A model reduction method for biochemical reaction networks

BackgroundIn 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.ResultsWe 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%.ConclusionsThe 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.

[1]  Mudita Singhal,et al.  COPASI - a COmplex PAthway SImulator , 2006, Bioinform..

[2]  Alexander N. Gorban,et al.  Robust simplifications of multiscale biochemical networks , 2008, BMC Systems Biology.

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

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

[5]  K. Brown,et al.  Graduate Texts in Mathematics , 1982 .

[6]  Gunnar Cedersund,et al.  Reduction of a biochemical model with preservation of its basic dynamic properties , 2006, The FEBS journal.

[7]  Klaas R. Westerterp,et al.  Development of catalytic hydrogenation reactors for the fine chemicals industry , 1988 .

[8]  L. A. Segel,et al.  The Quasi-Steady-State Assumption: A Case Study in Perturbation , 1989, SIAM Rev..

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

[10]  Béla Bollobás,et al.  Modern Graph Theory , 2002, Graduate Texts in Mathematics.

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

[12]  Marc R. Roussel,et al.  Invariant manifold methods for metabolic model reduction. , 2001, Chaos.

[13]  김삼묘,et al.  “Bioinformatics” 특집을 내면서 , 2000 .

[14]  Dimitris A. Goussis,et al.  Algorithmic asymptotic analysis of the NF-κBNF-κB signaling system , 2013, Comput. Math. Appl..

[15]  Dima Grigoriev,et al.  Tropical Geometries and Dynamics of Biochemical Networks Application to Hybrid Cell Cycle Models , 2011, SASB.

[16]  M. Apri,et al.  Complexity reduction preserving dynamical behavior of biochemical networks. , 2012, Journal of theoretical biology.

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

[18]  Irina Surovtsova,et al.  Approaches to Complexity Reduction in a Systems Biology Research Environment (SYCAMORE) , 2006, Proceedings of the 2006 Winter Simulation Conference.

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

[20]  Karen van Eunen,et al.  Biochemical Competition Makes Fatty-Acid β-Oxidation Vulnerable to Substrate Overload , 2013, PLoS Comput. Biol..

[21]  Gang Liu,et al.  Sensitivity, principal component and flux analysis applied to signal transduction: the case of epidermal growth factor mediated signaling , 2005, Bioinform..

[22]  S. Subramaniam,et al.  Reduced-order modelling of biochemical networks: application to the GTPase-cycle signalling module. , 2005, Systems biology.

[23]  Sven Sahle,et al.  Glycolytic oscillations in a model of a lactic acid bacterium metabolism. , 2013, Biophysical chemistry.

[24]  I. E. Nikerel,et al.  Model reduction and a priori kinetic parameter identifiability analysis using metabolome time series for metabolic reaction networks with linlog kinetics. , 2009, Metabolic engineering.

[25]  Henning Schmidt,et al.  Complexity reduction of biochemical rate expressions , 2008, Bioinform..

[26]  L. Petzold,et al.  Model reduction for chemical kinetics: an optimization approach , 1999 .

[27]  Bruce L. Clarke,et al.  General method for simplifying chemical networks while preserving overall stoichiometry in reduced mechanisms , 1992 .

[28]  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..

[29]  Ioannis P. Androulakis,et al.  Kinetic mechanism reduction based on an integer programming approach , 2000 .

[30]  Herbert M. Sauro,et al.  Bifurcation discovery tool , 2005, Bioinform..

[31]  Neil Swainston,et al.  Towards a genome-scale kinetic model of cellular metabolism , 2010, BMC Systems Biology.

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

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

[34]  Alexander N Gorban,et al.  Reduction of dynamical biochemical reactions networks in computational biology , 2012, Front. Gene..

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

[36]  F. G. Young.  Enzymes , 1951 .

[37]  Paul I. Barton,et al.  Optimally-reduced kinetic models: reaction elimination in large-scale kinetic mechanisms , 2003 .