Accurate quantification of intracellular metabolic fluxes is central to systems biology and biotechnology. Flux estimation relies on biochemical network models, with $^{13}$C 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 (BMA) provides a principled framework for this purpose, but its application to $^{13}$C-MFA has so far been restricted to uncertainty in reaction bidirectionality within fixed network topologies. We introduce a scalable Bayesian inference framework for $^{13}$C-MFA, Bayesian model set averaging, that applies BMA to encompass uncertainty in reactions and pathways. Our approach combines reversible jump Markov chain Monte Carlo for trans-dimensional exploration of model spaces with diffusive nested sampling for robust estimation of model evidences, enabling averaging over large families of metabolic network models. 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 data-supported model structures. Importantly, rather than committing to a single model, the framework manages structural uncertainty: under limited data, competing models are retained, whereas increasing data informativeness improved model and flux recovery. The approach scales to billions of model variants, providing a practical foundation for uncertainty- and misspecification-aware quantitative flux inference in $^{13}$C-MFA.

翻译：细胞内代谢通量的准确定量是系统生物学和生物技术的核心问题。通量估计依赖于生物化学网络模型，而$^{13}$C代谢通量分析（MFA）是目前最先进的方法。然而，同位素标记数据通常不足以唯一地支持单一网络结构。在这种情况下，通量估计变得依赖于模型，这突显出需要明确考虑结构不确定性的方法。贝叶斯模型平均（BMA）为此提供了一个有原则的框架，但迄今为止其在$^{13}$C-MFA中的应用仅限于固定网络拓扑内反应双向性的不确定性。我们提出了一种可扩展的贝叶斯推断框架——贝叶斯模型集平均，用于$^{13}$C-MFA，该框架应用BMA来涵盖反应和路径的不确定性。我们的方法结合了用于跨维模型空间探索的可逆跳跃马尔可夫链蒙特卡洛和用于稳健估计模型证据的扩散嵌套采样，从而能够对大量代谢网络模型族进行平均。通过说明性和应用规模合成案例研究，我们证明了该方法能产生稳健的通量估计，揭示多个网络配置何时在统计上不可区分，并恢复数据支持的模型结构。重要的是，该框架并非致力于单一模型，而是管理结构不确定性：在数据有限的情况下，保留竞争模型，而数据信息量的增加改善了模型和通量的恢复。该方法可扩展到数十亿个模型变体，为$^{13}$C-MFA中具有不确定性和错误指定意识的定量通量推断提供了实用基础。