A graphical method for determining inhibition parameters for partial and complete inhibitors.

A new simple graphical method is described for the determination of inhibition type and kinetic parameters of an enzyme reaction without any replot. The method consists of plotting experimental data as v/(vo--v) versus the reciprocal of the inhibitor concentration at different substrate concentrations, where v and vo represent the velocity in the presence and in the absence of the inhibitor respectively with a given concentration of the substrate. Partial inhibition gives straight lines that converge on the abscissa at a point away from the origin, whereas complete inhibition gives lines that go through the origin. The inhibition constants of enzymes and the reaction rate constant of the enzyme-substrate-inhibitor complex can be calculated from the abscissa and ordinate intercepts of the plot. The relationship between the slope of the plot and the substrate concentration shows characteristic features depending on the inhibition type: for partial competitive inhibition, the straight line converging on the abscissa at--Ks, the dissociation constant of the enzyme-substrate complex; for non-competitive inhibition, a constant slope independent of the substrate concentration; for uncompetitive inhibition, a hyperbola decreasing with the increase in the substrate concentration; for mixed-type inhibition, a hyperbola increasing with the increase in the substrate concentration. The properties of the replot are useful in confirmation of the inhibition mechanism.     

A linear equation that describes the steady-state kinetics of enzymes and subcellular particles interacting with tightly bound inhibitors

When an enzyme exhibits a high affinity for an inhibitor, the steady-state analysis of the mechanism is complicated by the non-linearity of normal dose-response plots or of reciprocal replots. It is shown here that dose-response measurements generate a linear plot of inhibitor concentration divided by degree of inhibition against velocity without inhibitor divided by velocity with inhibitor; the concentration of enzyme may be derived from the extrapolated intercept of such plots, and the mechanism of inhibition from replots of the variation of the slope with substrate concentration. The limiting cases where virtually all inhibitor molecules are bound or virtually all are free are described, together with the situation when a significant proportion of the substrate becomes bound. This type of analysis indicates that the inhibitors of oxidative phosphorylation, rutamycin and bongkrekic acid, are tightly bound to rat liver mitochondria.     

The kinetic mechanism of the hypothalamic progesterone 5 alpha-reductase

The kinetic mechanism of the hypothalamic NADPH-linked progesterone 5 alpha-reductase from female rats was determined to be equilibrium ordered sequential by initial velocity, product inhibition and dead-end inhibition studies. Analysis of the initial velocity data resulted in intersecting double reciprocal plots indicating a sequential mechanism (apparent Km (progesterone) = 95.4 +/- 4.5 nM; apparent Kia(NADPH) = 9.9 +/- 0.7 microM). The plot of 1/v vs 1/progesterone intersected on the ordinate which is consistent with an equilibrium ordered mechanism. Ordered addition of the substrates was also supported by product inhibition studies with NADP versus NADPH and NADP versus progesterone. NADP is a competitive inhibitor versus NADPH (apparent Kis = 4.3 +/- 1.3 microM) and a noncompetitive inhibitor versus progesterone (apparent Kis = 31.9 +/- 1.4 microM and apparent Kii = 145.4 +/- 15.5 microM). These inhibition patterns show that NADPH binds prior to progesterone. Taken together, these analyses indicate that the cofactor, NADPH, binds to the enzyme in rapid equilibrium and preferentially precedes the binding of progesterone.     

