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Nonlinear estimation of microbial and enzyme kinetic parameters from progress curve data.

A computer program (BIOKINFIT) was developed to estimate microbial and enzyme kinetic parameters from progress curve data by nonlinear regression. BIOKINFIT overcomes the limitations associated with parameter estimation in nonlinear equations that are implicit in the dependent variable by numerically approximating the substrate concentration in the integrated kinetic expressions. The simplex method was used to minimize the error between experimentally observed and theoretically predicted substrate depletion data. The robustness of this approach was initially verified using synthetic substrate depletion data that were characterized by either simple or relative errors of known magnitude. Subsequently, previously published data from three different experiments including the pyruvate kinase reaction, 2-chlorophenol biodegradation, and glucose uptake by Penicillium chrysogenum were used to verify the utility of the present approach for kinetic parameter estimation. In all cases, experimental substrate depletion data were accurately described by the theoretical curves and kinetic parameter estimates obtained in this study using the simplex method were in close agreement with those reported previously. BIOKINFIT, available free of charge on request, offers a convenient and robust method of analyzing progress curve data in implicit kinetic expressions.

Biodegradation, Environmental↗

Human hepatic beta-glucuronidase: an enzyme kinetic study.

beta-Glucuronidase (EC 3.2.1.31) was purified from human liver and its activity was determined by enzyme kinetic method employing phenolphthalein glucuronic acid (PGA) and conjugated bilirubin, primarily bilirubin diglucuronide purified from human bile, as substrates in the absence or presence of D-glucaro-1,4-lactone. The enzyme was capable of acting on both PGA and conjugated bilirubin with Michaelis constants of 0.435 mmol/l at 56 degrees C and 1.02 mmol/l at 37 degrees C, respectively. Both reactions were beta-glucuronidase-specific because both were inhibited by D-glucaro-1,4-lactone in a competitive fashion. Conjugated bilirubin acted as a noncompetitive inhibitor of the enzyme for PGA in a two-substrate system. The study indicates that these two substrates bind at different catalytic sites of the enzyme and, on molar base, conjugated bilirubin had higher affinity for the enzyme and less degree of inhibition by D-glucaro-1,4-lactone than PGA. Whether such catalytic sites are also common for other beta-D-glucuronid ethers and esters remains to be proven.

Bilirubin↗

Steady-state enzyme kinetics with high-affinity substrates or inhibitors. A statistical treatment of dose-response curves.

A statistical treatment of steady-state enzyme kinetic measurements is described that allows for depletion of free substrate or free inhibitor concentrations owing to significant binding to the enzyme. V(max.), K(m) or K(i), enzyme concentration, the concentration of substrate or inhibitor required for a half-maximal effect and standard errors of these parameters can be calculated from dose-response measurements; the concentration of each component of the system may be estimated also. The statistically best values of the parameters are used to convert dose-response curves into convenient linear forms. The method is applied to dose-response measurements of hydroxyquinoline N-oxide inhibition of bacterial respiration and aminopterin inhibition of dihydrofolate reductase. Two FORTRAN programs for this method have been deposited as Supplementary Publication no. SUP 50019 at the National Lending Library for Science and Technology, Boston Spa, Yorks. LS23 7BQ, U.K., from whom copies may be obtained on the terms indicated in Biochem. J. (1973) 131, 5.

Aminopterin↗

Estimating the dual-enzyme kinetic parameters for Cr (VI) reduction by Shewanella oneidensis MR-1 from soil column experiments.

Hexavalent chromium (Cr (VI)) contamination of soil and groundwater is considered a major environmental concern. Bioreduction of Cr (VI) to trivalent chromium (Cr (III)) can be considered an effective technology in remediating Cr (VI) contaminated sites. Among the Cr (VI) reducing bacteria, Shewanella oneidensis MR-1 (MR-1) is relatively effective. Reduction of Cr (VI) by MR-1 is defined by the dual-enzyme kinetic model. The feasibility of bioreduction of Cr (VI) is usually evaluated by performing batch experiments which may not accurately represent the subsurface environment. The objective of this paper is to present a rational approach to determine the dual-enzyme reaction kinetics of Cr (VI) reduction by MR-1 from continuous flow soil column experiments which more accurately simulate the subsurface environment. Kinetic parameters obtained from soil column data were found to be much smaller than that obtained from batch data. The stable enzyme induced reaction rate was found to be 127th and the average deactivating enzyme induced reaction rate was 117th of the corresponding values obtained from batch reactor data as reported in literature.

