The Variation of Isometric Energy Rates With Muscle Length: A Distribution-Moment Model Analysis

The Distribution-Moment Model of skeletal muscle, which has been enhanced recently to make possible the calculation of chemical energy release (E˙) and heat production (H˙) rates [1], is applied to isometric muscle. Under steady-state isometric conditions the model predicts a simple relation between the energy rates and the muscle length, namely , where Λ is the ratio of muscle length to the “optimal” length at which maximal isometric tension is produced, and α(Λ) is a function numerically equal to the ratio of the tetanic isometric force to its maximum value. The single dimensionless constant in this relation, B, can be calculated from model parameters characterizing muscle dynamics at the optimum length, and has a value near unity for frog sartorius at 0°C. The predicted behavior is shown to agree reasonably well with experimental measurements of heat production and phosphocreatine (PCr) hydrolysis. The model relates the isometric energy rates to PCr hydrolysis in (1) cross-bridge interactions, and (2) calcium pumping into the sarcoplasmic reticulum.