We present an integrated thermokinetic model describing control of cardiac mitochondrial bioenergetics. The model describes the tricarboxylic acid (TCA) cycle, oxidative phosphorylation, and mitochondrial Ca(2+) handling. The kinetic component of the model includes effectors of the TCA cycle enzymes regulating production of NADH and FADH(2), which in turn are used by the electron transport chain to establish a proton motive force (Delta mu(H)), driving the F(1)F(0)-ATPase. In addition, mitochondrial matrix Ca(2+), determined by Ca(2+) uniporter and Na(+)/Ca(2+) exchanger activities, regulates activity of the TCA cycle enzymes isocitrate dehydrogenase and alpha-ketoglutarate dehydrogenase. The model is described by twelve ordinary differential equations for the time rate of change of mitochondrial membrane potential (Delta Psi(m)), and matrix concentrations of Ca(2+), NADH, ADP, and TCA cycle intermediates. The model is used to predict the response of mitochondria to changes in substrate delivery, metabolic inhibition, the rate of adenine nucleotide exchange, and Ca(2+). The model is able to reproduce, qualitatively and semiquantitatively, experimental data concerning mitochondrial bioenergetics, Ca(2+) dynamics, and respiratory control. Significant increases in oxygen consumption (V(O(2))), proton efflux, NADH, and ATP synthesis, in response to an increase in cytoplasmic Ca(2+), are obtained when the Ca(2+)-sensitive dehydrogenases are the main rate-controlling steps of respiratory flux. These responses diminished when control is shifted downstream (e.g., the respiratory chain or adenine nucleotide translocator). The time-dependent behavior of the model, under conditions simulating an increase in workload, closely reproduces experimentally observed mitochondrial NADH dynamics in heart trabeculae subjected to changes in pacing frequency. The steady-state and time-dependent behavior of the model support the hypothesis that mitochondrial matrix Ca(2+) plays an important role in matching energy supply with demand in cardiac myocytes.