Biosynthesis of glycogen in Neurospora crassa. Kinetic mechanism of UDP-glucose: glycogen 4-alpha-glucosyltransferase.

The kinetic mechanism of glycogen synthase [UDP-glucose: glycogen 4-alpha-glucosyltransferase, EC 2.4.1.11], glucose-6-P-dependent form, from Neurospora crassa has been investigated by initial velocity experiments and studies with inhibitors in the presence of sufficient levels of glucose-6-P. The rate equation was different from those of common two-substrate systems because one of the substrates, glycogen, is also a product. The reaction rates were determined by varying the concentration of one of the substrates while keeping that of the other constant. Double-reciprocal plots of initial velocity measurements were linear and showed converging line patterns. UDP was found to act competitively when the substrate UDP-glucose was varied, but noncompetitively when glycogen was varied. On the basis of these results, it is concluded that glycogen synthase, glucose-6-P-dependent form, from N. crassa has a rapid equilibrium random Bi-Bi mechanism. Rate constant and dissociation constants for each step of this mechanism were estimated.     

Integrated steady state rate equations and the determination of individual rate constants.

Integrated steady state rate equations have been used to determine the kinetic constants (Vs, Ks, Vp, and Kp) and rate constants (k1, k2, k3, and k4) of the reversible enzyme mechanism: (see article). The fumarase reaction has been used as a model to illustrate the procedures for determining these constants. In contrast to initial velocity studies, the values of the constants have been obtained by examining the enzyme reaction in only one direction rather than in both forward and reverse directions. To accomplish this, a new procedure is described for fitting data to integrated rate equations which eliminates problems encountered when data are analyzed graphically. The advantages of examining on enzyme reaction in one direction with these new procedures allow this method to be extended to the examination of enzymes with simple mechanisms where initial velocities are difficult to measure because either the substrate or product is not readily available, or because the reaction is not readily reversible.     

Kinetic studies of alpha-galactosidase-containing mold pellets on PNPG hydrolysis.

Little is known about techniques for applying untreated microbial cells containing enzymes directly to industrial processes as a biocatalyst. The kinetic behavior of alpha-galactosidase-containing spherical pellets which are formed naturally under given conditions in a submerged culture of Mortierella vinacea was studied on the hydrolysis of PNPG (p-nitrophenyl-alpha-D-galactopyranoside). The effect on intraparticle diffusion on the overall reaction rate was assessed by the use of an effectiveness factor, which was calculated by the approximate solution to the equation derived from the mass balance within a pellet. The experimental effectiveness factors were found to be represented as a single function of the modified Thiele modulus, including such parameters as pellet size, enzyme concentration in the pellet, and substrate concentration. As the diffusional effect became more significant, the marked substrate inhibition as seen for a free enzyme disappeared gradually. The effect of product inhibition on the pellets was much weaker than that for a free enzyme at a given substrate concentration. In the region of diffusion controlled reaction, it was found that the rate is proportional to the square root of the enzyme concentration in the pellet. In addition, similarly to what was reported previously for a free enzyme,the reaction in a batch system was found to be approximately representable as simple first-order kinetics in which the rate constant was dependent on the initial substrate concentration.     

Production of lactobionic acid and sorbitol from lactose/fructose substrate using GFOR/GL enzymes from Zymomonas mobilis cells: a kinetic study

In this work, we have investigated the kinetics of the biotechnological production of lactobionic acid (LBA) and sorbitol by the catalytic action of glucose-fructose oxidoreductase (GFOR) and glucono-δ-lactonase (GL) enzymes. The cells of bacterium Zymomonas mobilis ATCC 29191 containing this enzymatic complex were submitted to permeabilization and reticulation procedures. The effect of the concentration of substrates on the rate of product formation using a mobilized cell system was investigated. The application of higher fructose concentration seems to not affect the initial rate of formation of the bionic acid. Under conditions of low initial concentration of lactose, the experimental kinetic data of the bi-substrate reaction were modelled by assuming a rate equation of the classical ping-pong mechanism. The found kinetic parameters displayed a low affinity of the GFOR enzyme for both substrates. The enzymatic system did not exhibit normal Michaelis-Menten kinetics in response to a change of concentration of lactose, when fructose was held constant, presenting a sigmoid relationship between initial velocity and substrate concentration. A rate equation based on Hill kinetics was used to describe the kinetic behaviour of this enzyme-substituted reaction at higher lactose concentrations. The results from batch experiments using immobilized cells within Ca-alginate beads revealed that there is no pronounced occurrence of mass transfer limitations on LBA production for beads with 1.2 mm in average diameter. This discussion aids for defining the best operating conditions to maximize the productivity for LBA and sorbitol in this bioconversion and also for reducing the complexity of downstream separation processes.     

