Theoretical treatment of tension transients in muscle following sudden changes in orthophosphate concentration: implications for energy transduction

The relative timing of the force-generating power stroke and release of the ATP-hydrolysis product orthophosphate (Pi) in actomyosin energy transduction is debated. It may be explored by studying the tension response to sudden changes in [Pi] during isometric muscle contraction (Pi-transients; rate constant k_Pi) and by the rate of redevelopment of isometric force (k_tr) after a period of unloaded shortening at varied [Pi]. Most studies of these types are interpreted using simple kinetic schemes that ignore the range of elastic strains of actin-attached myosin cross-bridges. We found that the only simple scheme which accounts for the experimental findings of single exponential Pi-transients with k_Pi ≈ k_tr has force-generation coincident with actin-myosin attachment. This characteristics could compromise the high power output of muscle. We therefore turned to a mechanokinetic model, allowing consideration of the varying elastic cross-bridge strains. Our model assumes Pi-release between cross-bridge attachment and the force-generating power stroke. However, power strokes only occur if cross-bridges attach in a pre-power-stroke state with zero or negative elastic strain (counteracting shortening). The model suggests two components of the Pi-transients. One is attributed to slow cross-bridge detachment from the pre-power-stroke state at positive elastic strain upon Pi-binding. The other is due to Pi-induced shifts in equilibrium with rapid power stroke reversal. The slow component dominates for all parameter values tested but the fast component is ubiquitous, predicting a biphasic Pi-transient in disagreement with experiments. Strikingly, however, the mechanokinetic model gives different predictions than apparently similar simple kinetic schemes and we do not rule out the existence of parameter values leading to a negligible fast component. We also show that the assumption of secondary Pi-binding sites on myosin outside the active site removes the fast component albeit without predicting that k_tr ≈ k_Pi. Additional studies are required to finally corroborate that k_tr ≈ k_Pi in experiments but also to further develop mechanokinetic models combined with multistep Pi-release.