Modeling the Actin.myosin ATPase Cross-Bridge Cycle for Skeletal and Cardiac Muscle Myosin Isoforms.

Modeling the complete actin.myosin ATPase cycle has always been limited by the lack of experimental data concerning key steps of the cycle, because these steps can only be defined at very low ionic strength. Here, using human ß-cardiac myosin-S1, we combine published data from transient and steady-state kinetics to model a minimal eight-state ATPase cycle. The model illustrates the occupancy of each intermediate around the cycle and how the occupancy is altered by changes in actin concentration for [actin] = 1-20Km. The cycle can be used to predict the maximal velocity of contraction (by motility assay or sarcomeric shortening) at different actin concentrations (which is consistent with experimental velocity data) and predict the effect of a 5 pN load on a single motor. The same exercise was repeated for human α-cardiac myosin S1 and rabbit fast skeletal muscle S1. The data illustrates how the motor domain properties can alter the ATPase cycle and hence the occupancy of the key states in the cycle. These in turn alter the predicted mechanical response of the myosin independent of other factors present in a sarcomere, such as filament stiffness and regulatory proteins. We also explore the potential of this modeling approach for the study of mutations in human ß-cardiac myosin using the hypertrophic myopathy mutation R453C. Our modeling, using the transient kinetic data, predicts mechanical properties of the motor that are compatible with the single-molecule study. The modeling approach may therefore be of wide use for predicting the properties of myosin mutations.

Three-dimensional stochastic model of actin-myosin binding in the sarcomere lattice.

The effect of molecule tethering in three-dimensional (3-D) space on bimolecular binding kinetics is rarely addressed and only occasionally incorporated into models of cell motility. The simplest system that can quantitatively determine this effect is the 3-D sarcomere lattice of the striated muscle, where tethered myosin in thick filaments can only bind to a relatively small number of available sites on the actin filament, positioned within a limited range of thermal movement of the myosin head. Here we implement spatially explicit actomyosin interactions into the multiscale Monte Carlo platform MUSICO, specifically defining how geometrical constraints on tethered myosins can modulate state transition rates in the actomyosin cycle. The simulations provide the distribution of myosin bound to sites on actin, ensure conservation of the number of interacting myosins and actin monomers, and most importantly, the departure in behavior of tethered myosin molecules from unconstrained myosin interactions with actin. In addition, MUSICO determines the number of cross-bridges in each actomyosin cycle state, the force and number of attached cross-bridges per myosin filament, the range of cross-bridge forces and accounts for energy consumption. At the macroscopic scale, MUSICO simulations show large differences in predicted force-velocity curves and in the response during early force recovery phase after a step change in length comparing to the two simplest mass action kinetic models. The origin of these differences is rooted in the different fluxes of myosin binding and corresponding instantaneous cross-bridge distributions and quantitatively reflects a major flaw of the mathematical description in all mass action kinetic models. Consequently, this new approach shows that accurate recapitulation of experimental data requires significantly different binding rates, number of actomyosin states, and cross-bridge elasticity than typically used in mass action kinetic models to correctly describe the biochemical reactions of tethered molecules and their interaction energetics.