CRYSTALLINE TRYPSIN : V. KINETICS OF THE DIGESTION OF PROTEINS WITH CRUDE AND CRYSTALLINE TRYPSIN

The rate of digestion, as determined by the increase in non-protein nitrogen or formol titration, of casein, gelatin, and hemoglobin with crystalline trypsin preparations increases nearly in proportion to the concentration of protein, but with crude pancreatic extract the rate of digestion becomes independent of the protein concentration in concentrations of more than 2.5 per cent. With both enzymes the rate of digestion of mixtures of 5 per cent casein and gelatin is greater than would be expected from the point of view of a compound between enzyme and substrate. The rate of digestion of 5 per cent casein in the presence of 5 per cent gelatin is exactly the same as that of 5 per cent casein alone. This result is obtained with both enzymes. The digestion of casein with crude trypsin follows the course of a monomolecular reaction quite closely while with purified trypsin the velocity constant decreases as the reaction proceeds. In the case of hemoglobin the monomolecular velocity constant decreases with both purified and crude enzyme. When the reaction is followed by changes in the viscosity of the solution the abnormal effect of changing substrate concentration disappears and the reaction is in fair agreement with the monomolecular equation. The results as a whole indicate that the abnormalities of the reaction are due to the occurrence of several consecutive reactions rather than to the formation of a substrate enzyme compound.     

Phosphorylation reaction of vertebrate smooth muscle myosin: an enzyme kinetic analysis

Phosphorylation of vertebrate smooth muscle myosin or its isolated 20 000-dalton light chains by myosin light-chain kinase (MLCK) was found to follow first-order kinetics not only at low ([M] much less than Km) but also at high ([M] greater than or equal to Km) substrate concentration. This observation can most simply be explained by a product inhibition for which the Michaelis constants (Km) of the enzyme for the substrate (dephosphorylated myosin) and for the product (phosphorylated myosin) are approximately the same. For such a case, integration of the kinetic velocity equation gives an exponential formula similar to that of a true first-order reaction, the only difference being that its rate constant (k) depends additionally on the initial substrate concentration ([M]0). The standard kinetic constants (k, Km, Vmax) have been calculated by using this pseudo-first-order relationship. Independent evidence for the validity of the derived kinetic relationship was obtained from binding studies with myosin and MLCK. These showed that MLCK binds to phosphorylated and dephosphorylated myosin with approximately equal affinity (Ks = 30 X 10(-9) M). The possible applicability of the same kinetic relationship to other enzyme systems is discussed.     

Kinetic studies of mold α-galactosidase on PNPG hydrolysis

The kinetic properties of α-galactosidase of Mortierella vinacea were investigated in detail using PNPG (p-nitrophenyl-α-D -galactopyranoside) as a substrate. Consequently, the enzyme was markedly inhibited not only by the substrate, but also by the galactose hydrolized. The initial rate of reaction at sufficiently high substrate concentrations, however, did not fall to zero and did approach a finite value. Galactose behaved as a mixed inhibitor and was neither totally competitive nor totally noncompetitive. A rate equation was obtained from a generalized equation derived from a kinetic model which took both the inhibitions into consideration. The constants used in the equation were appropriately estimated. The calculated rate agreed fairly well with the observed initial rate. Moreover, the PNPG hydrolysis progressing in a batch system was found to be approximately representable by simple first order kinetics in which the rate constant was dependent on the initial substrate concentration.     

