Viscometric determination of carboxymethylcellulase in standard international units

A direct theoretical approach is described for using viscometric data to determine standard units of carboxymethylcellulase as recommended by the Commission on Enzymes. Application of the theory showed that under suitably defined conditions calculated units were directly proportional to the quantity of enzyme used for assay. When the theory was applied to a kinetic analysis of enzyme action, a linear relationship was obtained from a Lineweaver-Burk plot and allowed the Michaelis-Menten constant to be readily calculated. The theory can also be modified so that relative though arbitrary enzyme units can be obtained from one simple calculation. The method should be applicable to other depolymerases that cleave their substrate randomly.     

The comparison of the estimation of enzyme kinetic parameters by fitting reaction curve to the integrated Michaelis-Menten rate equations of different predictor variables

The estimation of enzyme kinetic parameters by nonlinear fitting reaction curve to the integrated Michaelis-Menten rate equation ln(S(0)/S)+(S(0)-S)/K(m)=(V(m)/K(m))xt was investigated and compared to that by fitting to (S(0)-S)/t=V(m)-K(m)x[ln(S(0)/S)/t] (Atkins GL, Nimmo IA. The reliability of Michaelis-Menten constants and maximum velocities estimated by using the integrated Michaelis-Menten equation. Biochem J 1973;135:779-84) with uricase as the model. Uricase reaction curve was simulated with random absorbance error of 0.001 at 0.075 mmol/l uric acid. Experimental reaction curve was monitored by absorbance at 293 nm. For both CV and deviation <20% by simulation, K(m) from 5 to 100 micromol/l was estimated with Eq. (1) while K(m) from 5 to 50 micromol/l was estimated with Eq. (2). The background absorbance and the error in the lag time of steady-state reaction resulted in negative K(m) with Eq. (2), but did not affect K(m) estimated with Eq. (1). Both equations gave better estimation of V(m). The computation time and the goodness of fit with Eq. (1) were 40-fold greater than those with Eq. (2). By experimentation, Eq. (1) yielded K(m) consistent with the Lineweaver-Burk plot analysis, but Eq. (2) gave many negative parameters. Apparent K(m) by Eq. (1) linearly increased, while V(m) were constant, vs. xanthine concentrations, and the inhibition constant was consistent with the Lineweaver-Burk plot analysis. These results suggested that the integrated rate equation that uses the predictor variable of reaction time was reliable for the estimation of enzyme kinetic parameters and applicable for the characterization of enzyme inhibitors.     

A simple device for automated spectrophotometric kinetics using a diode array spectrophotometer

In this report we describe an automated system that rapidly and automatically mixes reagents and records results, such as spectrophotometric changes. It employs a commercial diode array spectrophotometer and a novel dilution chamber in a flow stream that allows repetitive spectrophotometric rate measurements at accurately measured incremental substrate concentrations. When applied to enzyme kinetic studies, initial velocities at 15 different substrate or inhibitor concentrations, or pH values, can be recorded in a few minutes with high reproducibility, i.e., standard deviations less than 1%, and high sensitivity. Reactions occur in an 8-microliters flow cell and the reagent consumption is minimal. The concentration of incrementally diluted reagent in the cell is measured directly by means of an indicator dye added to the substrate. Michaelis-Menten parameters, inhibition constants, and pH profiles are determined for several enzymes including dehydrogenases producing NADH, a kinase requiring a coupled assay, and a hydrolase, carboxypeptidase A, in a reaction that produces a small decrease in absorbance.     

EZ-FIT: a practical curve-fitting microcomputer program for the analysis of enzyme kinetic data on IBM-PC compatible computers

EZ-FIT, an interactive microcomputer software package, has been developed for the analysis of enzyme kinetic and equilibrium binding data. EZ-FIT was designed as a user-friendly menu-driven package that has the facility for data entry, editing, and filing. Data input permits the conversion of cpm, dpm, or optical density to molar per minute per milligram protein. Data can be fit to any of 14 model equations including Michaelis-Menten, Hill, isoenzyme, inhibition, dual substrate, agonist, antagonist, and modified integrated Michaelis-Menten. The program uses the Nelder-Mead simplex and Marquardt nonlinear regression algorithms sequentially. A report of the results includes the parameter estimates with standard errors, a Student t test to determine the accuracy of the parameter values, a Runs statistic test of the residuals, identification of outlying data, an Akaike information criterion test for goodness-of-fit, and, when the experimental variance is included, a chi 2 statistic test for goodness-of-fit. Several different graphs can be displayed: an X-Y, a Scatchard, an Eadie-Hofstee, a Lineweaver-Burk, a semilogarithmic, and a residual plot. A data analysis report and graphs are designed to evaluate the goodness-of-fit of the data to a particular model.     

