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J. Biol. Chem., Vol. 280, Issue 12, 11224-11232, March 25, 2005

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

Chin-Rang Yang¶, Bruce E. Shapiro||, She-pin Hung, Eric D. Mjolsness**, and G. Wesley Hatfield

From the Department of Microbiology and Molecular Genetics, College of Medicine, the ^**School of Information and Computer Science, and the Institute for Genomics and Bioinformatics, University of California at Irvine, Irvine, California 92697 and the ^||Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California 91109

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^TM. 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.

Received for publication, October 7, 2004 , and in revised form, January 18, 2005.

^* This work was supported in part by National Institutes of Health Grants GM55073 and GM68903 (to G. W. H.). The costs of publication of this article were defrayed in part by the payment of page charges. This article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

The on-line version of this article (available at http://www.jbc.org) contains further mathematical modeling data in the form of supplemental Fig. 1 and supplemental Table I.

^¶ A trainee of the Biomedical Informatics Training (BIT) Program of the University of California at Irvine Institute for Genomics and Bioinformatics and the recipient of National Library of Medicine Postdoctoral Fellowship T15 LM-07443.

To whom correspondence on computation questions should be addressed. E-mail: emj{at}uci.edu. To whom correspondence on biology questions should be addressed. E-mail: gwhatfie{at}uci.edu.

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