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 used a trypsin network as a model system to develop a realistic graph comprising 12 nodes and 32 edges. The graph (or, more specifically, species-species network) was validated using a random graph null model. Our analysis enabled an explicit illustration of the relationships among the nodes over time and, surprisingly, they revealed that a CRN may comprise various subgraphs but never the entire graph with all its edges present. Furthermore, we demonstrated that the application of degree, clustering coefficient, and betweenness centrality (network measures commonly employed in network science) could provide insights into when and if feedback interactions emerge in the CRN. 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.