The effects of inorganic phosphate on muscle force development and energetics: challenges in modelling related to experimental uncertainties

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 forcegenerating 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 nonuniformities, these discrepancies are insufficient to refute the tested models in favour of more complex alternatives.

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

“…From the findings listed above, although not statistically analyzed and established beyond doubt (as mentioned below in Conclusions), model A seems to fit in better with the experimental observations on the Pi effects on muscle force. This leads us to conclude, in agreement with Smith (35) and Ma ˚nsson (44), that the Pi release step occurs before, not after, the first tensing step. So, Pi can be thought of as triggering, i.e., gating, the first tensing step.…”

“…On the basis of the model fittings to Pi effects on force in experimental data, it does seem that the Pi release step precedes the first force-generation step rather than following it. This is similar to the conclusion reached by Smith (35) and Ma ˚nsson (44) from analyses of experimental data and modeling. 3) Considering the published experimental data of Woody et al (52) on single cardiac myosin molecules showing Pi release in the cross-bridge cycle is after force generation, further work is necessary to elucidate whether Pi release may be different in myosin types (muscle types, species, etc.).…”

“…His model gave a good account of the effect of Pi on tension and stiffness and of the phase II tension response after a Pi jump. This basic idea that Pi release occurred before the first force-generating step in the cross-bridge cycle has received support from a number of later experimental and modeling studies (36,43,44).…”

Phosphate binding induced force-reversal occurs via slow backward cycling of cross-bridges

“…Contrary to the fourth assumption, some studies suggest branched kinetic pathways (75)(76)(77), multiple structural pathways of Pi release through different backdoors (68) or binding of Pi to different chemical cross-bridge states (78). The analysis in the present study does not account for these alternatives.…”

Critical Evaluation of Current Hypotheses for the Pathogenesis of Hypertrophic Cardiomyopathy

“…Most likely, there are also differences along the length of cardiac fibers/cells (possibly between neighboring sarcomeres) [230] in analogy with what has been observed along a given skeletal muscle fiber [237][238][239]. Indeed, similar local non-uniformities have been observed in cardiac myofibrils [240] where important physiological roles of the non-uniformities include the speeding up relaxation [237,241] and, possibly, smoothening of halfsarcomere contractions, when summed over the length of the muscle [242]. Most likely, there are also differences along the length of cardiac fibers/cells (possibly between neighboring sarcomeres) [230] in analogy with what has been observed along a given skeletal muscle fiber [237][238][239].…”