  Searching for reaction pathways describing rare events in large systems
presents a long-standing challenge in chemistry and physics. Incorrectly
computed reaction pathways result in the degeneracy of microscopic
configurations and inability to sample hidden energy barriers. To this aim, we
present a general enhanced sampling method to find multiple diverse reaction
pathways of ligand unbinding through non-convex optimization of a loss function
describing ligand-protein interactions. The method successfully overcomes large
energy barriers using an adaptive bias potential, and constructs possible
reaction pathways along transient tunnels without the initial guesses of
intermediate or final states, requiring crystallographic information only. We
examine the method on the T4 lysozyme L99A mutant which is often used as a
model system to study ligand binding to proteins, provide a previously unknown
reaction pathway, and show that using the bias potential and the tunnel widths
it is possible to capture heterogeneity of the unbinding mechanisms between the
found transient protein tunnels.
