Identification of the intracellular control of the cardiac force-length relationship: Analysis of the hystereses in the force-length plane.

Revealing the mechanisms underlying the regulation of the cardiac muscle force-length relation is of immense importance for the understanding the normal and failing heart functions. Our model of the intracellular control of contraction includes two feedback loops: 1. The cooperativity (positive feedback) mechanisms, whereby the number of force generating cross-bridges (XBs) affects the rate of new XB recruitment. 2. The mechanical feedback, whereby the sarcomere velocity determines the time over which the XBs are at the strong state. The study aims to verify the ability of the model to explain the experimentally observed hystereses in the force-length relations (at constant activation) and to determine the role of each feedback loop. The force response to large (>4%) sarcomere length (SL) oscillation lags the length changes at low frequencies (<4Hz), leading to a counter-clock wise hysteresis. At high frequencies (>4Hz) the force precedes the SL oscillation and clockwise hysteresis appears. The model of the sarcomere, that couples calcium kinetics with XB dynamics, was built on Simulink. The force responses to SL oscillations were simulated at constant calcium concentration (activation). When the mechanical feedback is opened and only the cooperativity feedback exists, the force lags the SL. Opening the cooperativity mechanism and leaving only the mechanical feedback yields the opposite phenomenon and the force precedes the SL. The cooperativity dominates at low frequencies, when both feedbacks exist, while the mechanical feedback dominates at higher frequencies, in accordance with the experimental observations. The study emphasizes the role of each feedback.