The competition plot: A kinetic method to assess whether an enzyme that catalyzes multiple reactions does so at a unique site

Enzymes often act on more than one substrate, and the question then arises as to whether this can be attributed to the existence of two different enzymes that have not been separated or, more interesting, to the presence of two different active sites in the same enzyme. The competition plot is a kinetic method that allows us to test with little experimentation whether the two reactions occur at the same site or at different sites. It consists of making mixtures of the two substrates and plotting the total rate against a parameter p that defines the concentrations of the two substrates in terms of reference concentrations chosen to give the same rates at p = 0 and p = 1, i.e., when only one of the substrates is present. With a slight modification of the equations it can also be applied to enzymes that deviate from Michaelis-Menten kinetics. If the two substrates react at the same site, the competition plot gives a horizontal straight line; i.e., the total rate is independent of p. In contrast, if the two reactions occur at two separate and independent sites a curve with a maximum is obtained; separate reactions with cross-inhibition generate curves with either maxima or minima according to whether the Michaelis constants of the two substrates are smaller or larger than their inhibition constants in the other reactions. Strategies to avoid ambiguous results and to improve the sensitivity of the plot are described. A practical example is given to facilitate the experimental protocol for this plot.     

Inhibition of beta-lactamase of Bacillus licheniformis 749/C by compound PS-5, a new beta-lactam antibiotic.

By use of a new computer-assisted u.v.-spectrophotometric assay method, the kinetic parameters of the reaction catalysed by Bacillus licheniformis 749/C beta-lactamase were re-examined and the mode of inhibition of the enzyme by compound PS-5, a novel beta-lactam antibiotic, was studied with benzylpenicillin as substrate. (1) The fundamental assay conditions for the determination of Km and V were examined in detail with benzylpenicillin as substrate. In 0.1 M-sodium/potassium phosphate buffer, pH 6.8, at 30 degrees C, initial substrate concentrations of benzylpenicillin above 0.7 mM were very likely to lead to substrate inhibition. The Km value of the enzyme for benzylpenicillin at initial concentrations from 1.96 to 0.07 mM was calculated to be 97-108 microM. (2) The Km values of the enzyme for 6-aminopenicillanic acid, ampicillin and cephaloridine were found to be 25, 154-161 and 144-161 microM respectively. (3) Compound PS-5 was virtually unattacked by Bacillus licheniformis 749/C beta-lactamase. (4) The activity of the enzyme was diminished by compound PS-5, to extents depending on the duration of incubation and the concentration of the inhibitor. The rate of inactivation of the enzyme by compound PS-5 followed first-order kinetics. (5) In an Appendix, a new computer-assisted u.v.-spectrophotometric enzyme assay method, in which a single reaction progress curve of time-absorbance was analysed by the integrated Michaelis-Menten equation, was devised for the accurate and precise determination of the kinetic constants of beta-lactamase. For conversion of absorbance readings into molar substrate concentrations, the initial or final absorbance reading that was independent of the reaction time was used as the basis of calculation. In calculation of Km and V three systematic methods of data combination were employed for finer analysis of the reaction progress curve. A list of the computer program named YF6TAIM is obtainable from the author on request or as Supplementary Publication SUP 50100 (12 pages) from the British Library Lending Division, Boston Spa, Wetherby, West Yorkshire LS23 7BQ, U.K., on the terms indicated in Biochem. J. (1978) 169, 5.     

Effect of mass transfer resistance on the Lineweaver-Burk plots for flocculating microorganisms

It is shown that the mass transfer resistance can significantly distort the linearity of the Lineweaver-Burk plot of the kinetic data for a microbial culture which forms aggregates. For small flocs, the linearity of the Lineweaver-Burk plot is largely retained, but a different slope and intercept will be obtained compared with flocs free from mass transfer resistance. For large flocs, the Lineweaver-Burk plot shows pronounced curvature at high limiting substrate concentrations. Hence, if the true intrinsic kinetic parameters are to be extracted from a highly flocculating microbial culture, sufficient agitation has to be provided to remove the effect of mass transfer resistance. If the behavior of the flocculating microbial culture is to be explored, additional values for some physical parameters, such as the effective diffusion coefficient of the substrate in floc, the floc density, and the mean floc radius, are needed.     

