Abstract
Many interesting rare events in molecular systems, like ligand association, protein folding or conformational changes, occur on timescales that often are not accessible by direct numerical simulation. Therefore, rare event approximation approaches like interface sampling, Markov state model building, or advanced reaction coordinate-based free energy estimation have attracted huge attention recently. In this article we analyze the reliability of such approaches. How precise is an estimate of long relaxation timescales of molecular systems resulting from various forms of rare event approximation methods? Our results give a theoretical answer to this question by relating it with the transfer operator approach to molecular dynamics. By doing so we also allow for understanding deep connections between the different approaches.
Highlights
The problem of accurate estimation of long relaxation timescales associated with rare events in molecular dynamics like ligand association, protein folding, or conformational changes has attracted a lot of attention recently
How precise is an estimate of long relaxation timescales of molecular systems resulting from various forms of rare event approximation methods? Our results give a theoretical answer to this question by relating it with the transfer operator approach to molecular dynamics
We demonstrate how the new techniques for simulation of the effective dynamics can be used for efficient Markov state model (MSM) building or time-lagged independent component analysis (TiCA) applications
Summary
The problem of accurate estimation of long relaxation timescales associated with rare events in molecular dynamics like ligand association, protein folding, or conformational changes has attracted a lot of attention recently. One assumes that the effective dynamical behavior of the systems on long timescales can be described by a relatively low dimensional object given by some reaction coordinates Various advanced methods such as umbrella sampling [11,12], metadynamics [13,14], blue moon sampling [15], the adaptive biasing force method [16], or temperature-accelerated molecular dynamics (TAMD) [17], as well as trajectory-based techniques like milestoning [18], transition interface sampling [19], or forward flux sampling [20] may serve as some examples. We characterize the approximation quality for the (low-lying) eigenvalues of the infinitesimal generator This permits us to study the connection between the effective dynamics considered in [23] and Galerkin discretization schemes for the transfer operator.
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