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.     

Control of enzymatic velocity under near-equilibrium conditions

Algebraic derivations demonstrate that if a multireactant enzyme system is poised at equilibrium and the concentration of one of the reactants is then changed by a small fraction, the resulting net reaction velocity is hyperbolically related to the fractional perturbation rather than the initial or final absolute concentration of that reactant. For small fractional perturbations the velocity is almost identical regardless which reactant is perturbed. Similar results are obtained even if the reaction system is already displaced by up to 30% from equilibrium at the time of the perturbation. These conclusions are independent of the relationships between the reactant concentrations and the kinetic constants for the enzyme. Thus under any near-equilibrium condition each of the reactants for a multireactant enzyme system shares almost equally in control of the net reaction velocity.     

Determination of initial velocities of enzymic reactions from progress curves.

The present communication describes a novel method for estimating initial velocities (v) of enzyme-catalysed reactions. It is based on an approximation of experimental data obtained by the cubic spline function. The initial velocity of a reaction is calculated as a derivative of the approximating function at a time value equal to zero. The proposed method is usable on a computer with a FORTRAN IV program. The method can be successfully used in such cases as substantial extents of substrate conversion, the inactivation of an enzyme in the course of a reaction, the existence of large experimental error or when the reaction mechanism is unknown.     

Further studies on the purine phosphoribosyltransferase 'burst' velocity reaction.

In the assays used to determinate the adenine and hypoxanthine-guanine phosphoribosyltransferases activities from Artemia cysts two phases of velocity are observed in the synthesis of AMP, IMP and GMP: one initial burst and a second, slower, steady-state velocity. Both reaction velocities are divalent cation-dependent and temperature-resistant, as they are detectable at temperatures from 0 to 100 degrees C. Butanol, frequently employed to interrupt the purine phosphoribosyltransferase reactions, does not inhibit the enzyme activities. The 'burst' phase is not detected when the reaction is ended by the addition of EDTA. These data support that the initial velocities of these enzymatic reactions may be due to the accumulation of products formed by the overall reaction, developed subsequent to the controlled reaction period, being the 'burst' a result from the relative resistance of these enzymes to the agents that are often used to stop the reaction, such as heat or butanol.     

On the validity of using semilogarithmic plots to determine initial velocities of enzyme-catalyzed reactions

It has been proposed (Johnston & Diven, 1969a) that it is valid to use semilogarithmic (first-order) plots of the extent of reaction versus time for graphic determination of initial velocities of enzyme-catalyzed reactions. This proposition suggests the assumption that the initial velocity error expected to be introduced by the proposed procedure is smaller than or comparable to the error introduced by the customary graphic procedure. The latter is based on the assumption that the progress curves of enzyme-catalyzed reactions have an initial linear segment of sufficient duration to permit accurate determination of slope. The validity of the procedure proposed by Johnston and Diven is examined in this report. It is concluded that the procedure is applicable to a very small class of enzyme-catalyzed reactions and only under certain experimental conditions.     

Dimethyl sulfide, a volatile flavor constituent, is a slow-binding inhibitor of tyrosinase.

In this paper, the inhibition of tyrosinase by a volatile compound is kinetically analyzed for the first time. The results obtained show that the volatile flavor constituent dimethyl sulfide (DMS) inhibits the catecholase activity of tyrosinase in a nonclassical manner. A decrease in the initial velocity to a inhibited steady-state velocity can be observed within a few minutes. This time dependence, which is unaltered by prior incubation of the enzyme with the inhibitor, is consistent with a first-order transition. Both the initial and the constant rates decreased with increasing concentrations of inhibitor. The kinetic data obtained correspond to those for a postulated mechanism involving rapid formation of an enzyme-inhibitor complex that subsequently undergoes a relatively slow reversible reaction. These results, together with the high levels of DMS precursor in certain organisms, suggest a physiological role for this compound within plant tissues.     

The pre-steady state and steady-state kinetics of the ATPase activity of mitochondrial F1

1. The lag time before maximum velocity of ATP hydrolysis is reached upon mixing ATP with F1 is much greater than can be explained by a simple Michaelis-Menten mechanism, and must be due to an activation reaction. The lag time is dependent on the concentration of MgATP (half-maximal at 30 microM) and is equal to 30 ms at infinite MgATP concentration. The initial rate of hydrolysis by nucleotide-depleted F1 is much greater than with normal F1. It is tentatively suggested that the activation reaction with normal preparations is due to replacement of firmly bound ADP by MaATP. 2. After the initial time lag, the reaction follows very closely first-order kinetics provided that the concentration of MgATP is much less than the Km and the reaction is completed within 2 s. This is not expected if the dissociation constant of the enzyme-MgADP complex, an intermediate in the enzymic reaction, is much lower than the Km as has been reported in the literature. The value of V/Km, calculated from the exponential decay, is very close to that calculated from independent measurements of V and Km. 3. The low values for Ki(ADP) reported in the literature were found to be due to a slow (in the order of seconds) formation of an inhibited MgADP-enzyme complex. Dissipation of this inhibited complex by ATP requires seconds. The dissociation constant of the MgADP-enzyme complex that is an intermediate in the enzyme reaction was found to be 150 microM. 4. ADP but not ATP becomes firmly bound to nucleotide-depleted F1 in the absence of Mg2+.     

