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PubMed1991

Patch-clamp studies on the anomalous mole fraction effect of the K+ channel in cytoplasmic droplets of Nitella: an attempt to distinguish between a multi-ion single-file pore and an enzyme kinetic model with lazy state.

Patch-clamp studies have been employed in order to check whether the assumption of a multi-ion single-file pore is necessary for the explanation of the anomalous mole fraction effect or whether this effect can also be explained by a single-barrier enzyme kinetic model. Experiments in the cell-attached configuration were done on the tonoplast membrane of cytoplasmic droplets of Nitella in solutions containing 150 mol m-3 of K+ plus Tl+ with seven different K+/Tl+ ratios. At first sight, the results seem to support the multi-ion single-file pore, because apparent open channel conductivity displays the anomalous mole fraction effect, whereas open-probability has not been found to be dependent on the K+/Tl+ ratio. Changes in open probability would be expected for a single-barrier enzyme kinetic model with a lazy state. On the other hand, the lazy-state model is more successful in explaining the measured I-V curves. The entire slope of the apparent open channel current-voltage curves rotates with changing K+/Tl+ ratios in the whole voltage range between -100 and +80 mV. Numerical calculations on the basis of multi-ion single-file pores could create the anomalous mole fraction effect only in a limited voltage range with intersecting I-V curves. The apparent absence of an effect on open probability which is postulated by the lazy-state model can be explained if switching into and out of the lazy state is faster than can be resolved by the temporal resolution of 1 msec.

Biological Transport↗

PubMed1988

Identification and rejection of outliers in enzyme kinetics.

A program (AICOUT) for the correct choice of the experimental value and weight for replicate enzyme kinetic determinations is given. It is based on the method of identification of outliers proposed by Kitagawa (Technometrics, 21 (1979) 193-199). The program is written in BASIC and FORTRAN77. The FORTRAN77 version of AICOUT program coupled to a FORTRAN77 version of the non-linear regression program previously published by Canela (Int J Biomed Comput, 15 (1984) 121-130) is given. This joint program leads to an improvement of precision and confidence in the estimated parameters when the suitable strategy is used. This strategy is as follows: (i) the experimental points are selected, (ii) several replicates of each point are performed, (iii) data are analyzed and outliers are rejected, (iv) normal or biweighted regression is carried out.

Algorithms↗

PubMed1956

Enzyme kinetics.

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Enzymes↗

PubMed1995

Enzyme kinetics based on free-energy profiles.

A comprehensive theory for relating free-energy profiles to kinetic equations of enzyme reactions has been developed. It enables expression of the overall rate and the concentrations of reaction intermediates in terms of the heights of peaks in free-energy profiles for various reactions. The reactions include consecutive reactions with intermittent irreversible steps, those with dead-end side reactions and completely reversible reactions. The usefulness of the theory is shown by analysis of a single-substrate reaction, a reaction with a covalent intermediate, and product inhibition in a two-substrate reaction, in which kinetic parameters such as Vmax and Km are related to the peak heights in free-energy profiles. The paper refers also to the concept of rate-determining step (RDS) and shows the utility of a related concept rate-determining zone (RDZ) which indicates the reaction steps between the main intermediate and the RDS. The concept of RDZ is useful for resolving confusion related to the concept of RDS. It should be emphasized that the present approach is applicable only to linear reactions.

Enzymes↗

PubMed1998

An EXCEL template for calculation of enzyme kinetic parameters by non-linear regression.

MOTIVATION: An EXCEL template has been developed for the calculation of enzyme kinetic parameters by non-linear regression techniques. The tool is accurate, inexpensive, as well as easy to use and modify. AVAILABILITY: The program is available from http://www.ebi.ac.uk/biocat/biocat.html CONTACT: agustin. hernandez@bio.kuleuven.ac.be

Computational Biology↗

PubMed2001

Enzyme kinetics of cytochrome P450-mediated reactions.

