Identify structures underlying out-of-equilibrium reaction networks with random graph analysis

Network measures have proven very successful in identifying structural patterns in complex systems (e.g., a living cell, a neural network, the Internet). How such measures can be made applicable for the de novo design of chemical reaction networks (CRNs) is unknown. Here, we develop a procedure to model CRNs as a mathematical graph on which network measures and a random graph analysis can be applied. We used an enzymatic CRN (for which a mass-action model was previously developed) to show that the procedure provides insights into its network structure and properties. Temporal analyses, in particular, revealed when feedback interactions emerge in such a network, indicating that CRNs may comprise various subgraphs at different time steps but never the entire graph with all its edges present. We envision that the method developed here could be broadly applied in chemistry to characterize the network properties of many other CRNs, promising data-driven predictions designs of future molecular systems of ever greater complexity.