Free Energy Landscape of Biomolecules from Multiple Non-Equilibrium Molecular Simulations

Abstract

Computer simulations of biomolecules, e.g. molecular dynamics (MD), have gained widespread popularity in analyzing their behavior. One of the useful applications to reveal functional mechanisms of biomolecules is free energy calculation. Most of the current free energy calculation methods, however, rely heavily on the assumption that each trajectory approximates a quasi equilibrium ensemble of a target molecule. Since its violation may cause artifacts, practical use of short independent parallel simulations performed on massive parallel computer is still limited in the case of the system with slow equilibration time such as biomolecules. Hence it is highly demanded to develop the methods without this assumptions.We propose “Multiple Markov transition Matrix Method”, an algorithm by which a stationary probability distribution is estimated from non-equilibrium multiple MD trajectories independently generated with distinct Hamiltonians. Based on the Markovity assumption, we reconstructed a Markov transition matrix from the trajectories. Combining umbrella sampling technique and maximum likelihood estimation, we developed an optimization procedure to calculate the potential of mean force (PMF). The details will be described in the presentation.Figure 1:Free energy landscape of Met-enkephalin calculated from non-equilibrium simulations using this method.View Large Image | View Hi-Res Image | Download PowerPoint Slide