BPS2026 - Energy cost scales supralinearly with muscle force, and the emergence of this nonlinearity from fiber recruitment

Most muscle cross-bridge models predict that metabolic energy (ATP) consumption rate scales linearly with force (Ė∼aF 1 ) under steady-state isometric conditions. This behavior arises from the assumption that crossbridges act independently, so doubling force doubles active cross-bridges and ATP use. More complex models that account for cooperativity and calcium cycling predict a sublinear scaling, in reasonable agreement with muscle fiber experiments. The sublinearity arises because cross-bridge binding activates the thin filament, requiring less calcium-induced activation and therefore a lower cost for force. However, data from our human experiments suggest that metabolic energy rate (measured through indirect calorimetry) scales supralinearly with force (Ė∼aF 1.64 ) during an isometric force production task. In additional experiments, we found that human behavior in multiple isometric tasks involving sharing forces between legs, hands, and fingers can be explained by minimizing a cost function that depends on force with a similar exponent (1.64) suggesting that this supralinearity in force scaling with metabolic energy rate has behavioral implications. To understand our experiments, we developed a simple model of a muscle composed of 11 “regulatory units.” Each regulatory unit is a mixture of slow and fast fibers, with the composition of each varying from 100% slow to 100% fast in 10% increments. Slow fibers, with a higher duty ratio, generate more force per ATP than fast fibers. The model predicts that the optimal strategy is to initially recruit the slower, more “efficient” fibers and then recruit the faster ones. This generates an emergent supralinear scaling as we observed experimentally. This recruitment strategy seems related to Henneman's size principle, where slow motor units are recruited before faster ones. We conclude that fiber recruitment is a critical part of metabolic cost.