Detailed kinetics and regulation of mammalian NAD-linked isocitrate dehydrogenase

A mathematical model is presented to describe the catalytic mechanism of mammalian NAD-linked isocitrate dehydrogenase (NAD-IDH), a highly regulated enzyme in the tricarboxylic acid cycle, a crucial pathway in energy metabolism and biosynthesis. The mechanism accounts for allosteric regulation by magnesium-bound isocitrate and EGTA and calcium-bound ATP and ADP. The developed model is used to analyze kinetic data for the cardiac enzyme and to estimate kinetic parameter values. Since the kinetic mechanism is expressed in terms of chemical species (rather than biochemical reactants), the model explicitly accounts for the effects of biochemical state (ionic strength, pH, temperature, and metal cation concentration) on the kinetics. Because the substrate isocitrate competes with allosteric activators (ATP and ADP) and an inhibitor (EGTA) for metal ion cofactors (Ca(2+) and Mg(2+)), the observed kinetic relationships between reactants, activator and inhibitor concentrations, and catalytic flux are complex. Our analysis reveals that under physiological conditions, the ADP/ATP ratio plays a more significant role than Ca(2+) concentration in regulating the enzyme's activity. In addition, the enzyme is highly sensitive to Mg(2+) concentration in the physiological range, pointing to a potential regulatory role of [Mg(2+)] in mitochondrial energy metabolism.     

Kinetics and Regulation of Mammalian NADH-Ubiquinone Oxidoreductase (Complex I)

NADH-ubiquinone oxidoreductase (Complex I, European Commission No. 1.6.5.3) is one of the respiratory complexes that generate the proton-motive force required for the synthesis of ATP in mitochondria. The catalytic mechanism of Complex I has not been well understood, due to the complicated structure of this enzyme. Here, we develop a kinetic model for Complex I that accounts for electron transfer from NADH to ubiquinone through protein-bound prosthetic groups, which is coupled to the translocation of protons across the inner mitochondrial membrane. The model is derived based on the tri-bi enzyme mechanism combined with a simple model of the conformational changes associated with proton transport. To study the catalytic mechanism, parameter values are estimated by analyzing kinetic data. The model is further validated by independent data sets from additional experiments, effectively explaining the effect of pH on enzyme activity. Results imply that matrix pH significantly affects the enzyme turnover processes. The overall kinetic analysis demonstrates a hybrid ping-pong rapid-equilibrium random bi-bi mechanism, consolidating the characteristics from previously reported kinetic mechanisms and data.     

The role of Asn-212 in the catalytic mechanism of human endonuclease APE1: Stopped-flow kinetic study of incision activity on a natural AP site and a tetrahydrofuran analogue

Mammalian AP endonuclease 1 is a pivotal enzyme of the base excision repair pathway acting on apurinic/apyrimidinic sites. Previous structural and biochemical studies showed that the conserved Asn-212 residue is important for the enzymatic activity of APE1. Here, we report a comprehensive pre-steady-state kinetic analysis of two APE1 mutants, each containing amino acid substitutions at position 212, to ascertain the role of Asn-212 in individual steps of the APE1 catalytic mechanism. We applied the stopped-flow technique for detection of conformational transitions in the mutant proteins and DNA substrates during the catalytic cycle, using fluorophores that are sensitive to the micro-environment. Our data indicate that Asn-212 substitution by Asp reduces the rate of the incision step by ∼550-fold, while Ala substitution results in ∼70,000-fold decrease. Analysis of the binding steps revealed that both mutants continued to rapidly and efficiently bind to abasic DNA containing the natural AP site or its tetrahydrofuran analogue (F). Moreover, transient kinetic analysis showed that N212A APE1 possessed a higher binding rate and a higher affinity for specific substrates compared to N212D APE1. Molecular dynamics (MD) simulation revealed a significant dislocation of the key catalytic residues of both mutant proteins relative to wild-type APE1. The analysis of the model structure of N212D APE1 provides evidence for alternate hydrogen bonding between Asn-212 and Asp-210 residues, whereas N212A possesses an extended active site pocket due to Asn removal. Taken together, these biochemical and MD simulation results indicate that Asn-212 is essential for abasic DNA incision, but is not crucial for effective recognition/binding.     