Glucoamylase and glucose oxidase preparations and their combined application for conversion of maltose to gluconic acid

The kinetic behavior of a system of multiple enzyme in solution has been studied in a variable volume batch reactor at pH 5, controlled dissolved oxygen concentration, and T = 30°C. The enzymes used were glucoamylase (R. delemar), glucose oxidase (A. niger), and gluconolactonase (A. niger), all of which are important commercial biocatalysts, and a disaccharide was employed as the starting substrate. This study includes the basic kinetic properties of individual enzymes and interactions between components of the reaction mixture. Classical Michaelis–Menten single substrate or two substrate kinetic with parameters based on initial rate data predict correctly the batch time course of the sequential reaction network.     

An enzyme rate equation for the overall rate of reaction of gel-immobilized glucose oxidase particles under buffered conditions. I. Pseudo-one substrate conditions

The overall rate of reaction of buffered gel-immobilized glucose oxidase particles is described by means of an enzyme rate equation which relates the overall reaction rate of a particle to the free solution characteristics of the enzyme, the effective diffusivity of the limiting substrate in the gel, the characteristic particle size, and the limiting substrate concentration adjacent to the gel surface. This equation accounts quantitatively for the limitation of the overall rate of reaction by substrate diffusion, and it is used to illustrate the influence of the system parameters, i. e., particle size, enzyme concentration, and pH, on the extent of the diffusional resistance associated with gel-immobilized glucose oxidase particles. The enzyme rate equation is generally applicable to those enzymes whose kinetics approximately follow Michaelis-Menten form when in free solution.     

Mechanistic origin of the kinetic cooperativity of hexokinase type L1 from wheat germ

A theoretical analysis is presented which shows that initial velocity data for hexokinase L1 catalysis of glucose phosphorylation by MgATP cannot be reconciled with the observed rate of the 'mnemonical' conformational transition which has been proposed to account for the kinetic cooperativity of the enzyme. The basic kinetic properties of hexokinase L1 and other allegedly 'mnemonical' enzymes appear to be fully consistent with an ordered ternary-complex mechanism in which the leading substrate participates in abortive-complex formation. It is concluded that, so far, no enzyme displaying kinetic cooperativity has been convincingly demonstrated to operate by a 'mnemonical' type of reaction mechanism.     

Interdependence between cooperativity and control coefficients

Influence of the concentration of internal metabolites on the control coefficient (defined as fractional change in flux per fractional change in enzyme activity) and regulatory properties of a given enzyme have been studied theoretically using a cyclic model of three enzymes. This model is useful to investigate the properties of the flux control coefficient for an enzyme following different rate equations. Enzymes can have high or low values of control coefficient irrespective of the type of kinetic equation, but the results obtained show that the sensitivity of these values to substrate variations is strongly dependent on its rate equation. These results help identify which kinetic equation allows the best control of a given metabolic pathway. These results have been applied to the purine nucleotide cycle. It is demonstrated that the best control of the cycle is reached when the irreversible reaction catalyzed by AMP deaminase follows a rate law that corresponds to a rational function of 2:2 degree with respect to AMP concentration.     

Kinetic evidence for the formation of D-alanyl phosphate in the mechanism of D-alanyl-D-alanine ligase

