Theoretical treatment of striated muscle: Dynamic extension of four-state model.

We constructed a muscle model, based on the model first proposed by Gray and Gonda [6,7), that simulates the twitch contraction of striated muscle. Their original model postulated four basic states in the contraction cycle and predicted the properties of steady state contraction in striated muscle. Using the relationship between steady state tension and calcium concentration, we described several rate constants as functions of calcium concentration and calculated the number of attached crossbridges at various calcium concentration values. The results for both skeletal and cardiac muscle were approximately consistent with those of X-ray studies. Assuming that rate constants change immediately with the phasic alteration of intracellular calcium concentration, we estimated the time course of crossbridge distribution during twitch contraction; these findings were also consistent with those of X-ray studies. We also simulated the effects of calcium concentration and sarcomere length on the magnitude of twitch tension. These simulations suggest that the major determinants of crossbridge distribution during twitch contraction are the time courses of calcium transients and the rate constants of crossbridge kinetics. Our findings suggest that the model used in this study provides a theoretical basis for interpreting the characteristics of cardiac muscle encountered in the clinical setting.