A spectrophotometric assay for the transphosphatidylation activity of phospholipase D enzyme

We developed a specific spectrophotometric assay for the quantitative determination of phospholipase D-catalyzed transphosphatidylation activity. The assay measures p-nitrophenol liberated by phospholipase D-catalyzed reaction of phosphatidyl-p-nitrophenol and ethanol in an aqueous-organic emulsion system. The release of p-nitrophenol was linear to reaction time at an early stage of the reaction with phospholipase D from Streptomyces sp. In the spectrophotometric assay for the reaction with phospholipase D from Streptomyces chromofuscus, which has higher hydrolytic activity than transphosphatidylation activity, p-nitrophenol was not found. The advantages of this novel method for measuring the transphosphatidylation activity of phospholipase D are that (i) it does not use radioactive compounds, (ii) it can measure the initial velocity of the reaction, and (iii) it is rapid, easy, and accurate to perform.     

The hydrolysis of extracellular adenine nucleotides by cultured endothelial cells from pig aorta. Feed-forward inhibition of adenosine production at the cell surface

The time course of the extracellular reaction sequence ATP----ADP----AMP----adenosine has been examined during recirculation of substrate solutions over cultured pig aortic endothelial cells attached to polystyrene beads. This permits the study of reactions at volume to cell surface ratios approaching those of small blood vessels. When endothelial cells were presented with an initial bolus of ATP, high concentrations of the intermediates ADP and AMP developed before significant conversion of AMP to adenosine occurred. Further, the higher the initial ATP concentration, the slower the conversion of AMP to adenosine. Kinetic constants for each reaction were estimated by fitting simulated reaction curves to observed time courses. Apparent Km values estimated in this way agreed well with those reported for initial velocity measurements (ATPase = 300 microM; ADPase = 240 microM; and 5'-nucleotidase = 26 microM). The ratio of maximum velocities was ATPase:ADPase:AMPase = 6:1.5:1, with absolute values varying among cell batches. The data could only be fitted if the model incorporated inhibition of 5'-nucleotidase by ATP or ADP, and satisfactory fitting was achieved with a Ki value for ADP of 5 microM. These kinetic properties maximize the time separation of the intermediate pools. In vivo, at sites of platelet degranulation, they would create a time gap proportional to the size of the initial release between release of ADP (a proaggregatory milieu) and the appearance of adenosine (an anti-aggregatory milieu).     

Microphotometric measurement of initial maximum reaction rates in quantitative enzyme histochemistryin situ

Summary Final reaction product formation was recorded microphotometrically for succinate dehydrogenase in cross-sectioned muscle fibres at initial rate conditions and during prolonged incubations. Incubations with gel films and aqueous reaction medium both showed a decline of reaction rates. Maximum reaction rates could only be determined at initial rate conditions during the first minute of the incubation. Reaction rates recorded in different areas of the same tissue section were found to change with time to different degrees. From these results it was concluded that quantitative histochemical measurements of enzyme reactionsin situ can only be valid if measured under initial maximum velocity conditions.     

Kinetics of enzymes subject to very strong product inhibition: Analysis using simplified integrated rate equations and average velocities

Enzymes which catalyze energetically unfavorable reactions in the physiological direction are likely to be strongly inhibited by the reaction products. (Some energetically favorable reactions may also display strong "product inhibition" when assayed in the reverse direction.) In some cases, the inhibition caused by an accumulating product is so potent that true initial velocities cannot be directly determined using conventional assay methods. Continuous removal of the inhibitory product may be mitigated against by the nature of the assay or the unavailability of the appropriate coupling enzyme. It can be shown that if (a) only one inhibitory product is allowed to accumulate and (b) the substrate concentrations remain essentially constant over the assay period (i.e. Kproduct less than or equal to 10(-2)Ksubstrate, so that the decreasing reaction rate stems only from progressive product inhibition), then plots of reciprocal average (apparent) velocity (i.e. 1/v = t/[P]) versus [P] are linear and extrapolate to 1/v0, the reciprocal of the initial uninhibited velocity at the fixed substrate concentrations. Intercept replots give the usual initial velocity reciprocal plot patterns and permit Vmax and the substrate Km's to be determined. Slope replots are diagnostic of the type of inhibition exerted by the accumulating product and permit the inhibition constants to be determined. If all the appropriate coupling enzymes are available, some kinetic mechanisms can be diagnosed using data derived from the reaction progress curves in the presence of one accumulating product at a time.     

