A new multi-wavelength model-based method for determination of enzyme kinetic parameters

Lineweaver-Burk plot analysis is the most widely used method to determine enzyme kinetic parameters. In the spectrophotometric determination of enzyme activity using the Lineweaver-Burk plot, it is necessary to find a wavelength at which only the substrate or the product has absorbance without any spectroscopic interference of the other reaction components. Moreover, in this method, different initial concentrations of the substrate should be used to obtain the initial velocities required for Lineweaver-Burk plot analysis. In the present work, a multi-wavelength model-based method has been developed and validated to determine Michaelis-Menten constants for some enzyme reactions. In this method, a selective wavelength region and several experiments with different initial concentrations of the substrate are not required. The absorbance data of the kinetic assays are fitted by non-linear regression coupled to the numeric integration of the related differential equation. To indicate the applicability of the proposed method, the Michaelis-Menten constants for the oxidation of phenanthridine, 6-deoxypenciclovir and xanthine by molybdenum hydroxylases were determined using only a single initial concentration of the substrate, regardless of any spectral overlap.     

A microcomputer method for designing optimal experiments for estimating enzyme kinetic parameters

A computer program, written in BASIC, for designing optimal experiments with the aim of evaluating estimates of the parameters for any enzyme kinetic model is given. This computer program can be run on any microcomputer with less than 32 Kbytes of random access memory. The program uses the termed D-optimization design criterion, which minimizes the determinant of the variance-covariance matrix. The user only supplies the rate equation, the maximum and minimum concentrations of substrates and inhibitors, the weighting pattern, and the best possible values of the parameters. The computer supplies the optimal substrate and inhibitor concentrations (one for each parameters), for estimating the parameter values, and the determinant of the variance-covariance matrix. Likewise, the microcomputer supplies the eigenvalues and eigenvectors of information and redundancy matrices, the sensitivity and the global redundancy.     

A rapid method for determining kinetic parameters of enzymes exhibiting nonlinear thermal inactivation behavior

A rapid method is developed to analyze the kinetics of thermal inactivation of enzymes that exhibit a nonlinear biphasic log(activity)-time relationship. Thermal destruction experiments on alcohol dehydrogenase from baker's yeast demonstrate the applicability of the method. The method is based on physical considerations (as opposed to mathematical curve fitting/regression methods) and also serves as a quick check of results obtained using nonlinear regression. It is superior to fitting nonlinear enzyme inactivation data by first-order kinetics or taking the initial and final slopes of the inactivation data. In fact, the method is of general validity and can be applied to any decay process that can be represented by a sum of exponentials. (c) 1996 John Wiley & Sons, Inc.     

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.     

A kinetic investigation of fumarase reaction at high substrate concentrations

The hydration of fumarate to malate, catalyzed by fumarase was followed by infrared spectrometry. Substrate concentrations employed were all several orders of magnitude higher than K_m . The reciprocal plot of Lineweaver and Burke yielded an unusual curve of the type indicating auto-inhibition by substrate due perhaps to a two-point binding on the enzyme sites. The data obtained could not be treated satisfactorily by the conventional Michaelis-Menten kinetics. A slightly different type of analysis gave numerical values for some of the kinetics constants which are in reasonable agreement with published values.     

A kinetic study of Saccharomyces strains: Performance at high sugar concentrations

Alcoholic fermentation represents a significant example of production of compounds utilizable as alternative energy sources. High ethanol concentration in the fermented wort is needed in order to reduce the energy consumption in the process of alcohol recovery. A particular Saccharomyces strain, of the oviformis species, obtained from fermented worts exhibiting high ethanol concentrations is studied and compared with a common S. cerevisiae strain in order to show its skill in fermenting very concentrated sugar solutions with an energy saving of ca. 10%.     

A graphical method for determining inhibition parameters for partial and complete inhibitors.

