We present an integrated thermokinetic model describing control of cardiac mitochondrial bioenergetics. The model describes the tricarboxylic acid (TCA) cycle, oxidative phosphorylation, and mitochondrial Ca2+ handling. The kinetic component of the model includes effectors of the TCA cycle enzymes regulating production of NADH and FADH2, which in turn are used by the electron transport chain to establish a proton motive force (ΔμH), driving the F1F0-ATPase. In addition, mitochondrial matrix Ca2+, determined by Ca2+ uniporter and Na+/Ca2+ exchanger activities, regulates activity of the TCA cycle enzymes isocitrate dehydrogenase and α-ketoglutarate dehydrogenase. The model is described by twelve ordinary differential equations for the time rate of change of mitochondrial membrane potential (ΔΦm), and matrix concentrations of Ca2+, 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 Ca2+. The model is able to reproduce, qualitatively and semiquantitatively, experimental data concerning mitochondrial bioenergetics, Ca2+ dynamics, and respiratory control. Significant increases in oxygen consumption (VO2), proton efflux, NADH, and ATP synthesis, in response to an increase in cytoplasmic Ca2+, are obtained when the Ca2+-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 Ca2+ plays an important role in matching energy supply with demand in cardiac myocytes.
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