Mathematical Model of Oxygen Labeling to Study Heart Energy Transfer

Abstract

The mechanisms underlying the homeostasis of ATP, ADP, PCr and inorganic phosphate in heart under a wide range of workloads remain unclear. Fundamental to this search is an accurate understanding of the recycling fluxes of these metabolites between the mitochondrial inner membrane space and the ATPases on both the myofibrils and SERCA pumps. In addition to 31P-NMR inversion and saturation transfer studies, dynamic 18O labeling data has been used to analyze energy transfer. An integrative kinetic model that tracks the mass isotopomers of these four metabolites was constructed with the following compartments: mitochondrial matrix, mitochondrial intermembrane space, cytosol, and enzyme bound states of both ATPase and ATP synthase (since these reactions are not unidirectional with respect to oxygen exchange). A sensitivity analysis of this system was conducted with a jump to 30% H218O to find flux parameters that influenced the 18O labeling state. Both the creatine kinase and adenylate kinase shuttle fluxes were modeled as being bidirectional to test assumptions made in previous studies that analyzed dynamic 18O labeling data. It was found that the sum of forward and reverse fluxes through each shuttle determined the labeling state such that if the sum is kept constant and the net flux is reduced, a very similar labeling state is predicted. Total creatine kinase and adenylate kinase fluxes that exceeded the ATP synthase rate were also found to give almost the same predictions of the labeling state. Model predictions of the 18O labeling state of metabolites are very similar using energy fluxes reported in earlier studies of 18O labeling in the heart and energy transfer analysis by 31P-NMR inversion and saturation transfer.