BayFlux: A Bayesian method to quantify metabolic Fluxes and their uncertainty at the genome scale

by Tyler W. H. Backman, Christina Schenk, Tijana Radivojevic, David Ando, Jahnavi Singh, Jeffrey J. Czajka, Zak Costello, Jay D. Keasling, Yinjie Tang, Elena Akhmatskaya, Hector Garcia Martin

Metabolic fluxes, the number of metabolites traversing each biochemical reaction in a cell per unit time, are crucial for assessing and understanding cell function. ¹³C Metabolic Flux Analysis (¹³C MFA) is considered to be the gold standard for measuring metabolic fluxes. ¹³C MFA typically works by leveraging extracellular exchange fluxes as well as data from ¹³C 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 ¹³C 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 ¹³C MFA. The different results for some reactions when using genome-scale models vs core metabolic models advise caution in assuming strong inferences from ¹³C MFA since the results may depend significantly on the completeness of the model used. Based on BayFlux, we developed and evaluated novel methods (P-¹³C MOMA and P-¹³C ROOM) to predict the biological results of a gene knockout, that improve on the traditional MOMA and ROOM methods by quantifying prediction uncertainty.