Parameter Optimization Method in Multidimensional Umbrella Sampling.

J Chem Theory Comput

Department of Chemistry, Osaka Metropolitan University, 3-3-138, Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan.

Published: August 2024

AI Article Synopsis

  • Umbrella sampling (US) is used to calculate free-energy landscapes (FELs), but managing sampling positions for complex multidimensional calculations is challenging.
  • The study introduces a new method that optimizes US parameters by defining a target point and adjusting sampling around it, using normal distributions for better accuracy.
  • The method was tested on three different FEL calculations, demonstrating its ability to efficiently handle multidimensional problems, which traditional US methods struggle with.

Article Abstract

Umbrella sampling (US) is an effective method for calculating free-energy landscapes (FELs). However, the complexity of controlling the sampling positions complicates multidimensional FEL calculations. In this study, we proposed a method for controlling sampling by optimizing the US parameters. This method comprises the introduction of a target point and the optimization of the parameters to sample a window around this point. We approximated each window to normal distributions using an umbrella integration method and calculated the divergences between the window distributions and the state distributed at the target position by a variationally enhanced sampling method. Thus, the minimization of the divergence facilitated sampling around the target point, after which the parameters could be optimized on the fly while performing equilibration simulation. In practice, our method employs bias potentials with off-diagonal terms, ensuring a more efficient calculation of multidimensional FEL. Additionally, we developed an algorithm for determining the target point for automated FEL search; the algorithm samples in a specified direction while controlling the overlap of distributions. We performed three different FEL calculations as examples: (1) the calculation of the permeation of a water molecule through a lipid bilayer (one-dimensional FEL), (2) the calculation of the internal structural changes in alanine dipeptide in water (two-dimensional FEL), and (3) the calculation of the internal structural changes from a β-strand structure to an α-helix structure in alanine decapeptide (Ala10, 16-dimensional FEL). These results confirmed that our method could control the number of US windows and calculate the high-dimensional FELs that could not be evaluated by the conventional US method.

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Source
http://dx.doi.org/10.1021/acs.jctc.4c00282DOI Listing

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