On the rate-limiting dynamics of force development in muscle

Skeletal muscles produce forces relatively slowly compared with the action potentials that excite them. The dynamics of force production are governed by multiple processes, such as calcium activation, cycling of cross-bridges between myofilaments, and contraction against elastic tissues and the body. These processes have been included piecemeal in some muscle models, but not integrated to reveal which are the most rate limiting. We therefore examined their integrative contributions to force development in two conventional types of muscle models: Hill-type and cross-bridge. We found that no combination of these processes can self-consistently reproduce classic data such as twitch and tetanus. Rather, additional dynamics are needed following calcium activation and facilitating cross-bridge cycling, such as for cooperative myofilament interaction and reconfiguration. We provisionally lump such processes into a simple first-order model of 'force facilitation dynamics' that integrate into a cross-bridge-type muscle model. The proposed model self-consistently reproduces force development for a range of excitations including twitch and tetanus and electromyography-to-force curves. The model's step response reveals relatively small timing contributions of calcium activation (3%), cross-bridge cycling (3%) and contraction (27%) to overall force development of human quadriceps, with the remainder (67%) explained by force facilitation. The same set of model parameters predicts the change in force magnitude (gain) and timing (phase delay) as a function of excitatory firing rate, or as a function of cyclic contraction frequency. Although experiments are necessary to reveal the dynamics of muscle, integrative models are useful for identifying the main rate-limiting processes.