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

The release of inorganic phosphate (Pi) from the cross-bridge is a pivotal step in the cross-bridge ATPase cycle leading to force generation. It is well known that Pi release and the force-generating step are reversible, thus increase of [Pi] decreases isometric force by product inhibition and increases the rate constant kTR of mechanically-induced force redevelopment due to the reversible redistribution of cross-bridges among non-force-generating and force-generating states. The experiments on cardiac myofibrils from guinea pig presented here show that increasing [Pi] increases kTR almost reciprocally to force, i.e., kTR {approx} 1/force. To elucidate which cross-bridge models can explain the reciprocal kTR-force relation, simulations were performed for models varying in sequence and kinetics of 1) the Pi release-rebinding equilibrium, 2) the force-generating step and its reversal, and 3) the transitions limiting forward and backward cycling of cross-bridges between non-force-generating and force-generating states. Models consisting of fast reversible force generation before/after rapid Pi release-rebinding fail to describe the kTR-force relation observed in experiments. Models consistent with the experimental kTR-force relation have in common that Pi binding and/or force-reversal are/is intrinsically slow, i.e., either Pi binding or force-reversal or both limit backward cycling of cross-bridges from force-generating to non-force-generating states. STATEMENT OF SIGNIFICANCEPrevious mechanical studies on muscle fibers, myofibrils and myosin interacting with actin revealed that force production associated to phosphate release from myosins active site presents a reversible process in the cross-bridge cycle. The correlation of this reversible process to the process(es) limiting kinetics of backward cycling from force-generating to non-force-generating states remained unclear. Experimental data of cardiac myofibrils and model simulations show that the combined effects of [Pi] on force and the rate constant of force redevelopment (kTR) are inconsistent with fast reversible force generation before/after rapid Pi release-rebinding. The minimum requirement in sequential models for successfully describing the experimentally observed nearly reciprocal change of force and kTR is that either the Pi binding or the force-reversal step limit backward cycling.