Regulation of mitochondrial malate dehydrogenase: kinetic modulation independent of subunit interaction

Porcine heart mitochondrial malate dehydrogenase (EC 1.1.1.37), a dimeric enzyme of Mr = 70,000, is both allosterically activated and inhibited by citrate. Using an affinity elution procedure based upon citrate binding to malate dehydrogenase, the isolation of pure heterodimer (a dimeric species with one active subunit and one iodoacetamide-inactivated subunit) has been achieved. Investigations utilizing this heterodimer in conjunction with resin-bound monomers of malate dehydrogenase have allowed the formulation of a definite conclusion concerning the role of subunit interactions in catalysis and regulation of this enzyme. The citrate kinetic effects, oxaloacetate inhibition, malate activation, and the effects of 2-thenoyl-trifluoroacetone (TTFA) are shown to be independent of interaction between catalytically active subunits. Previous kinetic data thought to support a reciprocating catalytic mechanism for this enzyme may be reinterpreted upon closer analysis in relation to an allosteric, conformationally specific binding model for malate dehydrogenase.     

Insights into the catalytic mechanism of type VI sulfide:quinone oxidoreductases

Sulfide oxidation is catalyzed by ancient membrane-bound sulfide:quinone oxidoreductases (SQR) which are classified into six different types. For catalysis of sulfide oxidation, all SQRs require FAD cofactor and a redox-active centre in the active site, usually formed between conserved essential cysteines. SQRs of different types have variation in the number and position of cysteines, highlighting the potential for diverse catalytic mechanisms. The photosynthetic purple sulfur bacterium, Thiocapsa roseopersicina contains a type VI SQR enzyme (TrSqrF) having unusual catalytic parameters and four cysteines likely involved in the catalysis. Site-directed mutagenesis was applied to identify the role of cysteines in the catalytic process of TrSqrF. Based on biochemical and kinetic characterization of these TrSqrF variants, Cys121 is identified as crucial for enzyme activity. The cofactor is covalently bound via a heterodisulfide bridge between Cys121 and the C8M group of FAD. Mutation of another cysteine present in all SQRs (Cys332) causes remarkably decreased enzyme activity (14.6% of wild type enzyme) proving important, but non-essential role of this residue in enzyme catalysis. The sulfhydril-blocking agent, iodoacetamide can irreversibly inactivate TrSqrF but only if substrates are present and the enzyme is actively catalyzing its reaction. When the enzyme is inhibited by iodoacetamide, the FAD cofactor is released. The inhibition studies support a mechanism that entails opening and reforming of the heterodisulfide bridge during the catalytic cycle of TrSqrF. Our study thus reports the first detailed structure-function analysis of a type VI SQR enzyme which enables the proposal of a distinct mechanism of sulfide oxidation for this class.     

Substrate activation of porcine pancreatic kallikrein by N alpha derivatives of arginine 4-nitroanilides

Hydrolysis of several N alpha-substituted L-arginine 4-nitroanilides with porcine pancreatic kallikrein was studied under different conditions of pH, temperature, and salt concentration. At high substrate concentrations a deviation from Michaelis-Menten kinetics was observed with a significant increase in the hydrolysis rates of almost all substrates. Kinetic data were analyzed on the assumption that porcine pancreatic kallikrein presents an additional binding site with lower affinity for the substrate. Binding to this auxiliary site gives rise to a modulated enzyme species which can hydrolyze an additional molecule of the substrate through a second catalytic pathway. The values of both Michaelis-Menten and catalytic rate constants were higher for the modulated species than for the free enzyme, suggesting a mechanism of enzyme activation by substrate. Kinetic data indicated similar substrate requirements for binding at the primary and auxiliary sites of the enzyme. Tris(hydroxymethyl)aminomethane hydrochloride and NaCl were shown to alter the kinetic parameters of the hydrolysis of N alpha-acetyl-L-Phe-L-Arg 4-nitroanilide by porcine pancreatic kallikrein but not the enzyme activation pattern (ratio of the catalytic constants for the activated and the free enzyme forms). Similar observations were made when the hydrolysis of D-Val-L-Leu-L-Arg 4-nitroanilide was studied under different pH and temperature conditions.     

