The Location and Rate of the Phosphate Release Step in the Muscle Cross-Bridge Cycle

Abstract

It is controversial whether the phosphate (Pi) release step in the cross-bridge cycle occurs before or after the first tension-generating step and whether it is fast or slow. We have therefore modified our previous model of the frog cross-bridge cycle by including a Pi release step either before (model A) or after (model B) the first tension-generating step and refined the two models by downhill simplex runs against experimental data for the force-velocity relation and the tension transients after length steps. Pi release step was initially made slow (70 s À1 ), but after refinement, it became fast ($500 s À1 for model A and $6000 s À1 for model B). The two models gave similar fits to the experimental tension transients after length steps, but model A gave a better fit to the lengthening limb of the force-velocity relation than model B.

Recent insights into the relative timing of myosin's powerstroke and release of phosphate

“…An important caveat with this and similar models is that some of the fit parameters may be inconsistent with experimental observations. For example, in this report (Offer & Ranatunga, 2020) the rate of P i ‐release changed dramatically during refinement of the model, increasing from a rate of 70/s, a value taken from measurements in solution (White et al, 1997), to 500/s for the P i ‐release‐first model and over 6,000/s for the powerstroke‐first model. These values are two to three orders of magnitude higher than the measured values for myosin II in solution (White et al, 1997).…”

“…However, this interpretation of these data is not universally accepted (Månsson, Rassier, & Tsiavaliaris, 2015; Månsson, 2019; Offer & Ranatunga, 2020; D. A. Smith, 2014), and indeed, has been challenged recently by efforts to model these and related findings from muscle fibers, using kinetic models that treat P i ‐release and the powerstroke as distinct and separate events (Månsson, 2019; Offer & Ranatunga, 2020; D. A. Smith, 2014). The most direct test of the two hypotheses evaluated two models in which P i ‐release was made to occur either before or after the powerstroke (Offer & Ranatunga, 2020). Both models seemed to reproduce the effects on the shortening region of the force velocity‐relationship, but a P i ‐release‐first model seemed to reproduce the effects of P i on isometric force and tension transients in response to lengthening better than a powerstroke‐first model.…”

“…However, this interpretation of these data is not universally accepted (Månsson, Rassier, & Tsiavaliaris, 2015;Månsson, 2019;Offer & Ranatunga, 2020;D. A. Smith, 2014), and indeed, has been challenged recently by efforts to model these and related findings from muscle fibers, using kinetic models that treat P i -release and the powerstroke as distinct and separate events (Månsson, 2019;Offer & Ranatunga, 2020;D. A. Smith, 2014).…”

“…A. Smith, 2014). The most direct test of the two hypotheses evaluated two models in which P i -release was made to occur either before or after the powerstroke (Offer & Ranatunga, 2020). Both models seemed to reproduce the effects on the shortening region of the force velocity-relationship, but a P i -release-first model seemed to reproduce the effects of P i on isometric force and tension transients in response to lengthening better than a powerstroke-first model.…”

Sensitivity of muscle force response of a two-state cross-bridge model to variations in model parameters

“…2,3 Nonlinear and dynamic characteristics of muscle forces produced during isometric, concentric, and eccentric contractions can be represented to a certain degree using cross-bridge models. 4,5 The mathematical representation of the structural and biochemical events of contraction involves a system of differential equations. Huxley-type models have become more sophisticated since the first description in the 1957 model, involving an ever-growing number of mechanical and chemical states.…”