A model reduction method for biochemical reaction networks

BMC Systems Biology

Bayu Jayawardhana¹  Barbara M Bakker²  Karen van Eunen²  Arjan van der Schaft³  Shodhan Rao¹ 

[1] Institute of Technology and Management, Nijenborgh 4, University of Groningen, 9747 AG Groningen, Netherlands;Department of Pediatrics, Center for Liver, Digestive and Metabolic Diseases, University Medical Center Groningen, University of Groningen, Hanzeplein 1, 9713 GZ, Groningen, Netherlands;Johann Bernoulli Institute for Mathematics and Computer Science, University of Groningen, P.O. Box 407, 9700 AK Groningen, Netherlands

关键词: Rat liver beta oxidation;    Yeast glycolysis;    Weighted Laplacian;    Complex graph;    Enzyme kinetics;    Kinetic models;   

Others  :  866414
DOI  :  10.1186/1752-0509-8-52

 received in 2013-10-29, accepted in 2014-04-23,  发布年份 2014

【 摘 要 】

Background

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 reactions 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.

【 授权许可】

   
2014 Rao et al.; licensee BioMed Central Ltd.

【 图 表 】

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