Cellular energetics analysis by a mathematical model of energy balance: estimation of parameters in human skeletal muscle

Cellular energy balance requires that the physiological demands by ATP-utilizing functions be matched by ATP synthesis to sustain muscle activity. We devised a new method of analysis of these processes in data from single individuals. Our approach is based on the logic of current information on the major mechanisms involved in this energy balance and can quantify not directly measurable parameters that govern those mechanisms. We use a mathematical model that simulates by ordinary, nonlinear differential equations three components of cellular bioenergetics (cellular ATP flux, mitochondrial oxidative phosphorylation, and creatine kinase kinetics). We incorporate data under resting conditions, during the transition toward a steady state of stimulation and during the transition during recovery back to the original resting state. Making use of prior information about the kinetic parameters, we fitted the model to previously published dynamic phosphocreatine (PCr) and inorganic phosphate (P-i) data obtained in normal subjects with an activity-recovery protocol using P-31 nuclear magnetic resonance spectroscopy. The experiment consisted of a baseline phase, an ischemic phase (during which muscle stimulation and PCr utilization occurred), and an aerobic recovery phase. The model described satisfactorily the kinetics of the changes in PCr and P-i and allowed estimation of the maximal velocity of oxidative phosphorylation and of the net ATP flux in individuals both at rest and during stimulation. This work lays the foundation for a quantitative, model-based approach to the study of in vivo muscle energy balance in intact muscle systems, including human muscle.