# A mechanokinetic actomyosin model predicts different orthophosphate sensitivities of force and ATP turnover rate during isometric muscle contraction

## TL;DR

This paper proposes a new model explaining how muscle force and ATP usage respond differently to changes in orthophosphate during contraction.

## Contribution

A mechanokinetic model is introduced that explains Pi sensitivity differences in force and ATP turnover without requiring a branched pathway.

## Key findings

- Force sensitivity to Pi is explained by two components: pre-power-stroke cross-bridges with high strain and those with low strain.
- ATPase activity is less sensitive to Pi because only low-strain cross-bridges undergo ATP turnover.
- Reducing actin affinity in pre-power-stroke states proportionally reduces force and cross-bridge numbers with increased Pi.

## Abstract

The release of the ATP hydrolysis product, orthophosphate (Pi), from the myosin active site, together with force-generating structural changes, is central to actomyosin energy transduction, but the temporal order of these events remains unclear. A range of data, interpreted using simple kinetic schemes (that do not account for varying cross-bridge strains) suggests that force generation is closely associated with the attachment of the myosin head to actin, preceding Pi-release. However, the addition of a branched pathway to the kinetic scheme is needed to account for the lower sensitivity of the isometric ATP-turnover rate to Pi compared with that of force. In contrast, a branched pathway does not appear necessary if the data are analyzed using a mechanokinetic model that incorporates the myosin strain distribution. Here, we corroborated this idea using a model in which Pi-release from the active site precedes the force-generating power-stroke. We explain the effect based on two components underlying the reduction in isometric force with increased [Pi]. The larger component arises from pre-power-stroke cross-bridges with high large elastic strain, whereas the smaller component results from cross-bridges attaching with low elastic strain. Because only the latter myosin heads undergo ATPase cycles, force exhibits greater Pi-sensitivity than ATPase activity. Changes in model parameter values that minimize the width of the cross-bridge strain distribution do not eliminate the difference in Pi-sensitivity between isometric force and ATPase. Such changes, including reduced actin affinity in a pre-power-stroke state, also lead to a proportional reduction in isometric force and in the number of attached cross-bridges with increased [Pi]. In conclusion, our data suggest that a mechanokinetic model explains the combined changes in isometric force, ATPase activity, and the number of attached cross-bridges with varied [Pi] more directly than apparently simpler kinetic schemes. A central feature of these results is the explicit demonstration of two components of isometric force with different physiological roles.