A Mathematical Model for the Branched Chain Amino Acid Biosynthetic Pathways of Escherichia coli K12

As a first step toward the elucidation of the systems biology of the model organism Escherichia coli, it was our goal to mathematically model a metabolic system of intermediate complexity, namely the well studied end product-regulated pathways for the biosynthesis of the branched chain amino acids l-isoleucine, l-valine, and l-leucine. This has been accomplished with the use of kMech (Yang, C.-R., Shapiro, B. E., Mjolsness, E. D., and Hatfield, G. W. (2005) Bioinformatics 21, in press), a Cellerator (Shapiro, B. E., Levchenko, A., Meyerowitz, E. M., Wold, B. J., and Mjolsness, E. D. (2003) Bioinformatics 19, 677–678) language extension that describes a suite of enzyme reaction mechanisms. Each enzyme mechanism is parsed by kMech into a set of fundamental association-dissociation reactions that are translated by Cellerator into ordinary differential equations. These ordinary differential equations are numerically solved by Mathematica™. Any metabolic pathway can be simulated by stringing together appropriate kMech models and providing the physical and kinetic parameters for each enzyme in the pathway. Writing differential equations is not required. The mathematical model of branched chain amino acid biosynthesis in E. coli K12 presented here incorporates all of the forward and reverse enzyme reactions and regulatory circuits of the branched chain amino acid biosynthetic pathways, including single and multiple substrate (Ping Pong and Bi Bi) enzyme kinetic reactions, feedback inhibition (allosteric, competitive, and non-competitive) mechanisms, the channeling of metabolic flow through isozymes, the channeling of metabolic flow via transamination reactions, and active transport mechanisms. This model simulates the results of experimental measurements. As a first step toward the elucidation of the systems biology of the model organism Escherichia coli, it was our goal to mathematically model a metabolic system of intermediate complexity, namely the well studied end product-regulated pathways for the biosynthesis of the branched chain amino acids l-isoleucine, l-valine, and l-leucine. This has been accomplished with the use of kMech (Yang, C.-R., Shapiro, B. E., Mjolsness, E. D., and Hatfield, G. W. (2005) Bioinformatics 21, in press), a Cellerator (Shapiro, B. E., Levchenko, A., Meyerowitz, E. M., Wold, B. J., and Mjolsness, E. D. (2003) Bioinformatics 19, 677–678) language extension that describes a suite of enzyme reaction mechanisms. Each enzyme mechanism is parsed by kMech into a set of fundamental association-dissociation reactions that are translated by Cellerator into ordinary differential equations. These ordinary differential equations are numerically solved by Mathematica™. Any metabolic pathway can be simulated by stringing together appropriate kMech models and providing the physical and kinetic parameters for each enzyme in the pathway. Writing differential equations is not required. The mathematical model of branched chain amino acid biosynthesis in E. coli K12 presented here incorporates all of the forward and reverse enzyme reactions and regulatory circuits of the branched chain amino acid biosynthetic pathways, including single and multiple substrate (Ping Pong and Bi Bi) enzyme kinetic reactions, feedback inhibition (allosteric, competitive, and non-competitive) mechanisms, the channeling of metabolic flow through isozymes, the channeling of metabolic flow via transamination reactions, and active transport mechanisms. This model simulates the results of experimental measurements. Systems biology may be broadly defined as the integration of diverse data into useful biological models that allow scientists to easily observe complex cellular behaviors and predict the outcomes of metabolic and genetic perturbations. As a first step toward the elucidation of the systems biology of the model organism Escherichia coli, we have elected to limit our initial efforts to the development of a mathematical model for the complex but well studied metabolic pathways for the biosynthesis of the branched chain amino acids l-isoleucine, l-valine, and l-leucine. The biosynthetic pathways for the branched chain amino acids are shown in Fig. 1 (1Umbarger H.E. Annu. Rev. Biochem. 1978; 47: 532-606Crossref PubMed Scopus (417) Google Scholar, 2Umbarger H.E. Neidhardt F.C. Curtiss III, R. Ingraham J.L. Lin E.C.C. Low K.B. Magasanik B. Reznikoff W.S. Riley M. Schaechter M. Umbarger H.E. Escherichia coli and Salmonella: Cellular and Molecular Biology. 