Optimal control of molecular dynamics using Markov state models

• 成果类型: Article
• 署名作者: Schuette, Christof; Winkelmann, Stefanie; Hartmann, Carsten
• 署名单位: Free University of Berlin
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-012-0547-6
• 发表日期: 2012
• 页码: 259-282
• 关键词: RISK-SENSITIVE CONTROL; conformational-change; principal eigenvalue; time; metastability; TRANSITION; simulation; EQUATIONS; symmetry

摘要

A numerical scheme for solving high-dimensional stochastic control problems on an infinite time horizon that appear relevant in the context of molecular dynamics is outlined. The scheme rests on the interpretation of the corresponding Hamilton-Jacobi-Bellman equation as a nonlinear eigenvalue problem that, using a logarithmic transformation, can be recast as a linear eigenvalue problem, for which the principal eigenvalue and its eigenfunction are sought. The latter can be computed efficiently by approximating the underlying stochastic process with a coarse-grained Markov state model for the dominant metastable sets. We illustrate our method with two numerical examples, one of which involves the task of maximizing the population of alpha-helices in an ensemble of small biomolecules (alanine dipeptide), and discuss the relation to the large deviation principle of Donsker and Varadhan.