Reconstructing Potentials of Mean Force through Time Series Analysis of Steered Molecular Dynamics Simulations

Atomic force microscopy (AFM) experiments and steered molecular dynamics (SMD) simulations have revealed much about the dynamics of protein-ligand binding and unbinding, as well as the stretching and unfolding of proteins. Both techniques induce ligand unbinding or protein unfolding by applying external mechanical forces to the ligand or stretched protein. However, comparing results from these two techniques, such as the magnitude of forces required to unbind ligands, has remained a challenge since SMD simulations proceed six to nine orders of magnitude faster due to limitations in computational resources. Results of simulations and experiments can be compared through a potential of mean force (PMF). We describe and implement three time series analysis techniques for reconstructing the PMF from position and applied force data gathered from SMD trajectories. One technique, based on the WHAM theory, views the unbinding or stretching as a quasi-equilibrium process; the other two techniques, one based on van Kampen's Ω-expansion, the second on a least squares minimization of the Onsager-Machlup action with respect to the choice of PMF, assume a Langevin description of the dynamics in order to account for the nonequilibrium character of SMD data. The latter two methods are applied to SMD data taken from a simulation of the extraction of a lipid from a phospholipid membrane monolayer.