The most common drug-drug interactions may be understood in terms of alterations of metabolism, associated primarily with changes in the activity of cytochrome P450 (CYP) enzymes. Kinetic parameters such as Km, Vmax, Ki and Ka, which describe metabolism-based drug interactions, are usually determined by appropriate kinetic models and may be used to predict the pharmacokinetic consequences of exposure to one or multiple drugs. According to classic Michaelis-Menten (M-M) kinetics, one binding site models can be employed to simply interpret inhibition (pure competitive, non-competitive and uncompetitive) or activation of the enzyme. However, some cytochromes P450, in particular CYP3A4, exhibit unusual kinetic characteristics. In this instance, the changes in apparent kinetic constants in the presence of inhibitor or activator or second substrate do not obey the rules of M-M kinetics, and the resulting kinetics are not straightforward and hamper mechanistic interpretation of the interaction in question. These unusual kinetics include substrate activation (autoactivation), substrate inhibition, partial inhibition, activation, differential kinetics and others. To address this problem, several kinetic models can be proposed, based upon the assumption that multiple substrate binding sites exist at the active site of a particular P450, and the resulting kinetic constants are, therefore, solved to adequately describe the observed interaction between multiple drugs. The following is an overview of some cytochrome P450-mediated classic and atypical enzyme kinetics, and the associated kinetic models. Applications of these kinetic models can provide some new insights into the mechanism of P450-mediated drug-drug interactions.

Algorithms↗

PubMed1974

Statistical considerations in the estimation of enzyme kinetic parameters by the direct linear plot andother methods.

The statistical implications of the direct linear plot for enzyme kinetic data, described in the preceding paper (Eisenthal & Cornish-Bowden, 1974), are discussed for the case of the Michaelis-Menten equation. The plot is shown to lead directly to non-parametric confidence limits for the kinetic parameters, V and K(m), which depend on far less sweeping assumptions about the nature of experimental error than those implicit in the method of least squares. Median estimates of V and K(m) can also be defined, which are shown to be more robust than the least-squares estimates in a wide variety of experimental situations.

Computers↗

PubMed1989

Space-filling effects of inert solutes as probes for the detection and study of substrate-mediated conformational changes by enzyme kinetics: theoretical considerations.

From expressions derived for the space-filling effects of small inert solutes on kinetic parameters for univalent enzymes undergoing isomerizations that are substrate-induced and pre-existing, it is concluded that experimental observation of an enhanced maximal velocity in the presence of inert solute can only reflect the existence of the former type of conformational change; and that the isomerization must be governed by a relatively small equilibrium constant. Similar conclusions apply to multivalent enzymes exhibiting Michaelis-Menten kinetics. Extension of the theory to provide quantitative expressions for multivalent enzymes has made possible the numerical simulation of thermodynamic non-ideality effects on systems conforming with the Monod and Koshland models of allostery. In that regard the simulated Scatchard plots for the two models differ sufficiently in form to suggest that detailed examination of the space-filling effects of small solutes on the kinetics of an allosteric enzyme may, under favourable circumstances, allow identification of the appropriate allosteric mechanism. Finally, these considerations of thermodynamic non-ideality in relation to the kinetics of allosteric enzymes have revealed formal similarities between the consequences of space-filling by inert solutes and the specific effects of allosteric activators or inhibitors. Attention is drawn to the possible implications of this observation in relation to the functioning of allosteric enzymes in vivo, where catalytic performance may be modified by factors no more specific than the ability of unrelated solutes to occupy space in the highly concentrated cellular environment.

Chemical Phenomena↗

PubMed1983

Effects of conformational selectivity and of overlapping kinetically influential ionizations on the characteristics of pH-dependent enzyme kinetics. Implications of free-enzyme pKa variability in reactions of papain for its catalytic mechanism.

