the new weighted residual methods, thermodynamic integration, and WHAM are performed. When configuration space is perfectly sampled the high-order weighted residual methods are found to exhibit exponential convergence. For more realistic sampling, the weighted residual methods performed comparably to the other two. However, results suggest that spectral type methods are more robust with respect to parameter choices describing the solution space.},
doi = {10.1016/j.jcp.2006.12.015},
url = {https://www.osti.gov/biblio/20991600}, journal = {Journal of Computational Physics},
issn = {0021-9991},
number = 1,
volume = 225,
place = {United States},
year = {Sun Jul 01 00:00:00 EDT 2007},
month = {Sun Jul 01 00:00:00 EDT 2007}
}