Human glutathione transferase T2-2 discloses some evolutionary strategies for optimization of the catalytic activity of glutathione transferases

Steady state, pre-steady state kinetic experiments, and site-directed mutagenesis have been used to dissect the catalytic mechanism of human glutathione transferase T2-2 with 1-menaphthyl sulfate as co-substrate. This enzyme is close to the ancestral precursor of the more recently evolved glutathione transferases belonging to Alpha, Pi, and Mu classes. The enzyme displays a random kinetic mechanism with very low k(cat) and k(cat)/K(m)((GSH)) values and with a rate-limiting step identified as the product release. The chemical step, which is fast and causes product accumulation before the steady state catalysis, strictly depends on the deprotonation of the bound GSH. Replacement of Arg-107 with Ala dramatically affects the fast phase, indicating that this residue is crucial both in the activation and orientation of GSH in the ternary complex. All pre-steady state and steady state kinetic data were convincingly fit to a kinetic mechanism that reflects a quite primordial catalytic efficiency of this enzyme. It involves two slowly interconverting or not interconverting enzyme populations (or active sites of the dimeric enzyme) both able to bind and activate GSH and strongly inhibited by the product. Only one population or subunit is catalytically competent. The proposed mechanism accounts for the apparent half-site behavior of this enzyme and for the apparent negative cooperativity observed under steady state conditions. These findings also suggest some evolutionary strategies in the glutathione transferase family that have been adopted for the optimization of the catalytic activity, which are mainly based on an increased flexibility of critical protein segments and on an optimal orientation of the substrate.     

Biochemical analysis of Thermotoga maritima GH36 alpha-galactosidase (TmGalA) confirms the mechanistic commonality of clan GH-D glycoside hydrolases

Organization of glycoside hydrolase (GH) families into clans expands the utility of information on catalytic mechanisms of member enzymes. This issue was examined for GH27 and GH36 through biochemical analysis of GH36 alpha-galactosidase from Thermotoga maritima (TmGalA). Catalytic residues in TmGalA were inferred through structural homology with GH27 members to facilitate design of site-directed mutants. Product analysis confirmed that the wild type (WT) acted with retention of anomeric stereochemistry, analogous to GH27 enzymes. Conserved acidic residues were confirmed through kinetic analysis of D327G and D387G mutant enzymes, azide rescue, and determination of azide rescue products. Mutation of Asp327 to Gly resulted in a mutant that had a 200-800-fold lower catalytic rate on aryl galactosides relative to the WT enzyme. Azide rescue experiments using the D327G enzyme showed a 30-fold higher catalytic rate compared to without azide. Addition of azide to the reaction resulted in formation of azide beta-d-galactopyranoside, confirming Asp327 as the nucleophilic residue. The Asp387Gly mutation was 1500-fold catalytically slower than the WT enzyme on p-nitrophenyl alpha-d-galactopyranoside. Analysis at different pH values produced a bell-shaped curve of the WT enzyme, but D387G exhibited higher activity with increasing pH. Catalyzed reactions with the D387G mutant in the presence of azide resulted in formation of azide alpha-d-galactopryanoside as the product of a retaining mechanism. These results confirm that Asp387 is the acid/base residue of TmGalA. Furthermore, they show that the biochemical characteristics of GH36 TmGalA are closely related to GH27 enzymes, confirming the mechanistic commonality of clan GH-D members.     

Cloning, expression and characterisation of Erwinia carotovora L-asparaginase

Bacterial L-asparaginases (E.C. 3.5.1.1) have been used as therapeutic agents in the treatment of acute childhood lymphoblastic leukaemia. L-asparaginase from Erwinia carotovora NCYC 1526 (ErA) was cloned and expressed in E. coli. The enzyme was purified to homogeneity by a two-step procedure comprising cation-exchange chromatography and affinity chromatography on immobilised L-asparagine. The enzymatic properties of the recombinant enzyme were investigated and the kinetic parameters (K(m), k(cat)) for a number of substrates were determined. Molecular modelling studies were also employed to create a model of ErA, based on the known structure of the Erwinia chrysanthemi enzyme. The molecular model was used to help interpret biochemical data concerning substrate specificity and catalytic mechanism of the enzyme. The kinetic parameters of selected substrates were determined at various pH values, and the pH-dependence profiles of V(max) and V(max)/K(m) were analyzed. The pH-dependence of V(max) shows one transition in the acidic pH range with pK(a)=5.4, and the pH-dependence of V(max)/K(m) exhibits two transitions with pK(a)=5.4 and 8.5. Based on analysis of alternative substrates and molecular modelling studies, it was concluded that the pK(a) at the acidic pH range corresponds to the active site residues Asp115 or Glu82, whereas the pK(a) observed at the alkaline pH range is not due to substrate amino group ionisation, but rather is the result of enzyme ionisation. The effect of temperature and viscosity on the catalytic activity of the enzyme was also investigated and it was concluded that the rate-limiting step of the catalytic reaction is relevant to structural transitions of the protein. Thermodynamic analysis of the activity data showed that the activation energies are dependent on the substrate, and entropy changes appear to be the main determinant contributing to substrate specificity.     

