An Automated Model Reduction Method for Biochemical Reaction Networks

Abstract

We propose a new approach to the model reduction of biochemical reaction networks governed by various types of enzyme kinetics rate laws with non-autocatalytic reactions, each of which can be reversible or irreversible. This method extends the approach for model reduction previously proposed by Rao et al. which proceeds by the step-wise reduction in the number of complexes by Kron reduction of the weighted Laplacian corresponding to the complex graph of the network. The main idea in the current manuscript is based on rewriting the mathematical model of a reaction network as a model of a network consisting of linkage classes that contain more than one reaction. It is done by joining certain distinct linkage classes into a single linkage class by using the conservation laws of the network. We show that this adjustment improves the extent of applicability of the method proposed by Rao et al. We automate the entire reduction procedure using Matlab. We test our automated model reduction to two real-life reaction networks, namely, a model of neural stem cell regulation and a model of hedgehog signaling pathway. We apply our reduction approach to meaningfully reduce the number of complexes in the complex graph corresponding to these networks. When the number of species’ concentrations in the model of neural stem cell regulation is reduced by 33.33%, the difference between the dynamics of the original model and the reduced model, quantified by an error integral, is only 4.85%. Likewise, when the number of species’ concentrations is reduced by 33.33% in the model of hedgehog signaling pathway, the difference between the dynamics of the original model and the reduced model is only 6.59%.

Keywords

• graph theory
• biochemistry
• chemical reaction network theory
• systems biology
• mathematical modeling
• weighted Laplacian matrix