To be certain about the uncertainty: Bayesian statistics for ¹³ C metabolic flux analysis

¹³ C Metabolic Fluxes Analysis (¹³ C MFA) remains to be the most powerful approach to determine intracellular metabolic reaction rates. Decisions on strain engineering and experimentation heavily rely upon the certainty with which these fluxes are estimated. For uncertainty quantification, the vast majority of ¹³ C MFA studies relies on confidence intervals from the paradigm of Frequentist statistics. However, it is well known that the confidence intervals for a given experimental outcome are not uniquely defined. As a result, confidence intervals produced by different methods can be different, but nevertheless equally valid. This is of high relevance to ¹³ C MFA, since practitioners regularly use three different approximate approaches for calculating confidence intervals. By means of a computational study with a realistic model of the central carbon metabolism of E. coli, we provide strong evidence that confidence intervals used in the field depend strongly on the technique with which they were calculated and, thus, their use leads to misinterpretation of the flux uncertainty. In order to provide a better alternative to confidence intervals in ¹³ C MFA, we demonstrate that credible intervals from the paradigm of Bayesian statistics give more reliable flux uncertainty quantifications which can be readily computed with high accuracy using Markov chain Monte Carlo. In addition, the widely applied chi-square test, as a means of testing whether the model reproduces the data, is examined closer.