Hybrid dynamic modeling of Escherichia coli central metabolic network combining Michaelis-Menten and approximate kinetic equations

The construction of dynamic metabolic models at reaction network level requires the use of mechanistic enzymatic rate equations that comprise a large number of parameters. The lack of knowledge on these equations and the difficulty in the experimental identification of their associated parameters, represent nowadays the limiting factor in the construction of such models. In this study, we compare four alternative modeling approaches based on Michaelis-Menten kinetics for the bi-molecular reactions and different types of simplified rate equations for the remaining reactions (generalized mass action, convenience kinetics, lin-log and power-law). Using the mechanistic model for Escherichia coli central carbon metabolism as a benchmark, we investigate the alternative modeling approaches through comparative simulations analyses. The good dynamic behavior and the powerful predictive capabilities obtained using the hybrid model composed of Michaelis-Menten and the approximate lin-log kinetics indicate that this is a possible suitable approach to model complex large-scale networks where the exact rate laws are unknown.

[1]  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.

[2]  D A Fell,et al.  Control of the threonine-synthesis pathway in Escherichia coli: a theoretical and experimental approach. , 2001, The Biochemical journal.

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

[4]  Douglas B. Kell,et al.  Non-linear optimization of biochemical pathways: applications to metabolic engineering and parameter estimation , 1998, Bioinform..

[5]  E. Klipp,et al.  Bringing metabolic networks to life: convenience rate law and thermodynamic constraints , 2006, Theoretical Biology and Medical Modelling.

[6]  M. Savageau Biochemical systems analysis. III. Dynamic solutions using a power-law approximation , 1970 .

[7]  John J. Tyson,et al.  Modeling Molecular Interaction Networks with Nonlinear Ordinary Differential Equations , 2006 .

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

[9]  J. Preiss,et al.  Biosynthesis of bacterial glycogen. Kinetic studies of a glucose-1-phosphate adenylyltransferase (EC 2.7.7.27) from a glycogen-deficient mutant of Escherichia coli B. , 1975, The Journal of biological chemistry.

[10]  Maria Rodriguez-Fernandez,et al.  A hybrid approach for efficient and robust parameter estimation in biochemical pathways. , 2006, Bio Systems.

[11]  B. Palsson,et al.  k-Cone analysis: determining all candidate values for kinetic parameters on a network scale. , 2005, Biophysical journal.

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

[13]  David S. Wishart,et al.  The CyberCell Database (CCDB): a comprehensive, self-updating, relational database to coordinate and facilitate in silico modeling of Escherichia coli , 2004, Nucleic Acids Res..

[14]  Masaru Tomita,et al.  Theoretical Biology and Medical Modelling , 2022 .

[15]  M. Tomita,et al.  Quantitative metabolome analysis using capillary electrophoresis mass spectrometry. , 2003, Journal of proteome research.

[16]  Jonas S. Almeida,et al.  Parameter optimization in S-system models , 2008, BMC Systems Biology.

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

[18]  Mari Tabuchi Systems biology standards— the community speaks , 2007 .

[19]  D. Broomhead,et al.  Something from nothing − bridging the gap between constraint‐based and kinetic modelling , 2007, The FEBS journal.

[20]  J. Heijnen,et al.  Dynamic simulation and metabolic re-design of a branched pathway using linlog kinetics. , 2003, Metabolic engineering.

[21]  Attila Csikász-Nagy,et al.  Computational systems biology of the cell cycle , 2009, Briefings Bioinform..

[22]  Renate Kania,et al.  SABIO-RK: a database for biochemical reactions and their kinetics , 2007, BMC Systems Biology.

[23]  M. Reuss,et al.  In vivo analysis of glucose-induced fast changes in yeast adenine nucleotide pool applying a rapid sampling technique. , 1993, Analytical biochemistry.

[24]  B. Wright,et al.  Systems analysis of the tricarboxylic acid cycle in Dictyostelium discoideum. I. The basis for model construction. , 1992, The Journal of biological chemistry.

[25]  Barbara M. Bakker,et al.  Glycolysis in Bloodstream Form Trypanosoma brucei Can Be Understood in Terms of the Kinetics of the Glycolytic Enzymes* , 1997, The Journal of Biological Chemistry.

[26]  R. Takors,et al.  Quantification of intracellular metabolites in Escherichia coli K12 using liquid chromatographic-electrospray ionization tandem mass spectrometric techniques. , 2001, Analytical biochemistry.

[27]  Barbara M. Bakker,et al.  Can yeast glycolysis be understood in terms of in vitro kinetics of the constituent enzymes? Testing biochemistry. , 2000, European journal of biochemistry.

[28]  Joseph J. Heijnen,et al.  A method for estimation of elasticities in metabolic networks using steady state and dynamic metabolomics data and linlog kinetics , 2006, BMC Bioinformatics.

