Kinetic determination of tight-binding impurities in enzyme inhibitors

A novel rate equation to characterize the dose-response behavior of a moderately potent ("classical") enzyme inhibitor contaminated with a very potent ("tight-binding") impurity is derived. Mathematical properties of the new rate equation show that, for such contaminated materials, experimentally observed I(50) values are ambiguous. The four-parameter logistic equation, conventionally used to determine I(50) values, cannot be used to detect the presence of tight-binding impurities in inhibitor samples. In contrast, fitting the newly derived rate equation to inhibitor dose- response curves can, in favorable cases, reveal whether the unknown material is chemically homogeneous or whether it is contaminated with a tight-binding impurity. The limitations of our method with respect to the detectable range of inhibition constants (both classical and tight-binding) were examined by using Monte-Carlo simulations. To test the new analytical procedure experimentally, we added a small amount (0.02 mole%) of a tight-binding impurity (K(i)=0.065 nM) to an otherwise weak inhibitor of human mast-cell tryptase (K(i)=50.4 microM). The resulting material was treated as "unknown." Our kinetic equation predicts that such adulterated material should show I(50)=0.40 microM, which was identical to the experimentally observed value. The best-fit value of the apparent inhibition constants for the tight-binding inhibitor was K(i)=(0.107+/-0.035)nM, close to the true value of 0.065 nM.     

Determination of the mechanism and kinetic constants for hog kidney gamma-glutamyltransferase.

The initial-velocity kinetics of hog kidney gamma-glutamyltransferase were studied. Glutamate gamma-(4-nitroanilide) and its 3-carboxy derivative, glutamate gamma-(3-carboxy-4-nitroanilide), served as gamma-glutamyl donors, and glycylglycine as an acceptor. Reaction products were identified by paper chromatography and amino acid analysis. Inhibited Ping Pong mechanisms and a comprehensive initial- velocity expression were developed which account for the observed simultaneous gamma-glutamyl transfer and autotransfer, competitive inhibition by glycylglycine, and non-competitive inhibition by the carboxy donor. The validity of the proposed Ping Pong mechanisms are supported by enzyme-velocity data obtained with constant ratios of acceptor to donor concentrations. Kinetic constants were determined by a non-linear regression analysis. With glutamate gamma-(4-nitroanilide) as the donor, Michaelis constants for the donor, acceptor and donor-acting-as-acceptor are 1.87, 24.9, and 2.08 mM respectively. With glutamate gamma-(3-carboxy-4-nitroanilide) as the donor, these Michaelis constants are 1.63, 16.6, and 12.3 mM. Glyclyglycine competitive inhibition constants with the parent donor and its carboxy derivative are 275 and 205 mM respectively; the non-competitive inhibition constant of the carboxy donor is 34 mM.     

Theoretical treatment of tight-binding inhibition of an enzyme. Ribonuclease inhibitor as special case.

A general treatment of very tight-binding inhibition is described. It was applied to purified endogenous RNAase inhibitor from rat testis. This treatment discriminates among the different types of inhibition and allows for calculation of the inhibition parameters. When very tight-binding inhibitions are studied at similar molar concentrations of both enzyme and inhibitor, a further approach is required. This is also described and applied to the RNAase inhibitor. A Ki value of 3.2 x 10(-12) M was found for this inhibitor protein. On the basis of this result, it was considered inappropriate to classify this type of inhibitor in terms of competitive or non-competitive, as has been done for such inhibitors so far. Functional consequences of this analysis are discussed for the RNAase-RNAase inhibitor system.     

