An enzyme mechanism language for the mathematical modeling of metabolic pathways

MOTIVATION: As a first step toward the elucidation of the systems biology of complex biological systems, it was our goal to mathematically model common enzyme catalytic and regulatory mechanisms that repeatedly appear in biological processes such as signal transduction and metabolic pathways. RESULTS: We describe kMech, a Cellerator language extension that describes a suite of enzyme 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 Mathematica. In addition, we present methods that use commonly available kinetic measurements to estimate rate constants required to solve these differential equations.     

Application of a generalized MWC model for the mathematical simulation of metabolic pathways regulated by allosteric enzymes

In our effort to elucidate the systems biology of the model organism, Escherichia coli, we have developed a mathematical model that simulates the allosteric regulation for threonine biosynthesis pathway starting from aspartate. To achieve this goal, we used kMech, a Cellerator language extension that describes enzyme mechanisms for the mathematical modeling of metabolic pathways. These mechanisms are converted by Cellerator into ordinary differential equations (ODEs) solvable by Mathematica. In this paper, we describe a more flexible model in Cellerator, which generalizes the Monod, Wyman, Changeux (MWC) model for enzyme allosteric regulation to allow for multiple substrate, activator and inhibitor binding sites. Furthermore, we have developed a model that describes the behavior of the bifunctional allosteric enzyme aspartate kinase I-homoserine dehydrogenase I (AKI-HDHI). This model predicts the partition of enzyme activities in the steady state which paves the way for a more generalized prediction of the behavior of bifunctional enzymes.     

Biosynthesis and elongation of short- and medium-chain-length fatty acids

Short- and medium-chain-length fatty acids (FAs) are important constituents of a wide array of natural products. Branched and straight short-chain-length FAs originate from branched chain amino acid metabolism, and serve as primers for elongation in FA synthase-like reactions. However, a recent model proposes that the one-carbon extension reactions that utilize 2-oxo-3-methylbutyric acid in leucine biosynthesis also catalyze a repetitive one-carbon elongation of short-chain primers to medium-chain-length FAs. The existence of such a mechanism would require a novel form of regulation to control carbon flux between amino acid and FA biosynthesis. A critical re-analysis of the data used to support this pathway fails to support the hypothesis for FA elongation by one-carbon extension cycles of alpha-ketoacids. Therefore, we tested the hypothesis experimentally using criteria that distinguish between one- and two-carbon elongation mechanisms: (a) isotopomer patterns in terminal carbon atom pairs of branched and straight FAs resulting from differential labeling with [(13)C]?cetate; (b)(13)C]threonine labeling patterns in odd- and even chain length FAs; and (c) differential sensitivity of elongation reactions to inhibition by cerulenin. All three criteria indicated that biosynthesis of medium-chain length FAs is mediated primarily by FA synthase-like reactions.     

1H, 13C, 15N assignments of the dimeric regulatory subunit (ilvN) of the E. coli AHAS I

Acetohydroxyacid synthase (AHAS) is an enzyme involved in the biosynthesis of the branched chain amino acids viz, valine, leucine and isoleucine. The activity of this enzyme is regulated through feedback inhibition by the end products of the pathway. Here we report the backbone and side-chain assignments of ilvN, the 22 kDa dimeric regulatory subunit of E. coli AHAS isoenzyme I, in the valine bound form. Detailed analysis of the structure of ilvN and its interactions with the catalytic subunit of E. coli AHAS I will help in understanding the mechanism of activation and regulation of the branched chain amino acid biosynthesis.     

Cysteine synthase (CysM) of Mycobacterium tuberculosis is an O-phosphoserine sulfhydrylase: evidence for an alternative cysteine biosynthesis pathway in mycobacteria