2nd Ed. American Society for Microbiology Press, Washington, D. C.1996: 442-457Google Scholar, 3Hatfield G.W. Benham C.J. Annu. Rev. Genet. 2002; 36: 175-203Crossref PubMed Scopus (194) Google Scholar). l-Threonine deaminase (TDA), 1The abbreviations used are: TDA, l-threonine deaminase; AHAS, α-acetohydroxy acid synthase; aKB, α-ketobutyrate; MWC, Monod, Wyman, and Changeux (model); ODE, ordinary differential equation; Pyr, pyruvate; TB, transaminase B. the first enzyme specific for the biosynthesis of l-isoleucine, is end product-inhibited by l-isoleucine, and α-isopropylmalate synthase (IPMS), the first enzyme specific for the biosynthesis of l-leucine, is end product-inhibited by l-leucine. However, because the parallel pathways for l-valine and l-isoleucine biosynthesis are catalyzed by a set of bi-functional enzymes that bind substrates from either pathway, l-valine inhibition of the first enzyme specific for its biosynthesis catalyzed by a single α-acetohydroxy acid synthase (AHAS) could compromise the cell for l-isoleucine biosynthesis or result in the accumulation of a toxic metabolic intermediate, α-ketobutyrate (αKB). This type of regulatory problem is often solved by using multiple isozymes with different substrate preferences that are differentially regulated by multiple end products of parallel pathways. In this case, there are three AHAS isozymes that catalyze the first step of the l-valine and the second step of the l-isoleucine pathway (4Barak Z. Chipman D.M. Gollop N. J. Bacteriol. 1987; 169: 3750-3756Crossref PubMed Google Scholar). AHAS I has substrate preferences for the condensation of two pyruvate molecules required for l-valine biosynthesis and is end product-inhibited by l-valine (4Barak Z. Chipman D.M. Gollop N. J. Bacteriol. 1987; 169: 3750-3756Crossref PubMed Google Scholar). AHAS III shows no preference for pyruvate or αKB. Although this isozyme can produce intermediates for both l-valine and l-isoleucine, it is inhibited by l-valine (4Barak Z. Chipman D.M. Gollop N. J. Bacteriol. 1987; 169: 3750-3756Crossref PubMed Google Scholar). The AHAS II isozyme has substrate preferences for the condensation of pyruvate and the αKB required for l-isoleucine biosynthesis, and it is not inhibited by any of the branched chain amino acids (4Barak Z. Chipman D.M. Gollop N. J. Bacteriol. 1987; 169: 3750-3756Crossref PubMed Google Scholar). However, AHAS II is not active in the E. coli. K12 strain (5Lawther R.P. Calhoun D.H. Gray J. Adams C.W. Hauser C.A. Hatfield G.W. J. Bacteriol. 1982; 149: 294-298Crossref PubMed Google Scholar). Consequently, this strain cannot grow in the presence of high levels of l-valine unless l-isoleucine is also added to the growth medium (6Umbarger H.E. Brown B. J. Bacteriol. 1955; 70: 241-248Crossref PubMed Google Scholar). TDA is an allosteric enzyme whose kinetic behavior can be described by the concerted allosteric transition mode of the Monod, Wyman, and Changeux (MWC) model (7Monod J. Wyman J. Changeux J.P. J. Mol. Biol. 1965; 12: 88-118Crossref PubMed Scopus (6184) Google Scholar, 8Hatfield G.W. Umbarger H.E. J. Biol. Chem. 1970; 245: 1742-1747Abstract Full Text PDF PubMed Google Scholar). According to the MWC model, TDA can exist in an active state (R) or an inactive state (T) (8Hatfield G.W. Umbarger H.E. J. Biol. Chem. 1970; 245: 1742-1747Abstract Full Text PDF PubMed Google Scholar, 9Changeux J.P. Cold Spring Harbor Symp. Quant. Biol. 1963; 28: 497-504Crossref Google Scholar). The fraction of active enzyme in the R or T states is determined by the concentrations and relative affinities of the substrate (l-threonine), the inhibitor (l-isoleucine), and the activator (l-valine) for the R and T states. In addition to these regulatory circuits, the intracellular levels of the branched chain amino acids are influenced by the reversible transamination reactions of each pathway. When the intracellular levels of any of the end product amino acids become high, reverse reactions to their cognate ketoacids are favored; for example, high concentrations of l-valine can be converted to α-ketoisovalerate to supplement l-leucine production. In turn, intracellular amino acid levels can be affected by their active transport from the extracellular growth medium. Therefore, the enzyme reactions required for the active transport of the branched chain amino acids into the cell against a concentration gradient are included in our simulations. The Mathematical Model—Here we use kMech (10Yang C.-R. Shapiro B.E. Mjolsness E.D. Hatfield G.W. Bioinformatics. 