The kinetic mechanism of the anterior pituitary progesterone 5 alpha-reductase

An analysis of the kinetic mechanism of the microsomal NADPH-linked progesterone 5 alpha-reductase obtained from female rat anterior pituitaries was performed. Initial velocity, product inhibition and dead-end inhibition studies indicate that the kinetic mechanism for the progesterone 5 alpha-reductase is equilibrium ordered sequential. Analysis of the initial velocity data resulted in intersecting double reciprocal plots suggesting a sequential mechanism [apparent Km(progesterone) = 88.2 +/- 8.2 nM; apparent Kia(NADPH) = 7.7 +/- 1.1 microM]. Furthermore, the plot of 1/v vs 1/progesterone intersected on the ordinate which is indicative of an equilibrium ordered mechanism. Additional support for ordered substrate binding was provided by the product inhibition studies with NADPH versus NADP and progesterone versus NADP. NADP is a competitive inhibitor versus NADPH (apparent Kis = 7.8 +/- 1.0 microM) and a noncompetitive inhibitor versus progesterone (apparent Kis = 9.85 +/- 2.1 microM and apparent Kii = 63.2 +/- 12.5 microM). These inhibition patterns suggest that NADPH binds prior to progesterone. In sum, these kinetic studies indicate that NADPH binds to the microsomal enzyme in rapid equilibrium and preferentially precedes the binding of progesterone.     

pH-dependence of the triose phosphate isomerase reaction

1. Some kinetic properties of aspartate transcarbamoylase (EC 2.1.3.2), that had been purified approx. 20-fold from wheat germ, were studied. 2. A plot of enzyme activity against pH showed a low maximum at pH8.4 and a second, higher, maximum at pH10.5. A plot of percentage inhibition by 0.2mm-UMP against pH was approximately parallel to the plot of activity against pH, except that between pH6.5 and 7.5 the enzyme was insensitive to 0.2mm-UMP. 3. Kinetics were studied in detail at pH10.0 and 25 degrees C. In the absence of UMP, initial-rate plots were hyperbolic when the concentration of either substrate was varied. UMP decreased both V(max.) and K(m) in plots of initial rate against l-aspartate concentration, but the plots remained hyperbolic. However, UMP converted plots of initial rate against carbamoyl phosphate concentration into a sigmoidal shape, without significantly affecting V(max.). Plots of initial rate against UMP concentration were also sigmoidal. 4. The theoretical model proposed by Monod et al. (1965) gave a partial explanation of these results. When quasi-equilibrium conditions were assumed analysis in terms of this model suggested a trimeric enzyme binding the allosteric ligands, carbamoyl phosphate and UMP, nearly exclusively to the R and T conformational states respectively, and existing predominantly in the R state when ligands were absent. However, the values of the Hill coefficients for the co-operativity of each allosteric ligand were somewhat less than those predicted by the theory. 5. Some of the implications of these results are discussed, and the enzyme is contrasted with the well-known aspartate transcarbamoylase of Escherichia coli.     

Enzyme kinetics: partial and complete uncompetitive inhibition

A graphical method for analysing enzyme data to obtain kinetic parameters, to identify the types of inhibition and the enzyme mechanisms is described. The method consists of plotting experimental data as v/(V(0)-v) versus 1/(I) at different substrate concentrations. I is the inhibitor concentration; V(0) and v are the initial rates of enzyme reaction attained by the system in the presence of a fixed amount of substrate and in the absence and presence of inhibitor respectively. Complete inhibition gives straight lines that pass through the origin while partial inhibition gives straight lines that converge on the 1/I-axis at a point away from the origin. With uncompetitive inhibition the slopes of the lines decrease with increasing substrate concentration. The kinetic parameters K(m), K'(i) and beta (degree of partiality) can best be determined from respective secondary plots of slope and intercept versus reciprocal of substrate concentration.     

Mechanistic and kinetic studies of inhibition of enzymes

A graphical method for analyzing enzyme data to obtain kinetic parameters, and to identify the types of inhibition and the enzyme mechanisms, is described. The method consists of plotting experimental data as nu/(V0 - nu) vs 1/(I) at different substrate concentrations. I is the inhibitor concentration; V0 and nu are the rates of enzyme reaction attained by the system in the presence of a fixed amount of substrate, and in the absence and presence of inhibitor, respectively. Complete inhibition gives straight lines that go through the origin; partial inhibition gives straight lines that converge on the 1-I axis, at a point away from the origin. For competitive inhibition, the slopes of the lines increase with increasing-substrate concentration; with noncompetitive inhibition, the slopes are independent of substrate concentration; with uncompetitive inhibition, the slopes of the lines decrease with increasing substrate concentrations. The kinetic parameters, Km, Ki, Ki', and beta (degree of partiality) can best be determined from respective secondary plots of slope and intercept vs substrate concentration, for competitive and noncompetitive inhibition mechanism or slope and intercept vs reciprocal substrate concentration for uncompetitive inhibition mechanism. Functional consequencs of these analyses are represented in terms of specific enzyme-inhibitor systems.     

