Self-healing Umbrella Sampling:  A Non-equilibrium Approach for Quantitative Free Energy Calculations

Abstract

We propose a new approach for the umbrella sampling method in molecular dynamics simulations of complex systems. An accelerated sampling of the slow degrees of freedom is achieved by generating a single self-adaptive trajectory that tends to span uniformly the reaction coordinate using a time dependent bias potential derived from the preceding history of the system. To show the convergent behavior and the efficiency of the method, we present the free energy surface of alanine dipeptide in water as a function of the backbone dihedral angles.

PLUMED: A portable plugin for free-energy calculations with molecular dynamics

“…Various improvements have been introduced so as to refine the bias potential on the fly (see, among others, Refs. [5,6,25,26]). We focus here on metadynamics, in its standard form [6,27] or in the recently introduced well-tempered flavor [28].…”

“…This manner of biasing the evolution by discouraging the visited configurations was first introduced in the taboo search [30] and, in the context of MD, by the local elevation method [31]. The approach is also closely related to the Wang and Landau algorithm [25], adaptive force bias [5] and self-healing umbrella sampling [26]. In metadynamics, the bias at time t is written as an integral on the past trajectory r(t):…”

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“…This iterative approach to the problem 28,29 led to the development of adaptive biasing potential methods that improve the potential "on the fly", 16,17,19,30 i.e., while the simulation is performed. All these methods share the common basic idea, namely, "to introduce the concept of memory" 30 during a simulation by changing the potential of mean force perceived by the system, in order to penalize conformations that have been already sampled before.…”

“…36 This problem corresponds to finding an optimal protocol for the evolution of the modification factor in the original Wang-Landau algorithm. Various solutions have been proposed 19,[37][38][39] in which the energy h in eq. (19) is time-dependent.…”

“…Quasi-equilibrium techniques [16][17][18][19] build such biasing potential by periodically adding a small perturbation to the system Hamiltonian so as to progressively flatten the free energy surface along selected reaction coordinates. For example, in the so-called "metadynamics" simulation method, 16 a history-dependent potential, made of Gaussian functions deposed continuously at the instantaneous values of the given reaction coordinates, is imposed to the system.…”