Finding an Optimal Pathway on a Multidimensional Free-Energy Landscape

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 metadynamics-extended 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 importance-sampling scheme confers to the latter an
asymptotic convergence, while the overall algorithm inherits the advantage
of high sampling efficiency of its predecessor, meta-eABF, 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.