A simple model of aerobic metabolism: applications to work transitions in muscle

Adding kinetics to the model of the phosphate energy system [Connett. Am. J. Physiol. 254 (Regulatory Integrative Comp. Physiol. 23): R949-R959, 1988], we provide a framework for analyzing metabolic transients in muscle tissue. We modify the formalism of the earlier model and introduce a buffering factor, which measures buffering of adenine nucleotides by phosphocreatine. The time course of the phosphate energy state can be calculated given the following: 1) adenosinetriphosphatase (ATPase) rate, 2) pH, and 3) a mitochondrial driving function, i.e., ATP production in terms of the phosphate energy state. We use mitochondrial driving functions derived from steady-state measurements to predict the time courses for rest-work transitions. Predictions for transitions in the rat gastrocnemius muscle agree with published values. The model is used to test different existing hypotheses of oxygen consumption (VO2) regulation. Each hypothesis generates a specific mitochondrial driving function, which in turn generates a specific time course of phosphate energy state during transitions. A mitochondrial driving function based on enzyme kinetics with ADP as a substrate leads to time courses not matching the data. Mitochondrial driving functions that are linear with phosphocreatine, Pi, phosphorylation potential, or the pool of high-energy phosphate bonds (phosphate potential energy) gave good agreement with the data.