2005; a Cellerator B.E. Mjolsness E.D. Bioinformatics. PubMed Scopus Google language extension that describes a suite of enzyme reaction mechanisms. Each enzyme mechanism is parsed by kMech into a set of fundamental association-dissociation reactions that are translated by Cellerator into ordinary differential equations that are numerically solved by (10Yang C.-R. Shapiro B.E. Mjolsness E.D. Hatfield G.W. Bioinformatics. 2005; Scholar). a model for a metabolic pathway, to together appropriate kMech enzyme mechanism models and the physical and kinetic parameters for each The development of for model parameters as forward and reverse and from kinetic and is described (10Yang C.-R. Shapiro B.E. Mjolsness E.D. Hatfield G.W. Bioinformatics. 2005; Scholar). The kMech models for each of the pathway enzymes a and a with kMech and the kinetic and initial for the its Systems are the of for and the Bioinformatics The PDF of the and a of and enzyme kinetic and physical parameters used in are in the data in the of this is of to and use the kinetic for product reactions and the to equations for complex multiple These of equations enzyme mechanisms. Although metabolic PubMed Scopus Google it cannot for example, the that flow channeling through the three AHAS isozymes of the parallel l-isoleucine and l-valine pathways and the transamination This of mathematical a of enzyme kinetic and regulatory circuits as described (AHAS) AHAS isozymes are of flow into either the l-isoleucine or l-valine biosynthetic pathway. The Pong Bi Bi enzyme mechanism of these isozymes describes a Bi) mechanism in the of substrates and of products is is a Pong mechanism because the enzyme a and a intermediate state as and in Fig. flow through these isozymes is by the affinities of the enzyme intermediates for their second substrates as shown in Fig. Biochem. PubMed Scopus Google Scholar). example, the AHAS II enzyme reactions shown in Fig. 1 are described by the two reaction 1 and 1 is for the condensation of two pyruvate molecules for the biosynthesis of the of the l-valine and l-leucine pathways. is for the condensation of and αKB for the biosynthesis of the of the l-isoleucine pathway. As in the reactions, the initial reaction of with AHAS II to the enzyme intermediate is Therefore, these reactions two molecules of be of for each of or This can be by these reactions as shown in In the is used in with the kMech models to this of pathways The kMech in for the channeling of pyruvate through the AHAS II isozyme into l-valine or l-isoleucine are shown in In this and are and are is is the enzyme intermediate is in to that it is in the intermediate state with the first a kMech enzyme model that to that the enzyme model is Pong Bi with a are of the with a are of the enzyme substrate and with a are for the of kMech the three AHAS II reactions shown into association-dissociation reactions and the in B.E. Mjolsness E.D. Bioinformatics. PubMed Scopus Google shown in This is to Cellerator the differential equations that the of for each in the AHAS II isozyme reaction are in and presented in These differential equations and are to are solved by the and of enzyme product are The also was used for the of the AHAS I and AHAS III isozymes described in the data in the of this of kMech models used in this are (10Yang C.-R. Shapiro B.E. Mjolsness E.D. Hatfield G.W. Bioinformatics. 2005; Scholar). transaminase enzyme the reversible step of the biosynthetic pathways of all three of the branched chain amino acids 1 and The first step of each of these Pong Bi Bi transamination reactions as an amino to a enzyme intermediate in Fig. for the transamination of the three different of each pathway. flow through is by the affinities of the enzyme intermediates for their second substrates as shown in Fig. The enzyme reactions of Fig. 1 are described by the equations shown in the first substrate reaction with is the for all three of the branched chain second the is used to this as shown in transamination is kMech models be in both reaction for each of the three branched chain amino acid the is used to the second substrate reactions is to that the enzyme is in the intermediate state with the first of each transamination in Fig. as shown in These reactions are parsed by kMech into association-dissociation reactions and to are as described The was used for transaminase a reversible Pong Bi Bi mechanism enzyme that as the amino for the transamination of l-valine deaminase is an allosteric enzyme whose kinetic behavior can be described by the concerted allosteric transition model of Monod, Wyman, Changeux as the MWC model (7Monod J. Wyman J. Changeux J.P. J. Mol. Biol. 1965; 12: 