A new enzyme-coupled spectrophotometric method for the determination of arginase activity

A spectrophotometric method for the determination of arginase (EC 3.5.3.1) is presented. Arginase is coupled to urease and glutamate dehydrogenase and the decrease in absorbance at 340 nm due to the oxidation of NADPH is followed. The method is rapid, is sensitive, is economical and permits continuous monitoring. The initial velocities were directly proportional to the enzyme concentrations between 0.06 and 0.30 units per 0.5 ml. The Lineweaver-Burk plot yielded positive allosteric behavior for the tetrameric enzyme. The K' and the Hill coefficient, n, calculated from Hill plot were found to be 4.7 mM and 1.26 (r = 1.00), respectively. These values are in good agreement with the literature.     

Progress curves analysis as an alternative for exploration of activation-inhibition phenomena in cholinesterases

The kinetic behaviour of insect acetylcholinesterases deviates from the Michaelis-Menten pattern. These deviations are known as activation or inhibition at various substrate concentrations and can be more or less observable depending on mutations around the active site of the enzyme. Most kinetic studies on these enzymes still rely on initial rate measurements. It is demonstrated here that according to this method one of the deviations can be overlooked. We attempt to point out that in such cases a detailed step-by-step progress curves analysis is successful. The study is focused on two different methods of analysing progress curves: (i) the first one is based on an integrated initial rate equation which can sufficiently fit truncated progress curves under corresponding conditions; and (ii) the other one precludes the algebraic formulae, but uses numerical integration for searching a non analytical solution of ordinary differential equations describing a kinetic model. All methods are tested on three different acetylcholinesterase mutants from Drosophila melanogaster. The results indicate that kinetic parameters for the E107K mutant with highly expressive activation and inhibition can be well evaluated applying any analysis method. It is quite different for E107W and E107Y mutants where latent activation is present, but discovered only using one or the other progress curves analysis methods.     

Progress Curves Analysis as an Alternative for Exploration of Activation-inhibition Phenomena in Cholinesterases

The kinetic behaviour of insect acetylcholinesterases deviates from the Michaelis-Menten pattern. These deviations are known as activation or inhibition at various substrate concentrations and can be more or less observable depending on mutations around the active site of the enzyme. Most kinetic studies on these enzymes still rely on initial rate measurements. It is demonstrated here that according to this method one of the deviations can be overlooked. We attempt to point out that in such cases a detailed step-by-step progress curves analysis is successful. The study is focused on two different methods of analysing progress curves: (i) the first one is based on an integrated initial rate equation which can sufficiently fit truncated progress curves under corresponding conditions; and (ii) the other one precludes the algebraic formulae, but uses numerical integration for searching a non analytical solution of ordinary differential equations describing a kinetic model. All methods are tested on three different acetylcholinesterase mutants from Drosophila melanogaster. The results indicate that kinetic parameters for the E107K mutant with highly expressive activation and inhibition can be well evaluated applying any analysis method. It is quite different for E107W and E107Y mutants where latent activation is present, but discovered only using one or the other progress curves analysis methods.     

A new linear plot for standard curves in kinetic substrate assays extended above the Michaelis-Menten constant: application to a luminometric assay of glycerol

In conventional kinetic substrate assays the standard curve is plotted as observed reaction rate, upsilon obs, versus added substrate concentration, Sadd, and has a linearity limited to Sadd much less than Km. From this plot the blank reaction rate, upsilon bl, is easily estimated but not the contaminating substrate concentration, Scon, present in reagents (unless it is the only blank source). Thus the actual substrate concentration, S = Scon + Sadd, cannot be estimated as required for the various linear plots based on the Michaelis-Menten equation. We have derived an expression, (upsilon obs - upsilon bl)/Vapp = Sadd/(Kmapp + Sadd), containing only those parameters measured for a conventional standard curve (Vapp and Kmapp are obtained from a plot of (upsilon obs - upsilon bl) versus (upsilon obs - upsilon bl)/Sadd). A plot of (upsilon obs - upsilon bl)/Vapp versus Sadd/(Kmapp + Sadd) can be used as a standard curve with the following advantages over the conventional standard curve: (a) For all kinetic substrate assays it is identical and connects the points (0, 0) and (1, 1). Thus deviations from true Michaelis-Menten kinetics or erroneous kinetic constants are easily detected. (b) Since it is linear even above Km, the analytically useful range is considerably extended. (c) For assays with a wide dynamic range it can be used in lin-lin or log-log form. The procedure is illustrated for a kinetic assay of glycerol (Kmapp = 40 mumol/liter). The plot was found to be entirely linear in the range 0.07-100 mumol/liter (glycerol concentration in cuvette).     

