Investigating rare events by transition interface sampling

Abstract

We briefly review simulation schemes for the investigation of rare transitions and we resume the recently introduced Transition Interface Sampling, a method in which the computation of rate constants is recast into the computation of fluxes through interfaces dividing the reactant and product state.

Long‐Time Protein Folding Dynamics from Short‐Time Molecular Dynamics Simulations

“…These models, however, have yet to demonstrate that they can adequately describe the dynamics on timescales much longer than the trajectories from which the models were constructed; no attempt is made to compare the dynamics predicted by the model with long trajectories of explicitly solvated systems. Transition interface sampling [31] and "milestoning" [15] attempt to describe dynamics along a one-dimensional reaction coordinate, but these approaches are valid only if it can be shown that relaxation transverse to this coordinate happens very quickly. Some have suggested constructing stochastic models of dynamics by expansion of the dynamical operator in a smooth basis set [43,51,44], but this approach unfortunately suffers from the great difficulty of choosing rapidly convergent basis sets for large molecules.…”

Reaction Path Optimization and Sampling Methods and Their Applications for Rare Events

“…To enhance the sampling efficiency for such a complex system, the TPS with path replica exchange (Bolhuis 2008) and multi states transition TPS (Rogal & Bolhuis 2008) were developed. Based on the TPS framework, a transition interface sampling (TIS) method (Moroni et al 2004;Van Erp et al 2003;Vanerp & Bolhuis 2005) was developed to measure the positive flux through a series of hypersurfaces in phase space for the calculation of reaction rate constants. The TPS and TIS methods were applied to simulate the β-hairpin folding, (Bolhuis 2003) base-pair binding of DNA, (Hagan 2003) Trp-cage folding in explicit solvent, (Juraszek & Bolhuis 2006) and the reaction mechanism of lactate dehydrogenase.…”

Characterization of Rare Events in Molecular Dynamics

“…Figure 1), i.e., the computational effort of generating an entire ensemble of long reactive trajectories can be prohibitive; (2) convergence of the MC scheme in the infinite dimensional path space can be very poor; and (3) the limitation to a pre-defined trajectory length T can lead to biased statistics of the TPS ensemble. Advanced TPS schemes try to remedy these drawbacks by combining the original TPS idea with interface methods [9]. Even though TPS can be used no matter whether the underlying dynamics is deterministic or stochastic, the algorithm is usually used in connection with deterministic Hamiltonian dynamics [3].…”

“…There is a list of rather general techniques, with Forward Flux Sampling (FFS) [8], Transition Interface Sampling (TIS) [9] and Milestoning [10] as examples, that approximate transition rates by exploring how the transition progresses from one to the next interface that separates A from B.…”

“…Most notable among these techniques are (1) Transition Path Sampling (TPS) [3]; (2) the so-called String Methods [4], or optimal path approaches [5][6][7] and variants thereof; (3) techniques that follow the progress of the transition through interfaces, like Forward-Flux Simulation (FFS) [8], Transition Interface Sampling (TIS) [9] or the Milestoning techniques [10,11]; and (4) methods that drive the molecular system by external forces with the aim of making the required transition more frequent while still allowing one to compute the exact rare event statistics for the unforced system, e.g., based on Jarzynski's and Crook's identity [12,13]. All of these methods consider the problem in continuous state space, i.e., through reactive trajectories or transition channels in the original state space of the molecular system.…”