Metabolic modelling of microbes: the flux-balance approach.

One area of active research in this area has focused on bacterial metabolism (van Gulik and Heijnen, 1995; Liao et al., 1996; Lee et al., 1997; Sauer et al., 1998; Edwards and Palsson, 1999; Sauer and Bailey, 1999; Schilling et al., 1999; Edwards and Palsson, 2000a, b; Schilling et al., 2000; Edwards et al., 2001a, b). Genomic information, coupled with biochemical and strain-specific information, has been used to reconstruct whole-cell metabolic networks for sequenced organisms (Edwards and Palsson, 1999; Schilling and Palsson, 2000) (Fig. 1). However, this information is not sufficient to specify completely the metabolic phenotypes that will be expressed under given environmental conditions. Metabolic phenotypes can be defined in terms of flux distributions through a metabolic network. Interpreting and predicting metabolic flux distributions requires the application of mathematical modelling and computer simulation. There exists a long history of quantitative metabolic modelling (Bailey, 1998) that will not be detailed here. Currently, several well developed mathematical approaches exist for the dynamic analysis of cellular metabolism and its regulation (Shuler and Domach, 1983; Liao, 1993; Palsson and Lee, 1993; Fell, 1996; Barkai and Leibler, 1997; Bailey, 1998; Novak et al., 1999; Tomita et al., 1999; Varner and Ramkrishna, 1999; Vaseghi et al., 1999). Most of these methods require detailed kinetic and concentration information about enzymes and various cofactors. Even though biological information is growing rapidly, we still do not have enough information to describe cellular metabolism in mathematical detail for a single cell (Bailey, 2001). The human red blood cell remains the only exception (Holzhutter et al., 1985; Schuster et al., 1988; Joshi and Palsson, 1989; Rae et al., 1990; Lee and Palsson, 1991; Mulquiney and Kuchel, 1999)

[1]  L. Rédei.  CHAPTER I – SET-THEORETICAL PRELIMINARIES , 1967 .

[2]  Michael L. Shuler,et al.  Mathematical Models of the Growth of Individual Cells: Tools for Testing Biochemical Mechanisms , 1983 .

[3]  E. Papoutsakis.  Equations and calculations for fermentations of butyric acid bacteria , 1984, Biotechnology and bioengineering.

[4]  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.

[5]  E. Papoutsakis,et al.  Equations and calculations of product yields and preferred pathways for butanediol and mixed‐acid fermentations , 1985, Biotechnology and bioengineering.

[6]  E. Papoutsakis,et al.  Fermentation equations for propionic‐acid bacteria and production of assorted oxychemicals from various sugars , 1985, Biotechnology and bioengineering.

[7]  D. Fell,et al.  Fat synthesis in adipose tissue. An examination of stoichiometric constraints. , 1986, The Biochemical journal.

[8]  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.

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

[10]  M. Domach,et al.  Simple constrained‐optimization view of acetate overflow in E. coli , 1990, Biotechnology and bioengineering.

[11]  B O Palsson,et al.  A comprehensive model of human erythrocyte metabolism: extensions to include pH effects. , 1990, Biomedica biochimica acta.

[12]  C. Rae,et al.  Kinetic analysis of the human erythrocyte glyoxalase system using 1H NMR and a computer model. , 1990, European journal of biochemistry.

[13]  B O Palsson,et al.  Optimal selection of metabolic fluxes for in vivo measurement. I. Development of mathematical methods. , 1992, Journal of theoretical biology.

[14]  B O Palsson,et al.  Optimal selection of metabolic fluxes for in vivo measurement. II. Application to Escherichia coli and hybridoma cell metabolism. , 1992, Journal of theoretical biology.

[15]  B O Palsson,et al.  Model complexity has a significant effect on the numerical value and interpretation of metabolic sensitivity coefficients. , 1993, Journal of theoretical biology.

[16]  J. Liao.  Modelling and analysis of metabolic pathways. , 1993, Current opinion in biotechnology.

[17]  B. Palsson,et al.  Biochemical production capabilities of escherichia coli , 1993, Biotechnology and bioengineering.

[18]  B. Palsson,et al.  Metabolic capabilities of Escherichia coli: I. synthesis of biosynthetic precursors and cofactors. , 1993, Journal of theoretical biology.

[19]  G. Stephanopoulos,et al.  Metabolic flux distributions in Corynebacterium glutamicum during growth and lysine overproduction , 2000, Biotechnology and bioengineering.

