Enzyme kinetics for a two-step enzymic reaction with comparable initial enzyme-substrate ratios

We extend the validity of the quasi-steady state assumption for a model double intermediate enzyme-substrate reaction to include the case where the ratio of initial enzyme to substrate concentration is not necessarily small. Simple analytical solutions are obtained when the reaction rates and the initial substrate concentration satisfy a certain condition. These analytical solutions compare favourably with numerical solutions of the full system of differential equations describing the reaction. Experimental methods are suggested which might permit the application of the quasi-steady state assumption to reactions where it may not have been obviously applicable before.     

Time dependence of activation of muscle AMP-aminohydrolase by substrate and potassium ion

The kinetics of AMP-aminohydrolase, which under steady state conditions shows a typical sigmoid dependence of initial velocities versus substrate concentration, have been examined by rapid mixing methods. Using this technique it was observed that when substrate or substrate plus activator (K(+)) were mixed with enzyme, the rate of appearance of product markedly increased during the first few tenths of a second. The time course of this change in rate was taken to reflect the progress of activation by substrate or by K(+). On the other hand, addition of activator to enzyme prior to mixing with substrate gave process curves for the formation of product consistent with normal Michaelis-Menten behaviour.Under the conditions where the reaction was examined, the enzyme at time zero had less than 10% of the activity of the fully active enzyme. The time course for activation with K(+) followed a first order process with a rate constant of 10.6 sec(-1) at 20 degrees C. A simple mechanism consistent with the data and capable of explaining the sigmoid dependence of initial velocities versus substrate concentrations observed in steady state kinetics was proposed.     

Analysis of the quasi-steady-state approximation for an enzymatic one-substrate reaction

The validity of the quasi-steady state approximation for the calculation of the rate function of an isolated enzyme reaction is analysed by a detailed consideration of the time dependent process. For the characterization of the deviations of the real motion from the quasi-stationary state three kinds of error functions are used, the relaxation deficit, the relative relaxation time and the relaxation error. An improved approximation procedure is developed to calculate the transient states of the system. The maximum distance of the original motion from the quasi-stationary states is estimated by a general method. By consideration of different enzyme and substrate concentrations as well as different kinetic constants those parameter regions have been determined, where the errors of the quasi-steady state approximation do not exceed tolerated values. It is suggested how the methods can be applied to metabolic pathways.     

Bacillus subtilis chorismate mutase is partially diffusion-controlled.

The effect of viscosogens on the enzyme-catalyzed rearrangement of chorismate to prephenate has been studied. The steady-state parameters kcat and kcat/Km for the monofunctional chorismate mutase from Bacillus subtilis (BsCM) decreased significantly with increasing concentrations of glycerol, whereas the 'sluggish' BsCM mutants C75A and C75S were insensitive to changes in microviscosity. The latter results rule out extraneous interactions of the viscosogen as an explanation for the effects observed with the wild-type enzyme. Additional control experiments show that neither viscosogen-induced shifts in the pH-dependence of the enzyme-catalyzed reaction nor small perturbations of the conformational equilibrium of chorismate can account for the observed effects. Instead, BsCM appears to be limited by substrate binding and product release at low and high substrate concentrations, respectively. Analysis of the kinetic data indicates that diffusive transition states are between 30 and 40% rate-determining in these concentration regimes; the chemical step must contribute to the remaining kinetic barrier. The relatively low value of the 'on' rates for chorismate and prephenate (approximately 2 x 106 m-1.s-1) probably reflects the need for a rare conformation of the enzyme, the ligand, or both for successful binding. Interestingly, the chorismate mutase domain of the bifunctional chorismate mutase-prephenate dehydratase from Escherichia coli, which has steady-state kinetic parameters comparable to those of BsCM but has a much less accessible active site, is insensitive to changes in viscosity and the reaction it catalyses is not diffusion-controlled.     