Bioreactors↗

Enzyme kinetic studies and inhibition by oligopeptides of LH-RH degradation in rat hypothalamus and pituitary.

The enzyme kinetic parameters of the degradation of luteinizing hormone-releasing hormone (LH-RH) and L-cystine-bis-(4-nitroanilide) (Cys-NA) by rat hypothalamic (HYP) and pituitary (PIT) extracts and the effect of various oligopeptides on the rate of LH-RH inactivation were investigated in vitro. The 105,000 x g supernatant of 1 rat HYP inactivated 57 microgram LH-RH during a 30 min incubation (Km = 12.4 microM, V max = 2.33 microgram LH-RH/mg protein/min), and of one rat anterior PIT, 48 microgram LH-RH during 30 min of incubation (Km = 12.2 microM, V max = 8.0 microgram LH-RH/mg protein/min). The synthetic substrate Cys-NA competitively inhibited LH-RH degradation with a Ki of 8.5 microM in the HYP and 6 microM in the PIT enzyme preparation. Vice versa, LH-RH also competitively inhibited the cleavage of Cys-NA with inhibition constants of 14 microM (HYP) and 15 microM (PIT) indicating that the 2 substrates are probably cleaved by the same enzyme. The most effective inhibitors of LH-RH degradation were found to be angiotensin-related peptides, neurotensin, bradykinin, and bacitracin. A relatively weak effect was obtained with oxytocin, enkephalin and puromycin. It is concluded that endogenous oligopeptides such as angiotensins, neurotensin, bradykinin, etc., may possibly influence H-RH degradation in the PIT and the HYP. The synthetic substrate Cys-NA may be an appropriate substrate for measuring the activity of an LH-RH-degrading peptidase, which therefore could be classified as arylamidase.

Aminopeptidases↗

Adaptation of an HPLC system for transient-state enzyme kinetic experiments: pulse-flow method.

The components of an HPLC system can be easily reassembled into an instrument for transient-state enzyme kinetic experiments based on the continuous-flow technique. The scheme of reassembly, operation and data evaluation is described in detail for the Pharmacia FPLC system. The working quality of the suggested scheme was tested using a well-studied process of bacterial beta-galactosidase activation by Mg2+ ions. The found parameters were in a good agreement with the literature data. The pulse-flow mode was developed for the delivery of working solutions to reduce the required quantities of enzyme and/or other reaction components. The work presents new approach to HPLC modules as building blocks for sophisticated liquid flow reactors, such as automatic solid phase synthesizers, sequencers and so on.

Chromatography, High Pressure Liquid↗

Robust regression of enzyme kinetic data.

A method described previously [Cornish-Bowden & Endrenyi (1981) Biochem. J. 193, 1005-1008] for fitting theoretical equations to enzyme kinetic data without prior knowledge of weights or error distribution has been tested by computer simulation. With the equations for various kinds of linear inhibition as an example, the method performed well under all of the conditions examined, giving results that were often much better than those given by widely used least-squares alternatives, and were never appreciably worse. Although equations for two-substrate kinetics were not explicitly tested, the results for inhibition equations can be generalized to include two-substrate equations because the two are formally equivalent for simulation purposes. As a check on the results with inhibition equations the method was also tested for fitting bell-shaped pH-activity profiles and gave correspondingly good results.

Computers↗

Enzyme kinetic modelling as a tool to analyse the behaviour of cytochrome P450 catalysed reactions: application to amitriptyline N-demethylation.

