Mathematical modelling of energy demand and supply in the cardiac myocyte

Abstract

The mechanisms that regulate the control of energy demand and energy supply in the heart muscle are crucial for maintaining normal cardiac function, yet they are not very well understood. Although a number of mechanisms have been proffered by which mitochondrial supply of ATP can change to match varying workload in the myocardium, identifying the underlying regulatory pathways remains controversial. In this study, we have developed mathematical models of the sarcoplasmic endoplasmic reticulum Ca²⁺ ATPase (SERCA) pump and the acto-myosin cross-bridge cycle which, along with the Na+/K+ pump, are the key energy-consuming processes in the cardiomyocyte. These models encapsulate both thermodynamic considerations and metabolite sensitivity into a cycle-based framework. The parameters of these models are constrained by experimental data which characterise their physiological behaviour. These models are then placed within the context of a whole-cell electrophysiological framework, alongside a model of mitochondrial energy supply, to investigate the mechanisms that regulate energy control and to shed light on two experimental observations which, for many decades, have evaded a mechanistic explanation: the apparent linearity of the VO₂- PVA (pressure-volume area) relationship and the metabolic stability hypothesis, wherein demand-supply homeostasis is maintained despite negligible variation in metabolite concentrations at varying workloads. The predictions from our model simulations indicate that, under constant metabolite concentrations, the ATP-FTI (force-time integral) relationship is linear, while the ATP- FLA (force-length-area, cellular equivalent of VO₂- PVA) relationship is linear only at low work rates. The linearity of the ATP-FTI relationship is found to arise from kinetic properties of the cross-bridge model. This property is not retained in the ATP-FLA relationship and is lost when metabolite concentrations are allowed to vary, as during normal variation with changing workload. This suggests that FTI and FLA are not equivalent, and that the VO₂- PVA relationship may only be approximately linear. Finally, we show that metabolite concentrations change significantly with increasing workload if Pi feedback onto mitochondrial oxidative phosphorylation is removed from the model, suggesting that Pi-regulation alone is sufficient to maintain metabolic homeostasis in the absence of other regulatory mechanisms.