[20]  B. Palsson,et al.  Metabolic Capabilities of Escherichia coli II. Optimal Growth Patterns , 1993 .

[21]  B. Palsson,et al.  Metabolic Flux Balancing: Basic Concepts, Scientific and Practical Use , 1994, Bio/Technology.

[22]  George Stephanopoulos,et al.  Modeling of Isotope Distributions and Intracellular Fluxes in Metabolic Networks Using Atom Mapping Matrices , 1994 .

[23]  B. Palsson,et al.  Stoichiometric flux balance models quantitatively predict growth and metabolic by-product secretion in wild-type Escherichia coli W3110 , 1994, Applied and environmental microbiology.

[24]  B O Palsson,et al.  Predictions for oxygen supply control to enhance population stability of engineered production strains , 1994, Biotechnology and bioengineering.

[25]  J. Heijnen,et al.  A metabolic network stoichiometry analysis of microbial growth and product formation , 1995, Biotechnology and bioengineering.

[26]  Amit Varma,et al.  Parametric sensitivity of stoichiometric flux balance models applied to wild‐type Escherichia coli metabolism , 1995, Biotechnology and bioengineering.

[27]  J Tramper,et al.  Metabolic flux analysis of hybridoma cells in different culture media using mass balances , 1996, Biotechnology and bioengineering.

[28]  Peter D. Karp,et al.  Eco Cyc: encyclopedia of Escherichia coli genes and metabolism , 1999, Nucleic Acids Res..

[29]  F. Neidhart.  Escherichia coli and Salmonella. , 1996 .

[30]  W Wiechert,et al.  In vivo stationary flux analysis by 13C labeling experiments. , 1996, Advances in biochemical engineering/biotechnology.

[31]  D. Fell.  Understanding the Control of Metabolism , 1996 .

[32]  J. Liao,et al.  Pathway analysis, engineering, and physiological considerations for redirecting central metabolism. , 1996, Biotechnology and bioengineering.

[33]  Microbial genomics: the floodgates open. , 1997, Trends in microbiology.

[34]  H. Bonarius,et al.  Flux analysis of underdetermined metabolic networks: the quest for the missing constraints. , 1997 .

[35]  N. W. Davis,et al.  The complete genome sequence of Escherichia coli K-12. , 1997, Science.

[36]  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.

[37]  M. Domach,et al.  Supply-Side Analysis of Growth of Bacillus subtilis on Glucose-Citrate Medium: Feasible Network Alternatives and Yield Optimality , 1997, Applied and environmental microbiology.

[38]  S. Leibler,et al.  Robustness in simple biochemical networks , 1997, Nature.

[39]  U. Sauer,et al.  Metabolic fluxes in riboflavin-producing Bacillus subtilis , 1997, Nature Biotechnology.

[40]  M. Domach,et al.  Supply-Side Analysis of Growth of Bacillus subtilis on Glucose-Citrate Medium: Feasible Network Alternatives and Yield Optimality , 1997, Applied and environmental microbiology.

[41]  M. Kanehisa,et al.  Computation with the KEGG pathway database. , 1998, Bio Systems.

[42]  J E Bailey,et al.  Mathematical Modeling and Analysis in Biochemical Engineering: Past Accomplishments and Future Opportunities , 1998, Biotechnology progress.

[43]  A flux-based stoichiometric model of enhanced biological phosphorus removal metabolism , 1998 .

[44]  J E Bailey,et al.  Metabolic capacity of Bacillus subtilis for the production of purine nucleosides, riboflavin, and folic acid. , 1998, Biotechnology and bioengineering.

[45]  J. Keasling,et al.  Effect of Escherichia coli biomass composition on central metabolic fluxes predicted by a stoichiometric model. , 1998, Biotechnology and bioengineering.

[46]  Evgeni Selkov,et al.  MPW: the Metabolic Pathways Database , 1998, Nucleic Acids Res..

[47]  D. Ramkrishna,et al.  Metabolic Engineering from a Cybernetic Perspective. 1. Theoretical Preliminaries , 1999, Biotechnology progress.

[48]  K Nasmyth,et al.  Finishing the cell cycle. , 1999, Journal of theoretical biology.

[49]  J E Bailey,et al.  Estimation of P-to-O ratio in Bacillus subtilis and its influence on maximum riboflavin yield. , 1999, Biotechnology and bioengineering.

[50]  Stephanopoulos,et al.  Metabolite and isotopomer balancing in the analysis of metabolic cycles: I. Theory. , 1999, Biotechnology and bioengineering.

