A Spatially Detailed Model of Isometric Contraction Based on Competitive Binding of Troponin I Explains Cooperative Interactions between Tropomyosin and Crossbridges

Biophysical models of cardiac tension development provide a succinct representation of our understanding of force generation in the heart. The link between protein kinetics and interactions that gives rise to high cooperativity is not yet fully explained from experiments or previous biophysical models. We propose a biophysical ODE-based representation of cross-bridge (XB), tropomyosin and troponin within a contractile regulatory unit (RU) to investigate the mechanisms behind cooperative activation, as well as the role of cooperativity in dynamic tension generation across different species. The model includes cooperative interactions between regulatory units (RU-RU), between crossbridges (XB-XB), as well more complex interactions between crossbridges and regulatory units (XB-RU interactions). For the steady-state force-calcium relationship, our framework predicts that: (1) XB-RU effects are key in shifting the half-activation value of the force-calcium relationship towards lower [Ca2+], but have only small effects on cooperativity. (2) XB-XB effects approximately double the duty ratio of myosin, but do not significantly affect cooperativity. (3) RU-RU effects derived from the long-range action of tropomyosin are a major factor in cooperative activation, with each additional unblocked RU increasing the rate of additional RU's unblocking. (4) Myosin affinity for short (1-4 RU) unblocked stretches of actin of is very low, and the resulting suppression of force at low [Ca2+] is a major contributor in the biphasic force-calcium relationship. We also reproduce isometric tension development across mouse, rat and human at physiological temperature and pacing rate, and conclude that species differences require only changes in myosin affinity and troponin I/troponin C affinity. Furthermore, we show that the calcium dependence of the rate of tension redevelopment k(tr) is explained by transient blocking of RU's by a temporary decrease in XB-RU effects.