Reynolds’ transport theorem justifies an assumption in Huxley’s cross-bridge equation of muscle contraction

Huxley's cross-bridge model uses the sliding filament theory to formulate the contractile mechanism and force production in skeletal muscle. In this model, the force in a muscle becomes a function of the fraction of attached cross-bridges. Specifically, muscle contraction occurs through the attachment of myosin filament based cross-bridges to specific sites on the actin filaments. In his theory, Huxley introduces the fraction of attached cross-bridges in the form of an intuitive evolution equation that gives probabilities of attachment and detachment of the cross-bridges actin without a formal proof. In this study, we use Reynolds' transport theorem of continuum mechanics and show that this important and intuitively derived passage in Huxley's paper is indeed correct.