Enhancing conformational sampling by modifying the underlying velocity distribution: digitally filtered hybrid Monte Carlo

Abstract

The rugged energy landscape of proteins often leads conventional molecular dynamics simulations to get stuck in local minima leading to inefficient sampling and slow convergence. Two main methods exist to improve sampling. First, by smoothing the underlying energy surface thereby encouraging barrier crossing, and second, by modifying the simulation velocities. There are many examples in the literature of the former, but velocity modification is a comparatively less well exploited approach. In a method previously developed in our group called Reversible Digitally Filtered Molecular Dynamics (RDFMD), we have been able to induce conformational changes in proteins by amplifying low-frequency molecular vibrations via application of a digital filter to the velocity set [1]. However, the application of a digital filter to the molecules, disrupts the equilibrium of the system, leading to incorrect ensemble averages. To sample a statistical ensemble and still benefit from the application of the digital filter a novel method called Digitally Filtered Hybrid Monte Carlo (DFHMC) is proposed. This method builds on the work of Momentum Enhanced Hybrid Monte Carlo (MEHMC) [2]. Low frequency motions are selectively enhanced via application of a specifically designed Digital Filter (as in RDFMD), but equilibrium is maintained using a Hybrid Monte Carlo approach. In this thesis, the theory behind the DFHMC and the integration of the method into several optimised molecular dynamics packages is explained. The capability of sampling from the canonical ensemble and the enhancement in energy barrier crossing, and hence convergence, is demonstrated on a system with double well potential and with a curved transition path. As a model for the dihedral motions in proteins, the application of the DFHMC method to a single alanine dipeptide molecule in explicit and implicit water is discussed. We observed a reduction in sampling efficiency in DFHMC when the molecule has centre of mass rotation. Ideas on how to potentially overcome the rotation problem is discussed. And the Riemannian Manifold Hamiltonian Monte Carlo method [3] is introduced to investigate the application of the method to molecular systems.

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ORCID for Jonathan Essex: orcid.org/0000-0003-2639-2746

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