Impact of enzyme concentration and residence time on apparent activity recovery in jump dilution analysis

Jump dilution analysis is commonly used to evaluate the reversibility of inhibition and to quantify the residence time of the inhibitor–enzyme complex. During hit and lead characterization, one sometimes observes apparently linear progress curves after jump dilution that display activity recoveries that are intermediate between those expected for fully reversible and irreversible inhibition. Computer simulations of progress curves after jump dilution indicate that seemingly linear progress curves can result when dealing with tight-binding inhibitors if substoichiometric concentrations of inhibitor are preincubated with enzyme. In this situation, the activity recovered is comparable to that expected for instantaneously reversible inhibitors. In addition, simulations demonstrate that intermediate values of activity recovery may be observed for compounds with modestly slow dissociation rates (i.e., residence times >0 min but ?20 min) when the attending curvature of the data is not accounted for. The observation of intermediate values of recovery can, thus, serve as an indication of either modest residence time or a contaminating inactivator within an inhibitor sample, in either case prompting greater scrutiny of the test compound.     

UDPglucose dehydrogenase. Kinetics and their mechanistic implications.

Initial velocity and product inhibition studies were carried out on UDP-glucose dehydrogenase (UDPglucose: NAD+ 6-oxidoreductase, EC 1.1.1.22) from beef liver to determine if the kinetics of the reaction are compatible with the established mechanism. An intersecting initial velocity pattern was observed with NAD+ as the variable substrate and UDPG as the changing fixed substrate. UDPglucuronic acid gave competitive inhibition of UDPG and non-competitive inhibition of NAD+. Inhibition by NADH gave complex patterns.Lineweaver-Burk plots of 1/upsilon versus 1/NAD+ at varied levels of NADH gave highly non-linear curves. At levels of NAD+ below 0.05 mM, non-competitive inhibition patterns were observed giving parabolic curves. Extrapolation to saturation with NAD+ showed NADH gave linear uncompetitive inhibition of UDPG if NAD+ was saturating. However, at levels of NAD+ above 0.10 mM, NADH became a competitive inhibitor of NAD+ (parabolic curves) and when NAD+ was saturating NADH gave no inhibition of UDPG. NADH was non-competitive versus UDPG when NAD+ was not saturating. These results are compatible with a mechanism in which UDPG binds first, followed by NAD+, which is reduced and released. A second mol of NAD+ is then bound, reduced, and released. The irreversible step in the reaction must occur after the release of the second mol of NADH but before the release of UDPglucuronic acid. This is apparently caused by the hydrolysis of a thiol ester between UDPglucoronic acid and the essential thiol group of the enzyme. Examination of rate equations indicated that this hydrolysis is the rate-limiting step in the overall reaction. The discontinuity in the velocities observed at high NAD+ concentrations is apparently caused by the binding of NAD+ in the active site after the release of the second mol of NADH, eliminating the NADH inhibition when NAD+ becomes saturating.     

The ribonuclease inhibitors from porcine thyroid and liver are slow, tight-binding inhibitors of bovine pancreatic ribonuclease A

Ribonuclease inhibitors were purified from the latent ribonuclease fractions of porcine thyroid and liver and used to test the hypothesis that their inhibition of bovine pancreatic ribonuclease A is correctly described by tight-binding rather than Michaelis-Menton kinetics. Both proteins were found to act as slow, tight-binding inhibitors of the enzyme. These steady-state velocities also showed that both the thyroid and liver inhibitors were competitive inhibitors of bovine pancreatic ribonuclease A with Ki's of 0.1 and 0.4 nM, respectively. In contrast to interpretations based on Michaelis-Menton assumptions that show non-competitive inhibition, these results suggest that an enzyme:inhibitor:substrate complex does not exist.     

High-throughput screening of enzyme inhibitors: automatic determination of tight-binding inhibition constants

Determination of tight-binding inhibition constants by nonlinear least-squares regression requires sufficiently good initial estimates of the best-fit values. Normally an initial estimate of the inhibition constant must be provided by the investigator. This paper describes an automatic procedure for the estimation of tight-binding inhibition constants directly from dose-response data. Because the procedure does not require human intervention, it was incorporated into an algorithm for high-throughput screening of enzyme inhibitors. A suitable computer program is available electronically (http://www.biokin.com). Representative experimental data are shown for the inhibition of human mast-cell tryptase.     

