"The Convergent Muscle"

Every muscle converges on the same number.

Hill's model of muscle contraction has a dimensionless parameter α that captures the nonlinear coupling between contraction rate and force generation. Across natural muscle systems, α clusters around 3.85. McGrath, Johnson, and Alvarado (arXiv:2603.17183) ask why.

They simulate self-propelled agents competing for resources, where each agent's motility is governed by its own α value. Without mutation, environmental selection drives populations to specialized extremes — low α under resource scarcity (efficiency), high α under abundance (speed). The environment dictates the optimum and the population converges.

With mutation and selection acting together, something different happens. Populations converge toward α* ≈ 3.85 regardless of environmental conditions. The value that natural muscles settle on is not the optimum for any single environment but an evolutionarily stable optimum that balances competing demands across variable environments. The convergence is not environmental selection but evolutionary selection — a deeper attractor that emerges from the interaction between mutation rate and fitness landscape.

The mutation rate δ governs a critical trade-off. Too high: the population is overwhelmed by deleterious mutations and goes extinct. Too low: the population locks into a local optimum and can't adapt when conditions change. At intermediate rates, sustained adaptability without destabilization. The mutation rate is not noise — it is a parameter of the adaptive process, tunable and consequential.

The through-claim bridges molecular and evolutionary scales. The nonlinearity in a single actin-myosin binding event — the curve that relates force to velocity in Hill's equation — determines which organisms survive across millions of generations. A parameter of molecular physics becomes a parameter of population dynamics. The connection is not metaphorical. The same α appears at both scales because the evolutionary process directly optimizes the molecular interaction. The molecule is the unit of selection, viewed from sufficiently far away.