The effects of selection by a small molecule, when binding to a protein, of a particular conformation from an equilibrium stereopopulation on the characteristics of the pH-dependence of reaction with a reactivity probe or substrate were determined by analysis of an appropriate kinetic model. For reaction in one protonic state containing an equilibrium mixture of two conformational isomers, the pH-second-order rate constant (k) profile is of conventional sigmoidal form. The apparent pKa value is a composite of the pKa values of the two conformational states. The value of pKapp. for a given enzyme under given experimental conditions will always be the same (provided that the site-specificity assumed in the model is maintained) irrespective of whether only one conformation reacts or both react, with the same or with different rate constants. The experimentally determined pH-independent rate constant (kapp.) is an average of the reactivities of the two conformational states weighted in favour of the predominant form. The presence of an additional but unreactive conformational state also affects the value of kapp. The possibility that overlapping acid dissociations that affect the reactivity of the enzyme might provide pH-k profiles often indistinguishable in practice from simple sigmoidal dissociation curves and subject to variability in apparent pKa values was evaluated by a simulation study. If two reactive protonic states of the enzyme respond differently to changes in the structure of the substrate or site-specific reactivity probe, differences in apparent pKa values of up to approx. 1 unit can be exhibited without deviation from sigmoidal behaviour being reliably observed. Differences in apparent pKa values observed in some site-specific reactions of papain and their possible consequences for its catalytic mechanism are discussed.

Hydrogen-Ion Concentration↗

PubMed2000

Enzyme kinetics of hevamine, a chitinase from the rubber tree Hevea brasiliensis.

The enzyme kinetics of hevamine, a chitinase from the rubber tree Hevea brasiliensis, were studied in detail with a new enzyme assay. In this assay, the enzyme reaction products were derivatized by reductive coupling to a chromophore. Products were separated by HPLC and the amount of product was calculated by peak integration. Penta-N-acetylglucosamine (penta-nag) and hexa-N-acetylglucosamine (hexa-nag) were used as substrates. Hexa-nag was more efficiently converted than penta-nag, which is an indication that hevamine has at least six sugar binding sites in the active site. Tetra-N-acetylglucosamine (tetra-nag) and allosamidin were tested as inhibitors. Allosamidin was found to be a competitive inhibitor with a K(i) of 3.1 microM. Under the conditions tested, tetra-nag did not inhibit hevamine.

Acetylglucosamine↗

PubMed1988

Substrate as a source of thermodynamic nonideality in enzyme kinetic studies: invertase-catalyzed hydrolysis of sucrose.

Expressions for the effects of thermodynamic nonideality arising from the use of high concentrations of small substrate in enzyme kinetic studies are derived. Their application to experimental results for the hydrolysis of sucrose by yeast invertase (pH 4.9, 37 degrees C) signifies that the progressive decrease in initial velocity at high sucrose concentration is consistent with the occurrence of isomeric expansion during the transition of an enzyme-substrate complex to its activated state. Ultracentrifuge studies on the yeast enzyme preparation are then used to establish the physical acceptability of the volume change required to account for the kinetic effects in these terms: the postulated expansion of 1.3 liter/mol would represent a mere 0.16% increase in hydrated volume (or a corresponding increase in extent of asymmetry). Finally, although originally interpreted to signify an effect of sucrose on water concentration, published results for the invertase-sucrose system [J. M. Nelson and M. P. Schubert (1928) J. Amer. Chem. Soc. 50, 2188-2193] also find a rational explanation in terms of the present analysis based on effects of thermodynamic nonideality in enzyme kinetic studies.

Catalysis↗

PubMed2004

Validation and characterization of uninhibited enzyme kinetics performed in multiwell plates.

Several systematic errors may occur during the analysis of uninhibited enzyme kinetic data using commercially available multiwell plate reader software. A MATLAB program is developed to remove these systematic errors from the data analysis process for a single substrate-enzyme system conforming to Michaelis-Menten kinetics. Three experimental designs that may be used to validate a new enzyme preparation or assay methodology and to characterize an enzyme-substrate system, while capitalizing on the ability of multiwell plate readers to perform multiple reactions simultaneously, are also proposed. These experimental designs are used to (i) test for enzyme inactivation and the quality of data obtained from an enzyme assay using Selwyn's test, (ii) calculate the limit of detection of the enzyme assay, and (iii) calculate Km and Vm values. If replicates that reflect the overall error in performing a measurement are used, the latter two experiments may be performed with internal estimation of the error structure. The need to correct for the systematic errors discussed and the utility of the proposed experimental designs were confirmed by numerical simulation. The proposed experiments were conducted using recombinant inducible nitric oxide synthase preparations and the oxyhemoglobin assay.

Biochemistry↗

PubMed1996

ENZEDUC 1.0: a user-friendly software package for computation of hyperbolic enzyme kinetic data in biochemical education.