88-118Crossref PubMed Scopus (6184) Google Scholar, 8Hatfield G.W. Umbarger H.E. J. Biol. Chem. 1970; 245: 1742-1747Abstract Full Text PDF PubMed Google Scholar). According to the MWC model, TDA can exist in an active state (R) or an inactive state (T) (8Hatfield G.W. Umbarger H.E. J. Biol. Chem. 1970; 245: 1742-1747Abstract Full Text PDF PubMed Google Scholar, 9Changeux J.P. Cold Spring Harbor Symp. Quant. Biol. 1963; 28: 497-504Crossref Google Scholar). The fraction of enzyme in the R or T state is determined by the concentrations and relative affinities of the substrate (l-threonine), the inhibitor (l-isoleucine), and the activator (l-valine) for each This model is described by two 1 and and in and are and activator and are their is the of substrate and is the of the of the substrate for the active R state and the inhibited T is the for the R and T states in the of is the initial reaction and is the reaction 1 describes the fraction of the enzyme in the active state (R) as a of substrate and describes the of the enzyme by substrate as a of substrate and concentrations (7Monod J. Wyman J. Changeux J.P. J. Mol. Biol. 1965; 12: 88-118Crossref PubMed Scopus (6184) Google Scholar). have described of the MWC model in Cellerator (10Yang C.-R. Shapiro B.E. Mjolsness E.D. Hatfield G.W. Bioinformatics. 2005; Scholar). of the kinetic parameters and concentrations are often in the However, of and are often not These can be by substrate in the presence and of inhibitor concentrations (10Yang C.-R. Shapiro B.E. Mjolsness E.D. Hatfield G.W. Bioinformatics. 2005; Scholar, and of and Scholar, G. W. The of l-Threonine in by and Scholar). of intracellular enzyme concentrations are not However, with experimental these concentrations can be from the and specific of example, in the that the intracellular concentration of TDA is D.H. Hatfield G.W. J. Biol. Chem. Full Text PDF PubMed Google Scholar). have shown a levels with and in both E. coli Hatfield G.W. J. Biol. Chem. Full Text Full Text PDF PubMed Scopus Google and B. Mol. Biol. PubMed Scopus Google Scholar, R. J. R. R. PubMed Scopus Google Scholar). the intracellular levels of the enzymes of the branched chain amino acid biosynthetic pathway can be from the intracellular of TDA and the relative levels of the branched chain amino acid biosynthetic enzymes using data Hatfield G.W. J. Biol. Chem. 2002; Full Text Full Text PDF PubMed Scopus Google Scholar). The data in I in the of this that this is a using intracellular enzyme concentrations in this produce pathway intermediate and end product levels Chipman D.M. Z. J. Bacteriol. PubMed Google Scholar, J. Bacteriol. PubMed Google to of these of of enzyme kinetic and physical parameters to the differential equations for the and their are in I in the of this The to intracellular levels of pathway and end products are also for In for each enzyme there are three parameters namely the enzyme concentration the for each and the for each enzyme enzymes with regulatory parameters as the for each inhibitor and the for each activator also are required. In the initial from data as described and the and from in enzyme kinetic data of enzymes with the of transaminase and α-isopropylmalate used because of a of experimental These to the in levels of intermediate and end product Chipman D.M. Z. J. Bacteriol. PubMed Google Scholar, J. Bacteriol. PubMed Google Scholar). the and in because the are to of the initial However, because can in including the relative of for the of of the mathematical model was with the parameters in I in the of this it was used for the of the metabolic and genetic of the of through the of E. coli three metabolic pathways simulated here of metabolic and three enzyme The mathematical model for this metabolic system of with and and The enzymes of these pathways three enzyme Bi and Pong Bi Bi) that are regulated by competitive, or inhibition mechanisms. As described the physical parameters for these models have been from the from data in the or by experimental data I in the of this intracellular enzyme levels have been from enzyme and data Hatfield G.W. J. Biol. Chem. 2002; Full Text Full Text PDF PubMed Scopus Google Scholar). The levels for the pathway intermediates and end products are shown in Fig. enzyme levels to the flow of intermediates through these pathways to in levels of pathway intermediates and end products Chipman D.M. Z. J. Bacteriol. PubMed Google Scholar, J. Bacteriol. PubMed Google Scholar). The kMech kinetic and initial for the are presented in Fig. in the of this of allosteric regulatory mechanism of TDA was simulated with the MWC model physical parameters the or to experimental data (10Yang C.