High-throughput screening of enzyme inhibitors: simultaneous determination of tight-binding inhibition constants and enzyme concentration

Active site titration by a reversible tight-binding inhibitor normally depends on prior knowledge of the inhibition constant. Conversely, the determination of tight-binding inhibition constants normally requires prior knowledge of the active enzyme concentration. Often, neither of these quantities is known with sufficient accuracy. This paper describes experimental conditions under which both the enzyme active site concentration and the tight-binding inhibition constant can be determined simultaneously from a single dose-response curve. Representative experimental data are shown for the inhibition of human kallikrein.     

A quick method for the determination of inhibition constants.

The inhibition constant Ki in the common case of competitive inhibition can be obtained by simple comparison of progress curves in the presence and in the absence of inhibitor. The difference between the times taken for the concentration of substrate to fall to the same value is used to obtain Ki. The procedure to use when the product inhibits is described. When there is mixed inhibition, reactions at different substrate concentrations are used to obtain both inhibition constants.     

Allosteric regulation of beef liver arginase activity by L-ornithine

Inhibition of beef liver arginase by L-ornithine was investigated with two sets of independent experiments. Progress curves of the production of urea were simulated with two integrated Michaelis-Menten equations for competitive and non-competitive inhibition by ornithine. Both fitted the curves well, but failed to correctly predict the inhibition when the reaction was started with ornithine already present. Measurement of initial rates of reaction enabled an allosteric model to be built in accordance to Monod-Wyman-Changeux: arginine preferentially binds to the active state R and ornithine preferentially binds to the inactive state T. In the absence of both ligands, the R in equilibrium T equilibrium slightly favours the active state and both states bind ornithine more strongly than arginine. No great variation was observed in the 6 parameters of the model by assuming the enzyme to be a trimer or a tetramer. The model was able to predict not only the initial rate curves, from which it was derived, but also the progress curves independently obtained.     

Analysis of progress curves by simulations generated by numerical integration.

A highly flexible computer program written in FORTRAN is presented which fits computer-generated simulations to experimental progress-curve data by an iterative non-linear weighted least-squares procedure. This fitting procedure allows kinetic rate constants to be determined from the experimental progress curves. Although the numerical integration of the rate equations by a previously described method [Barshop, Wrenn & Frieden (1983) Anal. Biochem. 130, 134-145] is used here to generate predicted curves, any routine capable of the integration of a set of differential equations can be used. The fitting program described is designed to be widely applicable, easy to learn and convenient to use. The use, behaviour and power of the program is explored by using simulated test data.     

Diagnosis of enzyme inhibition based on the degree of inhibition

In this work, a method for the diagnosis of kinetic inhibition, based on the dependence of the degree of inhibition (epsilon(i)) on the inhibitor concentration [I] and on the substrate concentration [S], is presented. Because the degree of inhibition is a ratio between rates, kinetic data are normalized by the introduction of an internal control-the rate of the uninhibited reaction. Therefore, the error associated with the kinetic measurements decreases and less experimental measurements are necessary to achieve the diagnosis. The process described, which uses graphical and/or non-linear fitting procedures, allows distinguishing between 20 different kinds of inhibition, including not only linear and hyperbolic, but also parabolic and rational 2,2 inhibitions. Rational 2,2 indicates a new type of inhibition corresponding to an incomplete parabolic inhibition, i.e. mechanistically it corresponds to an inhibitor that binds to two inhibition sites producing enzymatic complexes that are still active. In spite of its comprehensiveness, the diagnosis process is greatly facilitated by the division of the diagnosis of the inhibition in a step-by-step procedure, where only two rival models are evaluated in each step. In the non-linear fittings, the choice between rival models uses a test based on information statistics theory, the Akaike information criterion test, in order to penalize complex models that tend to be favoured in fittings. Finally, equations that allow the determination of inhibition kinetic constants were also deduced. The formalism presented was tested by examining inhibition of acid phosphatase by phosphate (a linear competitive inhibitor).     