Mg2+, Asp-, and Glu--effects in the processive and distributive DNA relaxation catalyzed by a eukaryotic topoisomerase.

The salt requirement for the catalysis of DNA relaxation carried out by a eukaryotic DNA topoisomerase I from Candida was reexamined with plasmid pBR322 DNA. Two levels of analysis were considered: the initial velocity of the overall reaction and the mode of this reaction (processivity vs distributivity). When looking at the monovalent salts from the first level, the replacement of Cl- by Glu- or Asp- greatly enhanced the salt range over which the enzyme was active. Moreover, the initial velocity reached an optimal value for a higher salt concentration in this case. For the cationic counterpart, K+ was a little more effective than Na+ and much more so than NH4+. Addition of 4 mM magnesium chloride affected both the range and the optimum of the initial velocity differentially, depending upon the monovalent salt, but with a general stimulating tendency. On the other hand, when the Mg2+ salt was varied, substitution of chloride by aspartate enhanced the optimum of the initial velocity for a fixed KCl concentration. In addition, magnesium aspartate (MgAsp2) and magnesium glutamate (MgGlu2) allowed the reaction to occur even without monovalent salt and over an extended range. Magnesium was also shown to directly interact with the general catalysis (Kd = 2.5 mM). From the second level of analysis, the presence of Mg2+ (except with NH4Glu), the substitution of Cl- by Glu- or Asp-, and a lower monovalent salt concentration than that used for the velocity optimum were required to promote the processive mode.(ABSTRACT TRUNCATED AT 250 WORDS)     

Specific Time Course of Peroxidase Oxidation in the Presence of SH-Containing Inhibitors. Comparison with the Inhibition of Polyphenoloxidase Activities

The time courses of the peroxidase reaction in presence of SH-containinginhibitors are very specific. After a lag period resulting froma transitory absence of reaction, the oxidation develops butits initial velocity is in some cases decreased. The durationof the lag period depends on the inhibitor concentration butcan also be modified by incubating the inhibitor with hydrogenperoxide or with the enzyme. With respect to the inhibitionof polyphenoloxidase activities, two kinds of action of SH-containingcompounds might be recognized. The absence of the reaction observedduring the first phase may be related to the chelation of Feions contained in the peroxidases, inducing then an inactivationof the enzymes. The beginning of the reaction, at the end ofthe lag period, might be due to the oxidation of the inhibitorSH-radicals by hydrogen peroxide or by some early oxidationproducts. The second action of the inhibitors might be due toa reduction of some early oxidation products such as quinoneswhich prevents the formation of the coloured polymer. The initialvelocity of the reaction is therefore lowered. This second phasedepends on the nature of the substrate of the peroxidase reaction. (Received February 10, 1984; Accepted August 24, 1984)     

Channeling of a beta-oxidation intermediate on the large subunit of the fatty acid oxidation complex from Escherichia coli

The kinetic properties of the fatty acid oxidation complex from Escherichia coli were studied with the aim of elucidating the functional consequence of having enoyl-CoA hydratase and 3-hydroxyacyl-CoA dehydrogenase associated with a multifunctional polypeptide. The kinetic parameters of individual enzymes were determined and used in model calculations based on a published theory (Storer, A. C., and Cornish-Bowden, A. (1974) Biochem. J. 141, 205-209) to predict the kinetic behavior of a system of functionally unlinked enzymes. The validity of the theory for making these calculations was proven by demonstrating a good agreement between the calculated and observed rates of intermediate and product formation for the conversion of 2-decenoyl-CoA to 3-ketodecanoyl-CoA catalyzed by a mixture of bovine liver enoyl-CoA hydratase and pig heart L-3-hydroxyacyl-CoA dehydrogenase. The conversion of 2-decenoyl-CoA to 3-ketodecanoyl-CoA catalyzed by the sequential action of the hydratase and dehydrogenase of the complex from E. coli was determined by measuring the rate of NADH formation. Stopped-flow measurements showed the rate of NADH formation to be linear without any lag period. When the initial velocity of the hydratase was 10.2 microM min-1, that of the overall reaction was 8.41 microM min-1. In contrast, the results calculated by use of the Storer and Cornish-Bowden equation for a system of unlinked enzymes predicted the overall reaction to exhibit a lag time of 30 s and to result in the accumulation of 2.1 microM 3-hydroxydecanoyl-CoA before reaching a velocity corresponding to 82.5% of that of the hydratase reaction. The high initial rate and the unusual kinetic properties of the overall reaction observed in the present study are best explained by a channeling mechanism on the large subunit of the E. coli fatty acid oxidation complex. When the apparent degree of channeling is corrected for the percentage of the dehydrogenase active sites saturated with NAD+, more than 90% of the intermediate appears to be transferred directly from the active site of enoyl-CoA hydratase to that of 3-hydroxyacyl-CoA dehydrogenase.     