The biosynthesis of cysteine is a crucial metabolic pathway supplying a building block for de novo protein synthesis but also a reduced thiol as a component of the oxidative defense mechanisms that appear particularly vital in the dormant state of Mycobacterium tuberculosis. We here show that the cysteine synthase CysM is, in contrast to previous annotations, an O-phosphoserine-specific cysteine synthase. CysM belongs to the fold type II pyridoxal 5'-phosphate-dependent enzymes, as revealed by the crystal structure determined at 2.1-angstroms resolution. A model of O-phosphoserine bound to the enzyme suggests a hydrogen bonding interaction of the side chain of Arg220 with the phosphate group as a key feature in substrate selectivity. Replacement of this residue results in a significant loss of specificity for O-phosphoserine. Notably, reactions with sulfur donors are not affected by the amino acid replacement. The specificity of CysM toward O-phosphoserine together with the previously established novel mode of sulfur delivery via thiocarboxylated CysO (Burns, K. E., Baumgart, S., Dorrestein, P. C., Zhai, H., McLafferty, F. W., and Begley, T. P. (2005) J. Am. Chem. Soc. 127, 11602-11603) provide strong evidence for an O-phosphoserine-based cysteine biosynthesis pathway in M. tuberculosis that is independent of both O-acetylserine and the sulfate reduction pathway. The existence of an alternative biosynthetic pathway to cysteine in this pathogen has implications for the design strategy aimed at inhibition of this metabolic route.     

Cloning of the Bacillus subtilis glutamine phosphoribosylpyrophosphate amidotransferase gene in Escherichia coli. Nucleotide sequence determination and properties of the plasmid-encoded enzyme

The Bacillus subtilis gene encoding glutamine phosphoribosylpyrophosphate amidotransferase (amidophosphoribosyltransferase) was cloned in pBR322. This gene is designated purF by analogy with the corresponding gene in Escherichia coli. B. subtilis purF was expressed in E. coli from a plasmid promoter. The plasmid-encoded enzyme was functional in vivo and complemented an E. coli purF mutant strain. The nucleotide sequence of a 1651-base pair B. subtilis DNA fragment was determined, thus localizing the 1428-base pair structural gene. A primary translation product of 476 amino acid residues was deduced from the DNA sequence. Comparison with the previously determined NH2-terminal amino acid sequence indicates that 11 residues are proteolytically removed from the NH2 terminus, leaving a protein chain of 465 residues having an NH2-terminal active site cysteine residue. Plasmid-encoded B. subtilis amidophosphoribosyltransferase was purified from E. coli cells and compared to the enzymes from B. subtilis and E. coli. The plasmid-encoded enzyme was similar in properties to amidophosphoribosyltransferase obtained from B. subtilis. Enzyme specific activity, immunological reactivity, in vitro lability to O2, Fe-S content, and NH2-terminal processing were virtually identical with amidophosphoribosyltransferase purified from B. subtilis. Thus E. coli correctly processed the NH2 terminus and assembled [4Fe-4S] centers in B. subtilis amidophosphoribosyltransferase although it does not perform these maturation steps on its own enzyme. Amino acid sequence comparison indicates that the B. subtilis and E. coli enzymes are homologous. Catalytic and regulatory domains were tentatively identified based on comparison with E. coli amidophosphoribosyltransferase and other phosphoribosyltransferase (Argos, P., Hanei, M., Wilson, J., and Kelley, W. (1983) J. Biol. Chem. 258, 6450-6457).     

Production and characterization of bifunctional enzymes. Substrate channeling in the aspartate pathway

The direct channeling of an intermediate between enzymes that catalyze consecutive reactions in a pathway offers the possibility of an efficient, exclusive, and protected means of metabolite delivery. Aspartokinase-homoserine dehydrogenase I (AK-HDH I) from Escherichia coli is an unusual bifunctional enzyme in that it does not catalyze consecutive reactions. The potential channeling of the intermediate beta-aspartyl phosphate between the aspartokinase of this bifunctional enzyme and aspartate semialdehyde dehydrogenase (ASADH), the enzyme that catalyzes the intervening reaction, has been examined. The introduction of increasing levels of inactivated ASADH has been shown to compete against enzyme-enzyme interactions and direct intermediate channeling, leading to a decrease in the overall reaction flux through these consecutive enzymes. These same results are obtained whether these experiments are conducted with aspartokinase III, a naturally occurring monofunctional isozyme, with an artificially produced monofunctional aspartokinase I, or with a fusion construct of AK I-ASADH. These results provide definitive evidence for the channeling of beta-aspartyl phosphate between aspartokinase and aspartate semialdehyde dehydrogenase in E. coli and suggest that ASADH may provide a bridge to channel the intermediates between the non-consecutive reactions of AK-HDH I.     

