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The detailed kMech models for each of the pathway enzymes Fig. Cellerator, available at www. These types of equations focus on conversion between metabolites metabolic flux rather than enzyme mechanisms. Although metabolic flux provides valuable information about biomass conversions 12 , it cannot simulate, for example, the pathway-specific regulation patterns that control carbon flow channeling through the three AHAS isozymes of the parallel l -isoleucine and l -valine pathways and the final transamination reactions.

This level of mathematical modeling requires a detailed understanding of enzyme kinetic mechanisms and regulatory circuits Fig.

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Enzyme-centric, metabolic pathways for the biosynthesis of the branched chain amino acids l -isoleucine, l -valine, and l -leucine. The abbreviations of enzymes and metabolites are the same as those in Fig.

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Ovals represent enzyme molecules. White ovals indicate free enzyme states, and shaded ovals indicate intermediate enzyme states with a function group attached to enzymes. Enzyme reactions are indicated by lines with arrowheads. Reversible reactions are indicated by gray lines with arrowheads. Switching between free and intermediate enzyme states are indicated by dashed lines with double arrowheads. The Ping Pong Bi Bi enzyme mechanism of these isozymes describes a specialized two-substrate, two-product Bi Bi mechanism in which the binding of substrates and release of products is ordered. It is a Ping Pong mechanism because the enzyme shuttles between a free and a substrate-modified intermediate state indicated as white and shaded ovals , respectively, in Fig.

Carbon flow through these isozymes is controlled by the affinities K m of the enzyme intermediates for their second substrates as shown in Fig. As written in the reactions, the initial reaction of Pyr with free AHAS II to form the activated enzyme intermediate is represented twice. This redundancy can be resolved by rewriting these reactions as shown in Reaction 3.

Detailed descriptions of other kMech models used in this simulation are published elsewhere The first step of each of these Ping Pong Bi Bi transamination reactions uses glutamate as an amino donor to form a pyridoxamine-bound enzyme intermediate TBNH 2 , shaded oval in Fig. The TB enzyme reactions of Fig. These reactions are parsed by kMech into elementary association-dissociation reactions and passed on to Cellerator, where they are processed as described above. The same method was used for modeling transaminase C, a reversible Ping Pong Bi Bi mechanism enzyme that uses alanine as the amino donor for the transamination of l -valine Fig.

Allosteric Regulation— Threonine deaminase is an allosteric enzyme whose kinetic behavior can be described by the concerted allosteric transition model of Monod, Wyman, Changeux known as the MWC model 7 , 8. 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 state.

This model is described by two equations, designated Equations 1 and 2 , in which S, I , and A are substrate, inhibitor, and activator concentrations, respectively, K m , K i , and K a are their respective dissociation constants, n is the number of substrate and effector ligand binding sites, c is the ratio of the affinity of the substrate for the catalytically active R state and the inhibited T state, L 0 is the equilibrium constant allosteric constant for the R and T states in the absence of ligands, v o is the initial reaction velocity, and V max is the maximal reaction velocity.

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Equation 1 describes the fraction of the enzyme in the catalytically active state R as a function of substrate and effector concentrations. We have recently described implementation of the MWC model in Cellerator Experimental values of the kinetic parameters and ligand concentrations listed above are most often available in the literature. However, values of c and L 0 are often not available. These values can be calculated by fitting substrate saturation curves in the presence and absence of several inhibitor concentrations 10 , 14 , Approximation of Intracellular Enzyme Concentrations— With few exceptions, intracellular enzyme concentrations are not available.

However, with careful experimental documentation, these concentrations can be approximated from the yields and specific activities of purified enzymes. Furthermore, recent experiments have shown a positive correlation between mRNA levels measured with DNA microarrays and protein abundance in both E. Thus, the intracellular levels of the remaining enzymes of the branched chain amino acid biosynthetic pathway can be inferred from the calculated intracellular level of TDA and the relative mRNA levels of the other branched chain amino acid biosynthetic enzymes using DNA microarray data The data in supplemental Table I in the on-line version of this article demonstrate that this is a reasonable method.

Amino Acid Biosynthesis – Pathways, Regulation and Metabolic Engineering

Indeed, simulations using intracellular enzyme concentrations inferred in this manner produce experimentally observed steady-state pathway intermediate and end product levels 21 , 22 , usually within 2-fold to one-half adjustments of these inferred values. Optimization of Model Parameters— A list of reported enzyme kinetic and physical parameters needed to solve the differential equations for the simulations reported here, and their literature sources are available in supplemental Table I in the on-line version of this article.

The optimized values to simulate known steady-state intracellular levels of pathway substrates, intermediates, and end products are also listed for comparison. In brief, for each enzyme there are at least three parameters needed, namely the total enzyme concentration E T , the K m for each substrate, and the k cat for each enzyme reaction. For enzymes with additional regulatory mechanism, extra parameters such as the K i for each inhibitor and the K a for each activator also are required.

These values were manually adjusted to match the published in vivo steady-state levels of intermediate and end product metabolites 21 , Interestingly, the inferred E T and in vitro K m values work quit well, because the adjustments are usually within 2-fold to one-half of the initial values. However, because many variables can influence in vitro measurements, including the relative activities of purified enzymes, larger corrections were sometimes necessary for the estimation of k cat values 5 of 9 enzymes.