Conformational basis for substrate recognition and regulation of catalytic activity in Staphylococcus aureus nucleoside di-phosphate kinase

Nucleoside diphosphate kinases (NDK) are characterized by high catalytic turnover rates and diverse substrate specificity. These features make this enzyme an effective activator of a pro-drug-an application that has been actively pursued for a variety of therapeutic strategies. The catalytic mechanism of this enzyme is governed by a conserved histidine that coordinates a magnesium ion at the active site. Despite substantial structural and biochemical information on NDK, the mechanistic feature of the phospho-transfer that leads to auto-phosphorylation remains unclear. While the role of the histidine residue is well documented, the other active site residues, in particular the conserved serine remains poorly characterized. Studies on some homologues suggest no role for the serine residue at the active site, while others suggest a crucial role for this serine in the regulation and quaternary association of this enzyme in some species. Here we report the biochemical features of the Staphylococcus aureus NDK and the mutant enzymes. We also describe the crystal structures of the apo-NDK, as a transition state mimic with vanadate and in complex with different nucleotide substrates. These structures formed the basis for molecular dynamics simulations to understand the broad substrate specificity of this enzyme and the role of active site residues in the phospho-transfer mechanism and oligomerization. Put together, these data suggest that concerted changes in the conformation of specific residues facilitate the stabilization of nucleotide complexes thereby enabling the steps involved in the ping-pong reaction mechanism without large changes to the overall structure of this enzyme.     

Kinetic analysis of the mechanism for subtilisin in essentially anhydrous organic solvents

Steady-state kinetic analysis has been used to confirm the catalytic mechanism of lyophilized subtilisin suspended in a variety of organic solvents. Specifically, this article demonstrates that partial reactions can occur between subtilisin and ester substrates in organic solvents. Partitioning of common intermediates between competing acceptors at a constant ratio of products has also been described. The decomposition of a common intermediate formed from different substrates at the same rate is also further evidence of an acyl-enzyme mechanism for subtilisin suspended in anhydrous solvents. Partitioning of a common intermediate to give two products at a constant total rate, and saturation kinetics at varying substrate concentrations, complete a kinetic investigation of the enzyme mechanism. All the data generated support the formation of a stable acyl enzyme during the transesterification reaction catalzyed by subtilisin in the solvents used.     

On the mechanism of the metallo-beta-lactamase from Bacteroides fragilis.

The catalytic mechanism of metallo-beta-lactamase from Bacteroides fragilis, a dinuclear Zn(II)-containing enzyme responsible for multiple antibiotic resistance, has been investigated by using nitrocefin as a substrate. Rapid-scanning and single-wavelength stopped-flow studies revealed the accumulation during turnover of an enzyme-bound intermediate with intense absorbance at 665 nm (epsilon = 30 000 M(-1) cm(-1)). The proposed minimum kinetic mechanism for the B. fragilis metallo-beta-lactamase-catalyzed nitrocefin hydrolysis [Wang, Z., and Benkovic, S. J. (1998) J. Biol. Chem. 273, 22402-22408] was confirmed, and more accurate kinetic parameters were obtained from computer simulations and fitting. The intermediate was shown to be a novel anionic species bound to the enzyme through a Zn-acyl linkage and contains a negatively charged nitrogen leaving group. This is the first time such an intermediate was observed in the catalytic cycle of a Zn(II)-containing hydrolase and is evidence for a unique beta-lactam hydrolysis mechanism in which the amine can leave as an anion; prior protonation is not required. The electrostatic interaction between the negatively charged intermediate and the positively charged dinuclear Zn(II) center of the enzyme is important for stabilization of the intermediate. The catalytic reaction was accelerated in the presence of exogenous nucleophiles or anions, and neither the product nor the enzyme was modified during turnover, indicating that a Zn-bound hydroxide (rather than Asp-103) is the active site nucleophile. On the basis of all the information on hand, a catalytic mechanism of the B. fragilis metallo-beta-lactamase is proposed.     

