Finding an optimal pathway on a multidimensional free-energy landscape

Abstract

An ad-hoc, yet widely adopted approach to investigate complex molecular objects in motion using importance-sampling schemes involves two steps, namely (i) mapping the multidimensional free-energy landscape that characterizes the movements in the molecular object at hand and (ii) finding the most probable transition path connecting basins of the free-energy hyperplane. To achieve this goal, we turn to an importance-sampling algorithm, coined well-tempered metadynamicsextended adaptive biasing force (WTM-eABF), aimed at mapping rugged free-energy landscapes, combined with a path-searching algorithm, which we call multidimensional lowest energy (MULE), to identify the underlying minimum free-energy pathway in the collective-variable space of interest. First, the well-tempered feature of the importancesampling scheme confers to the latter an asymptotic convergence, while the overall algorithm inherits the advantage of high sampling efficiency of its predecessor, metaeABF, making its performance less sensitive to user-defined parameters. Second, the Dijkstra algorithm implemented in MULE is able to identify with utmost efficiency a pathway that satisfies minimum free energy of activation among all the possible routes in the multidimensional free-energy landscape. Numerical simulations of three molecular assemblies indicate that association of WTM-eABF and MULE constitutes a reliable, efficient and robust approach for exploring coupled movements in complex molecular objects. On account of its ease of use and intrinsic performance, we expect WTM-eABF and MULE to become a tool of choice for both experts and nonexperts interested in the thermodynamics and the kinetics of processes relevant to chemistry and biology.