Analysis of metabolite and strain effects on cardiac cross-bridge dynamics using model linearisation techniques

Multi-scale models of cardiac energetics are becoming crucial in better understanding the prevalent chronic diseases operating at the intersection of metabolic and cardiovascular dysfunction. Computationally efficient models of cardiac cross-bridge kinetics that are sensitive to changes in metabolite concentrations are necessary to simulate the effects of disease-induced changes in cellular metabolic state on cardiac mechanics across disparate spatial scales. While these models do currently exist, deeper analysis of how the modelling of metabolite effects and the assignment of strain dependence within the cross-bridge cycle affect the properties of the model is required. In this study, model linearisation techniques were used to simulate and interrogate the complex modulus of an ODE-based model of cross-bridge kinetics. Active complex moduli were measured from permeabilised rat cardiac trabeculae under five different metabolite conditions with varying ATP and P_i concentrations. Sensitivity to metabolites was incorporated into an existing three-state cross-bridge model using either a direct dependence or a rapid equilibrium approach. Combining the two metabolite binding methods with all possible locations of strain dependence within the cross-bridge cycle produced 64 permutations of the cross-bridge model. Using linear model analysis, these models were systematically explored to determine the effects of metabolite binding and their interaction with strain dependence on the frequency response of cardiac muscle. The results showed that the experimentally observed effects of ATP and P_i concentrations on the cardiac complex modulus could be attributed to their regulation of cross-bridge detachment rates. Analysis of the cross-bridge models revealed a mechanistic basis for the biochemical schemes which place P_i release following cross-bridge formation and ATP binding prior to cross-bridge detachment. In addition, placing strain dependence on the reverse rate of the cross-bridge power stroke produced the model which most closely matched the experimental data. From these analyses, a well-justified metabolite-sensitive model of rat cardiac cross-bridge kinetics is presented which is suitable for parameterisation with other data sets and integration with multi-scale cardiac models.