The effect of insulin on the catalytic efficacy of rat skeletal muscle hexokinase isoenzyme II]

The effect of insulin on the intracellular localization of rat skeletal muscle hexokinase isozyme II (hexokinase II) was studied in vivo. It was found that after injection of the hormone the glucose concentration in the muscle gradually increases in parallel with the hexokinase II redistribution between the cytosol and the mitochondrial fraction in the direction of the bound form of the enzyme. This effect of insulin is due to glucose, an indispensable participant of the complex formation between the enzyme and the mitochondrial membrane. It was shown that the effect of glucose as a hexokinase II adsorbing reagent is a highly specific one. The hexokinase II binding to mitochondria in the presence of glucose is accompanied by changes in some kinetic properties of the enzyme. A kinetic analysis of catalytic efficiency of the free and bound hexokinase II forms revealed that the catalytic efficiency of hexokinase II within the composition of the enzyme-membrane complex exceeds by two orders of magnitude that of the free enzyme. The data obtained are discussed in the framework of an adsorption mechanism of hexokinase activity regulation in the cell.     

Purification and kinetic analysis of eIF2B from Saccharomyces cerevisiae

Eukaryotic translation initiation factor 2B (eIF2B) is the heteropentameric guanine nucleotide exchange factor for translation initiation factor 2 (eIF2). Recent studies in the yeast Saccharomyces cerevisiae have served to characterize genetically the exchange factor. However, enzyme kinetic studies of the yeast enzyme have been hindered by the lack of sufficient quantities of protein suitable for biochemical analysis. We have purified yeast eIF2B and characterized its catalytic properties in vitro. Values for K(m) and V(max) were determined to be 12.2 nm and 250.7 fmol/min, respectively, at 0 degrees C. The calculated turnover number (K(cat)) of 43.2 pmol of GDP released per min/pmol of eIF2B at 30 degrees C is approximately 1 order of magnitude lower than values previously reported for the mammalian factor. Reciprocal plots at varying fixed concentrations of the second substrate were linear and intersected to the left of the y axis. This is consistent with a sequential catalytic mechanism and argues against a ping-pong mechanism similar to that proposed for EF-Tu/EF-Ts. In support of this model, our yeast eIF2B preparations bind guanine nucleotides, with an apparent dissociation constant for GTP in the low micromolar range.     

Origins of specificity and promiscuity in metabolic networks

How enzymes have evolved to their present form is linked to the question of how pathways emerged and evolved into extant metabolic networks. To investigate this mechanism, we have explored the chemical diversity present in a largely unbiased data set of catalytic reactions processed by modern enzymes across the tree of life. In order to get a quantitative estimate of enzyme chemical diversity, we measure enzyme multispecificity or promiscuity using the reaction molecular signatures. Our main finding is that reactions that are catalyzed by a highly specific enzyme are shared by poorly divergent species, suggesting a later emergence of this function during evolution. In contrast, reactions that are catalyzed by highly promiscuous enzymes are more likely to appear uniformly distributed across species in the tree of life. From a functional point of view, promiscuous enzymes are mainly involved in amino acid and lipid metabolisms, which might be associated with the earliest form of biochemical reactions. In this way, results presented in this paper might assist us with the identification of primeval promiscuous catalytic functions contributing to life's minimal metabolism.     

Catalytic acid-base groups in yeast pyruvate decarboxylase. 3. A steady-state kinetic model consistent with the behavior of both wild-type and variant enzymes at all relevant pH values.

