Measuring and Modelling the Effect of Inorganic Phosphate on Cross-bridge Mechanics in Human Cardiac Muscle.

Many common chronic diseases operate at the intersection of metabolic and cardiovascular dysfunction. In order to model the effects of these diseases and investigate underlying causes we are developing a cardiomyocyte model which incorporates both the mechanics and metabolic factors that underlie work done by the heart. In this paper we present the first experimental results from our study measuring mechanical properties in human cardiac trabeculae, including the effect of inorganic phosphate (Pi) on the complex modulus at 37 °C. Extending our previous mathematical model, we have developed a computationally efficient model of cardiac cross-bridge mechanics which is sensitive to changes in cellular Pi. This extended model was parameterised with human cardiac complex modulus data. It captured the changes to cardiac mechanics following an increase in Pi concentration that we measured experimentally, including a reduced elastic modulus and a right-shift in frequency. The human cardiac trabecula we studied had a low sensitivity to Pi compared to what has been previously reported in mammalian cardiac tissue, which suggests that the muscle may have cellular compensatory mechanisms to cope with elevated Pi levels. This study demonstrates the feasibility of our experimental-modelling pipeline for future investigation of mechanical and metabolic effects in the diseased human heart.Clinical Relevance- This study presents the first measurement of the effect of Pi on the stiffness frequency response of human cardiac tissue and extends an experimental-modelling framework appropriate for investigating effects of disease on the human heart.

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 Pi 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 Pi 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 Pi 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.

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.