Steady-state kinetic analysis of the quinoprotein methylamine dehydrogenase from Paracoccus denitrificans.

A steady-state kinetic analysis was performed of the reaction of methylamine and phenazine ethosulphate (PES) with the quinoprotein methylamine dehydrogenase from Paracoccus denitrificans. Experiments with methylamine and PES as varied-concentration substrates produced a series of parallel reciprocal plots, and when the concentrations of these substrates were varied in a constant ratio a linear reciprocal plot of initial velocity against PES concentration was obtained. Nearly identical values of V/Km of PES were obtained with four different n-alkylamines. These data suggest that this reaction proceeds by a ping-pong type of mechanism. The enzyme reacted with a variety of n-alkylamines but not with secondary, tertiary or aromatic amines or amino acids. The substrate specificity was dictated primarily by the Km value exhibited by the particular amine. A deuterium kinetic isotope effect was observed with deuterated methylamine as a substrate. The enzyme exhibited a pH optimum for V at pH 7.5. The absorbance spectrum of the pyrroloquinoline quinone prosthetic group of this enzyme was also effected by pH at values greater than 7.5. The enzyme was relatively insensitive to changes in ionic strength, and exhibited a linear Arrhenius plot over a range of temperatures from 10 degrees C to 50 degrees C with an energy of activation 46 kJ/mol (11 kcal/mol).     

Microcomputer simulation of steady-state enzyme kinetics for educational purposes

A BASIC program to assist the instruction of steady-state enzymekinetics has been developed for the IBM PC microcomputer. Itspurpose is to simulate laboratory experiments in order to minimizethe time required to obtain kinetic data from which studentsdeduce kinetic mechanisms and determine kinetic constants ofenzyme-catalyzed reactions. The program randomly selects a kineticscheme from various sequential, ping pong, and iso reactionsequences as well as values for the kinetic constants. The schemeand kinetic constants are unknown to the student at this time;the only thing he or she knows is the stoichiometry of the catalyzedreaction which can have two or three substrates and products.The student is prompted to enter values for concentrations ofsubstrates and products; several different concentrations foreach substrate and product can be entered in a single experiment.The program then calculates, displays and prints (if desired)the corresponding initial steadystate velocities. The studentcan perform as many experiments as desired until enough informationis obtained to determine the kinetic mechanism and to calculatevalues for the kinetic constants. Received on March 10, 1986; accepted on May 6, 1986     

Rat kidney porphobilinogen deaminase kinetics. Detection of enzyme-substrate complexes

BACKGROUND AND AIMS: Acute intermittent porphyria (AIP) is an inherited disease resulting from a reduced activity of the enzyme porphobilinogen deaminase (PBG-D). The kidney is an important target for numerous porphyrinogenic drugs and it may contribute to the clinical manifestations of porphyric attacks. An evaluation of kidney PBG-D role in the AIP pathophysiology requires detailed information on kidney PBG-D properties, under normal conditions. METHODS: Rat kidney PBG-D was purified to homogeneity and initial reaction velocities were calculated by measuring uroporphyrinogen I formation at pH 8.2 for different incubation times (0-20 min) and over a wide range of substrate concentrations (0.8-66 microM). RESULTS: Purified rat kidney PBG-D is a monomeric enzyme showing only a single protein band after SDS-PAGE, Western blot and isoelectric focusing (pI 4.9). Its molecular mass is 40 +/- 2.3 kDa, determined by SDS-PAGE and 39.8 +/- 2 kDa by gel filtration chromatography. Rat kidney PBG-D has an unusual kinetic behaviour, exhibiting a deviation from the Michaelis-Menten hyperbola. PBG-D kinetic data required a fitting to an equation of higher degree, leading to the following apparent kinetic constants: K(1) = 2.08 +/- 0.01 microM and K(2) = 0.102 +/- 0.003 microM. CONCLUSION: The values of these constants fulfil the restriction 4K(2) < or = K(1)(2), necessary for the occurrence of isoenzymes, interpreted in this work as enzyme-substrate intermediates. The initial reaction velocity expression here defined, correlates with an enzyme carrying only one active site but allowing, through conformational changes, the detection of at least two enzyme-substrate intermediates formed during PBG-D reaction.     

