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Effect of albumin and cytosol on enzyme kinetics of tolbutamide hydroxylation and on inhibition of CYP2C9 by gemfibrozil in human liver microsomes.

The effect of human serum albumin (Hsa) and human liver cytosol (Hlc) on the in vitro enzyme kinetics of the formation of hydroxytolbutamide (CYP2C9 marker reaction) and the inhibitory effect of gemfibrozil on tolbutamide hydroxylation were examined using human liver microsomes. The addition of Hsa greatly decreased the unbound concentrations of tolbutamide and gemfibrozil in the incubation medium, whereas Hlc only slightly decreased them. The unbound K(m) value for tolbutamide hydroxylation was 123 microM without Hsa and Hlc, and 73, 88, and 64 microM in the presence of Hsa (5 mg/ml), Hlc (0.5 mg/ml), and Hsa plus Hlc, respectively. The predicted in vivo hepatic clearance (CL(h)) of tolbutamide based on enzyme kinetics without Hsa and Hlc (0.06 ml/min/kg) was 40% of its in vivo clearance (0.15 ml/min/kg) based on published data. Addition of 5 mg/ml Hsa and 0.5 mg/ml Hlc to the incubation medium distinctly improved the prediction, with the coaddition of Hsa and Hlc yielding the most accurate value (0.14 ml/min/kg). The K(i) (6 microM) of gemfibrozil for CYP2C9, calculated using total drug concentrations, was increased by Hlc (8 microM), Hsa (40 microM), or both (72 microM). However, when the unbound substrate and inhibitor concentrations were considered, the K(i) (6 microM without Hsa and Hlc) was not markedly altered by Hsa (4 microM), Hlc (8 microM), or both Hsa and Hlc (9 microM). The present findings suggest that the addition of Hsa and Hlc to microsomal incubation media may yield enzyme kinetic estimates more comparable with in vivo results.

Albumins↗

The prediction of benzo[a]pyrene clearance by rat liver and lung from enzyme kinetic data.

The metabolic clearance of circulating benzo[a]pyrene (B[a]P) by liver and lung of control and 3-methylcholanthrene (3MC)-pretreated rats was predicted according to the perfusion-limited model from apparent enzyme kinetic constants determined in microsomal incubations. These predictions were tested in isolated organs perfused at normal organ flow. From microsomal incubations the apparent enzyme kinetic constants of B[a]P metabolism were determined. The apparent Km of liver microsomes was decreased 100 times by pretreatment with 3MC, while the Km of lung microsomes remained at about 0.2 microM. Maximal velocity of B[a]P metabolism was much greater in microsomes from liver than in those from lung of both control and 3MC-pretreated rats. Liver was found to have a far greater capacity for B[a]P metabolism (intrinsic free clearance) than lung. However, this large disparity was not evident in the predicted clearances. Perfused organs had B[a]P clearances very close to those predicted from the model. At normal (in vivo) organ flows, control rat lung had a clearance of 1.0 +/- 0.1 ml/min, whereas liver had a clearance of 5.9 +/- 0.2 ml/min. Corresponding clearances in organs from 3 MC-pretreated rats were 8.9 +/- 0.5 and 6.7 +/- 0.6 ml/min for lung and liver, respectively. Small discrepancies between predicted and observed values could not be explained by non-uniform distribution of B[a]P or shunting of flow. These results suggest that enzyme kinetic data can be used to assess accurately the ability of lung and liver to clear xenobiotic compounds such as B[a]P and that, despite the great disparity in their metabolic capacity, under certain conditions these two organs may function equally well in the removal of circulating compounds from the blood.

Animals↗

Measurement of enzyme kinetics using a continuous-flow microfluidic system.

