INTRODUCTIONÂ
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 (1–3). L-Threonine deaminase (TDA),1 the first enzyme specific for the biosynthesis of L-isoleucine, is end product-inhibited by L-isoleucine, and 
-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 -acetohydroxy acid synthase (AHAS) could compromise the cell for L-isoleucine biosynthesis or result in the accumulation of a toxic metabolic intermediate, -ketobutyrate (KB). 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 (4). 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 (4). AHAS III shows no preference for pyruvate or KB. Although this isozyme can produce intermediates for both L-valine and L-isoleucine, it is inhibited by L-valine (4). The AHAS II isozyme has substrate preferences for the condensation of pyruvate and the KB required for L-isoleucine biosynthesis, and it is not inhibited by any of the branched chain amino acids (4). However, AHAS II is not active in the E. coli. K12 strain (5). Consequently, this strain cannot grow in the presence of high levels of L-valine unless L-isoleucine is also added to the growth medium (6).
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 (7, 8). According to the MWC model, TDA can exist in an active state (R) or an inactive state (T) (8, 9). 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 -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.
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