Model-order reduction of biochemical reaction networks

In this paper we propose a model-order reduction method for chemical reaction networks governed by general enzyme kinetics, including the mass-action and Michaelis-Menten kinetics. The model-order reduction method is based on the Kron reduction of the weighted Laplacian matrix which describes the graph structure of complexes in the chemical reaction network. We apply our method to a yeast glycolysis model, where the simulation result shows that the transient behaviour of a number of key metabolites of the reduced-order model is in good agreement with those of the full-order model.

[1]  Arjan van der Schaft,et al.  On the graph and systems analysis of reversible chemical reaction networks with mass action kinetics , 2012, 2012 American Control Conference (ACC).

[2]  Gabriel Kron,et al.  Tensor analysis of networks , 1967 .

[3]  Iliya V. Karlin,et al.  Method of invariant manifold for chemical kinetics , 2003 .

[4]  Mikael Sunnåker,et al.  A method for zooming of nonlinear models of biochemical systems , 2011, BMC Systems Biology.

[5]  F. Horn.  Necessary and sufficient conditions for complex balancing in chemical kinetics , 1972 .

[6]  Arjan van der Schaft,et al.  A graph-theoretical approach for the analysis and model reduction of complex-balanced chemical reaction networks , 2012, Journal of Mathematical Chemistry.

[7]  Hanna Maria Hardin.  Handling biological complexity: as simple as possible but not simpler , 2010 .

[8]  Antonis Papachristodoulou,et al.  Guaranteed error bounds for structured complexity reduction of biochemical networks. , 2012, Journal of theoretical biology.

[9]  Arjan van der Schaft,et al.  Characterization and partial synthesis of the behavior of resistive circuits at their terminals , 2010, Syst. Control. Lett..

[10]  Eduardo D. Sontag.  Structure and stability of certain chemical networks and applications to the kinetic proofreading model of T-cell receptor signal transduction , 2001, IEEE Trans. Autom. Control..

[11]  Guangming Xie,et al.  Consensus in networked multi-agent systems via sampled control: Switching topology case , 2009, 2009 American Control Conference.

[12]  城塚 正,et al.  Chemical Engineering Scienceについて , 1962 .

[13]  R. Jackson,et al.  General mass action kinetics , 1972 .

[14]  M. Feinberg.  Chemical reaction network structure and the stability of complex isothermal reactors—I. The deficiency zero and deficiency one theorems , 1987 .

[15]  Hans V. Westerhoff,et al.  Testing Biochemistry Revisited: How In Vivo Metabolism Can Be Understood from In Vitro Enzyme Kinetics , 2012, PLoS Comput. Biol..

[16]  Arjan van der Schaft,et al.  On the Mathematical Structure of Balanced Chemical Reaction Networks Governed by Mass Action Kinetics , 2011, SIAM J. Appl. Math..