The idea that contraction of skeletal muscle and heart results from ATP-driven actomyosin cross-bridge cycles is generally accepted. However, operational details remain controversial. For instance, in conflict with most accepted views, evidence was recently presented [1] for appreciably non-linear elasticity with low stiffness for post-power-stroke cross-bridges. Moreover, a non-hyperbolic relationship was observed [2] between MgATP concentration and sliding velocity for actin filaments propelled in vitro by myosin subfragment 1 or full length myosin. Here we present convincing evidence for a hyperbolic [MgATP]-velocity relationship (r2=0.998; Michaelis-Menten constants, Vmax=15.28 ± 0.28 µm/s (mean±SEM) and KM= 0.389 ± 0.023 mM) when actin filaments are propelled by heavy meromyosin from rabbit fast skeletal muscle myosin (28-29oC; >3 independent experiments). Because the hyperbolic [MgATP]-velocity relationship is not readily consistent with inter-head cooperativity the results were interpreted using a cross-bridge model with independent myosin heads. The inter-state transition rates were strain-dependent and the model had one detached state and five attached actomyosin (AM) states with either MgATP (AMATP) or MgADP and/or inorganic phosphate (Pi) or no nucleotide at the active site. The AMADPPi state was a strongly bound pre-power-stroke state whereas the remaining states without Pi were post-power-stroke states required to account for strain-dependent MgADP-release on the one hand and MgATP-dependence of velocity and competitive inhibition of MgATP binding by MgADP (AM, AMADP, AMATP) on the other. The MgATP induced detachment was supplemented by MgATP independent, but strain-dependent, detachment from the rigor (AM) state. This model predicts a hyperbolic [MgATP]-velocity relationship if the cross-bridge elasticity is non-linear but a non-hyperbolic [MgATP]-velocity relationship (cf. [2]) if cross-bridge elasticity is linear.References:[1] Kaya, M. and Higuchi, H. (2010) Science 329(5992): 686-689.[2] Hooft, A. M. et al. (2007) Biochemistry46(11): 3513-3520.