Evolution of biosynthetic pathways: a common ancestor for threonine synthase, threonine dehydratase and D-serine dehydratase.

The Bacillus subtilis genes encoding threonine synthase (thrC) and homoserine kinase (thrB) have been cloned via complementation of Escherichia coli thr mutants. Determination of their nucleotide sequences indicates that the thrC stop codon overlaps the thrB start codon; this genetic organization suggests that the two genes belong to the same operon, as in E. coli. However, the gene order is thrC-thrB in B. subtilis whereas it is thrB-thrC in the thr operon of E. coli. This inversion of the thrC and thrB genes between E. coli and B. subtilis is indicative of a possible independent construction of the thr operon in these two organisms. In other respects, comparison of the predicted amino acid sequences of the B. subtilis and E. coli threonine synthases with that of Saccharomyces cerevisiae threonine dehydratase and that of E. coli D-serine dehydratase revealed extensive homologies between these pyridoxal phosphate-dependent enzymes. This sequence homology, which correlates with similarities in the catalytic mechanisms of these enzymes, indicates that these proteins, catalyzing different reactions in different metabolic pathways, may have evolved from a common ancestor.     

The biosynthesis of monolignols: a "metabolic grid", or independent pathways to guaiacyl and syringyl units?

Lignin is a complex polymer formed by the oxidative polymerization of hydroxycinnamyl alcohol derivatives termed monolignols. The major monolignols in dicotyledonous angiosperm lignin are monomethylated guaiacyl (G) units derived from coniferyl alcohol, and dimethylated syringyl (S) units derived from sinapyl alcohol. The biochemical pathways leading to the formation of monolignols feature successive hydroxylation and O-methylation of the aromatic ring and conversion of the side chain carboxyl to an alcohol function. The current view of the monolignol biosynthetic pathway envisages a metabolic grid leading to G and S units, through which the successive hydroxylation and O-methylation reactions may occur at different levels of side chain oxidation. The present article assesses biochemical and genetic evidence for and against such a model, including recent data on the methylation reactions of monolignol biosynthesis in alfalfa. We draw attention to portions of the currently accepted monolignol pathway that may require revision, and suggest an alternative model in which metabolic channeling allows for independent pathways to G and S lignin.     

The acetohydroxy acid synthase III isoenzyme of Escherichia coli K-12: regulation of synthesis by leucine.

Acetohydroxy acid synthase III (AHAS III) is one of the three isoenzymes which catalyze the condensation reaction for the biosynthesis of the branched chain amino acids in $\text{Escherichia coli}$ K-12. The synthesis of this enzyme is repressed by leucine. As a consequence of this regulatory feature, strain PS1035, in which AHAS III is the only AHAS isoenzyme expressed, does not grow in minimal medium containing leucine. The other two branched chain amino acids, isoleucine and valine, do not have regulatory effects on AHAS III synthesis.     

The induction of a dehydrogenase activity for branched chain amino acids in Bacillus subtilis

Summary In Bacillus subtilis a dehydrogenase activity for branched chain amino acids was induced twelvefold in glucose medium by isoleucine. To a lesser degree this activity was induced by metabolically related amino acids with the exception of leucine which hardly induced. The induced enzyme actvity is different from alanine dehydrogenase. The presumable role of this inducible enzyme in anteiso fatty acid biosynthesis is discussed.     

A novel two-gene requirement for the octanoyltransfer reaction of Bacillus subtilis lipoic acid biosynthesis

