Spatially-Compressed Cardiac Myofilament Models Generate Hysteresis that Is Not Found in Real Muscle

In the field of cardiac modeling, calcium- (Ca-) based activation is often described by sets of ordinary differential equations that do not explicitly represent spatial interactions of regulatory proteins or crossbridge attachment. These spatially compressed models are most often mean-field representations as opposed to methods that explicitly compute the surrounding field (or equivalently, the surrounding environment) of individual regulatory units and crossbridges. Instead, a mean value is used to represent the whole population. Almost universally, the mean-field approach assumes developed force produces positive feedback to globally increase the mean binding affinity of the regulatory proteins. We show that this approach produces hysteresis in the steady-state Force-Ca responses when developed force increases Ca-affinity troponin to the degree that is observed in real muscle. Specifically, multiple stable solutions exist as a function of Ca level that could be alternatively reached depending on stimulus history. The resulting hysteresis is quite pronounced and disagrees with experimental characterizations in cardiac muscle that generally show little if any hysteresis. Moreover, we provide data showing that hysteresis does not occur in carefully controlled myofibril preparations. Hence, we suggest that the most widely used methods to produce multiscale models of cardiac force generation show bistability and hysteresis effects that are not seen in real muscle responses