A product-inhibition study of bovine liver glutamate dehydrogenase.

1. Initial rates of oxidative deamination of L-glutamate with NAD+ as coenzyme, and of reductive aminiation of 2-oxoglutarate with NADH as coenzyme, catalysed by bovine liver glutamate dehydrogenase were measured in 0.111 M-sodium phosphate buffer, pH 7, at 25 degrees C, in the absence and presence of product inhibitors. All 12 possible combinations of variable substrate and product inhibitor were used. 2. Strict competition was observed between NAD+ and NADH, and between glutamate and 2-oxoglutarate. All other inhibition patterns were clearly non-competitive, except for inhibition by NH4+ with NAD+ as variable substrate. Here the extrapolation did not permit a clear distinction between competitive and non-competitive inhibition. 3. Mutually non-competitive behaviour between glutamate and NH4+ indicates that these substrates can be bound at the active site simultaneously. 4. Primary Lineweaver-Burk plots and derived secondary plots of slopes and intercepts against inhibitor concentration were linear, with one exception: with 2-oxoglutarate as variable substrate, the replot of primary intercepts against inhibitory NAD+ concentration was curved. 5. Separate Ki values were evaluated for the effect of each product inhibitor on the individual terms in the reciprocal initial-rate equations. With this information it is possible to calculate rates for any combination of substrate concentrations within the experimental range with any concentration of a single product inhibitor. 6. The inhibition patterns are consistent with neither a simple compulsory-order mechanism nor a rapid-equilibrium random-order mechanism without modification. They can, however, be reconciled with either type of mechanism by postulating appropirate abortive complexes. Of the two compulsory sequences that have been proposed, one, that in which the order of binding is NADH, NH4+, 2-oxoglutarate, requires an implausible pattern of abortive complex-formation to account for the results. 7. On the basis of a rapid-equilibrium random-order mechanism, dissociation constants can be calculated from the Ki values. Where these can be compared with independent estimates from the kinetics of the uninhibited reaction or from direct measurements of substrate binding, the agreement is reasonable good. On balance, therefore, the results provide further support for the rapid-equilibrium random-order mechanism under these conditions.     

The 48 kDa Ca2+-binding protein of bovine brain.

The integrated rate equation for reactions with stoichiometry A----P + Q is: e0t = -Cf . ln(1-delta P/A0) + C1 delta P + 1/2C2(delta P)2 where the coefficients C are linear or quadratic functions of the kinetic constants and the initial substrate and product concentrations. I have used the 21 progress curves described in the accompanying paper [Cox & Boeker (1987) Biochem. J. 245, 59-65] to develop computer-based analytical and statistical techniques for extracting kinetic constants by fitting this equation. The coefficients C were calculated by an unweighted non-linear regression: first approximations were obtained from a multiple regression of t on delta P and were refined by the Gauss-Newton method. The procedure converged in six iterations or less. The bias in the coefficients C was estimated by four methods and did not appear to be significant. The residuals in the progress curves appear to be normally distributed and do not correlate with the amount of product produced. Variances for Cf, C1 and C2 were estimated by four resampling procedures, which gave essentially identical results, and by matrix inversion, which came close to the others. The reliability of C2 can also be estimated by using an analysis-of-variance method that does not require resampling. The final kinetic constants were calculated by standard multiple regression, weighting each coefficient according to its variance. The weighted residuals from this procedure were normally distributed.     