This paper describes a microanalytical method for determining enzyme kinetics using a continuous-flow microfluidic system. The analysis is carried out by immobilizing the enzyme on microbeads, packing the microbeads into a chip-based microreactor (volume approximately 1.0 nL), and flowing the substrate over the packed bed. Data were analyzed using the Lilly-Hornby equation and compared to values obtained from conventional measurements based on the Michaelis-Menten equation. The two different enzyme-catalyzed reactions studied were chosen so that the substrate would be nonfluorescent and the product fluorescent. The first reaction involved the horseradish peroxidase-catalyzed reaction between hydrogen peroxide and N-acetyl-3,7-dihydroxyphenoxazine (amplex red) to yield fluorescent resorufin, and the second the beta-galactosidase-catalyzed reaction of nonfluorescent resorufin-beta-D-galactopyranoside to yield D-galactose and fluorescent resorufin. In both cases, the microfluidics-based method yielded the same result obtained from the standard Michaelis-Menten treatment. The continuous-flow method required approximately 10 microL of substrate solution and 10(9) enzyme molecules. This approach provides a new means for rapid determination of enzyme kinetics in microfluidic systems, which may be useful for clinical diagnostics, and drug discovery and screening.

Catalysis↗

On a nonelementary progress curve equation and its application in enzyme kinetics.

The analytical equation describing progress curves of an enzyme catalyzed reaction acting upon the Michaelis-Menten mechanism has been known for the case in which only the free enzyme incurs a loss of its activity, either spontaneously or as a result of an irreversible inhibitor action. The solution of differential equations which defines the rates of enzyme inactivation and substrate utilization is expressed by a nonelementary function in equation of an implicit type that precludes direct calculation of the extent of reaction at any time. Previously, the implicit equations have been rearranged to the alternative formulas and solved by the Newton-Raphson method, but this procedure may fail when used upon the presented equation. For this reason the other root-finding numerical method was applied, and the enzyme kinetic parameters of such numerically solved implicit equation for the reaction mechanism of irreversibly inhibited acetylcholinesterase were fitted to the experimental data by a nonlinear regression computer program.

Catalysis↗

Enzyme kinetics and inhibition of nimodipine metabolism in human liver microsomes.

AIM: To study the enzyme kinetics of nimodipine (NDP) metabolism and the effects of selective cytochrome P-450 (CYP-450) inhibitors on the metabolism of NDP in human liver microsomes in vitro. METHODS: Microsomes from six individual human liver specimens were used to perform enzyme kinetic studies and the kinetic parameters were estimated by Eadie-Hofstee equation. Various selective CYP-450 inhibitors were used to investigate their effects on the metabolism of NDP and the principal CYP-450 isoform involved in dehydrogenation of dihydropyridine ring of NDP in human liver microsomes. RESULTS: There was an important intersubject variability in NDP metabolism in human liver microsomes. For NDP dehydrogenase activity, the Km value was (36 +/- 11) mumol and the Vm value was (17 +/- 7) mumol.g-1.min-1. The dehydrogenation of dihydropyridine ring of NDP was competitively inhibited by ketoconazole (Ket) and troleandomycin (TAO), and the Ki values for Ket and TAO were 0.59 and 122.2 mumol, respectively. Phenacetin (Pnt), quinidine (Qui), diethyldithiocarbamate (DDC), sulfaphenazole (Sul), and tranylcypromine (Tra) had a little or no inhibitory effects on the dehydrogenation of NDP. CONCLUSION: The intersubject variability of NDP pharmacokinetics was attributed to the metabolic polymorphism of NDP in liver. Cytochrome P-4503A (CYP3A) is involved in the dehydrogenation of dihydropyridine ring of NDP.

Calcium Channel Blockers↗

A computer program for enzyme kinetics that combines model discrimination, parameter refinement and sequential experimental design.

A method of model discrimination and parameter estimation in enzyme kinetics is proposed. The experimental design and analysis of the model are carried out simultaneously and the stopping rule for experimentation is deduced by the experimenter when the probabilities a posteriori indicate that one model is clearly superior to the rest. A FORTRAN77 program specifically developed for joint designs is given. The method is very powerful, as indicated by its usefulness in the discrimination between models. For example, it has been successfully applied to three cases of enzyme kinetics (a single-substrate Michaelian reaction with product inhibition, a single-substrate complex reaction and a two-substrate reaction). By using this method the most probable model and the estimates of the parameters can be obtained in one experimental session. The FORTRAN77 program is deposited as Supplementary Publication SUP 50134 (19 pages) at the British Library (Lending Division), Boston Spa, Wetherby, West Yorkshire LS23 7BQ, U.K., from whom copies can be obtained on the terms indicated in Biochem. J. (1986) 233, 5.

