Self-guided Langevin dynamics via generalized Langevin equation

Abstract

Self-guided Langevin dynamics (SGLD) is a molecular simulation method that enhances conformational search and sampling via acceleration of the low frequency motions of the system. This acceleration is produced via introduction of a guiding force which breaks down the detailed-balance property of the dynamics, implying that some reweighting is necessary to perform equilibrium sampling. Here, we eliminate the need of reweighing and show that the NVT and NPT ensembles are sampled exactly by a new version of self-guided motion involving a generalized Langevin equation (GLE) in which the random force is modified so as to restore detailed-balance. Through the examples of alanine dipeptide and argon liquid, we show that this SGLD-GLE method has enhanced conformational sampling capabilities compared with regular Langevin dynamics (LD) while being of comparable computational complexity. In particular, SGLD-GLE is fully size extensive and can be used in arbitrarily large systems, making it an appealing alternative to LD. © 2015 Wiley Periodicals, Inc.

Keywords: canonical ensemble; conformational sampling; generalized Langevin equation; molecular simulation; self-guided Langevin dynamics.

Fig.1

An alanine dipeptide and its motions in LD and SGLD simulations. Motions are marked by colored arrays with blue, yellow, and red to represent cold, normal, and hot temperatures. T_lf and T_hf represent low frequency temperature and high frequency temperature, respectively.

Fig.2

the ϕ-φ distributions of an alanine dipeptide obtained from a 20 ns LD simulation at T=300 K, ξ=10/ps. Two popular regions, I around (−90°,−70°) and II around (−90°, 160°), are identified.

Fig.3

Average potential energies of the alanine dipeptide vs transitions between the the two ϕ–φ regions in high temperature LD, SGLD, and SGLD-GLE simulations. All the SGLD and SGLDGLE simulations were performed at T=300K with ξ=10/ps.

Fig.4

The φ angle distributions of the alanine dipeptide in the LD, SGLD, and SGLD-GLE simulations. All simulations were performed at T=300K, ξ=10/ps except the high temperature LD performed at T=350 K.

Fig.5

The potential energy distribution of the alanine dipeptide in LD at T=300K and T=350K, SGLD, and SGLD-GLE simulations at T=300K, ξ=10/ps, and λ=1.

Fig.6

The potential energy distributions of the liquid argon from LD, SGLD, and SGLD-GLE simulations. All simulations were performed at T=100 K, ξ=10/ps, except that the high temperature LD simulation that was performed at T=150 K. The guiding factor was λ=1 for both the SGLD and SGLD-GLE simulations.

Fig.7

The average potential energies and volumes of argon liquid are plot against the diffusion constants in high temperature LD, SGLD, and SGLD-GLE simulations. All simulations were performed at ξ=10/ps, T=100 K and P=1 atm except labeled otherwise. The high-temperature LD simulations are labeled with temperatures. The SGLD and SGLD-GLE simulations were labelled with the guiding factors.

Fig.8

The spectrum of the argon liquid from LD, SGLD, and SGLD-GLE simulations. All simulations were performed at T=100 K, P=1 atm, and ξ=10/ps, except that the high temperature LD was performed at T=150 K. The guiding factor was λ=1 for the SGLD and SGLD-GLE simulations.