Quantifying network uncertainty in chemical reaction network inference

Dynamical systems in biology are complex, and one often does not have comprehensive knowledge about the interactions involved. Chemical reaction network (CRN) inference aims to identify, from time-course observations of species concentrations, the reactions occurring between species. Existing approaches such as sparse regularisation largely focus on identifying a single, most likely CRN, without addressing uncertainty about the network structure. However, it is important to quantify network uncertainty to have confidence in our inference and predictions. In this work, we adapt sparse regularisation to quantify network uncertainty by mapping locally optimal solutions to CRN structures, which are subsequently weighted by approximate posterior probabilities. To validate our approach, we show in a simulation study that our method recovers CRNs that are structurally indistinguishable from the ground truth CRN. This involves extending theory on structural distinguishability to characterise the building blocks of structurally indistinguishable CRNs. We also find that nonconvex penalty functions give better coverage of plausible CRNs than the popular lasso regularisation. We also demonstrate that our method simultaneously recovers reactions proposed across multiple literature sources for a real-world reaction system. Our emphasis on network-level probabilities enables a novel, hierarchical representation of reaction ambiguities, which highlights alternative reaction pathways supported by the data and can guide future experimental design.