  Complex energy landscapes often arise in biological systems, e.g. for protein
folding, biochemical reactions or intracellular transport processes. Their
physical effects are often reflected in the first-passage times arising from
these energy landscapes. However, their calculation is notoriously challenging
and it is often difficult to identify the most relevant features of a given
energy landscape. Here we show how this can be achieved by coarse-graining the
Fokker-Planck equation to a master equation and decomposing its first-passage
times in an iterative process. We apply this method to the electrostatic
interaction between two rods of nonmuscle myosin II (NM2), which is the main
molecular motor for force generation in nonmuscle cells. Energy landscapes are
computed directly from the amino acid sequences of the three different
isoforms. Our approach allows us to identify the most relevant energy barriers
for their self-assembly into nonmuscle myosin II minifilaments and how they
change under force. In particular, we find that antiparallel configurations are
more stable than parallel ones, but also show more changes under mechanical
loading. Our work demonstrates the rich dynamics that can be expected for
NM2-assemblies under mechanical load and in general shows how one can identify
the most relevant energy barriers in complex energy landscapes.
