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PubMed1994

Evolutionary optimization of enzyme kinetic parameters; effect of constraints.

The distribution of the kinetic parameters of enzymic reactions is theoretically studied, on the assumption that, during evolution, the increase of reaction rates was an important target of natural selection. In extension of previous work on the optimization of enzyme kinetic parameters, the influence of constraints concerning upper limits of the individual rate constants is analyzed. The concept of "evolutionary effort" is applied to derive an expression for the cost function, leading to an overall upper limit for the values of the rate constants. The resulting optimization problem is solved for ordered mechanisms involving different numbers of elementary steps. It is shown that the optimum for the enzyme kinetic parameters strongly depends on the concentrations of the reactants. Low reactant concentrations lead generally to a tight binding of the reactants, while high concentrations result in a weak binding, favouring the rate constants of the other steps. In particular, states of maximum activity are not always characterized by maximal values of second-order rate constants. The results support the hypothesis that there is a mutual adaptation of Michaelis constants and reactant concentrations in an evolutionary timescale. In the limit of infinite values of the exponent of the cost function the results of the present "overall limit model" turn into the results of a model which takes into account individual upper limits for rate constants ("separate limit model"). The distributions of optimal rate constants are discussed in terms of free-energy profiles. The model is applied to the interpretation of the kinetic data of triosephosphate isomerase and inorganic pyrophosphatase.

Animals↗
PubMed1990

Description of enzyme kinetics in reversed micelles. 1. Theory.

In the literature measurements of kinetic data of enzymes in reversed micelles have been interpreted in two ways. In the first, all enzyme parameters are expressed with respect to the total volume of the reversed micellar solution. In the second, the enzymatic conversion is related only to the fraction of the volume consisting of aqueous solution (pseudophase model). In this paper equations are derived describing the rate of an enzymatic reaction for three different kinds of enzymes: enzymes obeying Michaelis-Menten kinetics, enzymes following a ping-pong bi-bi mechanism and enzymes which convert substrates according to an ordered mechanism. In deriving these equations, a distinction is made between intermicellar exchange reactions of substrate(s) and product(s) and the enzymatic reaction which takes place in the waterpool of a reversed micelle. In the description, all intrinsic rate constants of the enzyme are assumed to be independent of its environment. The rate equations show that the presence and efficiency of the intermicellar exchange reaction, which supplies the enzyme with substrate and removes product, can affect the rate of an enzymatic reaction under common experimental conditions. Whereas kinetic parameters derived from double-reciprocal plots often seem to be affected by enclosure in reversed micelles, these apparent deviations from kinetics in aqueous media can be explained by the model presented here as arising from exchange phenomena. Neither the experimentally determined maximum enzyme velocity, vmax, nor the Michaelis constants are affected by the incorporation of the enzyme in reversed micelles. The deviations of kinetic parameters from the aqueous values are shown to depend strongly on the concentration of reversed micelles, the intermicellar exchange rate and the volume fraction of water, a dependence in agreement with findings reported in the literature.

Colloids↗
PubMed1996

How to derive flux control coefficients from the rate equations of classical enzyme kinetics.

A recent report by Brown and Cooper demonstrated the usefulness of calculating "flux control coefficients" for each of the rate constants involved in the assumed kinetic mechanism of a single enzyme. The calculations of Brown and Cooper involved numerical differentiation. The present article substantiates this report by showing that the numerical results of Brown and Cooper can also be obtained in an explicit form. The analytical equations given establish the relationship between rigorously specified overall rate processes and "elementary rate constants," both being defined by the rate equations of classical enzyme kinetics. It is shown that analytical flux control coefficients can be obtained for all types of rate processes considered in classical enzyme kinetics, including, "initial rates," equilibrium exchange reactions, and reactions at limiting levels of substrate (and/or product) saturation. By restricting the discussion to strictly consecutive (ordered, unbranched, linear) mechanisms, the line of reasoning can be presented in a relatively simple form. The main conclusions are the following: (a) It is advantageous to carry out the analysis in terms of paired (conjugated) control coefficients. (b) Flux control analysis of "elementary rate constants" does not require any extra kinetic argument. (c) Neither the immediate aim nor the results of the presented type of analysis are directly relevant to theories of metabolic control. On the contrary, the type of control analysis considered completes classical enzyme kinetics with a new facet. (d) For illustrating its usefulness, the concept of flux control coefficients is applied to the problem of optimization of enzyme activity.