Once the mathematical model was optimized with the parameters reported in supplemental Table I in the on-line version of this article, it was used without further adjustment for the simulations of the metabolic and genetic perturbations reported below. The mathematical model for this metabolic system consists of ODEs with association and dissociation rate constants and 52 catalytic rate constants.

The enzymes of these interacting pathways employ three distinct enzyme mechanisms simple catalytic, Bi Bi, and Ping Pong Bi Bi that are regulated by allosteric, competitive, or noncompetitive inhibition mechanisms. Relative intracellular enzyme levels have been inferred from enzyme purification and DNA microarray data The steady-state levels for the thirteen pathway intermediates and end products are shown in Fig. Steady-state enzyme activity levels were optimized to properly channel the steady-state flow of intermediates through these pathways to match reported in vivo levels of pathway intermediates and end products 21 , Simulated flow of carbon through the branched chain amino acid biosynthetic pathways of E.

The intermediates are abbreviated as described in the legend of Fig.

The beginning substrates l -threonine and pyruvate levels, as well as the end product l -isoleucine, l -valine, and l -leucine levels, agree with measured intracellular values 21 , Allosteric Regulation of TDA— The allosteric regulatory mechanism of TDA was simulated with the MWC model employing physical parameters based on the literature or optimized to fit experimental data The data in Fig.

Correspondingly, the fraction of active TDA is initially decreased as l -isoleucine accumulates and countered to a steady level 5. Allosteric regulation of l TDA. A , the fraction of TDA in the active R state. At a final steady-state level of end product synthesis, it is only 1.

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Indeed, the simulation in Fig. Thus, as reproduced by our simulations, l -valine growth inhibition of E. Simulated effects of excess l -valine on branched chain amino acid biosynthesis in E. Conditions described in Fig. The simulation results in Fig. These simulations are verified by experimental results accumulated from multiple laboratories over a three decade period 6 , 24 , In the past, this has been largely accomplished by genetic manipulation and selection methods.

For example, a common strategy used to overproduce an amino acid has been to isolate a strain with a feedback-resistant mutation in the gene for the first enzyme for the biosynthesis of that amino acid.

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Here we use our model to determine the effects of a feedback-resistant TDA for the overproduction of l -isoleucine. The simulation in Fig. However, despite this increased amount of enzyme in the active state, the data in Fig. This is because E. The results in Fig.

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These simulated results, which show that high level overproduction of l -isoleucine in E. Simulation of an E. The simulation conditions described in the Fig. The simulation results in panel B show that l -isoleucine production in the TDA R mutant is 5—6-fold increased. However, acetohydroxy acid isomeroreductase-deficient strains can grow in the presence of only l -isoleucine and l -valine. An acetohydroxy acid isomeroreductase mutant ilvC E. The simulation conditions described in Fig. In this report, we describe a mathematical simulation of branched chain amino acid biosynthesis and regulation in E.

This approach involves the following steps. For well studied model organisms such as E. Examples include the approximation of rate constants k f and k r from kinetic measurements K m and k cat described by Yang et al. This type of deterministic continuous modeling of metabolic systems can provide valuable information such as predicted steady-state levels of metabolic substrates, intermediates, and end products and can predict the outcomes of biochemical and genetic perturbations that require detailed enzyme kinetic and regulatory mechanisms.

These types of equations are called steady-state velocity equations, because the derivatives of concentration of each reactant in the model over time are set to 0 in order to simplify a set of non-linear differential equations to linear algebra equations Therefore, the kinetic model based on this approach has embedded the steady-state hypothesis.

To build a pathway model, users need only to call upon kMech models for the enzyme mechanisms of a pathway without writing any differential equations. This graphical editor is designed to help users construct pathways, select enzyme mechanisms, and enter required physical and kinetic parameters with simple point and click methods. The model presented here is incomplete for many reasons, primarily, because it does not exist in the context of the bacteria cell.

In addition to the metabolic regulatory mechanisms considered here, carbon flow through metabolic pathways is affected by a hierarchy of additional controls of gene expression levels that affect pathway enzyme activities and amounts. These hierarchical levels of control, from the most general to the most specific, are as follows: i global control of gene activity mediated by chromosome structure 3 ; ii global control of the genes of stimulons and regulons 35 ; and iii operon-specific controls.

The first or highest level of control is exemplified by DNA topology-dependent mechanisms that coordinate basal level expression of all of the genes of the cell independent of operon-specific controls. This level is mediated by DNA architectural proteins and the actions of topoisomerases in response to nutritional and environmental growth conditions 3.

The second level of control is mediated by site-specific DNA-binding proteins, which, in cooperation with operon-specific controls, regulate often overlapping groups of metabolically related operons in response to environmental or metabolic transitions or stress conditions The third level of control is mediated by less abundant regulatory proteins that respond to operon-specific signals and bind in a site-specific manner to one or a few DNA sites to regulate single operons.

Each of these levels of control impacts metabolic regulation by influencing enzyme levels. Thus, a complete model of branched chain amino acid biosynthesis in E.

To incorporate these higher levels of regulation, we are currently developing a set of models that describe the genetic regulatory mechanisms that control the operons of the ilv regulon. To these ends, we face new challenges. Abstract Amino acids play several critical roles in plants, from providing the building blocks of proteins to being essential metabolites interacting with many branches of metabolism. Amino acid , feedback regulation , membrane , metabolism , plant , regulation , transcriptional level , transport.