Molecular-scale, nonlinear actomyosin binding dynamics drive population-scale adaptation and evolutionary convergence

Biological actuators -- from myosin motors to muscles -- follow Hill's model where a dimensionless parameter $α$ captures the nonlinear coupling between contraction rate and force generation. Our prior work identified a characteristic $α^* = 3.85 \pm 2.32$ across natural muscles and showed that $α^*$ optimizes a power-efficiency tradeoff, potentially explaining its prevalence in nature. However, those results reflected short-term actuation tasks whereas phenotypic distributions in $α$ emerge over evolutionary timescales. Here, we use numerical simulations of self-propelled agents to explore how nonlinear actomyosin actuation (parameterized by $α$) shapes population dynamics. Agents of different $α$ compete for resources and reproduce with slight mutations. Without mutations, resource availability drives populations in $α$ toward distinct behaviors: under abundance or scarcity, specialized $α$ survive. However, with mutations and selection, populations evolve toward distributions centered around the characteristic $α^*$ observed in nature. Further, we show that the mutation rate $δ$ governs a balance between adaptability and robustness: large $δ$ generates instability and extinction, small $δ$ prevents feedback, while intermediate $δ$ enables long-term adaptability while remaining robust to short-term noise. Our results suggest that nonlinear actuation provides a general understanding of energy management in actomyosin systems across a wide range of timescales, ranging from the task-specific to evolutionary. These insights may guide the rational design of active materials with adaptive properties.