Analysis of steady-state carbon tracer experiments using akaike information criteria

Introduction: Carbon isotope tracers have been used to determine relative rates of tricarboxylic acid cycle (TCA) cycle pathways since the 1950s. Steady-state experimental data are typically fit to a single mathematical model of metabolism to determine metabolic fluxes. Whether the chosen model is appropriate for the biological system has generally not been evaluated systematically. An overly-simple model omits known pathways while an overly-complex model may produce incorrect results due to overfitting. Objectives: The objectives were to develop and study a method that systematically evaluates multiple TCA cycle mathematical models as part of the fitting process. Methods: The problem of choosing overly-simple or overly-complex models was approached by developing software that automatically explores all possible combinations of flux through pyruvate dehydrogenase, pyruvate kinase, pyruvate carboxylase and anaplerosis at propionyl-CoA carboxylase, and equivalent pathways, all relative to TCA cycle flux. Typical TCA cycle metabolic tracer experiments that use ¹³C nuclear magnetic resonance for detection and quantification of ¹³C-enriched glutamate products were simulated and analyzed. By evaluating the multiple model fits with both the conventional sum-of-squares residual error (SSRE) and the Akaike Information Criterion (AIC), the software helps the investigator understand the interaction between model complexity and goodness of fit. Results: When fitting alternative models of the TCA cycle metabolism, the SSRE may identify more than one model that fits the data well. Among those models, the AIC provides guidance as to which is the simplest of the candidate models is sufficient to describe the observed data. However under some conditions, AIC used alone inappropriately discriminates against necessary metabolic complexity. Conclusion: In combination, the SSRE and AIC help the investigator identify the model that best describes the metabolism of a biological system.