A Differential Equation Model for Tropomyosin-induced Myosin Cooperativity Describes Myosin–Myosin Interactions at Low Calcium

Mechanochemical interactions between myosin and actin-troponin-tropomyosin (regulated thin filaments) underlie muscle contraction. Generally, the binding of a myosin molecule to a regulated thin filament facilitates the binding of nearby myosin; binding is cooperative. A simple yet accurate theoretical description of this cooperativity is lacking. From a general mechanochemical model that treats tropomyosin as a continuous beam, we show that cooperative interactions can be defined by two parameters: C; which specifies the number of neighboring molecules affected by myosin binding, and d, which specifies how regulation slows myosin’s binding rate to actin. We then propose two methods to derive differential equations describing cooperative ensembles of myosin interacting with regulated thin filaments: the weakly-correlated and the linear theory. The linear theory fits measurements of the speed of regulated thin filaments moving over a dense bed of myosin at low calcium, giving rapid and precise estimates of C 1⁄4 11" 2 and d = 0.003 ± 0.002. The theory clarifies the relationship between microscopic measurements and macroscopic properties, serving as a step toward a complete multi-scale description of muscle contraction. Keywords—Muscle, Regulation, Cooperative unit,