Actomyosin — the molecular motor system that drives muscle contraction — has a characteristic force-velocity relationship parametrized by a dimensionless number α. This number describes how contraction speed falls off with load: high α means the motor maintains speed under load; low α means it stalls quickly. Across species, from mollusks to mammals, the measured value clusters around α ≈ 3.85.
McGrath, Johnson, and Alvarado (arXiv:2603.17183) explain why. They simulate populations of competing agents whose actomyosin parameters are subject to mutation and selection. The agents compete for resources; those with better-matched motors reproduce more. Over evolutionary timescales, the population converges to α* ≈ 3.85 ± 2.32 — the value observed in nature.
The convergence is robust. Without mutations, populations select specialized α values that depend on environmental conditions — different resources favor different motor characteristics. But with mutations at intermediate rates, the population converges to α* regardless of the initial conditions or resource distribution. The mutations explore the parameter space; selection drives convergence; the equilibrium is set by the molecular-scale nonlinearity of the actomyosin binding dynamics.
The mutation rate itself has an optimal range. Too high, and the population cannot stabilize — each generation's adaptation is overwhelmed by the next generation's random variation. Too low, and the population cannot explore — it gets stuck at a locally optimal α that may not be globally optimal. Intermediate mutation rates enable long-term adaptability while maintaining robustness against short-term noise.
A dimensionless number at the molecular scale, fixed by evolutionary dynamics at the population scale. The binding kinetics of a single myosin head — a protein 10 nanometers long — propagates through seven orders of magnitude of biological organization to determine a macroscopic constant that characterizes muscle across the animal kingdom.