Michaelis-Menten kinetics at high enzyme concentrations

The total quasi-steady state approximation (tQSSA) for the irreversible Michaelis-Menten scheme is derived in a consistent manner. It is found that self-consistency of the initial transient guarantees the uniform validity of the tQSSA, but does not guarantee the validity of the linearization in the original derivation of Borghans et al. (1996, Bull. Math. Biol., 58, 43–63). Moreover, the present rederivation yielded the noteworthy result that the tQSSA is at least roughly valid for any substrate and enzyme concentrations. This reinforces and extends the original assertion that the parameter domain for which the tQSSA is valid overlaps the domain of validity of the standard quasi-steady state approximation and includes the limit of high enzyme concentrations. The criteria for the uniform validity of the original (linearized) tQSSA are corrected, and are used to derive approximate solutions that are uniformly valid in time. These approximations overlap and extend the domains of validity of the standard and reverse quasi-steady state approximations.     

Kinetics of an enzyme-catalyzed reaction measured by electrospray ionization mass spectrometry using a simple rapid mixing attachment

Mass spectrometry offers a potential means of measuring virtually all enzyme-catalyzed reactions by simultaneously measuring the concentrations of substrates, products, and intermediates where there are differences in mass between them. To perform these measurements the reaction mixture must be aged for different times and then ionized. Electrospray ionization mass spectrometry provides the most direct means of measuring these reactions. Here we describe a simple reaction mixing and ageing attachment for an electrospray ionization mass spectrometer, built from commercially available components. We have employed this device to measure the kinetics of a model reaction, namely the hydrolysis of N2-(carbobenzyloxy)-L-lysine-p-nitrophenyl ester-catalyzed by trypsin. In this way we were able to measure the kinetics of substrate depletion, product formation, and changes in both free enzyme and acyl-enzyme intermediate concentration in the approach to steady state. With this device we were able to measure reaction times down to about 640 ms.     

Catalytic properties of the HhaII restriction endonuclease

The catalytic properties of the HhaII restriction endonuclease were studied using plasmid pSK11 DNA containing a single 5'-G-A-N-T-C HhaII cleavage site as substrate. Reactions were followed by two methods: 1) gel electrophoretic analysis of nicked circular and linear DNA products, or 2) release of 32P-labeled inorganic phosphate from specifically labeled HhaII sites in a reaction coupled with bacterial alkaline phosphatase. The enzyme is optimally active at 37 degrees C in 10 mM Tris-HCl (pH 9.1) and 4-10 mM MgCl2 without added NaCl. Activity is stabilized by the presence of 2-mercaptoethanol and 0.2% Triton X-100 or 50 microgram/ml bovine serum albumin. At enzyme concentrations below 10 nM and using pSK11 as substrate, initial kinetic rates were dependent on the order of mixing of reactants. A lag of 3-4 min was observed if enzyme or substrate was added last. Preincubation of substrate and enzyme followed by initiation of the reaction with MgCl2 or preincubation of the enzyme with nonspecific DNA followed by initiation with substrate eliminated or reduced the lag, respectively, and speeded up the reactions. Under a wide range of reaction conditions, nicked pSK11 DNA accumulated early, while linear molecules appeared later, suggesting that HhaII cleaves one strand at a time in separate binding events. The apparent Km for covalently closed pSK11 DNA molecules was approximately 17 nM, and the turnover number for the conversion of covalent to nicked sites was 1.1 single strand scissions/min. Pre-steady state kinetic analysis indicated that cleavage of the first phosphodiester bond in a site is first order with a rate constant of about 0.8 min-1, while cleavage of the second phosphodiester bond is first order with a rate constant of about 0.2 min-1.     

Energetics of proline racemase: tracer perturbation experiments using [14C]proline that measure the interconversion rate of the two forms of free enzyme

Proline racemase exists in two states, one of which binds and isomerizes L-proline and the other of which binds and isomerizes D-proline. In the enzyme-catalyzed racemization of proline at high substrate concentrations, the interconversion of the two forms of the free enzyme becomes rate limiting. The tracer perturbation method of Britton (1966, 1973) vividly demonstrates the kinetic importance of this enzyme interconversion under oversaturating conditions and allows an estimate of the rate constant for this reaction of 10(5) s-1. It is further shown that the enzyme is bound state saturated and the peak-switch concentration, Cp, is 125 mM. At substrate concentrations higher than 125 mM the enzyme becomes oversaturated, and the reaction rate is limited by the transition state for the interconversion of two forms of the free enzyme. It seems likely that the two free enzyme forms differ only in the protonation states of the acidic and basic groups at the active site.     

