Cooperative effects due to calcium binding by troponin and their consequences for contraction and relaxation of cardiac muscle under various conditions of mechanical loading

A mathematical model for the regulation of mechanical activity in cardiac muscle has been developed based on a three-element rheological model of this muscle. The contractile element has been modeled taking into account the results of extensive mechanical tests that involved the recording of length-force and force-velocity relations and muscle responses to short-time deformations during various phases of the contraction-relaxation cycle. The best agreement between the experimental and the mathematical modeling results was obtained when a postulate stating two types of cooperativity to regulate the calcium binding by troponin was introduced into the model. Cooperativity of the first type is due to the dependence of the affinity of troponin C for Ca2+ on the concentration of myosin crossbridges in the vicinity of a given troponin C. Cooperativity of the second type assumes an increase in the affinity of a given troponin C for Ca2+ when the latter is bound by molecules neighboring troponin.