Uncovering cross-bridge properties that underlie the cardiac active complex modulus using model linearisation techniques

The properties underlying cardiac cross-bridge kinetics can be characterised by a muscle's active complex modulus. While the complex modulus can be described by a series of linear transfer functions, the biophysical mechanisms underlying these components are represented inconsistently among existing cross-bridge models. To address this, we examined the properties commonly implemented in cross-bridge models using model linearisation techniques and assessed their contributions to the complex modulus. From this analysis, we developed a biophysical model of cross-bridge kinetics that captures the three components of the active complex modulus: (1) the elastic modulus at low frequencies that arises from allowing the proportion of cross-bridges in the post-power stroke state to increase with sarcomere length, (2) the increase in elastic modulus at high frequencies that arises from the dependence of cross-bridge strain on sarcomere velocity, and (3) the negative viscous modulus which signifies the production of work by cross-bridges arises from either a sarcomere length or strain dependence, or both, on the rate of change of cross-bridge proportion in the post-power stroke state. While a model that includes all these features can theoretically reproduce the cardiac complex modulus, analysis of their transfer functions reveals that the relative contributions of these components are often not taken into account. As a result, the negative viscous component that signifies work production is not visible because the complex modulus is dominated by the effects of sarcomere velocity on cross-bridge strain.