Glycolysis and oxidative phosphorylation as a function of cytosolic phosphorylation state and power output of the muscle cell

A mathematical description of the regulation of ATP production in muscle cells is presented whereby the activity of OxP can be calculated as a function of (1) free [ADP] as the substrate and (2) a second driving force PhiDeltaG (kilojoules per mole) resulting from the difference of free energy DeltaG(ox,ap) (kilojoules per mole) - DeltaG(ATP,cyt) (kilojoules per mole). In turn, the term DeltaG(ox,ap) results from the proton motive force and the generation of ATP in the matrix space including the ATP-ADP exchange, whereas the phosphorylation state of the CHEP-sytem is described by DeltaG(ATP,cyt). Regulation of glycolysis is calculated as a function of free [ADP] and [AMP] at the level of PFK. The PFK is inhibited by a decreasing pH resulting from lactate accumulation. The ATP/PCr equilibrium of the CHEP-system is calculated by algebraic equations. The dynamic behaviour of the metabolic control of ATP production as a function of ATP consumption is calculated by a system of two 1st-order non-linear differential equations, including a time delay considering oxygen transport. Lactate distribution and elimination is calculated using a two-compartment model with an active lactate producing, and a passive, space including lactate elimination by combustion. The simulation of the dynamics of energy metabolism of muscle cells is performed by the stepwise solution of the differential equations with a 5th-order Runge-Kutta-Fehlberg-routine. Examples of various applications of the simulation of the dynamics of energy supply demonstrate the qualitative and quantitative congruence to the behaviour of metabolic processes in experiments during rest, exercise and recovery.