Use of the Metropolis algorithm to simulate the dynamics of protein chains

Abstract

The Metropolis implementation of the Monte Carlo algorithm has been developed to study the equilibrium thermodynamics of many-body systems. Choosing small trial moves, the trajectories obtained applying this algorithm agree with those obtained by Langevin's dynamics. Applying this procedure to a simplified protein model, it is possible to show that setting a threshold of 1 degree on the movement of the dihedrals of the protein backbone in a single Monte Carlo step, the mean quantities associated with the off-equilibrium dynamics (e.g., energy, RMSD, etc.) are well reproduced, while the good description of higher moments requires smaller moves. An important result is that the time duration of a Monte Carlo step depends linearly on the temperature, something which should be accounted for when doing simulations at different temperatures.