The widely quoted kinetic model for the mechanism of yeast pyruvate decarboxylase (YPDC, EC 4.1.1.1), an enzyme subject to substrate activation, is based on data for the wild-type enzyme under optimal experimental conditions. The major feature of the model is the obligatory binding of substrate in the regulatory site prior to substrate binding at the catalytic site. The activated monomer would complete the cycle by irreversible decarboxylation of the substrate and product (acetaldehyde) release. Our recent kinetic studies of YPDC variants substituted at positions D28 and E477 at the active center necessitate some modification of the mechanism. It was found that enzyme without substrate activation apparently is still catalytically competent. Further, substrate-dependent inhibition of D28-substituted variants leads to an enzyme form with nonzero activity at full saturation, requiring a second major branch point in the mechanism. Kinetic data for the E477Q variant suggest that three consecutive substrate binding steps may be needed to release product acetaldehyde, unlikely if YPDC monomer is the minimal catalytic unit with only two binding sites for substrate. A model to account for all kinetic observations involves a functional dimer operating through alternation of active sites. In the context of this mechanism, roles are suggested for the active center acid-base groups D28, E477, H114, and H115. The results underline once more the enormous importance that both aromatic rings of the thiamin diphosphate, rather than only the thiazolium ring, have in catalysis, a fact little appreciated prior to the availability of the 3-dimensional structure of these enzymes.     

A new mechanism and kinetic model for the enzymatic synthesis of short-chain fructooligosaccharides from sucrose

A kinetic model based on a ping-pong mechanism was developed under the steady-state hypothesis to account for the short-chain fructooligosaccharides (sc-FOS) synthesis using the commercial cellulolytic enzyme preparation, Rohapect CM. This new mechanism takes into account the interactions between the enzyme species and potential substrates (sucrose and sc-FOS) as a single complex reaction, allowing a better understanding of the reaction kinetics.The initial reaction rate laws appropriately describe the kinetic profiles of the examined substrates. Whereas sucrose exhibited Michaelis–Menten behavior with substrate inhibition, 1-kestose and nystose followed Michaelis–Menten and sigmoid enzyme kinetics. In addition, the enzyme was competitively inhibited by glucose and exhibited significant hydrolytic activity in the presence of nystose.The overall model was simultaneously fitted to experimental data from three initial sucrose concentrations (0.5, 1.5 and 2.1 M) using a multi-response regression with kinetic parameters that have biochemical relevance and are independent of the enzyme concentration. According to the model, sucrose acts almost exclusively as a fructosyl donor substrate. The mathematical development described herein is expected to be suitable for modeling similar enzymatic reaction systems.     

Analysis of progress curves of enzymatic reactions with unstable species

We present a general kinetic analysis of the Michaelis-Menten mechanism for the case in which the enzyme, the enzyme-substrate complex and the product are unstable. The kinetic data analysis which we suggest is based on the time progress curves of the product and/or on the time progress curve of the species into which the immediate product is transformed. This analysis, carried out under conditions of limiting enzyme concentration, allows the determination of the rate and equilibrium constants if adequate experimental results are available. We illustrate the method numerically by computer simulation of the reaction with added experimental errors.     

The Kinetic Reaction Mechanism of the Vibrio cholerae Sodium-dependent NADH Dehydrogenase

The sodium-dependent NADH dehydrogenase (Na⁺-NQR) is the main ion transporter in Vibrio cholerae. Its activity is linked to the operation of the respiratory chain and is essential for the development of the pathogenic phenotype. Previous studies have described different aspects of the enzyme, including the electron transfer pathways, sodium pumping structures, cofactor and subunit composition, among others. However, the mechanism of the enzyme remains to be completely elucidated. In this work, we have studied the kinetic mechanism of Na⁺-NQR with the use of steady state kinetics and stopped flow analysis. Na⁺-NQR follows a hexa-uni ping-pong mechanism, in which NADH acts as the first substrate, reacts with the enzyme, and the oxidized NAD leaves the catalytic site. In this conformation, the enzyme is able to capture two sodium ions and transport them to the external side of the membrane. In the last step, ubiquinone is bound and reduced, and ubiquinol is released. Our data also demonstrate that the catalytic cycle involves two redox states, the three- and five-electron reduced forms. A model that gathers all available information is proposed to explain the kinetic mechanism of Na⁺-NQR. This model provides a background to understand the current structural and functional information.     

Use and abuse of the quasi-steady-state approximation

The transient kinetic behaviour of an open single enzyme, single substrate reaction is examined. The reaction follows the Van Slyke-Cullen mechanism, a spacial case of the Michaelis-Menten reaction. The analysis is performed both with and without applying the quasi-steady-state approximation. The analysis of the full system shows conditions for biochemical pathway coupling, which yield sustained oscillatory behaviour in the enzyme reaction. The reduced model does not demonstrate this behaviour. The results have important implications in the analysis of open biochemical reactions and the modelling of metabolic systems.