A model reduction method for biochemical reaction networks

Shodhan Rao, Arjan van der Schaft, Karen van Eunen, Barbara M Bakker, Bayu Jayawardhana
2014 BMC Systems Biology  
In this paper we propose a model reduction method for biochemical reaction networks governed by a variety of reversible and irreversible enzyme kinetic rate laws, including reversible Michaelis-Menten and Hill kinetics. The method proceeds by a stepwise reduction in the number of complexes, defined as the left and right-hand sides of the reactions in the network. It is based on the Kron reduction of the weighted Laplacian matrix, which describes the graph structure of the complexes and
more » ... in the network. It does not rely on prior knowledge of the dynamic behaviour of the network and hence can be automated, as we demonstrate. The reduced network has fewer complexes, reactions, variables and parameters as compared to the original network, and yet the behaviour of a preselected set of significant metabolites in the reduced network resembles that of the original network. Moreover the reduced network largely retains the structure and kinetics of the original model. Results: We apply our method to a yeast glycolysis model and a rat liver fatty acid beta-oxidation model. When the number of state variables in the yeast model is reduced from 12 to 7, the difference between metabolite concentrations in the reduced and the full model, averaged over time and species, is only 8%. Likewise, when the number of state variables in the rat-liver beta-oxidation model is reduced from 42 to 29, the difference between the reduced model and the full model is 7.5%. Conclusions: The method has improved our understanding of the dynamics of the two networks. We found that, contrary to the general disposition, the first few metabolites which were deleted from the network during our stepwise reduction approach, are not those with the shortest convergence times. It shows that our reduction approach performs differently from other approaches that are based on time-scale separation. The method can be used to facilitate fitting of the parameters or to embed a detailed model of interest in a more coarse-grained yet realistic environment. A kinetic model of a biochemical reaction network consists of a set of ordinary differential equations describing the dynamics of the concentrations of all metabolites in the reaction network. Most biochemical reaction networks are complex and involve many enzyme-catalyzed processes with non-linear kinetics and intricate stoichiometric and regulatory interactions between the enzymes. Consequently, the mathematical models of such networks contain high-dimensional sets of coupled rational differential equations, which sometimes require huge computational effort to analyze. The current state-of-the-art numerical tools for stability analysis, for bifurcation study and for other types of dynamical analysis are known to suffer from a so-called curse-of-dimensionality. For example, the largest biological model that has numerically been analyzed for bifurcation in [1] consists of 25 metabolites and 37 parameters and the one in [2] has 22 metabolites.
doi:10.1186/1752-0509-8-52 pmid:24885656 pmcid:PMC4041147 fatcat:iraa2pm3rvcgndji6foaxnd23e