The kinetic mechanism and properties of the cytoplasmic acetoacetyl-coenzyme A thiolase from rat liver

1. Cytoplasmic acetoacetyl-CoA thiolase was highly purified in good yield from rat liver extracts. 2. Mg(2+) inhibits the rate of acetoacetyl-CoA thiolysis but not the rate of synthesis of acetoacetyl-CoA. Measurement of the velocity of thiolysis at varying Mg(2+) but fixed acetoacetyl-CoA concentrations gave evidence that the keto form of acetoacetyl-CoA is the true substrate. 3. Linear reciprocal plots of velocity of acetoacetyl-CoA synthesis against acetyl-CoA concentration in the presence or absence of desulpho-CoA (a competitive inhibitor) indicate that the kinetic mechanism is of the Ping Pong (Cleland, 1963) type involving an acetyl-enzyme covalent intermediate. In the presence of CoA the reciprocal plots are non-linear, becoming second order in acetyl-CoA (the Hill plot shows a slope of 1.7), but here this does not imply co-operative phenomena. 4. In the direction of acetoacetyl-CoA thiolysis CoA is a substrate inhibitor, competing with acetoacetyl-CoA, with a K(i) of 67mum. Linear reciprocal plots of initial velocity against concentration of mixtures of acetoacetyl-CoA plus CoA confirmed the Ping Pong mechanism for acetoacetyl-CoA thiolysis. This method of investigation also enabled the determination of all the kinetic constants without complication by substrate inhibition. When saturated with substrate the rate of acetoacetyl-CoA synthesis is 0.055 times the rate of acetoacetyl-CoA thiolysis. 5. Acetoacetyl-CoA thiolase was extremely susceptible to inhibition by an excess of iodoacetamide, but this inhibition was completely abolished after preincubation of the enzyme with a molar excess of acetoacetyl-CoA. This result was in keeping with the existence of an acetyl-enzyme. Acetyl-CoA, in whose presence the overall reaction could proceed, gave poor protection, presumably because of the continuous turnover of acetyl-enzyme in this case. 6. The kinetic mechanism of cytoplasmic thiolase is discussed in terms of its proposed role in steroid biosynthesis.     

Studies on the succinate dehydrogenating system. I. Kinetics of the succinate dehydrogenase interaction with a semiquindiimine radical of N,N,N',N'-tetramethyl-p-phenylenediamine.

1. The activities of the soluble reconstitutively active succinate dehydrogenase (EC 1.3.99.1) measured with three artificial electron acceptors, e.g. ferricyanide, phenazine methosulfate and free radical of N,N,N',N'-tetramethyl-p-phenylenediamine (WB), have been compared. The values estimated by extrapolation to infinite acceptor concentration using double reciprocal plots 1/v versus 1/[acceptor] are nearly the same for ferricyanide and phenazine methosulfate and about twice as high for the WB. 2. The double reciprocal plots 1/v versus 1/[succinate] in the presence of malonate at various concentrations of WB give a series of straight lines intercepting in the third quadrant. The data support the mechanism of the overall reaction, in which the reduced enzyme is oxidized by WB before dissociation of the enzyme-product complex. 3. The dependence of the rate of the overall reaction on WB concentration shows that only one kinetically significant redox site of the soluble succinate dehydrogenase is involved in the reduction of WB. 4. Studies of the change of V and Km values during aerobic inactivation of the soluble enzyme suggest that only 'the low Km ferricyanide reactive site' (Vinogradov, A.D., Gavrikova, E.V. and Goloveshkina, V.G. (1975) Biochem. Biophys, Res. Commun. 65, 1264--1269) is involved in reoxidation of the reduced enzyme by WB. 5. The pH dependence of V for the succinate-WB reductase reaction shows that the group of the enzyme with the pKa value of 6.7 at 22 degrees C is responsible for the reduction of dehydrogenase in the enzyme-substrate complex. 6. When WB interacts with the succinate-ubiquinone region of the respiratory chain, the double reciprocal plot 1/v versus 1/[WB] gives a straight line. The thenoyltrifluoroacetone inhibition of succinate-ubiquinone reductase or extraction of ubiquinone alter the 1/v versus 1/[WB] plots for the curves with a positive initial slope intercepting the ordinate at the same V as in the native particles. The data support the mechanism of succinate-ubiquinone reduction, in which no positive modulation of succinate dehydrogenase by ubiquinone exist in the membrane.     

