  Metabolic flux balance analyses are a standard tool in analysing metabolic
reaction rates compatible with measurements, steady-state and the metabolic
reaction network stoichiometry. Flux analysis methods commonly place
unrealistic assumptions on fluxes due to the convenience of formulating the
problem as a linear programming model, and most methods ignore the notable
uncertainty in flux estimates. We introduce a novel paradigm of Bayesian
metabolic flux analysis that models the reactions of the whole genome-scale
cellular system in probabilistic terms, and can infer the full flux vector
distribution of genome-scale metabolic systems based on exchange and
intracellular (e.g. 13C) flux measurements, steady-state assumptions, and
target function assumptions. The Bayesian model couples all fluxes jointly
together in a simple truncated multivariate posterior distribution, which
reveals informative flux couplings. Our model is a plug-in replacement to
conventional metabolic balance methods, such as flux balance analysis (FBA).
Our experiments indicate that we can characterise the genome-scale flux
covariances, reveal flux couplings, and determine more intracellular unobserved
fluxes in C. acetobutylicum from 13C data than flux variability analysis. The
COBRA compatible software is available at github.com/markusheinonen/bamfa
