An Enzyme Mechanism Language for the Mathematical Modeling of Metabolic Pathways

Chin-Rang Yang, Bruce E. Shapiro, Eric D. Mjolsness, and G. Wesley Hatfield

We have developed an enzyme mechanism language for the mathematical modeling of metabolic pathways. This language, kMech, is a comprehensive collection of single and multiple substrate enzyme reactions and regulatory mechanisms that extends Cellerator function for the mathematical modeling of enzyme reactions. Each mechanism has been codified to generate a set of elementary reactions that can be translated by Cellerator into ordinary differential equations (ODEs) solvable by Mathematica. We have also developed methods that use common kinetic measurements to estimate physical constants required to solve these ODEs. Because kMech assembles fundamental modular association-dissociation reaction mechanisms to describe complex enzyme mechanisms, the kMech/Cellerator dynamic modeling system is more flexible, and easily extended, than commonly used simulation systems based on Michaelis-Menten kinetic equations. We have initially used this system to model branched chain amino acid biosynthesis in *Escherichia coli*. Our simulations of metabolic and genetic perturbations predict experimentally observed results.

**Documents for Download:**

MathematicaTM executable, kMech.m, file : kMech

Instructions for kMech installation : Installation for kMech

kMech published in *Bioinformatics* (2005): Bioinformatics_Yang.pdf

A Sample Metabolic Pathway: MathematicaTM notebook: SamplePathway.nb

Parameters fitting for MWC model: c_L_fitting.nb and TDA_MWC.nb

The mathematical model for the simulation of branched chain amino acid biosynthesis:

Published in *The Journal of Biological Chemistry* (2005): JBC_Yang.pdf and Supplementary_Materials.

MathematicaTM notebook: Biosynthesis_of_Ile_Val_Leu.nb

SBML version: Biosynthesis_of_Ile_Val_Leu.sbml

HTML version: Biosynthesis_of_Ile_Val_Leu.html

The mathematical model for the simulation of Asparate-Threonine biosynthesis:

Manuscript (2004) : Najdi.pdf and Supplementary_Materials

MathematicaTM notebook: Biosynthesis_of_Asp-Thr.nb

HTML version: Biosynthesis_of_Asp-Thr.html