The steady state kinetic mechanism, molecular isotope exchange and the positional isotope exchange (PIX) reactions of D-alanyl-D-alanine ligase from Salmonella typhimurium have been studied. The kinetic mechanism has been determined to be ordered Ter-Ter from initial velocity and product inhibition experiments. The first substrate to bind is ATP followed by the addition of 2 mol of D-alanine. Pi is released, and then D-alanyl-D-alanine and ADP dissociate from the enzyme surface. In the reverse direction D-alanyl-D-alanine exhibits complete substrate inhibition (Ki = 1.15 +/- 0.05 mM) by binding to the enzyme-ATP complex. In the presence of D-alanine, D-alanyl-D-alanine ligase catalyzed the positional exchange of the beta,gamma-bridge oxygen in [gamma-18O4]ATP to a beta-nonbridge position. Two possible alternate dead-end substrate analogs, D-2-chloropropionic acid and isobutyric acid, did not induce a positional isotope exchange in [gamma-18O4]ATP. The positional isotope exchange rate is diminished relative to the net substrate turnover as the concentration of D-alanine is increased. This is consistent with the ordered Ter-Ter mechanism as determined by the steady state kinetic experiments. The ratio of the positional isotope exchange rate relative to the net chemical turnover of substrate (Vex/Vchem) approaches a value of 1.4 as the concentration of D-alanine becomes very small. This ratio is 100 times larger than the ratio of the maximal reverse and forward chemical reaction velocities (V2/V1). This situation is only possible when the reaction mechanism proceeds in two distinct steps and the first step is much faster than the second step. The enzyme was also found to catalyze the molecular isotope exchange of radiolabeled D-alanine with D-alanyl-D-alanine in the presence of phosphate. These results are consistent with the formation of D-alanyl phosphate as a kinetically competent intermediate.     

Estimation of the initial velocity of enzyme-catalysed reactions by non-linear regression analysis of progress curves.

Most methods for studying the kinetic properties of an enzyme involve the determination of initial velocities. When the reaction progress curve shows significant curvature due to depletion of the substrate, accumulation of inhibitory products or instability of the enzyme, estimation of the initial velocity is a subjective and inexact process. Two methods have been suggested [Cornish-Bowden (1975) Biochem. J. 144, 305-312; Boeker (1982) Biochem J. 203, 117-123] that attempt to eliminate this subjective element. The present study offers a third alternative, which is based on fitting a reparameterized form of the integrated Michaelis-Menten equation to the progress curves by non-linear regression. This method yields estimates and standard errors of the initial velocity and of the time to reach 50% reaction. No prior knowledge of the apparent product concentration at zero time or infinite time is required, since both of these quantities are also estimated from the data. It is shown that this method yields reliable estimates of the initial velocity under a wide range of circumstances, including those where the two previously published methods perform poorly.     

Energetics of enzyme catalysis. II. Oversaturation, case diagrams, reversible and irreversible behaviour

Most enzymes react in vivo under reversible conditions where the substrate and product concentrations are not far removed from equilibrium values. Under these conditions when the concentration of substrate is increased, in addition to the usual unsaturated and saturated behaviour we find a third type of kinetic regime at high substrate concentration-oversaturation. In this regime the rate limiting transition state involves interconversion of free enzyme forms. For a one substrate/one product enzyme, case diagrams can be constructed which depict the kinetic behaviour as a function of substrate and product concentrations. Six different cases are found and are discussed with the relevant free energy profiles. A systematic procedure is described for the investigation and construction of the case diagram.     

Bistability and the ordered bimolecular mechanism.

An equation describing the instantaneous velocity of an ordered bimolecular enzymatic reaction that exhibits inhibition by substrate and product was derived. Using kinetic constant values for horse liver alcohol dehydrogenase, the velocity expression was applied to an open-reaction system. The calculated steady-state surfaces displayed regions of bistability, which further substantiates the link between substrate inhibition and multiple steady states. This general computational approach may be applied to any system that can be described by an instantaneous velocity equation.     

Fatty acid synthetase. A steady state kinetic analysis of the reaction catalyzed by the enzyme from pigeon liver.

The kinetic mechanism of pigeon liver fatty acid synthetase action has been studied using steady state kinetic analysis. Initial velocity studies are consistent with an earlier suggestion that the enzyme catalyzes this reaction by a seven-site ping-pong mechanism. Although the range of substrate concentrations that could be used was limited by several factors, the initial velocity patterns showing the relationship between the substrates acetyl coenzyme CoA, malonyl-CoA, and NADPH appear to be a series of parallel lines, regardless of which substrate is varied at fixed levels of a second substrate. However, two of the substrates, acetyl-CoA and malonly-CoA, apparently exhibit a competitive substrate inhibition with respect to each other, but NADPH shows no inhibition of any kind. Product inhibition patterns suggest that free CoA is competitive versus acetyl-CoA and malonyl-CoA and is uncompetitive versus NADPH, and that NADP+ is competitive versus NADPH and uncompetitive versus acetyl-CoA or malonyl-CoA. These results are consistent with a seven-site ping-pong mechanism with intermediates covalently bound to 4'-phosphopantetheine (part of acyl carrier protein). Double competitive substrate inhibition by acetyl-CoA and malonyl-CoA is consistent with the rate equation derived for the over-all mechanism. The kinetic mechanism developed from these results is capable of explaining the formation of fatty acids from malonyl-CoA and NADPH alone (Katiyar, S. S., Briedis, A. V., and Porter, J. W. (1974) Arch. Biochem. Biophys. 162, 412-420) and also the formation of triacetic acid lactone from either malonyl-CoA alone or acetyl-CoA plus malonyl-CoA.     

