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Modelling of biochemical systems usually focuses on certain pathways, while the concentrations of so-called external metabolites are considered fixed. This approximation ignores feedback loops mediated by the environ-ment, that is, via external metabolites and reactions. To achieve a more realistic, dynamic description that is still numerically efficient, we propose a new methodology: the basic idea is to describe the environment by a lin-ear effective model of adjustable dimensionality. | ễFEBS Journal Biochemical network models simplified by balanced truncation Wolfram Liebermeister1 Ulrike Baur2 and Edda Klipp1 1 Max Planck Institute for Molecular Genetics Berlin Germany 2 TechnicalUniversity Berlin Institute of Mathematics Berlin Germany Keywords balanced truncation biochemical reaction system complexity reduction metabolic model modularity Correspondence W. Liebermeister Max Planck Institute for Molecular Genetics IhnestraBe 73 14195 Berlin Germany Fax 49 30 80409322 Tel 49 30 80409318 E-mail lieberme@molgen.mpg.de Website http www.molgen.mpg.de ag_klipp Received 24 December 2004 revised 10 May 2005 accepted 19 May 2005 doi 10.1111 j.1742-4658.2005.04780.x Modelling of biochemical systems usually focuses on certain pathways while the concentrations of so-called external metabolites are considered fixed. This approximation ignores feedback loops mediated by the environment that is via external metabolites and reactions. To achieve a more realistic dynamic description that is still numerically efficient we propose a new methodology the basic idea is to describe the environment by a linear effective model of adjustable dimensionality. In particular we a split the entire model into a subsystem and its environment b linearize the environment model around a steady state and c reduce its dimensionality by balanced truncation an established method for large-scale model reduction. The reduced variables describe the dynamic modes in the environment that dominate its interaction with the subsystem. We compute metabolic response coefficients that account for complexity-reduced dynamics of the environment. Our simulations show that a dynamic environment model can improve the simulation results considerably even if the environment model has been drastically reduced and if its kinetic parameters are only approximately known. The speed-up in computation gained by model reduction may become vital for parameter estimation in large cell models. Complexity .