Inhibition of jack bean urease by 1,4-benzoquinone and 2,5-dimethyl-1,4-benzoquinone. Evaluation of the inhibition mechanism

1,4-benzoquinone (BQ) and 2,5-dimethyl-1,4-benzoquinone (DMBQ) were studied as inhibitors of jack bean urease in 50 mM phosphate buffer, pH 7.0. The mechanisms of inhibition were evaluated by progress curves studies and steady-state approach to data achieved by preincubation of the enzyme with the inhibitor. The obtained reaction progress curves were time-dependent and characteristic of slow-binding inhibition. The effects of different concentrations of BQ and DMBQ on the initial and steady-state velocities as well as the apparent first-order velocity constants obeyed the relationships of two-step enzyme-inhibitor interaction, qualified as mechanism B. The rapid formation of an initial BQ-urease complex with an inhibition constant of Ki = 0.031 mM was followed by a slow isomerization into the final BQ-urease complex with the overall inhibition constant of Ki* = 4.5 x 10(-5) mM. The respective inhibition constants for DMBQ were Ki = 0.42 mM, Ki* = 1.2 x 10(-3) mM. The rate constants of the inhibitor-urease isomerization indicated that forward processes were rapid in contrast to slow reverse reactions. The overall inhibition constants obtained by the steady-state analysis were found to be 5.1 x 10(-5) mM for BQ and 0.98 x 10(-3) mM for DMBQ. BQ was found to be a much stronger inhibitor of urease than DMBQ. A test, based on reaction with L-cysteine, confirmed the essential role of the sulfhydryl group in the inhibition of urease by BQ and DMBQ.     

Transient kinetic approach to the study of acetylcholinesterase reversible inhibition by eseroline

The kinetic rate constants for interaction of (-)-eseroline-(3aS-cis)-1,2,3,3a,8,8a-hexahydro-1,3a,8-trimethylpyrrolo-[2,3-b]indol-5-ol with electric eel acetylcholinesterase (EC 3.1.1.7, acetylcholine acetylhydrolase) were measured at a low substrate concentration according to a transient kinetic approach by using a rapid experimental technique. The measurements were carried out on a stopped-flow apparatus where pre-incubated samples of enzyme with various inhibitor concentrations were diluted with a buffer solution containing the substrate. The experimental data in the form of sigmoid-shaped progress curves were analysed by applying an explicit progress curve equation that described the time dependence of product released during the reaction. The kinetic parameters were evaluated by non-linear regression treatment and the values of the corresponding constants showed approximately the equal affinities of eseroline and eserine (cf. Stojan, J. and Zorko, M. (1997) Biochim. Biophys. Acta, 1337, 75-84.) for binding into the active centre of the enzyme. On the other hand, the kinetic rates for association and dissociation of eseroline were two grades of magnitude higher than those of eserine. The explanation appears to be a substantionally impaired gliding of eserine into the active site gorge by the great mobility of the carbamoyl tail as well as by its numerous possible interactions with the residues lining the gorge. Additionally, a study of the dependence of the transition phase information on the inhibitor concentration was carried out using our experimental data.     

Modulation of glucokinase by glucose, small-molecule activator and glucokinase regulatory protein: steady-state kinetic and cell-based analysis

GK (glucokinase) is an enzyme central to glucose metabolism that displays positive co-operativity to substrate glucose. Small-molecule GKAs (GK activators) modulate GK catalytic activity and glucose affinity and are currently being pursued as a treatment for Type 2 diabetes. GK progress curves monitoring product formation are linear up to 1 mM glucose, but biphasic at 5 mM, with the transition from the lower initial velocity to the higher steady-state velocity being described by the rate constant kact. In the presence of a liver-specific GKA (compound A), progress curves at 1 mM glucose are similar to those at 5 mM, reflecting activation of GK by compound A. We show that GKRP (GK regulatory protein) is a slow tight-binding inhibitor of GK. Analysis of progress curves indicate that this inhibition is time dependent, with apparent initial and final Ki values being 113 and 12.8 nM respectively. When GK is pre-incubated with glucose and compound A, the inhibition observed by GKRP is time dependent, but independent of GKRP concentration, reflecting the GKA-controlled transition between closed and open GK conformations. These data are supported by cell-based imaging data from primary rat hepatocytes. This work characterizes the modulation of GK by a novel GKA that may enable the design of new and improved GKAs.     

