Abstract
Muscle force and power are developed by myosin cross-bridges, which cyclically attach to actin, undergo a force-generating transition and detach under turnover of ATP. The force-generating transition is intimately associated with release of inorganic phosphate (Pi) but the exact sequence of events in relation to the actual Pi release step is controversial. Details of this process are reflected in the relationships between [Pi] and the developed force and shortening velocity. In order to account for these relationships, models have proposed branched kinetic pathways or loose coupling between biochemical and force-generating transitions. A key hypothesis underlying the present study is that such complexities are not required to explain changes in the force–velocity relationship and ATP turnover rate with altered [Pi]. We therefore set out to test if models without branched kinetic paths and Pi-release occurring before the main force-generating transition can account for effects of varied [Pi] (0.1–25 mM). The models tested, one assuming either linear or non-linear cross-bridge elasticity, account well for critical aspects of muscle contraction at 0.5 mM Pi but their capacity to account for the maximum power output vary. We find that the models, within experimental uncertainties, account for the relationship between [Pi] and isometric force as well as between [Pi] and the velocity of shortening at low loads. However, in apparent contradiction with available experimental findings, the tested models produce an anomalous force–velocity relationship at elevated [Pi] and high loads with more than one possible velocity for a given load. Nevertheless, considering experimental uncertainties and effects of sarcomere non-uniformities, these discrepancies are insufficient to refute the tested models in favour of more complex alternatives.
Highlights
The contractile machinery of striated muscle, i.e. skeletal muscle and heart, is arranged in ~ 2 μm long repetitive units, sarcomeres that are serially connected along ~ 1 μm wide myofibrils running the length of the muscle
Mechanics and coarse-grain structure based on independent experimental data, probabilities of different cross-bridge states under steady-state conditions are calculated by solving a system of ordinary differential equations in the state probabilities (Hill 1974; Huxley 1957)
The predicted velocity is somewhat low at intermediate loads compared to experimental data
Summary
The contractile machinery of striated muscle, i.e. skeletal muscle and heart, is arranged in ~ 2 μm long repetitive units, sarcomeres that are serially connected along ~ 1 μm wide myofibrils running the length of the muscle. Combined information from solution biochemistry and single molecule mechanics, e.g. from optical tweezers based experiments, is sufficient to fully define the models including strain-dependence (Eisenberg et al 1980; Hill 1974; Månsson et al 2018), with minor exceptions regarding very fast strain-dependent rates The latter are obtained from independent experimental data (Månsson 2016). They often rely on the theoretical formalism of Hill (1974) but have become increasingly complex with time to account for a wider range of more detailed experimental findings To this end, recent models have incorporated states and transitions with far from universal support in independent studies such as solution biochemistry and single molecule mechanics. This includes branched pathways or loose chemo-mechanical coupling (Caremani et al 2013; Debold et al 2013) slippage between sites (Caremani et al 2013), cooperative phenomena
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