To be certain about the uncertainty: Bayesian statistics for¹³C metabolic flux analysis

Abstract

C Metabolic Fluxes Analysis ( 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 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 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 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.

The Design of FluxML: A Universal Modeling Language for 13C Metabolic Flux Analysis

“…These fluxes are then determined in an iterative fitting procedure in which the log-likelihood function, expressing the discrepancies between the model-predicted and measured quantities, is minimized. Finally, statistical measures estimate the confidence with which the fluxes are inferred from the data in view of their precision (Wiechert et al, 1997; Theorell et al, 2017).…”

Comprehensive assessment of measurement uncertainty in 13C-based metabolic flux experiments

“…As recently reported by Theorell et al [ 39 ], uncertainty quantification in the form of confidence intervals calculated by Monte Carlo simulation yields a rather optimistic estimation of flux uncertainty. However, this method was selected for our analysis for its simple implementation (including the consideration of covariances) and robustness and, even more importantly, because of its implementation in internationally accepted guidelines such as in the Guide to the Expression of Uncertainty in Measurement guidelines [ 23 ].…”

“…Similarly, the X 2 test for goodness of fit is recommended as standard practice in 13 C-based MFA [ 40 ]. However, it depends heavily on a correct estimation of measurement uncertainty given by the covariance matrix [ 39 ]. This increases the need for curation of the metabolic model structure (e.g., by enzymatic assays or tailored 13 C labeling experiments) [ 41 ].…”

Benchmarking kinetic models ofEscherichia colimetabolism

“…Most experimental research is now reported with at least some notion of uncertainty (46) . Ideally models should propagate uncertainty from training data and parameters to the actual predictions (47,48) .…”