Non-linear reduction for kinetic models of metabolic reaction networks.

Kinetic models of metabolic networks are essential for predicting and optimizing the transient behavior of cells in culture. However, such models are inherently high dimensional and stiff due to the large number of species and reactions involved and to kinetic rate constants of widely different orders of magnitude. In this paper we address the problem of deriving non-stiff, reduced-order non-linear models of the dominant dynamics of metabolic networks with fast and slow reactions. We present a method, based on singular perturbation analysis, which allows the systematic identification of quasi-steady-state conditions for the fast reactions, and the derivation of explicit non-linear models of the slow dynamics independent of the fast reaction rate expressions. The method is successfully applied to detailed models of metabolism in human erythrocytes and Saccharomyces cerevisiae.

[1]  S. Jørgensen,et al.  A biochemically structured model for Saccharomyces cerevisiae. , 2001, Journal of biotechnology.

[2]  M. Reuss,et al.  In vivo analysis of metabolic dynamics in Saccharomyces cerevisiae : I. Experimental observations. , 1997, Biotechnology and bioengineering.

[3]  P. Daoutidis,et al.  Model reduction for reaction-convection processes with fast and slow reactions , 2003, 2003 European Control Conference (ECC).

[4]  M M Domach,et al.  Computer model for glucose‐limited growth of a single cell of Escherichia coli B/r‐A , 1984, Biotechnology and bioengineering.

[5]  H. Shimizu,et al.  Optimization of agitation and aeration conditions for maximum virginiamycin production , 1999, Applied Microbiology and Biotechnology.

[6]  H. Holzhütter,et al.  Interrelations between glycolysis and the hexose monophosphate shunt in erythrocytes as studied on the basis of a mathematical model. , 1988, Bio Systems.

[7]  M. Mavrovouniotis,et al.  Simplification of Mathematical Models of Chemical Reaction Systems. , 1998, Chemical reviews.

[8]  H. Holzhütter,et al.  Mathematical modelling of metabolic pathways affected by an enzyme deficiency. A mathematical model of glycolysis in normal and pyruvate-kinase-deficient red blood cells. , 1985, European journal of biochemistry.

[9]  R. Heinrich,et al.  Quasi-steady-state approximation in the mathematical modeling of biochemical reaction networks , 1983 .

[10]  R Heinrich,et al.  Metabolic regulation and mathematical models. , 1977, Progress in biophysics and molecular biology.

[11]  J. Keasling,et al.  A Dynamic Model of theEscherichia coliPhosphate-Starvation Response , 1998 .

[12]  D. Fell,et al.  Detection of elementary flux modes in biochemical networks: a promising tool for pathway analysis and metabolic engineering. , 1999, Trends in biotechnology.

[13]  H. Holzhütter,et al.  Mathematical modelling of metabolic pathways affected by an enzyme deficiency. Energy and redox metabolism of glucose-6-phosphate-dehydrogenase-deficient erythrocytes. , 1989, European journal of biochemistry.

[14]  H. Holzhütter,et al.  Use of mathematical models for predicting the metabolic effect of large-scale enzyme activity alterations. Application to enzyme deficiencies of red blood cells. , 1995, European journal of biochemistry.

[15]  Prodromos Daoutidis,et al.  Singular perturbation modeling of nonlinear processes with nonexplicit time-scale multiplicity , 1998 .

[16]  Danail Bonchev,et al.  Chemical Reaction Networks: A Graph-Theoretical Approach , 1996 .

[17]  J. Nielsen,et al.  Metabolic engineering: techniques for analysis of targets for genetic manipulations. , 1998, Biotechnology and bioengineering.

[18]  D. Kompala,et al.  A structured kinetic modeling framework for the dynamics of hybridoma growth and monoclonal antibody production in continuous suspension cultures , 1989, Biotechnology and bioengineering.

[19]  Reinhart Heinrich,et al.  Mathematical analysis of multienzyme systems. I. Modelling of the glycolysis of human erythrocytes. , 1975, Bio Systems.

[20]  R. Heinrich,et al.  The Regulation of Cellular Systems , 1996, Springer US.

[21]  A. Gambhir,et al.  Multiple steady states with distinct cellular metabolism in continuous culture of mammalian cells. , 2000, Biotechnology and bioengineering.

[22]  P. Daoutidis,et al.  Nonlinear model reduction of chemical reaction systems , 2001 .

[23]  G. Lee,et al.  Enhancement of monoclonal antibody production by immobilized hybridoma cell culture with hyperosmolar medium , 1995, Biotechnology and bioengineering.

[24]  M. Reuss,et al.  In vivo analysis of metabolic dynamics in Saccharomyces cerevisiae: II. Mathematical model. , 1997, Biotechnology and bioengineering.

[25]  R. Heinrich,et al.  Metabolic Pathway Analysis: Basic Concepts and Scientific Applications in the Post‐genomic Era , 1999, Biotechnology progress.

[26]  J. Keasling,et al.  Stoichiometric model of Escherichia coli metabolism: incorporation of growth-rate dependent biomass composition and mechanistic energy requirements. , 1997, Biotechnology and bioengineering.

[27]  J. A. Roels,et al.  Energetics and Kinetics in Biotechnology , 1983 .

[28]  J. Keasling,et al.  Effect of Polyphosphate Metabolism on the Escherichia coli Phosphate‐Starvation Response , 1999, Biotechnology progress.

[29]  B. Palsson,et al.  Metabolic dynamics in the human red cell. Part I--A comprehensive kinetic model. , 1989, Journal of theoretical biology.

[30]  David F. Ollis,et al.  Biochemical Engineering Fundamentals , 1976 .

[31]  M A Savageau,et al.  Model assessment and refinement using strategies from biochemical systems theory: application to metabolism in human red blood cells. , 1996, Journal of theoretical biology.

[32]  K. Mauch,et al.  Tendency modeling: a new approach to obtain simplified kinetic models of metabolism applied to Saccharomyces cerevisiae. , 2000, Metabolic engineering.

[33]  B O Palsson,et al.  Metabolic dynamics in the human red cell. Part III--Metabolic reaction rates. , 1990, Journal of theoretical biology.

[34]  C. Goochee,et al.  The effect of cell-culture conditions on the oligosaccharide structures of secreted glycoproteins. , 1994, Current opinion in biotechnology.

[35]  C T Verrips,et al.  A structured, minimal parameter model of the central nitrogen metabolism in Saccharomyces cerevisiae: the prediction of the behavior of mutants. , 1998, Journal of theoretical biology.

[36]  A Joshi,et al.  Reducing complexity in metabolic networks: making metabolic meshes manageable. , 1987, Federation proceedings.

[37]  F. Kargı,et al.  Bioprocess Engineering: Basic Concepts , 1991 .

[38]  A. Lehninger.  Principles of Biochemistry , 1984 .