Graphical analysis of steady-state kinetic data of multireactant enzymes.

The graphical analysis of steady-state kinetic data according to Eadie-Augustinsson-Hofstee (EAH plot) is illustrated for multisubstrate systems and compared with the double reciprocal plot (Lineweaver-Burk plot) commonly used. It is emphasized that the choice of graphical representation may be of crucial importance when a discrimination between alternative rate laws has to be made. A major advantage of the EAH plot is the high sensitivity to deviations from linearity at low substrate concentrations.     

A theoretical equation describing the time evolution of the concentration of a selected range of substrate molecular weights in depolymerization processes mediated by single-attack mechanism endo-enzymes

Monitoring the time evolution of the concentration of a selected range of molecular weights of substrate, referred to as "detectable" substrate, has been used to determine endo-enzymic activities in polysaccharide depolymerizing processes. In the methodologies based on the use of dye-labeled substrates, the "detectable" substrate extends from a given molecular weight threshold downward. On the contrary, in the fluorescent probe-flow injection analysis methodology, initially developed to determine (1 --> 3)-(1 --> 4)-beta-D-glucanase activities, the "detectable" substrate extends from a given molecular weight threshold upward. Assuming that the time evolution of the molecular weight distribution of the substrate follows the most probable distribution (the enzymic attack is random and its mechanism is single attack), a theoretical equation describing the time evolution of the concentration of "detectable" substrate (from a given molecular weight threshold upward or downward) has been deduced. This equation, Wd = Wo. (1 + alphat). e-alphat, where Wd is the concentration of "detectable" substrate, Wo is the initial concentration of the substrate, t is the depolymerization time, and alpha is a parameter correlated through a hyperbola with the initial concentrations of enzyme and substrate and the Michaelis-Menten constant, Km, has been tested against different (1 --> 3)-(1 --> 4)-beta-D-glucan/(1 --> 3)-(1 --> 4)-beta-D-glucanase systems using the fluorescent probe-flow injection analysis methodology and Calcofluor as the fluorescent probe. The most important predictions of the theoretical equation, which allow accurate determination of both endo-enzymic activities and kinetic constants, have been experimentally confirmed.     

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.     

Kinetic studies of the enzymatic isomerization of xylose

d-Xylose isomerase catalyses the conversion of the common pentose, d-xylose, to its keto-isomer, d-xylose. This reaction is of interest because many microorganisms that are unable to metabolize d-xylose can utilize d-xylulose. The kinetics of a commonly used immobilized whole-cell isomerase, Sweetzyme Q, have been determined from initial rate studies on the forward and reverse reactions. The effect of pH, temperature, and substrate and product concentration on enzyme activity have all been examined. Reaction rates were modelled with the Michaelis-Menten equation. Using constants determined from Lineweaver-Burk plots, the rate equation accurately simulated experimental conversion data.     

Exact and user-friendly kinetic analysis of the two-step rapid equilibrium Michaelis-Menten mechanism

Most enzyme kinetic experiments are carried out under pseudo-first-order conditions, that is, when one of the reactant species (the enzyme or the substrate) is in a large excess of the other species. More accurate kinetic information about the system can be gained without the restrictions of the pseudo-first-order conditions. We present a practical and general method of analysis of the common two-step rapid equilibrium Michaelis-Menten mechanism. The formalism is exact in that it does not involve any other approximations such as the steady-state, limitations on the reactant concentrations or on reaction times. We apply this method to the global analysis of kinetic progress curves for bovine alkaline phosphatase assays carried out under both pseudo-first-order and pseudo-second-order conditions.     

双底物酶促反应的底物抑制分析

存在于双底物随机机制的途径中,偏离米氏方程行为的底物抑制现象被作为一个问题进行探讨．通过计算机模拟出双底物浓度和稳态下的初始速率构成的三维图形,提出底物抑制、速率常数和底物浓度之间的关系．