A new simple graphical method is described for the determination of inhibition type and kinetic parameters of an enzyme reaction without any replot. The method consists of plotting experimental data as v/(vo--v) versus the reciprocal of the inhibitor concentration at different substrate concentrations, where v and vo represent the velocity in the presence and in the absence of the inhibitor respectively with a given concentration of the substrate. Partial inhibition gives straight lines that converge on the abscissa at a point away from the origin, whereas complete inhibition gives lines that go through the origin. The inhibition constants of enzymes and the reaction rate constant of the enzyme-substrate-inhibitor complex can be calculated from the abscissa and ordinate intercepts of the plot. The relationship between the slope of the plot and the substrate concentration shows characteristic features depending on the inhibition type: for partial competitive inhibition, the straight line converging on the abscissa at--Ks, the dissociation constant of the enzyme-substrate complex; for non-competitive inhibition, a constant slope independent of the substrate concentration; for uncompetitive inhibition, a hyperbola decreasing with the increase in the substrate concentration; for mixed-type inhibition, a hyperbola increasing with the increase in the substrate concentration. The properties of the replot are useful in confirmation of the inhibition mechanism.     

The direct linear plot. A new graphical procedure for estimating enzyme kinetic parameters

A new plot is described for analysing the results of kinetic experiments in which the Michaelis-Menten equation is obeyed. Observations are plotted as lines in parameter space, instead of points in observation space. With appropriate modifications the plot is applicable to most problems of interest to the enzyme kineticist. It has the following advantages over traditional methods of plotting kinetic results: it is very simple to construct, because it is composed entirely of straight lines and requires no calculation or mathematical tables; the kinetic constants are read off the plot directly, again without calculation; it may be used during the course of an experiment to judge the success of the experiment, and to modify the experimental design; it provides clear and accurate information about the quality of the observations, and identifies aberrant observations; it provides a clear indication of the precision of the kinetic constants; constructed with care, it provides unbiased estimates of the kinetic constants, the same as those provided by a computer program; it may be used to simulate results for illustrative purposes very rapidly and simply.     

A flow method for determination of the kinetic parameters for immobilized enzymes.

A flow method is described for determination of the kinetics parameters (V-m and K-m) for enzymes that are bound to particles, to membranes, and to the interior surfaces of tubes. Substrate solution is pumped through Tygon tubing to a microvolume flow cell and back into the reaction mixture, the flow rate being adjusted to be faster than the rate of formation of product. To illustrate the technique, it is applied to the determination of the parameters for electric-eel acetylcholinesterase attached to particles, to membranes, and to the inner surface of nylon tubing.     

A semi-integrated method for the determination of enzyme kinetic parameters and graphical representation of the Michaelis-Menten equation

A semi-integrated method for the determination of the enzyme kinetics parameters (Km and V) and graphical representation of the Michaelis-Menten equation is proposed as a variation of determination of initial reaction rate (v) as a function of initial substrate concentration ([S]0). The method is based on the determination of the time required to exhaust half of the initial substrate concentration as a function of the initial substrate concentration. The advantages and limitations of this method are discussed.     

A linearization method for low catalytic activity enzyme kinetic analysis

A kinetic analysis was made and a linear plot based on the general rate equation derived by Laidler [Can. J. Chem. 33, 1614-1624] is proposed. This linearization method allows determining the kinetic parameters (K(m), k(cat)) and [E](0) for enzymes with low catalytic activity. The method was applied to chloroperoxidase from Caldariomyces fumago [EC 1.11.1.10], whose kinetic parameters K(m)(app), k(cat)(app), and [E](0) with monochlorodimedone as substrate, were obtained by using the linearization plot and the V(max) value (calculated by Eadie-Hofstee plot). This plot could also be useful to the study of abenzyme kinetics provided the concentration of the latter is either higher or equal than K(m) value.     

A novel method for determining the parameters of microbial kinetics

It is conventional to describe the relationship between the specific rate of microbial growth and the concentration of the inhibitory substrate in terms of the Andrews–Edwards equation. A novel method for establishing the constants of this equation is presented. The equation is transformed to a polynomial and the empirical data are approximated by a quadratic polynomial. The results obtained for the biodegradation of phenol in a mixed culture (activated sludge) are discussed.     