The Bacillus subtilis genome encodes three apparent lipoyl ligase homologues: yhfJ, yqhM and ywfL, which we have renamed lplJ, lipM and lipL respectively. We show that LplJ encodes the sole lipoyl ligase of this bacterium. Physiological and biochemical characterization of a ΔlipM strain showed that LipM is absolutely required for the endogenous lipoylation of all lipoate-dependent proteins, confirming its role as the B. subtilis octanoyltransferase. However, we also report that in contrast to Escherichia coli, B. subtilis requires a third protein for lipoic acid assembly, LipL. B. subtilis ΔlipL strains are unable to synthesize lipoic acid despite the presence of LipM and the sulphur insertion enzyme, LipA, which should suffice for lipoic acid biosynthesis based on the E. coli model. LipM is only required for the endogenous lipoylation pathway, whereas LipL also plays a role in lipoic acid scavenging. Expression of E. coli lipB allows growth of B. subtilisΔlipL or ΔlipM strains in the absence of supplements. In contrast, growth of an E. coliΔlipB strain can be complemented with lipM, but not lipL. These data together with those of the companion article provide evidence that LipM and LipL catalyse sequential reactions in a novel pathway for lipoic acid biosynthesis.     

Prediction of effects of amino acid supplementation on growth of E. coli B/r

A mathematical model for the growth of a single cell of E. coli on medium containing amino acid is presented. A mixture of purified amino acids (glutamate, aspartate, serine, tyrosine, and leucine) combined in the ratios found in a natural digest (casein) were employed as the nitrogen source. Each of these amino acids is the representative of a different family of amino acids. The transport mechanisms and assimilation routes for each amino acid were inserted into the prototype model. The enzyme activities and saturation constants used in the model were based on literature data. The maximum velocities for uptake systems were calculated from experimental data. The formation and homeostasis of amino acid pools were regulated through cross-control of the activities of biosynthetic enzymes and of membrane transport of exogenous nutrients. The size of each amino acid pool was determined with mass balance equations that included terms for a transport system, a biosynthesis system, a transaminase enzyme system for interchange between the amino acid families, and a consumption system. The predictions of the extended model with regard to nutrient concentrations and growth rates compared well with the experimental data.     

Global Stability of Reversible Enzymatic Metabolic Chains

We consider metabolic networks with reversible enzymatic reactions. The model is written as a system of ordinary differential equations, possibly with inputs and outputs. We prove the global stability of the equilibrium (if it exists), using techniques of monotone systems and compartmental matrices. We show that the equilibrium does not always exist. Finally, we consider a metabolic system coupled with a genetic network, and we study the dependence of the metabolic equilibrium (if it exists) with respect to concentrations of enzymes. We give some conclusions concerning the dynamical behavior of coupled genetic/metabolic systems.     

基于文献挖掘的巨大芽胞杆菌代谢网络模型的构建与分析

【目的】通过挖掘实验性文献,建立巨大芽胞杆菌事实型代谢网络模型,以详尽解析生理特性,优化其生理功能。【方法】从PubMed、Derwent Innovations Index、中国知网等公共文献(专利)数据库中获取与巨大芽胞杆菌(Bacillus megaterium)相关的实验性文献建立本地文献数据库。采用文献挖掘工具获取功能基因、酶、代谢物和生化反应等信息,以其为基础构建代谢网络粗模型,进一步借助KEGG等数据库修正以及Matlab程序的模拟得到精细模型(系统生物学标记语言的形式)。【结果】最终的精细模型共有292个生化反应、378个代谢物、220个酶和217个基因。以1.62 mmol/g cell/h的葡萄糖底物吸收速率为限制性条件,模拟的菌体比生长速率为0.089 h-1,略低于实验值0.11 h-1。此外,嘧啶代谢途径的单基因敲除模拟结果表明,准确率为90%。【结论】该代谢网络模型涵盖了中心代谢途径、维生素B12合成途径和氨基酸代谢途径,并在一定程度上反映了营养底物与基因对巨大芽胞杆菌生长性能的影响。     

4-Oxalocrotonate tautomerase, an enzyme composed of 62 amino acid residues per monomer.

