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

Abstract

Complex energy landscapes often arise in biological systems, e.g. for protein folding, biochemical reactions, or intracellular transport processes. Their physical effects are frequently reflected in the first-passage times (FPTs) 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 FPTs 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 NM2 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.

Keywords

• stochastic dynamics
• coarse-graining
• master equation
• molecular motors
• self-assembly