Thermodynamic and kinetic aspects of the hydrolysis of ethyl(R)-2- (benzyloxycarbonylamino)-3-sulfamoylpropionate in the presence of free and immobilized alpha-chymotrypsin

The hydrolysis of ethyl (R)-2-(benzyloxycarbonylamino)-3-sulfamoylpropionate (blocked cysteic acid S-amide) by native and immobilized alpha-chymotrypsin was studied. The experiments were performed using a constant enzyme/substrate ratio of 1:8 and at a temperature of 10-40 degrees C; the immobilized enzyme was bound to a dialdehyde cellulose matrix. A kinetic equation (Eq.10) was found to be applicable which confirms that the mechanism of the enzyme reaction consists of several stages, irrespective of the enzyme state. The temperature dependence of the reaction velocity was investigated and applied using the Arrhenius equation. The constant value thus obtained for the activating energy showed that the active centres retained their character during immobilization. The differences between the velocities of the reaction with immobilized and with native enzyme corresponded to the different number of active centres during the reaction time. Based on these results a kinetic model of the mechanism of the studied reaction is presented which includes an initial balanced stage of the chemosorption type.     

Slow- and tight-binding inhibition of aspartate aminotransferase by L-hydrazinosuccinate

The inhibition of aspartate aminotransferase (L-aspartate: 2-oxoglutarate aminotransferase, EC 2.6.1.1) by L-hydrazinosuccinate has been studied. The velocity of the enzyme reaction decreased with time when the reaction was initiated by the addition of enzyme to a mixture of the assay components and L-hydrazinosuccinate, while it increased slowly from a low level when a preincubated mixture of the enzyme and the inhibitor was added to the reaction mixture to initiate the reaction. Nearly 50% decrease in the initial reaction velocity was produced by a prolonged preincubation of the enzyme with the inhibitor, both at low concentrations of about 2 nM. These findings indicate that the inhibition is of the slow- and tight-binding type. The time-course of the reaction of the enzyme and the inhibitor, examined by the change in activity, was not in accord with single-step mechanisms, but rather appeared to follow biphasic kinetics. The inhibition could be fully reversed only in the presence of L-cysteine sulfinate or large excess of L-aspartate to convert the regenerated enzyme to its pyridoxamine form. The time-course of the reversal followed pseudo-first-order kinetics. Quantitative analysis of the experimental data has shown that the results are consistent with a mechanism of enzyme-inhibitor interaction which involves a reaction of two consecutive, reversible steps. The overall inhibition constant for L-hydrazinosuccinate was calculated to be approx. 0.2 nM.     

Condensation of Dextran-dialdehyde with Amino Acids under Nonreductive Conditions

The reaction between dextran-dialdehyde, prepared by periodate oxidation, and glycine was examined in detail. In contrast to that of aldose with amino acids, the dialdehyde reaction proceeded very rapidly. Higher temperatures and pH were favorable for the reaction and the initial velocity was proportional to the reaction time and the concentration of dextran-dialdehyde. Although the dextran-glycine adduct was stable during the gel filtration step to remove excess glycine, the adduct was readily dissociated by 0.3 m HC1. Among the amino acids tested, histidine and glycine gave higher reactivity than lysine and arginine. This basic information is useful for condensation of dextran-dialdehyde with various proteins and enzymes.     

An automated method to evaluate the enzyme kinetics of β‐glucosidases

Enzyme kinetic measurements are important for the characterization and engineering of biocatalysts, with applications in a wide range of research fields. The measurement of initial reaction velocity is usually slow and laborious, which motivated us to explore the possibilities for automating this process. Our model enzyme is the maize β‐glucosidase Zm‐p60.1. Zm‐p60.1 plays a significant role in plant growth and development by regulating levels of the active plant hormone cytokinin. Zm‐p60.1 belongs to a wide group of hydrolytic enzymes. Members of this group hydrolyze several different types of glucosides, releasing glucose as a secondary product. Enzyme kinetic measurements using artificial substrates are well established, but burdensome and time‐consuming. Thus, they are a suitable target for process automation. Simple optical methods for enzyme kinetic measurements using natural substrates are often impossible given the optical properties of the enzymatic reaction products. However, we have developed an automated method based on glucose detection, as glucose is released from all substrates of glucosidase reactions. The presented method can obtain 24 data points from up to 15 substrate concentrations to precisely describe the enzyme kinetics. The combination of an automated liquid handling process with assays that have been optimized for measuring the initial hydrolysis velocity of β‐glucosidases yields two distinct methods that are faster, cheaper, and more accurate than the established protocols.