[51]  R. Ramakrishna,et al.  Characterizing phenotypic plasticity: a phase plane analysis , 1999, Proceedings of the First Joint BMES/EMBS Conference. 1999 IEEE Engineering in Medicine and Biology 21st Annual Conference and the 1999 Annual Fall Meeting of the Biomedical Engineering Society (Cat. N.

[52]  A J Sinskey,et al.  Metabolite and isotopomer balancing in the analysis of metabolic cycles: II. Applications. , 1999, Biotechnology and bioengineering.

[53]  B. Palsson,et al.  Toward Metabolic Phenomics: Analysis of Genomic Data Using Flux Balances , 1999, Biotechnology progress.

[54]  J. Edwards,et al.  Systems Properties of the Haemophilus influenzaeRd Metabolic Genotype* , 1999, The Journal of Biological Chemistry.

[55]  Masaru Tomita,et al.  E-CELL: software environment for whole-cell simulation , 1999, Bioinform..

[56]  M. Reuss,et al.  In vivo dynamics of the pentose phosphate pathway in Saccharomyces cerevisiae. , 1999, Metabolic engineering.

[57]  P W Kuchel,et al.  Model of 2,3-bisphosphoglycerate metabolism in the human erythrocyte based on detailed enzyme kinetic equations: computer simulation and metabolic control analysis. , 1999, The Biochemical journal.

[58]  Philip W. Kuchel,et al.  Model of 2,3-bisphosphoglycerate metabolism in the human erythrocyte based on detailed enzyme kinetic equations: computer simulation and Metabolic Control Analysis , 1999 .

[59]  David Jenkins,et al.  Development and validation of a flux-based stoichiometric model for enhanced biological phosphorus removal metabolism , 1999 .

[60]  M. Reuss,et al.  In VivoDynamics of the Pentose Phosphate Pathway inSaccharomyces cerevisiae , 1999 .

[61]  O. Fiehn,et al.  Metabolite profiling for plant functional genomics , 2000, Nature Biotechnology.

[62]  B. Palsson,et al.  The Escherichia coli MG1655 in silico metabolic genotype: its definition, characteristics, and capabilities. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[63]  I. Grossmann,et al.  Recursive MILP model for finding all the alternate optima in LP models for metabolic networks , 2000 .

[64]  B. Palsson,et al.  Assessment of the metabolic capabilities of Haemophilus influenzae Rd through a genome-scale pathway analysis. , 2000, Journal of theoretical biology.

[65]  B. Palsson.  The challenges of in silico biology , 2000, Nature Biotechnology.

[66]  Bernhard O. Palsson,et al.  Metabolic flux balance analysis and the in silico analysis of Escherichia coli K-12 gene deletions , 2000, BMC Bioinformatics.

[67]  B. Palsson,et al.  Combining pathway analysis with flux balance analysis for the comprehensive study of metabolic systems. , 2000, Biotechnology and bioengineering.

[68]  Edward J. Caramana.  Mathematical Modeling and Analysis , 2000 .

[69]  A. Burgard,et al.  Probing the performance limits of the Escherichia coli metabolic network subject to gene additions or deletions. , 2001, Biotechnology and bioengineering.

[70]  B. Palsson,et al.  In silico predictions of Escherichia coli metabolic capabilities are consistent with experimental data , 2001, Nature Biotechnology.

[71]  M. Waterfield,et al.  Proteomics--post-genomic cartography to understand gene function. , 2001, Trends in pharmacological sciences.

[72]  B. Palsson,et al.  Regulation of gene expression in flux balance models of metabolism. , 2001, Journal of theoretical biology.

[73]  D. Kell,et al.  A functional genomics strategy that uses metabolome data to reveal the phenotype of silent mutations , 2001, Nature Biotechnology.

[74]  T. Gaasterland,et al.  Whole-genome analysis: annotations and updates. , 2001, Current opinion in structural biology.

[75]  C. Jacq,et al.  Transcriptomes, transcription activators and microarrays , 2001, FEBS letters.

[76]  Monica Riley,et al.  A functional update of the Escherichia coli K-12 genome , 2001, Genome Biology.

[77]  J. Bailey.  Complex biology with no parameters , 2001, Nature Biotechnology.

[78]  J. Shendure,et al.  Selection analyses of insertional mutants using subgenic-resolution arrays , 2001, Nature Biotechnology.

[79]  B. Palsson,et al.  Characterizing the metabolic phenotype: A phenotype phase plane analysis , 2002, Biotechnology and bioengineering.