Graphic presentation and analysis of inhibition data from ligand-binding experiments

One technique for the characterization of receptor subtypes involves measuring the inhibition of the binding of a radioligand which is not subtype selective by agonists or antagonists which are subtype selective. Although such data are routinely calculated using computer programs, it is often useful to have a graphical representation of the data. Until now, a "modified Scatchard" or "Hofstee" plot of the form P = -(P/I)(IC50) + 1 (where P is percentage inhibition and I is the inhibitor concentration) has been used. We describe an alternate plot of the form B = -(B X I)(1/IC50) + B0 (where B is the concentration of bound radioligand and B0 is the concentration of radioligand bound in the absence of the inhibitor). This method has the important advantage that the data need not be calculated as percentage inhibition which eliminates the error involved in the experimentally determined B0 value being included in the other values.     

Substrate inhibition in a human variant of hypoxanthine-guanine phosphoribosyltransferase

Hypoxanthine-guanine phosphoribosyltransferase from a young man with purine overproduction and decreased purine salvage in fibroblast cultures was found to have low activity at concentrations of purine substrates at which the enzyme from normal individuals showed near maximal activity. The low enzyme activity was not associated with changes in the values of the Km(app) and Vmax(app) for any of the enzyme substrates. However, the enzyme activity was susceptible to substrate inhibition by hypoxanthine and guanine. The values obtained for the true Km, true Vmax, and true Ki for hypoxanthine were 26 +/- 10 microM, 1761 +/- 382 microunits/mg of protein, and 80 +/- 20 microM, respectively. The pattern of the substrate inhibition, as seen on a plot of 1/v versus hypoxanthine concentration, was characteristic of that associated with the formation of a dead-end complex between the inhibitory substrate and an enzyme form with which it normally does not react. The nature of this enzyme form and that of the dead-end complex was determined from double inhibition experiments, which indicated that hypoxanthine interacted with an enzyme-PPi intermediate to form an enzyme-hypoxanthine-PPi dead-end complex. The trapping of the enzyme in this inactive form explains the low activity at high purine base concentrations. Further information as to the nature of the reaction mechanism was obtained from plots of the reciprocal of enzyme activity versus the reciprocal of PP-ribose-P concentration at different fixed hypoxanthine concentrations. A pattern characteristic of uncompetitive substrate inhibition was obtained. This is indicative of an ordered sequential binding of substrates on the enzyme; PP-ribose-P binding before hypoxanthine. Thus, the variant enzyme showed an ordered sequential reaction mechanism, with the inhibitory substrate forming a dead-end complex with an enzyme-PPi intermediate.     

