Reversible multiple time scale molecular dynamics

Abstract

The Trotter factorization of the Liouville propagator is used to generate new reversible molecular dynamics integrators. This strategy is applied to derive reversible reference system propagator algorithms (RESPA) that greatly accelerate simulations of systems with a separation of time scales or with long range forces. The new algorithms have all of the advantages of previous RESPA integrators but are reversible, and more stable than those methods. These methods are applied to a set of paradigmatic systems and are shown to be superior to earlier methods. It is shown how the new RESPA methods are related to predictorcorrector integrators. Finally, we show how these methods can be used to accelerate the integration of the equations of motion of systems with Nose thermostats.

ORAC: A molecular dynamics simulation program to explore free energy surfaces in biomolecular systems at the atomistic level

“…As thermodynamics is concerned, scaling the potential energy of a canonical system is equivalent to an inverse temperature scaling, since exp(−βcV (X)) = exp(−β V (X)), where T = T /c. From the point of view of a molecular dynamics simulation, the advantage of using the Hamiltonian REM approach is two-fold: (i) as all the replica have the same operating temperature, one does not have, like in temperature REM, to reinitialize the velocities after one successful configuration exchange and (ii) since the mean atomic velocities are the same throughout the extended system, one does not have to adapt the time step size for preserving the quality of r-RESPA integrator, 6 as it should be done in temperature REM. Moreover, Hamiltonian REM can also be applied to a specific part of the potential, weakening only the interactions that slow down the sampling along an interesting reaction coordinate.…”

“…In particular the numerical integration of the equations of motion was efficiently carried on with multiple time step schemes by taking advantage of the disparate time scale dynamics of complex molecular systems. 6 Versions of these effective integrators were devised 4 for simulating the system via the extended Lagrangian method 1 under a variety of thermodynamic conditions. Electrostatic interactions, notoriously a major stumbling computational block in the simulation of polar systems in periodic boundary conditions, were treated using the smooth particle mesh Ewald technique, [7][8][9] an algorithm delivering astonishing performances 3 both in accuracy and efficiency.…”

Molecular Dynamics with the United-Residue Model of Polypeptide Chains. I. Lagrange Equations of Motion and Tests of Numerical Stability in the Microcanonical Mode

“…The time-split algorithms are derived by splitting the Liouville propagator of the time evolution of the system under study. [65][66][67][68][69] In this study, in part of our calculations (section 3) we adapted the reversible reference system propagator algorithm (RESPA). 65 In the RESPA algorithm, each integration step consists of the following operations:…”

Enhanced sampling simulations to construct free-energy landscape of protein–partner substrate interaction

“…Under low-viscosity conditions, the biomolecule moves smoothly. Another method for a larger time-step is the reversible multiple time-scale algorithm (RESPA) (Tuckerman et al 1992), which enables a larger time-step of about 4 fs for the long-distant interaction terms because the long-distant interactions vary slowly. Combining such longer time-step methods with the enhanced sampling method may realize less computational cost to obtain the conformational ensemble.…”