Structural reduction of chemical reaction networks based on topology

Abstract

We develop a model-independent reduction method of chemical reaction systems based on the stoichiometry, which determines their network topology. A subnetwork can be eliminated systematically to give a reduced system with fewer degrees of freedom. This subnetwork removal is accompanied by rewiring of the network, which is prescribed by the Schur complement of the stoichiometric matrix. Using homology and cohomology groups to characterize the topology of chemical reaction networks, we can track the changes of the network topology induced by the reduction through the changes in those groups. We prove that, when certain topological conditions are met, the steady-state chemical concentrations and reaction rates of the reduced system are ensured to be the same as those of the original system. This result holds regardless of the modeling of the reactions, namely, chemical kinetics, since the conditions only involve topological information. This is advantageous because the details of reaction kinetics and parameter values are difficult to identify in many practical situations. The method allows us to reduce a reaction network while preserving its original steady-state properties, thereby complex reaction systems can be studied efficiently. We demonstrate the reduction method in hypothetical networks and the central carbon metabolism of Escherichia coli.