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We develop a model-independent reduction method of chemical reaction systemsbased on the stoichiometry, which determines their network topology. Asubnetwork can be eliminated systematically to give a reduced system with fewerdegrees of freedom. This subnetwork removal is accompanied by rewiring of thenetwork, which is prescribed by the Schur complement of the stoichiometricmatrix. Using homology and cohomology groups to characterize the topology ofchemical reaction networks, we can track the changes of the network topologyinduced by the reduction through the changes in those groups. We prove that,when certain topological conditions are met, the steady-state chemicalconcentrations and reaction rates of the reduced system are ensured to be thesame as those of the original system. This result holds regardless of themodeling of the reactions, namely chemical kinetics, since the conditions onlyinvolve topological information. This is advantageous because the details ofreaction kinetics and parameter values are difficult to identify in manypractical situations. The method allows us to reduce a reaction network whilepreserving its original steady-state properties, thereby complex reactionsystems can be studied efficiently. We demonstrate the reduction method inhypothetical networks and the central carbon metabolism of Escherichia coli.

Structural reduction of chemical reaction networks based on topology