A phenomenological theory of muscular contraction. I. Rate equations at a given length based on irreversible thermodynamics.

A phenomenological theory for contracting muscle based on irreversible thermodynamics and the sliding filament theory is developed. The individual cross bridges, considered as subunits, are viewed as linear energy converters with constant transport coefficients. With this view of the subunits, phenomenological equations applicable to the whole muscle are obtained. The transport coefficients are shown to be a function of a single parameter which is the number of activated cross bridges at any instant. By requiring Hill's force-velocity relation (1) to be satisfied, the response of the muscle is related to the number of activated cross bridges. The resulting theory differs significantly from the theory developed by Caplan (2) and a comparison of the theories is presented. The theory is shown to correlate well with the heat data of Woledge (3) for a tortoise muscle and gives a value of Y (ratio of chemical affinity to enthalpy of reaction) equal to 0.945. The comparison of the theory with Hill's frog muscle data (1) and (4) is also encouraging. In part II of this series, length variations are considered and the resulting theoretical predictions are shown to be consistent with experimental data.