The Minimal Group Size for Globally Coordinated Stepping of Muscle Myosins Depends on ATP Hydrolysis Free Energy

Abstract

In motility assays of muscle myosins, a distinct motile state emerges with increasing number of mechanically coupled myosin binding sites (N). This is explicable by coordinated myosin stepping (CMS): build-up of pre power stroke (PS) myosins is followed by a whole group PS and detachment cascade [1]. At low N, singular infrequent detachment cascades occur; at intermediate N, cascades group into bursts; for high N, interruptions between bursts disappear [1]. Here, we investigate how changing ATP hydrolysis free energy (ΔG) affects N-dependent emergence of CMS. We executed motility assays of muscle myosins and changed Pi concentration ([Pi]=0,1,2.5,5,15,30 mM, ionic strength adjusted by [KCl], [ATP]=2 mM, [ADP]=0.2 mM). Resolving actin sliding velocities by N [2] showed that increasing [Pi] increased the N at which bursts and continuous filament motion emerge. Lowering the rate of Pi release reproduced these observations in our detailed mechanochemical model of linearly elastic myosins mechanically coupled via an actin filament [1]. In this model, the rate of myosins' mechanical steps increases monotonically by ∼6 orders of magnitude dependent on the skew in myosin crossbridge strains (S). Plotting S and the fraction of myosin in the pre and the post PS state (n1,n2) reveals globally coordinated behavior that changes with N. N∼5: a quiescent state with high n1 dominates; N∼15: a quiescent state and cascading behavior with lowered n1 alternate; N∼30: cascading behavior dominates. An according continuous model shows two N-dependent stable steady states representing quiescence and cascading. Adding stochastic fluctuations in S lead to N-dependent cascade-like cycles. This suggests global coordination of myosins, which occurs above a minimal myosin group size that depends on ΔG.[1] Hilbert et al., Biophys J, 105(6):1466(2013) [2] Hilbert et al., PLoS Comp Biol, (2013).