Sensitivity Analysis of Flux Determination in Heart by H ₂ ¹⁸O -provided Labeling Using a Dynamic Isotopologue Model of Energy Transfer Pathways

Abstract

To characterize intracellular energy transfer in the heart, two organ-level methods have frequently been employed: inversion and saturation transfer, and dynamic labeling. Creatine kinase (CK) fluxes obtained by following oxygen labeling have been considerably smaller than the fluxes determined by saturation transfer. It has been proposed that dynamic labeling determines net flux through CK shuttle, whereas saturation transfer measures total unidirectional flux. However, to our knowledge, no sensitivity analysis of flux determination by oxygen labeling has been performed, limiting our ability to compare flux distributions predicted by different methods. Here we analyze oxygen labeling in a physiological heart phosphotransfer network with active CK and adenylate kinase (AdK) shuttles and establish which fluxes determine the labeling state. A mathematical model consisting of a system of ordinary differential equations was composed describing enrichment in each phosphoryl group and inorganic phosphate. By varying flux distributions in the model and calculating the labeling, we analyzed labeling sensitivity to different fluxes in the heart. We observed that the labeling state is predominantly sensitive to total unidirectional CK and AdK fluxes and not to net fluxes. We conclude that measuring dynamic incorporation of into the high-energy phosphotransfer network in heart does not permit unambiguous determination of energetic fluxes with a higher magnitude than the ATP synthase rate when the bidirectionality of fluxes is taken into account. Our analysis suggests that the flux distributions obtained using dynamic labeling, after removing the net flux assumption, are comparable with those from inversion and saturation transfer.

Author Summary

In heart, the movement of energy metabolites between force-producing myosin, other ATPases, and mitochondria is vital for its function and closely related to heart pathologies. In addition to diffusion, transport of ATP, ADP, Pi, and phosphocreatine occurs along parallel pathways such as the adenylate kinase and creatine kinase shuttles. Two organ-level methods have been developed to study the relative flux through these pathways. However, their results differ. It was recently demonstrated that studies often suffer from the exclusion of compartmentation from their metabolic models. One study overcame this limitation by using compartmental models and statistical methods on multiple experiments. Here, we analyzed the sensitivity of the other method - dynamic labeling of phosphoryl groups and inorganic phosphate. For that, we composed a mathematical model tracking enrichment of the metabolites and evaluated sensitivity of labeling to different flux distribution scenarios. Our study shows that the dynamic method provides a measure of total flux, and not net flux as presumed previously, making the fluxes predicted from both methods consistent. Importantly, conclusions derived on the basis of labeling analysis, particularly those regarding the net flux through the shuttles in control and pathological cases, need to be reevaluated.