Model Uncertainty Analysis for Metabolic Network Inference: A Case Study in Bayesian Model Averaging

A distinguishing feature of systems biology is the interrogation of models as a means of making predictions or generating deeper understanding of the systems under study. However, when using a given data set to address a specific question, a unique and provably correct model formulation to apply is rarely known. Instead, a large selection of alternative formulations of varying scopes ensues from combinatorial composition of entities. In this scenario, computational methods that allow us to make statistically valid inferences and predictions, while accounting for the uncertainty in model formulation are desired. We investigate into Bayesian Model Averaging (BMA), which accounts for model uncertainty by considering an ensemble of candidate models instead of a single model instance. To show the computational tractability of BMA, we perform model uncertainty analysis for a realistically sized reaction network from the domain of metabolic flux analysis, featuring an ensemble of millions of models. This is made possible using a Markov Chain Monte Carlo (MCMC) method, tailored to handle parameter and model structure uncertainty simultaneously. To investigate the computational burden of solving the multi-model problem, a super-model is created that includes the reactions of all models in the multi-model problem. The computational burden of the multi-model problem is compared to that of conventional MCMC inference on the single super-model. The comparison yields the surprising insight that the multi-model problem is computationally less expensive than the single super-model problem. Furthermore, we demonstrate, with the example at hand, that BMA yields valid structural network inferences.