Computers↗

Analysis of rabbit pulmonary angiotensin converting enzyme kinetics in vivo.

We investigated the kinetics of pulmonary angiotensin converting enzyme (ACE) in vivo by measuring the hydrolysis of a bolus dose of a synthetic ACE substrate, benzoyl-phenylalanyl-alanyl-proline (BPAP). Estimates of apparent Km and Vmax were calculated by multiple regression analysis using a nonlinear model of enzyme kinetics. A bolus injection of indocyanine green and BPAP was given into the jugular vein of anesthetized rabbits (3-4 kg b. wt.) and serial blood samples were collected at 1-sec intervals from the carotid artery. The concentration of indocyanine green, [3H]BPAP and its metabolite in each sample was used to construct pulmonary venous outflow concentration-time curves and to assess ACE activity. Addition of 0.04 to 2.6 mumol of unlabeled BPAP per kg to the injectate reduced [3H]BPAP metabolism in a dose-dependent manner, with a calculated ID50 of 0.37 mumol/kg at the peak of the outflow curve and 0.58 mumol/kg over the integral. There was a similar correlation between the concentration of BPAP in pulmonary blood, estimated from indocyanine green outflow curves, and the metabolism of [3H] BPAP. For each animal, application of the mathematical model provided statistically significant estimates of the kinetic constants for pulmonary BPAP metabolism in vivo. The apparent Km and Vmax were 9.3 +/- 0.8 and 63.1 +/- 9.5 mumol/sec/organ, respectively; the Vmax/Km was 6.8 +/- 1.0 ml/sec/organ. BPAP did not affect any of the hemodynamic parameters measured. The technique described provides a method for detailed study of the kinetics of pulmonary ACE in vivo and effects of inhibitor drugs or other experimental treatments on the function of this enzyme in the intact animal.

Animals↗

Analysis of one-component saturable systems such as ligand binding, enzyme kinetic, uptake, and transport data.

Statistical methods for analyzing enzyme kinetic or drug binding assays involving simple first-order kinetics have been reviewed. The Eadie-Hofstee format combines many attractive features. Specifically, this plot is as efficient as any of the alternatives, shows no tendency to produce grossly aberrant values, does not require explicit weighting, does not require an iterative fitting process, gives the parameters of interest and their errors of estimate directly, and is unbiased (after correction). A correction for the bias inherent in the Eadie-Hofstee format has been developed. A numerical example and computer program are given in appendices.

Biological Transport↗

Quantum mechanical methods for enzyme kinetics.

This review discusses methods for the incorporation of quantum mechanical effects into enzyme kinetics simulations in which the enzyme is an explicit part of the model. We emphasize three aspects: (a) use of quantum mechanical electronic structure methods such as molecular orbital theory and density functional theory, usually in conjunction with molecular mechanics; (b) treating vibrational motions quantum mechanically, either in an instantaneous harmonic approximation, or by path integrals, or by a three-dimensional wave function coupled to classical nuclear motion; (c) incorporation of multidimensional tunneling approximations into reaction rate calculations.

Computer Simulation↗

The evolution of enzyme kinetic power.

