Simultaneous Construction of Free Energy Surfaces via Multisite λ Dynamics and Umbrella Sampling.

Umbrella sampling (US) is a cornerstone enhanced sampling technique that constructs potentials of mean force (PMF) by biasing a system of interest along a set of collective variables (CV). With a good choice of CVs, one can uncover the free energy landscapes governing a plethora of biological processes such as protein-ligand (un)binding, protein (un)folding, and enzyme catalysis. However, multiple sets of umbrella simulations have to be run when one is interested in exploring how the free energy landscape of a particular process varies with chemical space, such as the effects of different mutations on the (un)folding landscape or how different ligands (un)bind to the same protein. We propose an enhanced sampling framework called MSλD + US that couples umbrella sampling with multisite λ dynamics (MSλD) to leverage MSλD's hallmark feature of sampling multiple chemical species in one simulation. In doing so, we recast the characterization of free energy landscapes for multiple chemical species into a simultaneous search of conformational and chemical landscapes. We validate MSλD + US's ability to construct multiple PMFs from a single set of umbrella simulations using three test systems of increasing complexity, with the most complex system involving the (un)binding PMFs of two ligands from trypsin.