Trans-dimensional Bayesian model averaging for 13C-metabolic flux analysis: Evidence-based flux inference under structural model uncertainty

MOTIVATION: Accurate quantification of intracellular metabolic fluxes is central to systems biology and biotechnology. Flux estimation relies on biochemical network models, with 13C-metabolic flux analysis (MFA) being the state-of-the-art approach. However, isotope labeling data are often insufficient to uniquely support a single network formulation. In such cases, flux estimates become model-dependent, highlighting the need for methods that explicitly account for structural uncertainty. Bayesian model averaging provides a principled framework for this purpose, but its application to 13C-MFA has so far been restricted to uncertainty in reaction bidirectionality within fixed network topologies. RESULTS: We introduce a scalable Bayesian inference framework for 13C-MFA, Bayesian model set averaging, that applies Bayesian model averaging to encompass uncertainty in reactions and pathways. Our approach combines reversible jump Markov chain Monte Carlo for trans-dimensional exploration of structural hypotheses with diffusive nested sampling for robust estimation of model evidences, enabling averaging over large families of metabolic network structures. Using illustrative and application-scale synthetic case studies, we demonstrate that the method yields robust flux estimates, reveals when multiple network configurations are statistically indistinguishable, and recovers the correct data-supported pathway configuration as data informativeness increases. Rather than conditioning inference on a single assumed network structure, the framework quantifies posterior support for alternative reaction and pathway hypotheses and propagates the resulting structural uncertainty into flux estimates. The approach scales to billions of model variants, providing a practical foundation for quantitative Bayesian flux inference under structural model uncertainty in 13C-MFA. AVAILABILITY AND IMPLEMENTATION: Sources and scripts to replicate results are available at https://github.com/JuBiotech/Supplement-to-Jadebeck-et-al.-2026. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.