A re-interpretation of the rate of tension redevelopment (k TR) in active muscle

A slackening to zero tension by large length release (similar to 20 %) and a restretch of active muscle fibres cause a fall and a redevelopment in tension. According to the model of Brenner (Proc Natl Acad Sci USA 85(9):3265-3269, 1988), the rate constant of tension redevelopment (k (TR)) is the sum of attachment and detachment rate constants, hence is limited by the fast reaction. Here we propose a model in which, after restretch, cross-bridges cycle many times by stretching series elastic elements, hence k (TR) is limited by a slow reaction. To set up this model, we made an assumption that the stepping rate (v) decreases linearly with tension (F), which is consistent with the Fenn effect. The distance traveled by a cross-bridge stretches series elastic elements with stiffness sigma. With these assumptions, we set up a first order differential equation, which results in an exponential time course with the rate constant k (TR) = sigma eta (0) nu (0)(1 - lambda)/F (1), where lambda = nu (1)/nu (0), eta = step size, the subscript 0 indicates unloaded condition, and the subscript 1 indicate isometric condition. We demonstrate that the ATP hydrolysis rate (=[myosin head]/nu (0)) is proportionate to k (TR) as the ambient temperature is changed, and that the published data fit to this relationship well if lambda = 0.28. We conclude that k (TR) is limited by the cross-bridge turnover rate; hence it represents the rate constant of the slowest reaction of the cross-bridge cycle, i.e. the ADP isomerization step before ADP is released.