Ising models of cooperativity in muscle contraction

Regulation of contraction in striated muscle is controlled by a dual mechanism involving both thin filaments containing actin and thick filaments containing myosin. The thin filament is activated by calcium ions binding to troponin, leading to tropomyosin azimuthal displacement, which allows the activation of a regulatory unit (composed of one troponin, one tropomyosin, and seven actin monomers) that exposes the actin sites for interaction with the myosin motors. Motor attachment to actin contributes to spreading activation within and beyond a regulatory unit along the thin filament through a cooperative mechanism. We introduce a one-dimensional Ising model to elucidate the mechanism of cooperativity in thin filament activation in relation to the force generated by the attached myosin motor. The model characterizes thin filament activation and cooperativity using only two parameters: one related to calcium concentration and the other to the force exerted by the attached myosin motor, which is modulated by temperature. At any force, the model is able to determine the extent of actin-myosin interactions on a correlation length ranging from two to seven actin monomers, in addition to the seven actin monomers of the regulatory unit. Our theoretical predictions are successfully tested on experimental data, and our tests also include the condition of hindered filament activation by the use of the specific drug omecamtiv mecarbil (OM). According to our model, the effect of OM results in an anticooperativity mechanism accounting for the experimental data.