Substrate ground state binding energy concentration is realized as transition state stabilization in physiological enzyme catalysis

Previously published kinetic data on the interactions of seventeen different enzymes with their physiological substrates are re-examined in order to understand the connection between ground state binding energy and transition state stabilization of the enzyme-catalyzed reactions. When the substrate ground state binding energies are normalized by the substrate molar volumes, binding of the substrate to the enzyme active site may be thought of as an energy concentration interaction; that is, binding of the substrate ground state brings in a certain concentration of energy. When kinetic data of the enzyme/substrate interactions are analyzed from this point of view, the following relationships are discovered: 1) smaller substrates possess more binding energy concentrations than do larger substrates with the effect dropping off exponentially, 2) larger enzymes (relative to substrate size) bind both the ground and transition states more tightly than smaller enzymes, and 3) high substrate ground state binding energy concentration is associated with greater reaction transition state stabilization. It is proposed that these observations are inconsistent with the conventional (Haldane) view of enzyme catalysis and are better reconciled with the shifting specificity model for enzyme catalysis.     

Evidence for a phosphoenzyme intermediate in the reaction pathway of rat hepatic fructose-2,6-bisphosphatase

We re-examined the kinetics of the bisphosphatase reaction of rat hepatic 6-phosphofructo-2-kinase/fructose-2,6-bisphosphatase after depleting the enzyme of bound fructose 6-phosphate and found a hyperbolic dependence on fructose 2,6-bisphosphate at concentrations below 100 nM. The Michaelis constant was 4 nM, the Vmax was about 12 nmol X mg-1 X min-1 at 22 degrees C but the substrate inhibited at concentrations above 100 nM. Both phosphate and alpha-glycerol phosphate strongly inhibited phosphoenzyme formation and hydrolytic rate below 100 nM, but relieved the inhibition by substrate at higher concentrations probably by antagonizing substrate binding. A number of observations support the proposition that the phosphoenzyme is a necessary participant in catalysis. 1) The amount of phosphoenzyme measured during steady-state hydrolysis as a function of substrate concentration correlated with the velocity profile. 2) Rapid mixing experiments demonstrated that over a broad range of substrate concentrations phosphoenzyme formation was faster than the net rate of hydrolysis. 3) Both phosphate and alpha-glycerol phosphate inhibited the rate of phosphoenzyme formation and, at low substrate concentrations, reduced the steady-state phosphoenzyme levels. The latter correlated with inhibition of substrate hydrolysis. 4) Both phosphate and alpha-glycerol phosphate stimulate the rate of phosphoenzyme breakdown, consistent with their stimulation of substrate hydrolysis at high substrate concentrations. 5) The fractional rate of phosphoenzyme breakdown, which was pH and substrate dependent, multiplied by the amount of phosphoenzyme obtained in the steady state at that pH and substrate concentration approximated the observed rate of hydrolysis. We conclude that the phosphoenzyme is a reaction intermediate in the hepatic fructose-2,6-bisphosphatase reaction.     

Introducing total substrates simplifies theoretical analysis at non-negligible enzyme concentrations: pseudo first-order kinetics and the loss of zero-order ultrasensitivity