氨基葡萄糖对酪氨酸酶的抑制作用

通过对酪氨酸酶催化底物L-DOPA反应速率的观察测定,研究了氨基葡萄糖（G-NH2）对酪氨酸酶的抑制作用。在反应液中加入50μL浓度为2.2 mg/mL G-NH2时（体系中G-NH2终浓度为36μg/mL）,酶抑制率为50%。GNH2对酪氨酸酶的抑制作用是个复杂的过程,酶反应呈先促进后抑制。分析酶抑制曲线Lineweaver-Burk双倒数图,得出G-NH2为混合抑制剂,进一步研究发现多巴醌生产量会减少,抑制类型是不可逆抑制。     

Some examples of the use of computer-produced contour plots in the fitting of enzyme rate equations to reaction-velocity measurements

The use of computer-based isotach plots, relating reaction velocity to simultaneous variation of two substrates or effectors of an enzyme, in producing estimates of the parameters of enzyme rate equations was investigated. The computer program (;SYMAP') incorporates an interpolation algorithm, and the superiority of this over visual estimation in producing interpolated velocity values for the estimation of parameter values by conventional double-reciprocal plots is described. The usefulness of the SYMAP program in monitoring the process of fitting data obtained by simultaneous changes in two experimental variables is also described. It is shown that if the residual errors are weighted by a procedure described elsewhere (Ottaway, 1971b, 1973), the percentage error of the computed velocity is distributed evenly over a plot which contains a 100-fold variation in the concentration of one substrate and a 500-fold variation in the concentration of Mg(2+), and in which the velocity of the reaction (that catalysed by NAD kinase) varies over a 60-fold range. The two-dimensional percentage error plot was used to assess the limits within which an incomplete inhibition equation is valid, and to detect a discrepancy in an expected good fit, caused by an impurity in one of the substrates.     

Regulatory properties of purified 3-phosphoglycerate dehydrogenase from Bacillus subtilis.

3-Phosphoglycerate dehydrogenase (3-phosphoglycerate:NAD oxidoreductase, EC. 1.1.1.95) was purified from Bacillus subtilis by conventional methods. The final preparation was homogeneous by electrophoretic analysis and had a sedimentation constant of 6.3 S. On the basis of gel filtration data the enzyme had a molecular weight of about 166000. The plot of velocity versus phosphoglycerate concentration was biphasic while similar plots for hydroxypyruvate phosphate and NADH were the conventional hyperbolic type. The enzyme was specifically inhibited by serine. The inhibition was time dependent, requiring several minutes incubation before a constant level of inhibition was achieved. Serine inhibition was of the "mixed type" with respect to 3-phosphoglycerate and Hill plots of these data had slopes that approached 2. Desensitization of the enzyme to serine inhibition was achieved by incubation in the absence of dithiothreitol. The desensitized enzyme was different from the native enzyme in fluoresence properties, sedimentation characteristics and in the absence of the biphasic phosphoglycerate saturation curve. Evidence was obtained for the participation of sulphydryl groups in the changes in protein structure responsible for serine inhibition as well as the dehydrogenase activity of the enzyme.     

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.     

Brain region differences and some characteristics of monoamine oxidase type a and b activities in the vervet monkey

Monoamine oxidase in the vervet monkey showed greater variations in activity in six brain regions when tyramine or phenylethylamine was used as the substrate (3.8- to 4.1-fold differences) than when serotonin was the substrate (1.8-fold differences). With phenylethylamine and tyramine as substrates, the highest MAO specific activities were found in the hypothalamus and the lowest in the cerebellum and cortex. With serotonin as the substrate, the highest specific activities were in the mesencephalon and cortex. The inhibition of tyramine deamination by clorgyline and deprenyl yielded biphasic plots indicative of the presence of MAO-A and MAO-B enzyme forms in the vervet brain. On the basis of these inhibitor curves, the vervet brain could be estimated to contain approximately 85% MAO-B and 15% MAO-A, in contrast to rat brain which contains 45% MAO-B and 55% MAO-A. The inhibition of serotonin deamination by deprenyl in vervet brain yielded a biphasic plot, suggesting that some serotonin deamination in the vervet is accomplished by the MAO-B enzyme form. Estimations of the relative amounts of MAO-A and MAO-B based on inhibitor curves or based on substrate ratios yielded proportionate results which were in close agreement across the different brain regions, supporting the validity of these approaches to estimating MAO-A and MAO-B activities.     