Binding Sites↗
PubMed1989

Graphic rules in steady and non-steady state enzyme kinetics.

Graphic methods, when applied to enzyme kinetics, can provide a visually intuitive relation between calculations and reaction graphs. This will not only greatly raise the efficiency of calculations but also significantly help the analysis of enzyme kinetic mechanisms. In this paper, four graphic rules are presented. Rules 1-3 are established for steady state enzyme-catalyzed reaction systems and Rule 4 is for non-steady state ones. In comparison with conventional graphic methods which can only be applied to steady state systems, the present rules have the following merits. 1) Complicated and tedious calculations can be greatly simplified; for example, in calculating the concentrations of enzyme species for the bi-bi random mechanism, the calculation work can be reduced 8-fold compared with the King-Altman's method. 2) A great deal of wasted labor can be avoided; for example, in calculating the rate of product formation for the same mechanism, the operation of finding and removing the 96 reciprocally canceled terms is no longer needed because they automatically disappear during the derivation. 3) Final results can be easily and safely checked by a formula provided in each of the graphic rules. 4) Non-steady state systems can also be treated by the present graphic method; for example, applying Rule 4, one can directly write out the solution for a non-steady state enzyme-catalyzed system, without the need to follow more difficult and complicated operations to solve differential equations. The mathematical proofs of Rules 1-4 are given in Appendices A-D (in the Miniprint), respectively.

Enzymes↗
PubMed2006

A literature review of enzyme kinetic parameters for CYP3A4-mediated metabolic reactions of 113 drugs in human liver microsomes: structure-kinetics relationship assessment.

Cytochrome P450 (CYP) enzymes represent a superfamily of hemoproteins that are involved in the metabolism of a wide variety of endogenous and exogenous compounds. For a given CYP enzyme, kinetic properties of a substrate are usually related to substrate lipophilicity (log P or log D(7.4)). In this review, enzyme kinetic parameters (K(m), V(max), and V(max)/K(m)) of 215 CYP3A4-mediated metabolic reactions of 113 drugs in human liver microsomes were obtained from the literature, and lipophilicity values of the 113 drugs were calculated using the ACD/Labs 8.0 program. A low degree of K(m)- or (V(max)/K(m))-lipophilicity correlation, but no V(max)-lipophilicity correlation, is exhibited for the CYP3A4-mediated reactions. Overall, K(m) decreases, but V(max)/K(m) increases, with increasing substrate lipophilicity, and V(max) appears to be independent of substrate lipophilicity. In other words, a low K(m) generally confers a high V(max)/K(m) ratio for a substrate. The degree of lipophilicity-kinetics correlations is related to both reaction types (or reaction mechanisms) and regiochemical positions (or physicochemical properties) of the reaction groups of the substrates. Among the categorized CYP3A4-mediated reactions, the best lipophilicity-kinetics correlation is achieved for carbon hydroxylation, followed by N-dealkylation. No or little lipophilicity-kinetics correlations are seen for N, S-oxidation and other reactions. Within the hydroxylation group, aliphatic hydroxylation shows the best lipophilicity-kinetics correlation while hydroxylation on a carbon atom adjacent to an aromatic ring does not show any lipophilicity-kinetics correlation. The detailed structural and kinetic data sets of the human liver microsomal CYP3A4-mediated reactions represent a specialized database useful for researchers working in the area of structure-metabolism relationship modeling and analysis.

Animals↗
PubMed1992

A simple computer program with statistical tests for the analysis of enzyme kinetics.

A simple computer program that calculates the kinetic parameters of enzyme reactions is described. Parameters are determined by nonlinear, least-squares regression using either Marquardt-Levenberg or Gauss-Newton algorithms to find the minimum sum of squares. Three types of enzyme reactions can be analyzed: single substrate reactions (Michaelis-Menten and sigmoidal kinetics), enzyme activation at a fixed substrate value or enzyme inhibition at a fixed substrate value. The user can monitor goodness of fit through nonparametric statistical tests (performed automatically by the computer) and through visual examination of the pattern of residuals. The program is unique in providing equations for activator and inhibition analysis as well as in enabling the user to fix some of the parameters before regression analysis. The simplicity of the program makes it extremely useful for quickly determining kinetic parameters during the data-gathering process.

Biometry↗
PubMed1994

Tyrosine-48 is the proton donor and histidine-110 directs substrate stereochemical selectivity in the reduction reaction of human aldose reductase: enzyme kinetics and crystal structure of the Y48H mutant enzyme.