1. To determine kinetic parameters (Vmax, K(m)) for cytochrome P450 (CYP) mediated metabolic pathways, nonlinear least squares regression is commonly used to fit a model equation (e.g., Michaelis Menten [MM]) to sets of data points (reaction velocity vs substrate concentration). This method can also be utilized to determine the parameters for more complex mechanisms involving allosteric or multi-enzyme systems. Akaike's Information Criterion (AIC), or an estimation of improvement of fit as successive parameters are introduced in the model (F-test), can be used to determine whether application of more complex models is helpful. To evaluate these approaches, we have examined the complex enzyme kinetics of amitriptyline (AMI) N-demethylation in vitro by human liver microsomes. 2. For a 15-point nortriptyline (NT) formation rate vs substrate (AMI) concentration curve, a two enzyme model, consisting of one enzyme with MM kinetics (Vmax = 1.2 nmol min-1 mg-1, K(m) = 24 microM) together with a sigmoidal component (described by an equation equivalent to the Hill equation for cooperative substrate binding; Vmax = 2.1 nmol min-1 mg-1, K' = 70 microM; Hill exponent n = 2.34), was favoured according to AIC and the F-test. 3. Data generated by incubating AMI under the same conditions but in the presence of 10 microM ketoconazole (KET), a CYP3A3/4 inhibitor, were consistent with a single enzyme model with substrate inhibition (Vmax = 0.74 nmol min-1 mg-1, K(m) = 186 microM, K1 = 0.0028 microM-1). 4. Sulphaphenazole (SPA), a CYP2C9 inhibitor, decreased the rate of NT formation in a concentration dependent manner, whereas a polyclonal rat liver CYP2C11 antibody, inhibitory for S-mephenytoin 4'-hydroxylation in humans, had no important effect on this reaction. 5. Incubation of AMI with 50 microM SPA resulted in a curve consistent with a two enzyme model, one with MM kinetics (Vmax = 0.72 nmol min-1 mg-1, K(m) = 54 microM) the other with 'Hill-kinetics' (Vmax = 2.1 nmol min-1 mg-1, K' = 195 microM; n = 2.38). 6. A fourth data-set was generated by incubating AMI with 10 microM KET and 50 microM SPA. The proposed model of best fit describes two activities, one obeying MM-kinetics (Vmax = 0.048 nmol min-1 mg-1, K(m) = 7 microM) and the other obeying MM kinetics but with substrate inhibition (Vmax = 0.8 nmol min-1 mg-1, K(m) = 443 microM, K1 = 0.0041 microM-1). 7. The combination of kinetic modelling tools and biological data has permitted the discrimination of at least three CYP enzymes involved in AMI N-demethylation. Two are identified as CYP3A3/4 and CYP2C9, although further work in several more livers is required to confirm the participation of the latter.

Amitriptyline↗

Steady-state enzyme kinetics in the Escherichia coli periplasm: a model of a whole cell biocatalyst.

This study provided analysis of in vivo enzyme kinetics in a model system which consisted of alkaline phosphatase in the periplasm of Escherichia coli. Modeling of complete substrate titration curves was achieved for a wide range of intraperiplasmic enzyme levels and outer membrane permeabilities. The results helped to identify the features most important to optimize in vivo reaction velocity. For many situations, a surprising finding was that maximum enzyme expression was not a major concern. For example, for moderate enzyme expression levels and moderate substrate levels (ca 0-5 mM), the limiting step for the enzyme in the periplasm was substrate (para-nitrophenylphosphate) diffusion through the outer membrane. In vivo reaction velocity was directly proportional to substrate concentration, outer membrane permeability, and the cell concentration. Velocity was also quite insensitive to a potent inhibitor of the enzyme. Even though diffusion-limited, periplasmic reaction velocity was quite sensitive to temperature, suggesting that the conformation of porin proteins in the E. coli outer membrane governed the average size of the pore. This model system therefore defined important features of bacterial whole cell biocatalyst design, which may also apply to other reactors using intact cells as catalysts.

Alkaline Phosphatase↗

Determination of catecholamines and O-methylated metabolites by reversed-phase high-performance liquid chromatography with fluorimetric detection and its application to enzyme kinetics.

