Find slow dynamic modes via analyzing molecular dynamics simulation trajectories

doi:10.1088/1674-1056/abad24

Abstract

It is a central issue to find the slow dynamic modes of biological macromolecules via analyzing the large-scale data of molecular dynamics simulation (MD). While the MD data are high-dimensional time-successive series involving all-atomic details and sub-picosecond time resolution, a few collective variables which characterizing the motions in longer than nanoseconds are needed to be chosen for an intuitive understanding of the dynamics of the system. The trajectory map (TM) was presented in our previous works to provide an efficient method to find the low-dimensional slow dynamic collective-motion modes from high-dimensional time series. In this paper, we present a more straight understanding about the principle of TM via the slow-mode linear space of the conformational probability distribution functions of MD trajectories and more clearly discuss the relation between the TM and the current other similar methods in finding slow modes.

Keywords: molecular dynamics simulation slow modes trajectory map

Received: 18 June 2020
Revised: 27 July 2020
Accepted manuscript online: 07 August 2020

PACS:	87.15.A-	(Theory, modeling, and computer simulation)
	02.70.Ns	(Molecular dynamics and particle methods)
	82.20.Wt	(Computational modeling; simulation)

Corresponding Authors: ^†Corresponding author. E-mail: xzhou@ucas.ac.cn

About author:

†Corresponding author. E-mail: xzhou@ucas.ac.cn

* Project supported by the National Natural Science Foundation of China (Grant No. 11904086).

Cite this article:

Chuanbiao Zhang(张传彪) and Xin Zhou(周昕)† Find slow dynamic modes via analyzing molecular dynamics simulation trajectories 2020 Chin. Phys. B 29 108706

Fig. 1.

(a) Time evolution of the RMSD of the Trp-cage to its native structure, the slow variables B₁ and B₂ obtained in the TM. Red line is time-window-smoothed one (Δ t = 200 ns). (b) Eigenvalue of the variance–covariance matrix of the trajectory-mapped points. The inset is the contribution of each basis function to the slow variables B₁ and B₂. (c) The free-energy landscape (in units of k_BT) in the slow-variable space (B₁, B₂).

Fig. 2.

Time-ordered similarity matrix of the MD trajectory. The similarity between two samples C(t₂, t₁) = B(t₂) ⋅ B(t₁). (b) The time-rearranged similarity matrix, suggesting three metastable states. (c) Kinetic transition network. Numbers near the arrows are the corresponding transition rates. The population of each state in the 208-μs MD trajectory is listed in bracket (which approaches to the equilibrium one, in consistent with the fact the folding and unfolding transitions occur more than ten times during the MD simulation). Residue TRP6 and PRO17 are shown in blue, GLY11 in red.

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Find slow dynamic modes via analyzing molecular dynamics simulation trajectories

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