A method of graphically analyzing substrate-inhibition kinetics

A model of substrate inhibition for enzyme catalysis was extended to describe the kinetics of photosynthetic production of ethylene by a recombinant cyanobacterium, which exhibits light-inhibition behavior similar to the substrate-inhibition behavior in enzyme reactions. To check the validity of the model against the experimental data, the model equation, which contains three kinetic parameters, was transformed so that a linear plot of the data could be made. The plot yielded reasonable linearity, and the parameter values could be estimated from the plot. The linear-plot approach was then applied to other inhibition kinetics including substrate inhibition of enzyme reactions and inhibitory growth of bacteria, whose analyses would otherwise require nonlinear least-squares fits or data measured in constrained ranges. Plots for three totally different systems all showed reasonable linearity, which enabled visual validation of the assumed kinetics. Parameter values evaluated from the plots were compared with results of nonlinear least-squares fits. A normalized linear plot for all the results discussed in this work is also presented, where dimensionless rates as a function of dimensionless concentration lie in a straight line. The linear-plot approach is expected to be complementary to nonlinear least-squares fits and other currently used methods in analyses of substrate-inhibition kinetics. Copyright 1999 John Wiley & Sons, Inc.     

Differential effects of manganese ions on Blastocladiella emersonii adenylate cyclase.

Adenylate cyclase (ATP pyrophosphate-lyase (cyclizing), EC 4.6.1.1) activity in Blastocladiella emersonii is associated with particulate subcellar fractions. Solubilization after treatment with detergent suggests its localization in a membrane fraction of the zoospore homogenate. The enzyme specifically requires Mn2+ for activity and is not stimulated by NaF. The kinetic characteristics of substrate utilization by B. emersonii adenylate cyclase were investigated with various concentrations of ATP and Mn2+, and in the presence of inhibitors. Plots of enzyme activity versus the actual concentration of the MnATP2- complex give sigmoid curves. An excess of Mn2+ activates the enzyme at low concentrations of substrate and leads to a modification of the enzyme kinetics. The nucleotides 5'-AMP and GTP were shown to be competitive inhibitors of the enzyme. In addition, kinetic data, obtained under conditions in which an inhibitor (ATP) is added in constant proportion to the variable substrate (MnATP2-) concentration, produced reciprocal plots that were linear and intersecting to the right of the ordinate, and secondary replots that were hyperbolic. These kinetic patterns support a model in which: MnATP2- is the substrate; free Mn2+ is an activator at low substrate concentrations, but an inhibitor at high substrate concentrations; and free ATP is not an efficient inhibiyor (Ki greater than 1.10(-4) M).     

Time-dependent inhibition of sucrose sweetness with gymnemic acid: Mode of action

A time-dependent study of the sweet response of sucrose allows a Lineweaver-Burk type of plot (reciprocal of magnitude estimation rate versus reciprocal of sucrose concentration) to be obtained, from which considerable deviation is observed after inhibition of sweetness with gymnemic acid. The plots after inhibition do not appear to be analogous to any of the known forms of competitive, uncompetitive or non-competitive inhibition of enzyme kinetics. Rather a “mixed-type” of inhibition is suggested, combining the attributes of competitive and non-competitive inhibition.     

A new plot for the kinetic analysis of dead-end enzyme inhibitors

A new procedure to characterize reversible dead-end inhibitors is presented. Preliminary identification of the inhibitor type is made by plotting vo/vi against the inhibitor concentration at different substrate concentrations. The inhibition constants for competitive, uncompetitive and mixed dead-end inhibitors are determined by secondary plots of l/(slope) vs [S], l/(slope) vs l/[S] and (slope)(Ks + [S] vs [S] respectively. These secondary plots render straight lines only for their corresponding type of inhibitor. For noncompetitive inhibitors all the secondary plots used yield straight lines. Therefore, the application of this plotting procedure leads to unambiguous diagnosis of the inhibitor type. An important feature of the procedure presented here is that the variable used (vo/vi) is independent on Vmax values. Therefore, experimental values obtained from enzyme preparations showing significant differences in their specific activities -i.e. enzyme coming from different purification steps- can be used.