The xylH gene encoding 4-oxalocrotonate tautomerase (4-OT) has been located on a subclone of the Pseudomonas putida mt-2 TOL plasmid pWW0 and inserted into an Escherichia coli expression vector. Several of the genes of the metafission pathway encoded by pWW0 have been cloned in E. coli, but the overexpression of their gene products has met with limited success. By utilizing the E. coli alkaline phosphatase promoter (phoA) coupled with the proper positioning of a ribosome-binding region, we are able to express functional 4-OT in yields of at least 10 mg of pure enzyme/liter of culture. 4-OT has been previously characterized and shown to be an extremely efficient catalyst (Whitman, C. P., Aird, B. A., Gillespie, W. R., and Stolowich, N. J. (1991) J. Am. Chem. Soc. 113, 3154-3162). Kinetic and physical characterization of the E. coli-expressed protein show that it is identical with that of the 4-OT isolated from P. putida. The functional unit is apparently a pentamer of identical subunits, each consisting of only 62 amino acid residues. This is the smallest enzyme subunit reported to date. The amino acid sequence, determined in part from automated Edman degradation and also deduced from the primary sequence of xylH, did not show homology with any of the sequences in the current data bases nor with any of the sequences of enzymes that catalyze similar reactions. We propose that the active site of 4-OT may be established by an overlap of subunits and comprised of amino acid residues belonging to several, if not all, of the subunits.     

Methionyl-tRNA synthetase from Bacillus stearothermophilus: structural and functional identities with the Escherichia coli enzyme.

The metS gene encoding homodimeric methionyl-tRNA synthetase from Bacillus stearothermophilus has been cloned and a 2880 base pair sequence solved. Comparison of the deduced enzyme protomer sequence (Mr 74,355) with that of the E. coli methionyl-tRNA synthetase protomer (Mr 76,124) revealed a relatively low level (32%) of identities, although both enzymes have very similar biochemical properties (Kalogerakos, T., Dessen, P., Fayat, G. and Blanquet, S. (1980) Biochemistry 19, 3712-3723). However, all the sequence patterns whose functional significance have been probed in the case of the E. coli enzyme are found in the thermostable enzyme sequence. In particular, a stretch of 16 amino acids corresponding to the CAU anticodon binding site in the E. coli synthetase structure is highly conserved in the metS sequence. The metS product could be expressed in E. coli and purified. It showed structure-function relationships identical to those of the enzyme extracted from B. stearothermophilus cells. In particular, the patterns of mild proteolysis were the same. Subtilisin converted the native dimer into a fully active monomeric species (62 kDa), while trypsin digestion yielded an inactive form because of an additional cleavage of the 62 kDa polypeptide into two subfragments capable however of remaining firmly associated. The subtilisin cleavage site was mapped on the enzyme polypeptide, and a gene encoding the active monomer was constructed and expressed in E. coli. Finally, trypsin attack was demonstrated to cleave a peptidic bond within the KMSKS sequence common to E. coli and B. stearothermophilus methionyl-tRNA synthetases. This sequence has been shown, in the case of the E. coli enzyme, to have an essential role for the catalysis of methionyl-adenylate formation.     

Purification and properties of guanosine triphosphate cyclohydrolase II from Escherichia coli.

An enzyme that uses GTP as substrate for the formation in stoichiometric quantities of formate, inorganic pyrophosphate, and 2,5-diamino-6-hydroxy-4-(ribosylamino)pyrimidine-5'-phosphate has been purified 2200-fold from extracts of Escherichia coli B. This enzyme is named GTP cyclohydrolase II to distinguish it from a previously studied E. coli enzyme, named GTP cyclohydrolase (and called GTP cyclohydrolase I in this paper), that catalyzes the first of a series of enzymatic reactions leading to the biosynthesis of the pteridine portion of folic acid (Burg, A. W., and Brown, G. M. (1968) J. Biol. Chem. 243, 2349-2358). Some of the properties of GTP cyclohydrolase II are: (a) divalent cations are required for activity (Mg2+ is most effective); (b) its molecular weight, estimated by filtration on Sephadex G-200, is 44,000; (c) the K-m for GTP is 41 mum; (d) its pH optimum is 8.5; and (e) its activity is inhibited by inorganic pyrophosphate, one of the products of the reaction. Compounds not used as substrate are: GDP, GMP, guanosine, dGTP, ATP, ITP, and XTP. Properties a, b, c, and e (above), as well as the nature of the products, distinguish this enzyme from GTP cyclohydrolase I. Since GTP cyclohydrolase II apparently is not concerned with the biosynthesis of folic acid, the possible physiological role of this enzyme in the biosynthesis of riboflavin is considered in the light of the present investigations and the previously published work on riboflavin biosynthesis by other investigators.