Kinetics of glucose isomerization to fructose by immobilized glucose isomerase: anomeric reactivity of D-glucose in kinetic model

The substrate specificity of immobilized D-glucose isomerase (EC 5.3. 1.5) is investigated with an immobilized enzyme-packed reactor. A series of isomerization experiments with alpha-, beta-, and equilibrated D-glucose solutions indicates that beta anomer as well as alpha anomer is a substrate of the glucose isomerase at pH 7.5 and 60 degrees C. For substrate concentration of 0.028 mol l(-1) (1% w/v), the initial conversion rate of alpha-D-glucose was 43% higher than that with equilibrated glucose at the same concentration and 113% higher than beta-D-glucose conversion rate. This anomeric reactivity of glucose isomerase is mathematically described with a set of kinetic equations based on the reaction steps complying with Briggs-Haldane mechanism and the experimentally determined kinetic constants. The proposed reaction mechanism includes the mutarotation and the isomerization reactions of alpha- and beta-D-glucose with different rate constants.     

On the use of apparent kinetic parameters for immobilized enzyme with noncompetitive substrate inhibition

The use of a simple rate equation with apparent parameters to describe the kinetic behavior of an immobilized enzyme with noncompetitive substrate inhibition was assessed. To do so, the reaction rate was calculated as a function of the interfacial substrate concentration, and the results were used to identify the apparent kinetic parameters by nonlinear regression. This procedure was repeated for different values of the diffusional constraints and of the inhibition constant. The equation using apparent parameters can describe the global kinetic behavior, provided that the diffusional and inhibitory constraints are not too high. When the constraints are high, a Michaelis-Menten equation can be used to model the kinetics for interfacial concentrations lower than the concentration leading to the maximum reaction rate.     

Studies on sucrose synthetase. Kinetic mechanism

The kinetic properties of Helianthus tuberosus sucrose synthetase, which catalyzes the reaction UDP-glucose + fructose = UDP + sucrose, have been studied. A plot of the reciprocal initial velocity versus reciprocal substrate concentration gave a series of intersecting lines indicating a sequential mechanism. Product inhibition studies showed that UDP-glucose was competitive with UDP, whereas fructose was competitive with sucrose and uncompetitive with UDP. On the other hand, a dead-end inhibitor, salicine, was competitive with sucrose and uncompetitive with UDP. The results of initial velocity, product, and dead-end inhibition studies suggested that the addition of substrates to the enzyme follows an ordered mechanism.     

The determination of specificity constants in enzyme-catalysed reactions.

A convenient and accurate procedure for determining the kinetic parameter Vmax./Km is described. This avoids the error in the usual method of taking the observed first-order rate constant of an enzymic reaction at low substrate concentration as Vmax./Km. A series of reactions is used in which the initial concentration of substrate is below Km (e.g. from 5% to 50% of Km). Measurements are taken over the same extent of reaction (e.g. 70%) for each member of the series, and treated as if the kinetics were truly first-order. The reciprocal of the observed first-order rate constant is then plotted against the initial concentration of substrate: the reciprocal of the ordinate intercept is Vmax./Km. The procedure, as well as being applicable to simple reactions, is shown to be valid when there is competitive inhibition by the product, or when the reaction is reversible, or when there is competitive or mixed inhibition. The hydrolysis of cephalosporin C by a beta-lactamase from Pseudomonas aeruginosa is used to illustrate the method.