The Briggs–Haldane standard quasi-steady state approximation and the resulting rate expressions for enzyme driven biochemical reactions provide crucial theoretical insight compared to the full set of equations describing the reactions, mainly because it reduces the number of variables and equations. When the enzyme is in excess of the substrate, a significant amount of substrate can be bound in intermediate complexes, so-called substrate sequestration. The standard quasi-steady state approximation is known to fail under such conditions, a main reason being that it neglects these intermediate complexes. Introducing total substrates, i.e., the sums of substrates and intermediate complexes, provides a similar reduction of the number of variables to consider but without neglecting the contribution from intermediate complexes. The present theoretical study illustrates the usefulness of such simplifications for the understanding of biochemical reaction schemes. We show how introducing the total substrates allows a simple analytical treatment of the relevance of significant enzyme concentrations for pseudo first-order kinetics and reconciles two proposed criteria for the validity of the pseudo first-order approximation. In addition, we show how the loss of zero-order ultrasensitivity in covalent modification cycles can be analyzed, in particular that approaches such as metabolic control analysis are immediately applicable to scenarios described by the total substrates with enzyme concentrations higher than or comparable to the substrate concentrations. A simple criterion which excludes the possibility of zero-order ultrasensitivity is presented.     

The size and curvature of anionic covesicle substrate affects the catalytic action of cytosolic phospholipase A2.

Cytosolic phospholipase A2 (cPLA2) is normally located in the cytosol, but in response to cellular activation the enzyme binds to the membrane at the lipid/water interface where it catalyzes the hydrolysis of the sn-2 ester of arachidonate-containing phospholipids. Synthetic phospholipid vesicle systems have been used in kinetic and mechanistic analyses of cPLA2, but these systems result in a rapid loss of enzyme activity. In the present research, covesicles of 1,2-dimyristoyl-sn-glycero-3-phosphomethanol (DMPM) containing 相似文献   

Regulation of UDPG pyrophosphorylase in Acetabularia mediterranea

The kinetic properties of UDPG pyrophosphorylase (glucosyl-1-phosphate uridyl transferase, EC 2.7.7.9) suggest that it may play a key role in the regulation of metabolism in Acetabularia mediterranea. The enzyme-catalyzed reaction is readily reversible in vitro, and has been assayed in both directions. The enzyme shows substrate inhibition by UDPG and UTP at substrate concentrations in excess of 2 mM. The kinetic behavior of the enzyme is consistent with the hypothesis that it catalyzes an ordered bisubstrate biproduct reaction in which G-1-P is the leading substrate, and UTP is the leading product. A plot of initial velocity vs. PPi concentration is sigmoid, indicating a cooperative homotropic effect. PGAL inhibits the reaction in the direction: UTP + G-1-P leads to UDPG + PPi It has no effect on the reverse reaction. The responses of the enzyme may serve to regulate the allocation of G-1-P between anabolic and catabolic pathways.     

Optimization of reaction conditions for enzymatic viscosity reduction and hydrolysis of wheat arabinoxylan in an industrial ethanol fermentation residue

This study examined enzyme-catalyzed viscosity reduction and evaluated the effects of substrate dry matter concentration on enzymatic degradation of arabinoxylan in a fermentation residue, "vinasse", resulting from industrial ethanol manufacture on wheat. Enzymatic catalysis was accomplished with a 50:50 mixture of an enzyme preparation from Humicola insolens, Ultraflo L, and a cellulolytic enzyme preparation from Trichoderma reesei, Celluclast 1.5 L. This enzyme mixture was previously shown to exhibit a synergistic action on arabinoxylan degradation. The viscosity of vinasse decreased with increased enzyme dosage and treatment time at pH 5, 50 degrees C, 5 wt % vinasse dry matter. After 24 h of enzymatic treatment, 76-84%, 75-80%, and 43-47%, respectively, of the theoretically maximal arabinose, xylose, and glucose releases were achieved, indicating that the viscosity decrease was a result of enzyme-catalyzed hydrolysis of arabinoxylan, beta-glucan, and cellulose. In designed response surface experiments, the optimal enzyme reaction conditions with respect to pH and temperature of the vinasse, the vinasse supernatant (mainly soluble material), and the vinasse sediment (mainly insoluble substances) varied from pH 5.2-6.4 and 41-49 degrees C for arabinose release and from pH 4.9-5.3 and 42-46 degrees C for xylose release. Even though only limited hydrolysis of the arabinoxylan in the vinasse sediment fraction was obtained, the results indicated that the same enzyme activities acted on the arabinoxylan in the different vinasse fractions irrespective of the state of solubility of the substrate material. The levels of liberated arabinose and xylose increased with increased dry matter concentration during enzymatic hydrolysis in the vinasse and the vinasse supernatant, but at the same time, increased substrate dry matter concentrations gave corresponding linear decreases in the hydrolytic efficiency as evaluated from levels of monosaccharide release per weight unit dry matter. The study thus documents that enzymatic arabinoxylan hydrolysis of the vinasse significantly decreases the vinasse viscosity and that a compromise in the dry matter must be found if enzymatic efficiency must be balanced with monosaccharide yields.     

