BayFlux: A <i>Bay</i> esian method to quantify metabolic <i>Flux</i> es and their uncertainty at the genome scale

Abstract Metabolic fluxes, the number of metabolites traversing each biochemical reaction in a cell per unit time, are crucial for assessing and understanding cell function. 13 C Metabolic Flux Analysis ( 13 C MFA) is considered to be the gold standard for measuring metabolic fluxes. 13 C MFA typically works by leveraging extracellular exchange fluxes as well as data from 13 C labeling experiments to calculate the flux profile which best fit the data for a small, central carbon, metabolic model. However, the nonlinear nature of the 13 C MFA fitting procedure means that several flux profiles fit the experimental data within the experimental error, and traditional optimization methods offer only a partial or skewed picture, especially in “non-gaussian” situations where multiple very distinct flux regions fit the data equally well. Here, we present a method for flux space sampling through Bayesian inference (BayFlux), that identifies the full distribution of fluxes compatible with experimental data for a comprehensive genome-scale model. This Bayesian approach allows us to accurately quantify uncertainty in calculated fluxes. We also find that, surprisingly, the genome-scale model of metabolism produces narrower flux distributions (reduced uncertainty) than the small core metabolic models traditionally used in 13 C MFA. The different results for some reactions when using genome-scale models vs core metabolic models advise caution in assuming strong inferences from 13 C MFA since the results may depend significantly on the completeness of the model used. Based on BayFlux, we developed and evaluated novel methods (P- 13 C MOMA and ROOM) to predict the biological results of a gene knockout, that improve on the traditional MOMA and ROOM methods. We provide an open source Python implementation of BayFlux at https://github.com/JBEI/bayflux . Author summary 13 C MFA practitioners know that modeling results can be sensitive to minor modifications of the metabolic model. Certain parts of the metabolic model that are not well mapped to a molecular mechanism ( e.g. drains to biomass or ATP maintenance) can have an inordinate impact on the final fluxes. The only way to ascertain the validity of the model is by checking that the result does not significantly differ from previously observed flux profiles. However, that approach diminishes the possibility of discovering truly novel flux profiles. Because of this strong dependence on metabolic model details, it would be very useful to have a systematic and repeatable way to produce these metabolic models. And indeed there is one: genome-scale metabolic models can be systematically obtained from genomic sequences, and represent all the known genomically encoded metabolic information. However, these models are much larger than the traditionally used central carbon metabolism models. Hence, the number of degrees of freedom of the model (fluxes) significantly exceeds the number of measurements (metabolite labeling profiles and exchange fluxes). As a result, one expects many flux profiles compatible with the experimental data. The best way to represent these is by identifying all fluxes compatible with the experimental data. Our novel method BayFlux, based on Bayesian inference and Markov Chain Monte Carlo sampling, provides this capability. Interestingly, this approach leads to the observation that traditional optimization approaches can significantly overestimate flux uncertainty, and that genome-scale models of metabolism produce narrower flux distributions than the small core metabolic models that are traditionally used in 13 C MFA. Furthermore, we show that the extra information provided by this approach allows us to improve knockout predictions, compared to traditional methods. Although the method scales well with more reactions, improvements will be needed to tackle the large metabolic models found in microbiomes and human metabolism.