The active site of human aldose reductase contains two residues, His110 and Tyr48, either of which could be the proton donor during catalysis. Tyr48 is a candidate since its hydroxyl group is in proximity to Lys77 and thus may have an abnormally low pKa value. To distinguish between these possibilities, we used site-directed mutagenesis to create the H110Q and H110A, the Y48F, Y48H, and Y48S, and the K77M mutant enzymes. The two His110 mutants resulted in a 1000-20,000-fold drop in kcat/Km, respectively, for the reduction of DL-glyceraldehyde at pH 7. The Y48F mutation caused total loss of activity, whereas the Y48H and Y48S mutants retained catalytic activity with kcat/Km reduced by 5 orders of magnitude. The K77M mutant is an inactive enzyme. Kinetic studies using xylose stereoisomers show that the wild-type enzyme distinguishes between D-xylose, L-xylose, and D-lyxose up to 150-fold better than the H110A or H110Q mutants. The His110 mutants do not effectively discriminate between these isomers (4-11-fold). The crystal structure of the Y48H mutant refined at 1.8-A resolution shows that the overall structure is not significantly different from the wild-type structure. Electron densities for the histidine side chain and a new water molecule fill the space occupied by Tyr48 in the wild-type enzyme. The water molecule is in hydrogen-bonding distance to the N zeta group of Lys77 and to the N epsilon of His48 and fills the space occupied by the hydroxyl group of tyrosine in the wild-type structure. These findings suggest that proton transfer is mediated in the Y48H mutant enzyme by the water molecule. The Y48H mutant shows large and equal primary deuterium isotope effects on kcat and kcat/Km (1.81 +/- 0.03), providing direct evidence for hydride transfer as the rate-determining step in this mutant. Deuterium solvent isotope effects indicate that the relative contribution of proton transfer to this step of the catalytic cascade is much less important for the Y48H mutant than for the wild-type enzyme [D2O(kcat/Km) = 1.06 +/- 0.02 and 4.73 +/- 0.23, respectively]. The kinetic and mutagenesis data, together with structural data, indicate that His 110 plays an important role in the orientation of substrates in the active site pocket, while Tyr48 is the proton donor during aldehyde reduction by aldose reductase.

Aldehyde Reductase↗
PubMed2001

Enzyme kinetics determined using calorimetry: a general assay for enzyme activity?

Two techniques for determining enzyme kinetic constants using isothermal titration microcalorimetry are presented. The methods are based on the proportionality between the rate of a reaction and the thermal power (heat/time) generated. (i) An enzyme can be titrated with increasing amounts of substrate, while pseudo-first-order conditions are maintained. (ii) Following a single injection, the change in thermal power as substrate is depleted can be continuously monitored. Both methods allow highly precise kinetic characterization in a single experiment and can be used to measure enzyme inhibition. Applicability is demonstrated using a representative enzyme from each EC classification, including (i) oxidation-reduction activity of DHFR (EC 1.5.1.3); (ii) transferase activity of creatine phosphokinase (EC 2.7.3.2) and hexokinase (EC 2.7.1.1); (iii) hydrolytic activity of Helicobacter pylori urease (EC 3.5.1.5), trypsin (EC 3.4.21.4), and the HIV-1 protease (EC 3.4.21.16); (iv) lyase activity of heparinase (EC 4.1.1.7); and (v) ligase activity of pyruvate carboxylate (EC 6.4.1.1). This nondestructive method is completely general, enabling precise analysis of reactions in spectroscopically opaque solutions, using physiological substrates. Such a universal assay may have wide applicability in functional genomics.

Adenosine Triphosphate↗
PubMed1983

Investigations on beta-lactamase stability of recently developed beta-lactam compounds: study of enzyme kinetics.

The plasmid-mediated TEM-1 enzyme (E. coli K12 R6K) and chromosomally mediated enzymes from Enterobacter cloacae (IEP 8.5) and Citrobacter freundii (IEP 9.5) were highly purified. Enzyme kinetics were studied with various therapeutic compounds as substrates and lamoxactam, azthreonam, and N-formimidoyl thienamycin as inhibitors. Lamoxactam and azthreonam failed to inhibit the TEM-1 enzyme, whereas N-formimidoyl thienamycin was a competitive inhibitor. KI was 5 mumol/l--thus corresponding to KM--and independent of the substrate. With respect to chromosomally mediated enzymes, there was a time-dependent inhibition of beta-lactam hydrolysis. KI ranged from 0.06 to 0.2 mumol/l in dependence of the inhibitor. Enzyme kinetics suggested a non-competitive type of inhibition thus indicating that binding of these compounds to both chromosomally mediated enzymes must be followed by a further reaction step. It is evident that the stability against beta-lactamases of recently developed compounds is based on different mechanisms--characteristic for the enzyme being considered.