A quantitative assay for the hydrolysis of structurally intact basement membranes

A quantitative assay has been developed for the hydrolysis of native bovine anterior lens capsule basement membrane fragments. The rationale for using structurally intact membrane fragments as the substrate in enzyme assays is that the proteinase susceptibility of the various basement membrane components differs when examined individually compared to when they are present in their native state. The assay is based upon the solubilization of 3H-bound protein from a finely ground suspension of [3H]acetylated basement membranes. The acetylation reaction and the fragmentation procedure do not alter the morphology or proteinase susceptibility of the membranes. The initial rate of release of radiolabeled digestion fragments by six different proteinases is approximately linear over the first 15% of hydrolysis, and the initial rates obtained are proportional to the amount of enzyme over a wide range of enzyme concentrations. The labeling index of 3810 cpm/micrograms of basement membrane used in this study permits the solubilization of 50 ng of protein to be detected easily. Some information about the size of the protein fragments solubilized can be obtained by addition of trichloroacetic (5% w/v)-tannic acid (0.25% w/v) reagent to the supernatants from the assays, since this reagent appears to selectively precipitate larger fragments. An additional feature of this assay is that, since the substrate is radiolabeled, one can selectively visualize and analyze the size distribution of the digestion products by carrying out sodium dodecyl sulfate-gel electrophoresis with fluorographic detection. Based on the observation that these intact membranes are extensively digested by a number of common proteinases which have widely different substrate specificities, it appears that the hypothesis that a highly specific proteinase or class of proteinases is necessary for basement membrane catabolism is specious .     

Kinetics of the extracellular cellulases of Clostridium thermocellum acting on pretreated mixed hardwood and Avicel

Initial hydrolysis rates were examined for mixed hardwood flour pretreated with 1% sulfuric acid for 9 s at 220 °C (PTW220) and Avicel. Linear rates were observed for fractional conversion relative to the theoretical up to 0.2 for PTW220 and 0.4 for Avicel. Initial rates were essentially unaffected by the presence of growth medium components over a range of pH values. Avicel-hydrolyzing activity was inhibited linearly by ethanol, with a 50% rate reduction at 8 wt.% ethanol. Rate saturation with either substrate or enzyme was observed in a manner qualitatively consistent with previously reported adsorption data. Although somewhat less reactive than Avicel at very low enzyme loadings, much higher reaction rates were observed for PTW220 at moderate and high enzyme loading because of its higher capacity to bind cellulase. At equal subtrate concentrations (as potential glucose) and fractional substrate coverage of 0.09, the initial rate of pretreated wood hydrolysis exceeded that of Avicel by 15-fold. For fractional substrate coverage values up to 0.09 (the maximum value achieved for PTW220), the initial rate was proportional to adsorbed enzyme for PTW220. However, the rate per adsorbed enzyme declined sharply with increasing fractional coverage for Avicel hydrolysis.     

Calculation of immobilized enzyme reaction progress curves from nested ordered-sequential rate expressions

A method for estimating immobilized enzyme reaction progress curves, using simultaneous non-linear regression analysis of 2–3 substrate concentrations with time, is presented. These facile procedures involve using nested Gauss–Newton curve fitting algorithms on a Microsoft EXCEL spreadsheet. We refer to our technique as "nested" because the analysis consists of two or three mutually parameter-dependent sets of computations associated with bi- or termolecular enzyme-catalyzed reactions, respectively. We have applied the method to immobilized glucose oxidase-catalyzed reactions ([ -glucose] and [O₂] with time) and found that the kinetic parameters from initial velocity data were similar to those determined by the nested curve fitting method discussed herein.     

