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Complex energy landscapes often arise in biological systems, e.g. for proteinfolding, biochemical reactions or intracellular transport processes. Theirphysical effects are often reflected in the first-passage times arising fromthese energy landscapes. However, their calculation is notoriously challengingand it is often difficult to identify the most relevant features of a givenenergy landscape. Here we show how this can be achieved by coarse-graining theFokker-Planck equation to a master equation and decomposing its first-passagetimes in an iterative process. We apply this method to the electrostaticinteraction between two rods of nonmuscle myosin II (NM2), which is the mainmolecular motor for force generation in nonmuscle cells. Energy landscapes arecomputed directly from the amino acid sequences of the three differentisoforms. Our approach allows us to identify the most relevant energy barriersfor their self-assembly into nonmuscle myosin II minifilaments and how theychange under force. In particular, we find that antiparallel configurations aremore stable than parallel ones, but also show more changes under mechanicalloading. Our work demonstrates the rich dynamics that can be expected forNM2-assemblies under mechanical load and in general shows how one can identifythe most relevant energy barriers in complex energy landscapes.

First-passage times in complex energy landscapes: a case study with nonmuscle myosin II assembly