Anti-Bacterial Agents↗
PubMed2006

Real-time analysis of enzyme kinetics via micro parallel liquid chromatography.

A generic method for real-time monitoring of enzyme kinetics is described in this paper. This approach enables rapid development of assays for high-throughput screening or reaction monitoring in the linear range of the enzyme kinetic curve. In this paper, we used protein kinase A and kemptide (a well-studied assay system) to demonstrate assay optimization by using micro parallel liquid chromatography. The optimal substrate and enzyme concentrations were determined rapidly and conveniently compared with the traditional methods for determining these parameters. Additionally, the data collected from the same experiment permitted calculations of K (m) for the substrate, V (max), and time-course study. In general, this approach provides two advantages. First, the broad ranges of detectable product conversions facilitate selection and implementation of assay conditions for high-throughput screening. Second, the system permits determination of 50% inhibitory concentration values at less than 1% conversion of substrate to product, thereby validating screening hits in the linear range of the enzyme kinetic curve. Overall, this optimization process can be done in less than 8 h. To demonstrate the ability to monitor a wide range of assay conditions, we varied initial concentrations over eight orders of magnitude within a single experiment. Compared with a classical enzyme kinetics study, this method significantly speeds the target validation process and reduces time associated with assay development and high-throughput screening implementation.

Chromatography, Liquid↗
PubMed1990

Regulation of S-adenosyl-L-methionine decarboxylase by 1-aminooxy-3-aminopropane: enzyme kinetics and effects on the enzyme activity in cultured cells.

The kinetics of inactivation of adenosylmethionine decarboxylase of rat liver and of baby hamster kidney cells (BHK21/C31) by 1-aminooxy-3-aminopropane was studied. The apparent dissociation constants (Ki) for the hepatic and BHK21/C13 enzymes were 1.5 and 2.0 mM and the times of half-inactivation at infinite concentration of the inhibitor (tau 1/2) were 1.2 and 3.8 min, respectively. Treatment of BHK21/C13 with 0.5 mM 1-aminooxy-3-aminopropane prevented cell growth and depleted the cells of putrescine and spermidine within 1 day. The depletion of spermidine resulted in increased activity of S-adenosylmethionine decarboxylase which was due, at least partly, to the increase in the half-life of the enzyme activity. Because spermine levels were not significantly affected, it appears that spermidine is the principal feedback regulator of S-adenosylmethionine decarboxylase. So, 1-aminooxy-3-aminopropane is a very weak inhibitor of S-adenosylmethionine decarboxylase and the cellular effects can be correlated primarily with its inhibitory effects on ornithine decarboxylase and spermidine synthase. In cell-free systems, however, 1-aminooxy-3-aminopropane is likely to find use in unraveling the reaction mechanism of S-adenosylmethionine decarboxylase.

Adenosylmethionine Decarboxylase↗
PubMed1979

Convenient method for studying enzyme kinetics.

A convenient method for enzyme kinetic studies is introduced. The method includes identification of reaction mechanism and estimation of the associated kinetic constants with a minimum number of experiments. The application of the method is illustrated by using literature data. Factors limiting the application of this method are also discussed.

Binding, Competitive↗
PubMed2000

Influence of water activity and aqueous solvent ordering on enzyme kinetics of alcohol dehydrogenase, lysozyme, and beta-galactosidase.

Effects of the water activity (a(w)) and the solvent ordering, as determined by the activity coefficient of water, were investigated on the enzyme kinetics of alcohol dehydrogenase, lysozyme, and beta-galactosidase in various aqueous solutions. The water activity and the solvent ordering were adjusted by addition of electrolytes (NaCl, KCl, CsCl, etc.) or nonelectrolytes (sugars, alcohols, urea, etc.) at various concentrations. Although the enzyme kinetics were strongly dependent on a(w), a(w) was not a complete determinant of the enzyme behavior in aqueous solutions. Enzyme kinetics were also dependent on the solvent ordering. At a fixed a(w), all the enzyme kinetic parameters tested had a good correlation with the solvent ordering parameter as represented by the parameter alpha, an index of the deviation of the water state from the ideal solution, determined from the activity coefficient of water in solutions. Solvent ordering was expected to affect the enzyme kinetics through its effect on the hydrophobic interaction between the enzyme and the substrate and also on the thermal fluctuation.