Progress curves of reactions catalyzed by unstable enzymes. A theoretical approach

When an enzyme is incubated with its substrate, the rate of catalysis will decline with time due to the combined effects of substrate utilization and product accumulation. These effects will be superimposed upon a progressive loss of catalytic activity if the enzyme is unstable, either spontaneously or as a result of an added reagent. In this report, the effect of enzyme inactivation on the progress curve for an enzyme-catalyzed reaction is considered. It is shown that under most circumstances catalysis will stop before the substrate is totally exhausted and that the amount of substrate remaining is related to the inactivation rate constants for various intermediates on the catalytic pathway. A graphical method for estimating these inactivation rate constants is suggested for several situations, including one which encompasses the effect of a suicide substrate. Expressions for the half time of the reaction are also given for some special cases.     

Enzymatic breakdown of threonine by threonine aldolase

1. The enzyme which splits threonine to acetaldehyde and glycine has been partially purified from rat liver (five- to sixfold purification) and the name threonine aldolase proposed for it. 2. The general properties of threonine aldolase have been studied. The enzyme is unstable to a pH below 5. The pH optimum of the enzyme reaction is at 7.5-7.7. The initial rate of production of acetaldehyde is proportional to the enzyme concentration, and when the enzyme concentration is constant, the production of acetaldehyde is proportional to the time, provided that the substrate is in excess. The enzyme is inhibited by the carbonyl group reagent, hydroxylamine. Attempts to demonstrate that pyridoxal phosphate is a cofactor were unsuccessful. 3. The enzyme splits only L-allothreonine and L-threonine and is inactive against the D-forms of these amino acids. 4. The enzyme reaction on DL-allothreonine follows first order kinetics. From the first order velocity constants and the initial rates of the rates of the reaction at various substrate concentrations the Michaelis constant, Ks, for this substrate has been evaluated. Michaelis constants have also been determined for threonine. 5. The optimum temperature for the enzymatic breakdown of DL-allothreonine at pH 7.65 was found to be 50 degrees C. in phosphate buffer and 48 degrees C. in tris-maleate buffer. The rate of thermal inactivation of the enzyme threonine aldolase obeys a first order reaction. The heat of thermal inactivation was calculated by the aid of the van't Hoff-Arrhenius equation to be 43,000 cal. per mole for the temperature range 41.2-46.6 degrees C. 6. Equivalent amounts of acetaldehyde and glycine were formed from DL-allothreonine and the enzymatic breakdown of DL-allothreonine was found to be irreversible.     

Kinetics and effect of salts and polyamines on T4 polynucleotide ligase.

The kinetics of T4 polynucleotide ligase has been investigated at pH 8,20 degrees C and using the double-stranded DNA substrate (dA)n - [(dT)10]n/10. Double-reciprocal plots of initial rates vs substrate concentrations as well as product inhibition studies have indicated that the enzyme reacts according to a ping-pong mechanism. The overall mechanism was found to be non-processive. The true Km for the DNA substrate was 0.6 muM and that of ATP 100 muM. Several attempts were made to reverse the T4 polynucleotide ligase joining reaction using 32-p-labelled (dA)n - [(DT)40]n/40 as substrate. No breakdown of this DNA could be detected. The joining reaction was inhibited by high concentrations, i.e. above approximately 70mM, of salts such as KCl, NaCl, NH4Cl and CsCl. At a concentration of 200 mM almost 100% inhibition was observed. Polyamines also caused inhibition of the enzyme, the most efficient inhibitor being spermine followed by spermidine. At a concentration of 1 mM spermine, virtually no joining took place. Addition of salts or polyamines resulted in a large increase in the apparent Km for the DNA substrate whereas the apparent Km for ATP remained unchanged. It is suggested that the affinity of the enzyme for the DNA substrate is decreased in the presence of inhibiting agents.