Biomolecular Sampling: Algorithms, Test Molecules, and Metrics

We compare the effectiveness of different simulation sampling techniques by illustrating their application to united atom butane, alanine dipeptide, and a small solvated protein, BPTI. We introduce an optimization of the Shadow Hybrid Monte Carlo (SHMC) algorithm, a rigorous method that removes the bias of molecular dynamics (MD). We also evaluate the ability of constant-temperature MD methods (based on Langevin and Nosé-Hoover dynamics) to achieve uniform thermal equilibrium. Our results show the the superiority of Langevin dynamics over Nosé-Hoover dynamics to achieve thermal equilibrium. They also illustrate the inherent limitation of sampling protocols that rely on sampling the microcanonical and canonical ensemble at only one temperature, and the importance of generalized ensemble approaches such as replica exchange that sample using different temperatures. Finally, we show how SHMC is able to remove bias and scale with timestep and system size. Presented, herein, are a set of sampling algorithms, test molecules, 2 and metrics. We make the sampling methods discussed available via the open source and freely distributed ProtoMol molecular simulation framework. For a system of N atoms, define configuration space as a dN dimensional vector of positions, where d is the number of degrees of freedom per atom. Similarly , phase space is defined by both configuration and momenta and is 2dN dimensional. The problem of sampling the configuration space of biomolecules such as proteins is an inherently difficult problem. The difficulties are due to the high dimensionality of phase space (6N), the ruggedness of the energy functions, the presence of multiple time scales, high energy barriers, and the introduction of systematic error (bias) by sampling methods.