Evolution of the kinetic potential of enzyme reactions is discussed. Quantitative assessment of the evolution of enzyme action has usually focused on optimization of the parametric ratio kcat./Km, which is the apparent second-order rate constant for the reaction of free substrate with free enzyme to give product. We propose that the general form kcat.[E]T/Km (where [E]T is total enzyme concentration), which is designated the 'kinetic power', is the real measure of kinetic/catalytic potential in situ. The standard paradigm of 'perfection' dictates the evolutionary maximum of 'kinetic power' to be k+s[E]T/2, where k+s is the diffusion-controlled rate constant for formation of the ES complex (and, hence, for the overall enzyme reaction). We discuss the role of protein conformational mobility in determining this state of 'perfection', via gating of substrate binding and determination of the catalytic configuration. Going beyond the level of the individual enzyme, we indicate the manner by which the organizational features of enzyme action in vivo may enhance the 'kinetic power'. Through evolutionary 'perfection' of the microenvironment, one finds that the 'kinetic power' of enzymes can be affected by alteration of [E]T as well as the unitary rate constants. At this level of complexity, we begin to realize that the 'kinetic' description of cell metabolism must be supplemented with thermodynamic concepts.

Biological Evolution↗

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.

Algorithms↗

A residence-time analysis of enzyme kinetics.

A 'first-passage-time' analysis is applied to enzyme kinetics. It is shown that the residence times determined in this way are directly related to the steady-state parameters and are particularly useful in analysis of isotopic exchange. A simple linear means is used for the calculation of these residence times that makes this method easily applicable to the numerical evaluation of complex models. This stochastic type of approach provides an alternative that avoids the classical steady-state approximation that the concentrations of enzyme intermediates are constant. Instead, steady state is defined as the randomization of the states of the enzyme following initial mixing due to completion of the turnovers of individual enzyme molecules at different times.

Enzymes↗

Modeling of human hepatic CYP3A4 enzyme kinetics, protein, and mRNA indicates deviation from log-normal distribution in CYP3A4 gene expression.

AIMS: To determine whether the variability in cytochrome P(450) (CYP)3A4 metabolic function is exhibited at both transcription and translation levels and to examine the population distribution of CYP3A4 enzyme kinetics, protein, and mRNA. METHODS: Enzyme kinetics of testosterone 6beta-hydroxylation, immunoblot CYP3A4 protein, and CYP3A4 mRNA were determined in a microsomal bank of human livers. The distribution of these determinations was analyzed using cumulative distribution (probit) plots and normality test variable (NTV) to detect deviation from normality. RESULTS: Mean hepatic CYP3A4 protein and relative CYP3A4 mRNA were 35+/-23 pmol/mg and 79+/-59 (CYP3A4/beta-actin), respectively. Kinetic parameter estimates of testosterone 6beta-hydroxylation were 611+/-684 pmol/mg/min for maximum rate of the reaction (V(max)) and 206+/-48 micro M for the Michaelis constant (K(m)). The CYP3A4 gene expression and its activity exhibited a relatively high degree of interindividual variability. Furthermore, significant correlation between CYP3A4 protein and V(max) of testosterone 6beta-hydroxylation (r=0.82, P<0.001) as well as CYP3A4 protein and its mRNA (r=0.52, P<0.01) was observed. Cumulative distribution plots and histograms for the CYP3A4 protein, its mRNA, and maximum testosterone 6beta-hydroxylation exhibited evidences of deviation from log-normal distribution. The minimum NTV value for the distribution of CYP3A4 protein corresponding to the inflection point in the probit occurred at approximately 10% cumulative frequency. The percentage of low CYP3A4 protein phenotype was consistent for CYP3A4 activity and its mRNA. In contrast, the distribution of K(m) of testosterone 6beta-hydroxylation does not show evidence of bimodality. CONCLUSIONS: The distribution of CYP3A4 metabolic function, protein, and mRNA is non-normal and may represent a regulatory polymorphism in hepatic CYP3A4 gene expression. In contrast, assessment of the possibility of a structural variant of CYP3A4 through evaluation of the standard deviation relative to the mean kinetic constant value suggests that structural mutation of CYP3A4 may not be a major factor affecting interindividual variation in CYP3A4 metabolic function.

Adolescent↗

[Nonlinear regression analysis of cardiac enzyme kinetic model with modified simplex method and DUD method using SAS software].