[29]  L. Petzold Automatic Selection of Methods for Solving Stiff and Nonstiff Systems of Ordinary Differential Equations , 1983 .

[30]  J. Heijnen,et al.  The mathematics of metabolic control analysis revisited. , 2002, Metabolic engineering.

[31]  R. Takors,et al.  Metabolomics: quantification of intracellular metabolite dynamics. , 2002, Biomolecular engineering.

[32]  K. Izui,et al.  Phosphoenolpyruvate carboxylase of Escherichia coli. Affinity labeling with bromopyruvate. , 1979, Journal of biochemistry.

[33]  W Wiechert,et al.  Unravelling the regulatory structure of biochemical networks using stimulus response experiments and large-scale model selection. , 2006, Systems biology.

[34]  Bernhard O. Palsson,et al.  Dynamic simulation of the human red blood cell metabolic network , 2001, Bioinform..

[35]  Ana Rute Neves,et al.  The intricate side of systems biology. , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[36]  J. Bailey,et al.  Effects of spatiotemporal variations on metabolic control: approximate analysis using (log)linear kinetic models. , 1997, Biotechnology and bioengineering.

[37]  Barbara M. Bakker,et al.  What Controls Glycolysis in Bloodstream Form Trypanosoma brucei?* , 1999, The Journal of Biological Chemistry.

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

[39]  J. Heijnen Approximative kinetic formats used in metabolic network modeling , 2005, Biotechnology and bioengineering.

[40]  Yu Zong Chen,et al.  KDBI: Kinetic Data of Bio-molecular Interactions database , 2003, Nucleic Acids Res..

[41]  Zhike Zi,et al.  SBML-SAT: a systems biology markup language (SBML) based sensitivity analysis tool , 2008, BMC Bioinformatics.

[42]  Felix Streichert,et al.  Comparing mathematical models on the problem of network inference , 2006, GECCO.

[43]  C. Chassagnole,et al.  Dynamic modeling of the central carbon metabolism of Escherichia coli. , 2002, Biotechnology and bioengineering.

[44]  James D. Murray Mathematical Biology: I. An Introduction , 2007 .

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

[46]  Masaru Tomita,et al.  Dynamic simulation of an in vitro multi‐enzyme system , 2007, FEBS letters.

[47]  J E Bailey,et al.  MCA has more to say. , 1996, Journal of theoretical biology.

[48]  Eberhard O. Voit,et al.  Kinetic modeling using S-systems and lin-log approaches , 2007 .

[49]  Antje Chang,et al.  BRENDA, enzyme data and metabolic information , 2002, Nucleic Acids Res..

[50]  Carmen G. Moles,et al.  Parameter estimation in biochemical pathways: a comparison of global optimization methods. , 2003, Genome research.

[51]  Lawrence J. Fogel,et al.  Artificial Intelligence through Simulated Evolution , 1966 .

[52]  Peter D. Karp,et al.  The EcoCyc and MetaCyc databases , 2000, Nucleic Acids Res..

[53]  D. Lauffenburger,et al.  Receptors: Models for Binding, Trafficking, and Signaling , 1993 .

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

[55]  Ian T. Paulsen,et al.  TransportDB: a comprehensive database resource for cytoplasmic membrane transport systems and outer membrane channels , 2006, Nucleic Acids Res..

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

[57]  H. Kitano,et al.  Computational systems biology , 2002, Nature.

[58]  Masaru Tomita,et al.  Theoretical Biology and Medical Modelling , 2022 .

[59]  M C Mossing,et al.  Variability of the intracellular ionic environment of Escherichia coli. Differences between in vitro and in vivo effects of ion concentrations on protein-DNA interactions and gene expression. , 1987, The Journal of biological chemistry.

[60]  Jacky L. Snoep,et al.  BioModels Database: a free, centralized database of curated, published, quantitative kinetic models of biochemical and cellular systems , 2005, Nucleic Acids Res..

[61]  J. Heijnen,et al.  Rapid sampling for analysis of in vivo kinetics using the BioScope: a system for continuous-pulse experiments. , 2002, Biotechnology and bioengineering.

[62]  B. Hess,et al.  Allosteric kinetics of pyruvate kinase of Saccharomyces carlsbergensis. , 1973, Journal of molecular biology.

[63]  F. Doyle,et al.  Dynamic flux balance analysis of diauxic growth in Escherichia coli. , 2002, Biophysical journal.

[64]  Eberhard O. Voit,et al.  Power-Law Approach to Modeling Biological Systems : I. Theory , 1982 .

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

[66]  Robert Hooke,et al.  `` Direct Search'' Solution of Numerical and Statistical Problems , 1961, JACM.

[67]  M. Schauer,et al.  Analysis of the quasi-steady-state approximation for an enzymatic one-substrate reaction. , 1979, Journal of theoretical biology.