Inhibition of yeast inositol phosphorylceramide synthase by aureobasidin A measured by a fluorometric assay

Inositol phosphorylceramide synthase (IPC synthase) is an essential and unique enzyme in fungal sphingolipid biosynthesis and is the target of the cyclic nonadepsipeptide antibiotic aureobasidin A. As a first step towards understanding the mechanism of aureobasidin A inhibition, we developed a fluorometric HPLC assay for IPC synthase using the Saccharomyces cerevisiae enzyme and the fluorescent substrate analog 6-[N-(7-nitro-2,1, 3-benzoxadiazol-4-yl)amino]-hexanoyl ceramide (C(6)-NBD-cer). The kinetic parameters for C(6)-NBD-cer were comparable to those for the synthetic substrate N-acetylsphinganine used previously. Aureobasidin A acted as a tight-binding, non-competitive inhibitor with respect to C(6)-NBD-cer and had a K(i) of 0.55 nM.     

Equilibrium competition binding assay: inhibition mechanism from a single dose response

Inhibition of a receptor by a small-molecule compound in many cases is achieved via a competitive, uncompetitive or non-competitive mechanism. The receptor-inhibitor interaction is often probed through the displacement of a ligand in an equilibrium competition binding experiment. The previous solutions to receptor inhibition mechanisms were borrowed from steady-state enzyme inhibition mechanisms. The inhibition mechanism is determined by a visual inspection or a global fit of ligand dose response curves at a series of inhibitor concentrations. However these solutions only apply to situations when both the ligand and the inhibitor are not significantly depleted by the receptor. In most published equilibrium receptor binding studies, only the relative potency of the inhibitor is calculated. Ranking inhibitors tested under differing experimental conditions is often not possible. In the current paper, we offer exact mathematical solutions to uncompetitive and non-competitive inhibition, and demonstrate that in most cases both the inhibition mechanism and absolute potency of an inhibitor can be simultaneously determined from a single dose response of the inhibitor at a fixed concentration of the ligand. Therefore, an equilibrium competition assay provides a quick and facile method to determine the inhibition mechanism of a large number of inhibitors. The theory herein described is applicable to equilibrium competition binding experiments such as radioligand assays and fluorescence polarization assays.     

Transient Kinetic Approach to the Study of Acetylcholinesterase Reversible Inhibition by Eseroline

The kinetic rate constants for interaction of (?)-eseroline-(3aS-cis)-1,2,3,3a,8,8a-hexahydro-1,3a,8-trimethylpyrrolo-[2,3-b]indol-5-ol with electric eel acetylcholinesterase (EC 3.1.1.7, acetylcholine acetylhydrolase) were measured at a low substrate concentration according to a transient kinetic approach by using a rapid experimental technique. The measurements were carried out on a stopped-flow apparatus where pre-incubated samples of enzyme with various inhibitor concentrations were diluted with a buffer solution containing the substrate. The experimental data in the form of sigmoid-shaped progress curves were analysed by applying an explicit progress curve equation that described the time dependence of product released during the reaction. The kinetic parameters were evaluated by non-linear regression treatment and the values of the corresponding constants showed approximately the equal affinities of eseroline and eserine (cf. Stojan, J. and Zorko, M. (1997) Biochim. Biophys. Acta, 1337, 75-84.) for binding into the active centre of the enzyme. On the other hand, the kinetic rates for association and dissociation of eseroline were two grades of magnitude higher than those of eserine. The explanation appears to be a substantionally impaired gliding of eserine into the active site gorge by the great mobility of the carbamoyl tail as well as by its numerous possible interactions with the residues lining the gorge. Additionally, a study of the dependence of the transition phase information on the inhibitor concentration was carried out using our experimental data.