Conformational change of a biomolecule studied by the weighted ensemble method: Use of the diffusion map method to extract reaction coordinates

Abstract

We simulate the nonequilibrium ensemble dynamics of a biomolecule using the weighted ensemble method, which was introduced in molecular dynamics simulations by Huber and Kim and further developed by Zuckerman and co-workers. As the order parameters to characterize its conformational change, we here use the coordinates derived from the diffusion map (DM) method, one of the manifold learning techniques. As a concrete example, we study the kinetic properties of a small peptide, chignolin in explicit water, and calculate the conformational change between the folded and misfolded states in a nonequilibrium way. We find that the transition time scales thus obtained are comparable to those using previously employed hydrogen-bond distances as the order parameters. Since the DM method only uses the 3D Cartesian coordinates of a peptide, this shows that the DM method can extract the important distance information of the peptide without relying on chemical intuition. The time scales are compared well with the previous results using different techniques, non-Markovian analysis and core-set milestoning for a single long trajectory. We also find that the most significant DM coordinate turns out to extract a dihedral angle of glycine, and the previously studied relaxation modes are well correlated with the most significant DM coordinates.

Analysis of molecular dynamics simulations of 10-residue peptide, chignolin, using statistical mechanics: Relaxation mode analysis and three-dimensional reference interaction site model theory

“…44). Manifold learning techniques for analyzing nonlinear data have been also applied to protein systems; for example, isomap method [45] and diffusion map method [46].…”

“…Core-set milestoning analysis has also been applied [69]. Isomap and diffusion map methods were used to cluster states for dynamical analysis methods [45,46].…”

“…44). Manifold learning techniques for analyzing nonlinear data have been also applied to protein systems; for example, isomap method [45] and diffusion map method [46].Analysis methods have also been developed depending on the increase in simulation time. In recent years, prolonged simulations can be performed; thus, dynamic analysis methods are required to identify local-minimum energy states and analyze the transitions between them.…”

“…Core-set milestoning analysis has also been applied [69]. Isomap and diffusion map methods were used to cluster states for dynamical analysis methods [45,46].RMA was developed to investigate the "dynamic" properties of spin systems [13] and homopolymer systems for Monte Carlo (MC) [14] and MD [15] simulations and has…”

Exploring Configuration Space and Path Space of Biomolecules Using Enhanced Sampling Techniques—Searching for Mechanism and Kinetics of Biomolecular Functions

“…Here the order parameters are the two hydrogen bond distances, which can discriminate the native and misfolded states. For details, see [88].…”