Journal Article↗
PubMed1996

Model for magnetic field effects on radical pair recombination in enzyme kinetics.

A prototypical model for describing magnetic field effects on the reaction kinetics of enzymes that exhibit radical pair recombination steps in their reaction cycle is presented. The model is an extended Michaelis-Menten reaction scheme including an intermediate enzyme-substrate complex where a spin-correlated radical pair state exists. The simple structure of the scheme makes it possible to calculate the enzyme reaction rate explicitly by combining chemical kinetics with magnetic field-dependent spin kinetics (radical pair mechanism). Recombination probability is determined by using the exponential model. Simulations show that the size of the magnetic field effect depends on relations between different rate constants, such as 1) the ratio between radical pair-lifetime and the magnetic field-sensitive intersystem crossing induced by the hyperfine interaction and the delta g mechanisms and 2) the chemical rate constants of the enzyme reaction cycle. An amplification factor that is derived from the specific relations between the rate constants is defined. It accounts for the fact that although the magnetic field-induced change in radical pair recombination probability is very small, the effect on the enzyme reaction rate is considerably larger, for example, by a factor of 1 to 100. Model simulations enable a qualitative comparison with recent experimental studies reporting magnetic field effects on coenzyme B12-dependent ethanolamine ammonia lyase in vitro activity that revealed a reduction in Vmax/KM at low flux densities and a return to the zero-field rate or an increase at high flux densities.

Computer Simulation↗
PubMed2005

Characterization of the cytochrome P450 enzymes and enzyme kinetic parameters for metabolism of BVT.2938 using different in vitro systems.

An important step in the drug development process is identification of enzymes responsible for metabolism of drug candidates and determination of enzyme kinetic parameters. These data are used to increase understanding of the pharmacokinetics and possible metabolic-based drug interactions of drug candidates. The aim of the present study was to characterize the cytochrome P450 enzymes and enzyme kinetic parameters for metabolism of BVT.2938 [1-(3-{2-[(2-ethoxy-3-pyridinyl)oxy]ethoxy}-2-pyrazinyl)-2(R)-methylpiperazine], a potent and selective 5HT2c-receptor agonist. The enzyme kinetic parameters were determined for formation of three main metabolites of BVT.2938 using human liver microsomes and expressed cytochrome P450 (CYP) isoforms. The major metabolite was formed by hydroxylation of the pyridine ring (CL(int)=27 microl/mgmin), and was catalysed by both CYP2D6*1 and CYP1A1, with K(m) values corresponding to 1.4 and 2.7 microM, respectively. The results from enzyme kinetic studies were confirmed by incubation of BVT.2938 in the presence of the chemical inhibitor of CYP2D6*1, quinidine. Quinidine inhibited the formation of the major metabolite by approximately 90%. Additionally, studies with recombinant expressed CYP isoforms from rat indicated that formation of the major metabolite of BVT.2938 was catalysed by CYP2D2. This result was further confirmed by experiments with liver slices from different rat strains, where the formation of the metabolite correlated with phenotype of CYP2D2 isoform (Sprague-Dawley male, extensive; Dark Agouti male, intermediate; Dark Agouti female, poor metabolizer). The present study showed that the major metabolite of BVT.2938 is formed by hydroxylation of the pyridine ring and catalysed by CYP2D6*1. CYP1A1 is also involved in this reaction and its role in extra-hepatic metabolism of BVT.2938 might be significant.

Animals↗
PubMed1988

Enzyme kinetics for a two-step enzymic reaction with comparable initial enzyme-substrate ratios.

We extend the validity of the quasi-steady state assumption for a model double intermediate enzyme-substrate reaction to include the case where the ratio of initial enzyme to substrate concentration is not necessarily small. Simple analytical solutions are obtained when the reaction rates and the initial substrate concentration satisfy a certain condition. These analytical solutions compare favourably with numerical solutions of the full system of differential equations describing the reaction. Experimental methods are suggested which might permit the application of the quasi-steady state assumption to reactions where it may not have been obviously applicable before.

Enzymes↗