OBJECTIVE: To compare the efficacy of modified simplex method and DUD method using SAS software for nonlinear regression analysis of cardiac enzyme kinetic model. METHOD: By using cardiac enzyme kinetic one-compartment mathematical model, nonlinear regression results obtained from DUD methods using SAS software and modified simplex method were compared with the same starting values to fit the creatine kinase curves in 22 patients with acute myocardial infarction. RESULTS: The parameters calculated by DUD method and modified simplex method were the same in 4 cases, and smaller least square was resulted from DUD method in 4 cases. In the other 14 cases, modified simplex method yielded smaller least square. The mean value of the least square calculated by modified simplex method was less than that by DUD method (867 747 vs 6 712 989, P=0.013). CONCLUSION: Modified simplex method appears to be more adequate than DUD method in estimating circulatory parameters of the one-compartment model.

Humans↗

Saturation of enzyme kinetics in circadian clock models.

From the mathematical study of simple models for circadian rhythm, the authors identified a clear effect of saturation in the enzyme kinetics on the promotion or suppression of a sustained oscillation. In the models, a clock gene (per gene) is transcribed to produce mRNAs, which are translated to produce proteins in the cytosol which are then transported to the nucleus and suppress the transcription of the gene. The negative feedback loop with a long time delay creates sustained oscillation. All the enzymatic reactions (e.g., degradation, translation, and modification) are assumed to be of Michaelis-Menten type. The reaction rate increases with the amount of substrate but saturates when it is very large. The authors prove mathematically that the saturation in any of the reactions included in the feedback loop (in-loop reaction steps) suppresses the oscillation, whereas the saturation of both degradation steps and the back transport of the protein to cytosol (branch reaction steps) makes the oscillation more likely to occur. In the experimental measurements of enzyme kinetics and in published circadian clock simulators, in-loop reaction steps have a small saturation index whereas branch reaction steps have a large saturation index.

Animals↗

Atypical enzyme kinetics: their effect on in vitro-in vivo pharmacokinetic predictions and drug interactions.

The most common method for estimating a drug's in vivo clearance from in vitro data has involved using the classical Michaelis-Menten model to describe the observed in vitro data and from this estimate intrinsic clearance. This process assumes that the drug obeys standard enzyme kinetics that can be described by this model. However, the observation of atypical enzyme kinetics, particularly involving cytochrome P450 enzymes, has become relatively common, and occurrences have been reported with virtually all of the cytochrome P450 isoforms. Since predictions of a drug's in vivo clearance are made based on kinetic parameters observed during in vitro experiments (in vitro estimated intrinsic clearance), mis-identification of the drug's kinetic profile can lead to inaccurate predictions of intrinsic clearance. In addition to these potential ramifications of in vitro-in vivo predictions, information is becoming available concerning the in vivo implications of drugs that exhibit atypical kinetic profiles. This review will discuss the various types of atypical kinetic profiles that may be observed during in vitro experiments, hypotheses for why they may occur, examples of how a drug's intrinsic clearance may be mis-estimated when atypical kinetics are incorrectly assessed, and the potential ramifications of these issues for prediction of drug interactions. Furthermore, potential, artifactual causes of atypical kinetic phenomena will be described.

Algorithms↗

Discrete design of enzyme kinetic experiments.

The usefulness of discrete designs in enzyme kinetics as an alternative to continuous designs is discussed in this paper, focusing on designs satisfying the D-optimality criterion. This study has been carried out using a program called DODID, specifically devised for this purpose, which is available by request to the authors. The results presented in this paper show that the relative efficiency of the D-optimal discrete designs with respect to the continuous ones increases rapidly when increasing the number of possible values for the control variables. Relative efficiencies higher than 0.98 are achieved when using 20 possible values for each variable. The power of the tools provided by the computational approach of this work is proved by the analysis made on the robustness of different designs for estimating the kinetic parameters when a wrong assumption on the error structure has been made. The robustness of the designs made assuming medium constant error (error variance proportional to the true response) is thus confirmed. A comparative study of several discriminating designs is also presented. The results obtained show that the designs produced by adding the optimal discrete designs corresponding to both candidate models plus the point where the weighted difference between the predicted values is maximum, is a good choice when designing an experiment for discrimination.

Algorithms↗