A stopped-flow assay for glycogen phosphorylase appropriate to measure catalytic activity at high enzyme concentrations

Glycogen phosphorylase (EC 2.4.1.1) may be assayed in the glycogen degradation direction by a continuous spectrophotometric method. The formation of glucose 1-phosphate from glycogen and phosphate produces a controlled change of pH which can be measured by the changes in absorbance of phenol red added to the system. The procedure may be conveniently applied to a stopped-flow spectrophotometer to measure the rate of the reaction. Therefore the activity of the enzyme may be determined at low conventional concentrations and, by the same technique, at high enzyme concentrations approaching those supposed to exist in vivo.     

Evaluation of distribution-free confidence limits for enzyme kinetic parameters

Monte Carlo experiments have been used to test the robustness of distribution-free confidence limits for the parameters of the Michaelis-Menten equation (Porter & Trager, 1977). When used in conjunction with the modified form of the direct linear plot (Cornish-Bowden & Eisenthal, 1978), they prove to be more robust than least-squares confidence limits. In circumstances where the least-squares assumptions are correct, the distribution-free confidence limits define the parameters somewhat less precisely than the corresponding least-squares confidence limits, but this effect is negligible unless there are eight or fewer observations.     

A method to describe enzyme-catalyzed reactions by combining steady state and time course enzyme kinetic parameters

Background

Complete analysis of single substrate enzyme-catalyzed reactions has required a separate use of two distinct approaches. Steady state approximations are employed to obtain substrate affinity and initial velocity information. Alternatively, first order exponential decay models permit simulation of the time course data for the reactions. Attempts to use integrals of steady state equations to describe reaction time courses have so far met with little success.

Methods

Here we use equations based on steady state approximations to directly model time course plots.

Results

Testing these expressions with the enzyme β-galactosidase, which adheres to classical Michaelis–Menten kinetics, produced a good fit between observed and calculated values.

General significance

This study indicates that, in addition to providing information on initial kinetic parameters, steady state approximations can be employed to directly model time course kinetics.Integrated forms of the Michaelis–Menten equation have previously been reported in the literature. Here we describe a method to directly apply steady state approximations to time course analysis for predicting product formation and simultaneously obtain multiple kinetic parameters.     

Estimation of the overall kinetic parameters of enzyme inactivation using an isoconversional method

An isoconversional method is proposed in order to calculate the kinetic parameters of enzyme inactivation. The method provides an efficient and low-cost procedure to describe both operational and thermal inactivation. Unlike the ordinary kinetic assays performed at constant enzyme concentration and at various substrate concentrations, the isoconversional method requires several extended kinetic curves for constant initial substrate concentration and different enzyme concentrations. The procedure was tested and validated using simulated data obtained for several kinetic models frequently discussed in the literature. After the validation, the isoconversional method was used for the investigation of the thermoinactivation of urease during urea hydrolysis in self buffered medium and the operational inactivation (destructive oxidation by excess peroxide) of catalase at high concentration of hydrogen peroxide. The results showed that the isoconversional method gives good results of global inactivation constant for both simple and more complex models.     

Evaluation of true kinetic parameters for reversible immobilized enzyme reactions

For a reversible one-substrate reaction system that follows the Haldane reaction mechanism, a new and effective method has been proposed to extract true or intrinsic kinetic parameters of immobilized enzymes from diffusion limited rate data. The method utilizes the effectiveness factors correlated in terms of the general modulus defined by Aris and Bischoff, and a new modulus defined in the present study. It requires a trial-and-error calculation, but only a few data points. Furthermore, it provides a saving of materials such as substrates and enzymes, and takes less time for experiments compared to the initial rate methods. The usefulness of the method is demonstrated by determining the kinetic parameters for membrane bound fumarase which catalyzes the reaction of the conversion of fumarate to L-malate, for which the equilibrium constant is ca. 4.