-R. Shapiro B.E. Mjolsness E.D. Hatfield G.W. Bioinformatics. 2005; Scholar). The data in Fig. that TDA αKB a with that in Chipman D.M. Z. J. Bacteriol. PubMed Google Scholar, J. Bacteriol. PubMed Google Scholar). the for l-isoleucine is the for l-valine an initial in the of αKB as l-isoleucine is by an to a that the accumulation of l-valine the fraction of active TDA is as l-isoleucine and to a of the enzyme is in the active R l-valine was for the of TDA with l-threonine in to in the levels of its l-isoleucine and its TDA is with l-threonine of the AHAS AHAS isozymes I and III a Pong Bi Bi enzyme mechanism described AHAS II isozyme is inactive in E. coli (5Lawther R.P. Calhoun D.H. Gray J. Adams C.W. Hauser C.A. Hatfield G.W. J. Bacteriol. 1982; 149: 294-298Crossref PubMed Google Scholar). The l-valine inhibition of AHAS I and III is in the of AHAS III, is because of the substrate concentrations in the presence of l-valine concentrations Biochem. PubMed Scopus Google Scholar). The data in Fig. that the of by AHAS isozymes I and III as l-valine These data also that by the AHAS isozyme III, to a as its end product inhibitor (l-valine) and as its because l-isoleucine and TDA of E. coli K12 to αKB is well that l-valine a concentration of 1 to a of E. coli K12 in a medium their growth and that this l-valine inhibition can be by l-isoleucine addition (6Umbarger H.E. Brown B. J. Bacteriol. 1955; 70: 241-248Crossref PubMed Google Scholar). the AHAS I and AHAS III isozymes of E. coli K12 are inhibited by l-valine and because the for AHAS II in E. coli K12 a that AHAS II (5Lawther R.P. Calhoun D.H. Gray J. Adams C.W. Hauser C.A. Hatfield G.W. J. Bacteriol. 1982; 149: 294-298Crossref PubMed Google it was that l-valine inhibition of AHAS I and AHAS III growth by with l-isoleucine However, that the intracellular l-isoleucine is not by l-valine because its biosynthesis is l-valine by AHAS III that active Biochem. PubMed Scopus Google Scholar, PubMed Scopus Google and by the l-valine of TDA that substrate into the l-isoleucine pathway. the in Fig. shows in the presence of extracellular l-valine, the intracellular l-isoleucine in the the pathway of l-isoleucine, This of αKB is by l-valine of TDA its and by l-valine inhibition of the AHAS I and AHAS III isozymes, its is that this αKB accumulation is toxic to because of its to the transport system J. Mol. Genet. PubMed Scopus Google Scholar, J. Mol. Genet. PubMed Scopus Google Scholar). as by our l-valine growth inhibition of E. coli K12 is not a of l-isoleucine The results in Fig. that the of αKB accumulation can be by l-isoleucine through its to TDA This shows in the presence of 1 l-valine, the of αKB and that in the presence of l-isoleucine, αKB levels are to the in the of The results in Fig. with the in αKB in the presence of 1 l-valine, of the cellular TDA is converted to the active R However, with the in αKB in the presence of l-isoleucine, the cellular TDA in the active R state is to the in the of These are by experimental results from multiple a three (6Umbarger H.E. Brown B. J. Bacteriol. 1955; 70: 241-248Crossref PubMed Google Scholar, J. Mol. Genet. PubMed Scopus Google Scholar, J. Mol. Genet. PubMed Scopus Google Scholar). the of an E. coli K12 goal of biological systems is to metabolic for the of as amino In the this has been accomplished by genetic and example, a used to an amino acid has been to a strain with a in the for the first enzyme for the biosynthesis of that amino we use our model to the of a TDA for the of can a TDA strain by the for l-isoleucine to a The in Fig. shows that in the of l-isoleucine the activator and substrate of cellular to the active R state with the type enzyme that is in the active R However, this of enzyme in the active the data in Fig. that AHAS III is to a to in l-isoleucine in a E. coli K12 with a type the the of the AHAS III is This is because E. coli K12 not have an active AHAS II isozyme that the condensation of pyruvate and αKB for l-isoleucine αKB to toxic These results that in to l-isoleucine, the αKB accumulation be The results in Fig. that a type AHAS II isozyme and an that the levels of all of the enzymes of the l-isoleucine and l-valine parallel pathways C.W. M. Hatfield G.W. J. Biol. Chem. Full Text PDF PubMed Google both of αKB and pathway intermediates and results in a in l-isoleucine production. These simulated that high of l-isoleucine in E. coli a AHAS II isozyme and a genetic with by of the E. Biochem. PubMed Scopus Google Scholar). E. coli K12 strain acid cannot produce and intermediates