In a study of the enzymatic methylation of individual catecholamines, high-performance liquid chromatography was used for the separation from their O-methylated metabolites. A RP-8 column and an aqueous mobile phase containing dodecylsodium sulphonate were used, and the eluate was analysed fluorimetrically (the detection limit was 20 pg). Each catecholamine used and its O-methylated compounds could be detected individually without interference from the catechol-O-methyltransferase and S-adenosylmethionine present. The application of the method to the study of enzyme kinetics is described.

Catecholamines↗

Rapid enzyme kinetic assays of individual Drosophila and comparisons of field-caught D. melanogaster and D. simulans.

Techniques for performing numerous enzyme kinetic assays with minimum time and effort would be valuable to studies of the evolutionary genetics of metabolic control and the quantitative genetics of determinants of kinetic parameters. Microtiter plate readers have been used for a variety of repetitious analytical techniques, and instruments are available that can take repetitive readings with sufficient speed to perform kinetic assays. The ability of these instruments to assay rapidly the kinetic properties of small samples makes them potentially useful for a number of problems in population genetics. While the ability to handle large numbers of samples is very attractive, the small sample volumes and optical imprecision of microtiter plates result in some sacrifice in accuracy. This paper presents methods for performing kinetic assays on individual field-caught Drosophila, quantifies the precision of these methods, and characterizes differences among Drosophila melanogaster and D. simulans from samples caught in California and Pennsylvania. Comparisons between field-caught and laboratory reared D. melanogaster show that most of the characters are very similar, with the exception of alpha GPDH, which has a threefold higher mean activity among field-caught flies. The phenotypic correlations are presented with a brief discussion of their relevance to assessing the evolution of metabolic control of these enzymes.

Animals↗

Volume and enzyme kinetics of human pancreatic secretion after endogenous stimulation with the Lundh test meal.

The present study was undertaken to investigate the volume and enzyme kinetics of human pancreatic secretion, after endogenous stimulation with a Lundh test meal, and evaluate the most reliable enzyme and collection period. The prestimulatory volume rates did not differentiate normal from pathologic pancreatic function. After ingestion of the test meal, the immediate increase in volume secretion was identical in healthy subjects and patients with pancreatic insufficiency. The latter showed a drastic reduction of prestimulatory and postprandial enzyme secretion. Cimetidine taken orally 12 and 2 h before the test meal study had no effect on volume and enzyme secretion and endogenous CCK release. Especially in severe pancreatic insufficiency, this modification simplified the performance of the Lundh test. The estimation of lipase and trypsin gave a significant correlation between Lundh test and secretin-cerulein test. The endogenous stimulation by Lundh test meal is a reliable test for routine diagnostic and scientific purposes.

Adult↗

Potential misconceptions arising from the application of enzyme kinetic equations to ligand-receptor systems at equilibrium.

The interactions of ligands with their receptors and the modulation of those interactions by other ligands are commonly described in the (verbal and mathematical) language of enzymology. While this analogy is appropriate in that velocity-substrate concentration curves and ligand-receptor binding isotherms often conform to similar rectangular hyperbolic relationships, the mathematical and conceptual similarities between the two systems strictly apply only to the simplest cases (absence or presence of a pure competitive inhibitor). To conclude that other classic forms of enzyme inhibition (uncompetitive, noncompetitive, mixed) have their exact mechanistic counterparts in "receptorology" can be misleading if due consideration is not given to the differences between the two types of system (steady-state versus equilibrium). In this communication, it is shown that relating receptor binding mechanisms to enzymological models results in Scatchard plots that are markedly different in appearance from the equivalent Eadie plots displaying enzyme kinetic data for all cases other than those in the absence of inhibitor or in the presence of a purely competitive inhibitor. It follows that receptor binding systems, which do produce inhibition patterns similar to those indicative of uncompetitive, noncompetitive, or mixed inhibition of an enzyme system, must do so through mechanisms that are different from those that produce these effects on enzymes. Consequently, terms such as uncompetitive or noncompetitive inhibition have different meanings when applied to receptors as compared with enzymes.

Binding, Competitive↗