Approaches to modeling crossbridges and calcium-dependent activation in cardiac muscle

While the primary function of the heart is a pump, ironically, the development of myofilament models that predict developed force have generally lagged behind the modeling of the electrophysiological and Ca²⁺-handling aspects of heart cells. A major impediment is that the basic events in force generating actin–myosin interactions are still not well understood and quantified despite advanced techniques that can probe molecular levels events and identify numerous energetic states. As a result, the modeler must decide how to best abstract the many identified states into useful models with an essential tradeoff in the level of complexity. Namely, complex models map more directly to biophysical states but experimental data does not yet exist to well constrain the rate constants and parameters. In contrast, parameters can be better constrained in simpler, lumped models, but the simplicity may preclude versatility and extensibility to other applications. Other controversies exist as to why the activation of the actin–myosin is so steeply dependent on activator Ca²⁺. More specifically steady-state force–[Ca²⁺] (F–Ca) relationships are similar to Hill functions, presumably as the result of cooperative interactions between neighboring crossbridges and/or regulatory proteins. We postulate that mathematical models must contain explicit representation of nearest-neighbor cooperative interactions to reproduce F–Ca relationships similar to experimental measures, whereas spatially compressing, mean-field approximation used in most models cannot. Finally, a related controversy is why F–Ca relationships show increased Ca²⁺ sensitivity as sarcomere length (SL) increases. We propose a model that suggests that the length-dependent effects can result from an interaction of explicit nearest-neighbor cooperative mechanisms and the number of recruitable crossbridges as a function of SL.