of the pathway for the biosynthesis of all three branched chain amino l-isoleucine, l-valine, and l-leucine However, acid can grow in the presence of l-isoleucine and These not l-leucine because l-valine can be to a of l-leucine biosynthesis, by the reverse reactions of and transaminase The results in Fig. that in the extracellular presence of l-valine and l-isoleucine, l-leucine can be to the of an In this we a mathematical of branched chain amino acid biosynthesis and in E. coli. This the 1 is the of all of the including and as well as the enzyme kinetic and regulatory mechanism of each enzyme in Fig. 1 and I in the of this well studied model as E. coli, these of are often in of and W. M. PubMed Scopus Google Scholar, E. PubMed Scopus Google Scholar, M. G. D. PubMed Google Scholar, E. N. R. E. E. PubMed Scopus Google Scholar, Riley M. M. J. 2002; PubMed Scopus Google Scholar). is the development of for model the of and from kinetic and described by (10Yang C.-R. Shapiro B.E. Mjolsness E.D. Hatfield G.W. Bioinformatics. 2005; the of from the of and the of intracellular enzyme concentrations from enzyme and is the use of the in 1 and to as as models that the and regulatory of each step is the stringing together of appropriate kMech models and providing the physical and kinetic parameters for each enzyme in the pathway. is the of ordinary differential equations to each enzyme mechanism in of fundamental is the of model parameters to intracellular levels of pathway and end is the of simulated and results of and genetic This type of of metabolic systems can as levels of metabolic and end products and can predict the outcomes of and genetic that enzyme kinetic and regulatory mechanisms. use the kinetic for product reactions and the to equations for complex multiple These of equations are because the of concentration of each in the model are set to in to a set of differential equations to equations J. Full Text Full Text PDF PubMed Scopus Google Scholar). Therefore, the kinetic model this has the In the model by of differential equations that the of of each in the model a pathway model, to kMech models for the enzyme of a pathway any differential equations. of this and the integration of and are (10Yang C.-R. Shapiro B.E. Mjolsness E.D. Hatfield G.W. Bioinformatics. 2005; Scholar). allow to be by an with or no a is This is to pathways, enzyme mechanisms, and required physical and kinetic parameters with and In to metabolic J.L. Biol. Google enzyme mechanism and PubMed Scopus Google the models described here a to an of complex metabolic The model presented here is for because it not exist in the of the In addition to the metabolic regulatory flow through metabolic pathways is affected by a of of levels that pathway enzyme and These levels of from the to the are as of by G.W. Benham C.J. Annu. Rev. Genet. 2002; 36: 175-203Crossref PubMed Scopus (194) Google of the of and F.C. Curtiss R. Neidhardt F.C. Curtiss III, R. Ingraham J.L. Lin E.C.C. Low K.B. Magasanik B. Reznikoff W.S. Riley M. Schaechter M. Umbarger H.E. Escherichia coli and Salmonella: Cellular and Molecular Biology. 2nd Ed. American Society for Microbiology Press, Washington, D. C.1996: and The first or of is by that of all of the of the cell of This is by and the of in to and growth G.W. Benham C.J. Annu. Rev. Genet. 2002; 36: 175-203Crossref PubMed Scopus (194) Google Scholar). The second of is by in with often of in to or metabolic or F.C. Curtiss R. Neidhardt F.C. Curtiss III, R. Ingraham J.L. Lin E.C.C. Low K.B. Magasanik B. Reznikoff W.S. Riley M. Schaechter M. Umbarger H.E. Escherichia coli and Salmonella: Cellular and Molecular Biology. 2nd Ed. American Society for Microbiology Press, Washington, D. C.1996: Scholar). The of is by regulatory that to and bind in a to or a to single Each of these levels of metabolic by enzyme a model of branched chain amino acid biosynthesis in E. coli these levels of these levels of we are a set of models that the genetic regulatory that the of the these we example, the ordinary differential equations we are using for metabolic pathways are a and for an of of molecules enzymes and and that because each cell there can be in the in regulatory a cell that can produce outcomes PubMed Scopus Google Scholar). this and we are for genetic regulatory mechanisms, that as J. Chem. Scopus Google and the J. Chem. Scopus Google This models for genetic regulatory as and as well as Therefore, the presented here be as a first step of a that from the and and relative data from to a metabolic pathway in E. coli. As high for and we that a be in are of from with