Generalised canonical–isokinetic ensemble: speeding up multiscale molecular dynamics and coupling with 3D molecular theory of solvation

Abstract

We have proposed a new canonical–isokinetic ensemble for efficient sampling of conformational space in molecular dynamics (MD) simulations which leads to the optimised isokinetic Nosé–Hoover (OIN) chain algorithm for atomic and molecular systems. We applied OIN to multiple time step (MTS) MD simulations of the rigid and flexible models of water to demonstrate its advantage over the standard canonical, isokinetic and canonical–isokinetic ensembles. With the stabilising effect of OIN thermostatting in MTS-MD, gigantic outer time steps up to picoseconds can be employed to accurately calculate equilibrium and conformational properties. Furthermore, we developed the atomic version of OIN for MTS-MD of a biomolecule in a solvent potential of mean force obtained at sequential MD steps by using the molecular theory of solvation, aka three-dimensional reference interaction site model with the Kovalenko–Hirata closure (3D-RISM-KH). The solvation forces are obtained analytically by converging the 3D-RISM-KH integral equations once per several OIN outer time steps, and are calculated in between by using solvation force-coordinate extrapolation (SFCE) in the subspace of previous successive solutions to 3D-RISM-KH. For illustration, we applied the multiscale OIN/SFCE/3D-RISM-KH algorithm to a fully flexible model of alanine dipeptide in aqueous solution. Although the computational rate of solvent sampling in OIN/SFCE/3D-RISM-KH is already 20 times faster than standard MD with explicit solvent, further substantial acceleration of sampling stems from making solute evolution steps in a statistically averaged potential of mean force obtained from 3D-RISM-KH. The latter efficiently samples the phase space for essential events with rare statistics such as exchange and localisation of solvent and ligand molecules in confined spaces, pockets and at binding sites of the solute macromolecule, as distinct from MD with explicit solvent which requires enormous computational time and number of steps in such cases.

Keywords:

• multiple time step (MTS) molecular dynamics (MD) simulation
• canonical and isokinetic ensembles thermostat algorithms
• optimised isokinetic Nosé–Hoover (OIN) chain algorithm
• 3D-RISM-KH molecular theory of solvation
• multiscale OIN/SFCE/3D-RISM-KH algorithm

Acknowledgements

We gratefully acknowledge the financial support from the ArboraNano – the Canadian Forest NanoProducts Network. I.O. thanks for the hospitality during his stay at the University of Alberta and the National Institute for Nanotechnology. The authors are grateful to Dr Tyler Luchko, Dr Nikolay Blinov and Dr Sergey Gusarov for fruitful discussions. We also thank Dr Tyler Luchko for help with the set of data for the MD simulations of alanine dipeptide [52].