Bioinformatics Original Paper Bayesian-based Selection of Metabolic Objective Functions

Motivation: A critical component of in silico analysis of under-determined metabolic systems is the identification of the appropriate objective function. A common assumption is that the objective of the cell is to maximize growth. This objective function has been shown to be consistent in a few limited experimental cases, but may not be universally appropriate. Here a method is presented to quantitatively determine the most probable objective function. Results: The genome-scale metabolism of Escherichia coli growing on succinate was used as a case-study for analysis. Five different objective functions, including maximization of growth rate, were chosen based on biological plausibility. A combination of flux balance analysis and linear programming was used to simulate cellular metabolism , which was then compared to independent experimental data using a Bayesian objective function discrimination technique. After comparing rates of oxygen uptake and acetate production, minimization of the production rate of redox potential was determined to be the most probable objective function. Given the appropriate reaction network and experimental data, the discrimination technique can be applied to any bacterium to test a variety of different possible objective functions. Supplementary information: Additional files, code and a program for carrying out model discrimination are available at

[1]  L. Wackett Metabolic engineering , 2009, Nature biotechnology.

[2]  Nagasuma R. Chandra,et al.  Flux Balance Analysis of Mycolic Acid Pathway: Targets for Anti-Tubercular Drugs , 2005, PLoS Comput. Biol..

[3]  U. Sauer,et al.  Large-scale in vivo flux analysis shows rigidity and suboptimal performance of Bacillus subtilis metabolism , 2005, Nature Genetics.

[4]  G. Stephanopoulos,et al.  Strain improvement by metabolic engineering: lysine production as a case study for systems biology. , 2005, Current opinion in biotechnology.

[5]  G. Stephanopoulos,et al.  Identifying gene targets for the metabolic engineering of lycopene biosynthesis in Escherichia coli. , 2005, Metabolic engineering.

[6]  Ranjan Srivastava,et al.  Evaluation of HIV-1 kinetic models using quantitative discrimination analysis , 2005, Bioinform..

[7]  Harvey J. Greenberg,et al.  Reconstruction and Functional Characterization of the Human Mitochondrial Metabolic Network Based on Proteomic and Biochemical Data* , 2004, Journal of Biological Chemistry.

[8]  B. Palsson,et al.  Genome-scale in silico models of E. coli have multiple equivalent phenotypic states: assessment of correlated reaction subsets that comprise network states. , 2004, Genome research.

[9]  G. Stephanopoulos,et al.  Systematic quantification of complex metabolic flux networks using stable isotopes and mass spectrometry. , 2003, European journal of biochemistry.

[10]  B. Palsson,et al.  An expanded genome-scale model of Escherichia coli K-12 (iJR904 GSM/GPR) , 2003, Genome Biology.

[11]  A. Burgard,et al.  Optimization-based framework for inferring and testing hypothesized metabolic objective functions. , 2003, Biotechnology and bioengineering.

[12]  B. Palsson,et al.  Genome-scale reconstruction of the Saccharomyces cerevisiae metabolic network. , 2003, Genome research.

[13]  B. Palsson,et al.  Escherichia coli K-12 undergoes adaptive evolution to achieve in silico predicted optimal growth , 2002, Nature.

[14]  G. Church,et al.  Genome-Scale Metabolic Model of Helicobacter pylori 26695 , 2002, Journal of bacteriology.

[15]  H. Kitano Systems Biology: A Brief Overview , 2002, Science.

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

[17]  B O Palsson,et al.  Flux-balance analysis of mitochondrial energy metabolism: consequences of systemic stoichiometric constraints. , 2001, American journal of physiology. Regulatory, integrative and comparative physiology.

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

[19]  G. Stephanopoulos,et al.  Metabolic flux analysis of postburn hepatic hypermetabolism. , 2000, Metabolic engineering.

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

[21]  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.

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

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

[24]  G. Stephanopoulos,et al.  Metabolic flux analysis: a powerful tool for monitoring tissue function. , 1999, Tissue engineering.

[25]  M M Ataai,et al.  Metabolic fluxes, pools, and enzyme measurements suggest a tighter coupling of energetics and biosynthetic reactions associated with reduced pyruvate kinase flux. , 1999, Biotechnology and bioengineering.

[26]  G Stephanopoulos,et al.  Metabolic flux analysis of hybridoma continuous culture steady state multiplicity. , 1999, Biotechnology and bioengineering.

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

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

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

[30]  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.

[31]  James C. Schaff,et al.  The Virtual Cell , 1998, Pacific Symposium on Biocomputing.

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

[33]  W. E. Stewart,et al.  Discrimination and goodness of fit of multiresponse mechanistic models , 1998 .

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

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

[36]  H. Holms,et al.  Flux analysis and control of the central metabolic pathways in Escherichia coli. , 1996, FEMS microbiology reviews.

[37]  George E. P. Box,et al.  Model Discrimination and Criticism with Single-Response Data , 1996 .

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

[39]  U. Sauer,et al.  Physiology and metabolic fluxes of wild-type and riboflavin-producing Bacillus subtilis , 1996, Applied and environmental microbiology.

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

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

[42]  H. Kacser,et al.  The control of flux. , 1995, Biochemical Society transactions.

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

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

[45]  M M Ataai,et al.  Analysis of metabolic fluxes in batch and continuous cultures of Bacillus subtilis , 1993, Biotechnology and bioengineering.

[46]  Michael L. Mavrovouniotis,et al.  Synthesis of biochemical production routes , 1992 .

[47]  Warren E. Stewart,et al.  Parameter estimation from multiresponse data , 1992 .

[48]  B. Palsson,et al.  Network analysis of intermediary metabolism using linear optimization. I. Development of mathematical formalism. , 1992, Journal of theoretical biology.

[49]  G. Stephanopoulos,et al.  Network rigidity and metabolic engineering in metabolite overproduction , 1991, Science.

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

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

[52]  B O Palsson,et al.  Metabolic dynamics in the human red cell. Part IV--Data prediction and some model computations. , 1990, Journal of theoretical biology.

[53]  B O Palsson,et al.  Metabolic dynamics in the human red cell. Part II--Interactions with the environment. , 1989, Journal of theoretical biology.

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

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

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

[57]  G. T. Tsao,et al.  Investigation of bacterial growth on mixed substrates: Experimental evaluation of cybernetic models , 1986, Biotechnology and bioengineering.

[58]  Warren E. Stewart,et al.  Bayesian Estimation of Common Parameters From Multiresponse Data With Missing Observations , 1981 .

[59]  Shuichi Aiba,et al.  Identification of metabolic model: Citrate production from glucose by Candida lipolytica , 1979 .

[60]  M. Savageau Biochemical systems analysis. II. The steady-state solutions for an n-pool system using a power-law approximation. , 1969, Journal of theoretical biology.

[61]  M. Savageau Biochemical systems analysis. II. The steady-state solutions for an n-pool system using a power-law approximation. , 1969, Journal of theoretical biology.

[62]  Rishi Jain,et al.  Bayesian-based selection of metabolic objective functions , 2007 .

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

[64]  G. Stephanopoulos Metabolic fluxes and metabolic engineering. , 1999, Metabolic engineering.

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

[66]  B O Palsson,et al.  Computer model of human erythrocyte metabolism. , 1989, Progress in clinical and biological research.