ENZEDUC 1.0 is a software package developed in Microsoft QuickBASIC v7.1 for computation of hyperbolic enzyme kinetics. The educational focus of the package is laboratory practical teaching. The program can manage a maximum of 18 substrate concentration values and 72 reaction rate values for each substrate concentration (1296 pairs of values). Samples can also be of unequal sizes. More than one reaction rate value for each substrate concentration can be handled. Real-time screen plots are obtained for the Michaelis-Menten function and the most popular linear transformations. Printer outputs are available. Hardware requirements are minimum 640 Kb RAM, EGA graphics card and 80286 processor.

Algorithms↗

PubMed1984

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.

Enzyme Inhibitors↗

PubMed1995

In vivo measurements of pulmonary angiotensin-converting enzyme kinetics. I. Theory and error analysis.

We developed a procedure for measuring pulmonary angiotensin-converting enzyme kinetics with fluorine-18 fluorocaptopril and positron emission tomography (PET). The method is based on the application of a compartmental receptor model that represents the kinetics of two species of ligand, presumably the trans and cis conformers of captopril. The input function was characterized and includes corrections for the labeled metabolites of fluorocaptopril. Application of the procedure to lung time-activity data obtained with PET produced estimates of kinetic parameters demonstrating fast kinetics for one conformer and slower kinetics for the other. Simulation studies were performed to evaluate the sensitivity of the estimated parameters to errors in the model assumptions and in measured values for variables required for analysis of the PET data. Estimates for two of the kinetic parameters, the amount of perfused unbound functional enzyme normalized to regional lung volume and the association rate constant for the trans conformer, were relatively stable even with large errors in the input data, varying < 30% from true values for all perturbations. Thus, the procedure produces reliable estimates of the kinetics of the trans conformer of captopril as well as theoretical curves that are close to the observed data.

Animals↗

PubMed2002

Effective experimental design: enzyme kinetics in the bioinformatics era.

Acquiring details about the kinetic parameters of enzymes is crucial to both drug development and clinical diagnosis. The correct design of an experiment is crucial to collecting data suitable for analysis, modelling and deriving the correct information. As classical design methods are not targeted to the more complex kinetics now frequently studied, further work is required to estimate parameters of such models with low variance. This review examines the different options available to produce major gains in information, productivity and the accuracy of each experiment.

Animals↗

PubMed1985

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 parameter), 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.

Biometry↗

PubMed2003

[Enzyme kinetics of clausenamide enantiomers in rat liver microsomes].

AIM: To investigate the enzyme kinetics of (-)3S,4R,5R,6S-clausenamide[(-)-Clau] and (+)-3R,4S,5S,6R-clausenamide[(+)-Clau] catalyzed by rat liver microsomes and compare their stereoselective differences. METHODS: An in vitro metabolic system was built by using rat liver microsomes and NADPH-generating system. Clau and its metabolites were determined simultaneously by a reversed-phase high performance liquid chromatography. The kinetic parameters, K(m), Vmax, and metabolic rate, Vmax/K(m), were calculated by Eadie-Hofstee plot. RESULTS: In the metabolic system, (-)-Clau was found to be mainly metabolized to 7-hydroxy-, 5-hydoxy- and 4-hydroxy-Clau, and 7-hydroxylation was a preferential pathway which exhibited higher Vmax/K(m) value (0.135 microL.min-1.mg-1) than those of 5- and 4-hydroxylation (0.063 and 0.068 microL.min-1.mg-1, respectively). For (+)-Clau, it was mainly metabolized to 4-hydroxy-Clau, whereas 7-hydroxy- and 4-hydroxy-Clau were so small that they could not be detected systematically. 4-Hydroxylation of (+)-Clau showed highest Vmam/K(m) value (0.547 microL.min-1.mg-1) among all the metabolites tested, which was 8.0 times higher than that of 4-hydroxylation of its antipode. CONCLUSION: The data indicated that there were obvious substrate stereoselective differences in the hydroxylation metabolism of (+)- and (-)-Clau, which provided an explanation of the difference of pharmacokinetic characteristics of Clau enantiomers in rats.

Animals↗