Description
A mathematical model that focuses on the interaction between a single actin and myosin filament is used to look at precise regulation of muscle activity at the micro-scale. Specifically, it is used to study how varying calcium pulse trains and myosin motor head spacing influences force generation by an array of motors using two different regulatory mechanisms: the control of total number of active myosin heads and the availability of myosin binding sites on the actin filament. This regulation is achieved by a change in structure and positioning of individual myosin heads along the thick filament, and the movement of tropomyosin on the actin filament via calcium-dependent troponin, respectively. The current model is distinct from previous models in multiple specific aspects: its inclusion of both thick and thin filament regulation methods, use of precise microsecond based modeling of crossbridge cycle events, and the varying of shape, number, and spacing of calcium pulse trains that allow manipulation of the timing and rate of change of calcium delivery and removal within the specified muscle system. A numerical model approach, whereby a system of differential equations is used to describe motor states and force generation, was ineffective largely because it was a deterministic approximation of a stochastic process. Other crucial restrictions included the inability to change motor alignment with respect to actin binding sites, and being unable to incorporate the effect of forces on individual motor transition rates. These limitations ultimately led to a linear force-velocity relationship that is not in agreement with the hyperbolic relationship obtained by experimental data. A stochastic cellular automaton approach was taken to overcome the drawbacks of the numerical approach, and effectively included individual strain-dependent motor transition rates and precise tracking of individual motor alignment. This ultimately led to a production of results more in agreement with experimental findings and the well-established hyperbolic force-velocity relationship.
