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.     

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.     

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.     

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.     

Inhibition of alkaline phosphatase by sialic acid.

The interaction of human organ alkaline phosphatases (orthophosphoric-monoester phosphohydrolases (alkaline optimum), EC 3.1.3.1) with sugars was studied. Hexosamines, N-acetylneuraminic acid (NANA or sialic acid), N-acetylmuramic acid and N-acetylglycolylneuraminic acid inhibited human organ alkaline phosphatase activities. Of these, sialic acid was the most effective inhibitor. The pH profiles for the enzymes in the absence and presence of sialic acid were similar. The sialic acid - enzyme complex was more heat stable than the free enzyme between 20 and 45 degrees C. Lineweaver-Burk plots of 1/v versus 1/S at various concentrations of sialic acid showed intersecting straight lines indicating that the mechanism of inhibition was a mixed type. The Ki value obtained from the plots of 1/v versus the square of sialic acid concentration was 0.07 mM for the hepatic, sialidase-treated hepatic, and intestinal alkaline phosphatases. The respective Hill coefficients varied somewhat with the alkaline phosphatase isoenzyme. Hyperbolic curves were obtained when the percentage of remaining activity was plotted against the substrate concentration at different concentrations of sialic acid. The Hill coefficient was lowered in the presence of sialic acid. The sialidase-treated hepatic enzymes used gave the most effective conversion. Partial denaturation of the enzyme with urea, or pronase digestion had a little if any effect on the sialic acid inhibition with constant time.     

Activity of gamma-glutamyl transferase of sheep cerebral cortex with respect to amino acids and glutathione]

gamma-glutamyl Transferase fron Sheep brain cortex capillaries was studied from the point of view of transport of aminoacids across blood brain barrier. Excess substrate inhibition was competitive and observed both with donor (glutathione) and various acceptors (methionine, alanine, tryptophan) but not with arginine. Excess glutathione inhibition of transfer reaction is concomitant with an increase of total reaction (transfer + hydrolysis + autotranspeptidation). With regard to aminoacids, the greater the K'm the stronger the inhibition. This inhibition is the result of formation of a dead complex. Lineweaver-Burk plots 1/v versus 1/[acceptor] give straight lines meeting at the same point, whereas 1/v verus 1/[donor] plots are roughly parallel for high aminoacid concentrations and become secant for the low ones. Replots of slopes vs. 1/[acceptor] are not linear: the lower the aminoacid affinity the more pronounced the slope replot curvature. Thus kinetic patterns are consistent with a branched ping-pong mechanism including a ternary complex (Enzyme-acceptor-H2O) at high or low relative concentration, which balances the two branches. The estimated value of kinetic parameters does not support the hypothesis of major implication of the enzyme in brain uptake of aminoacids.     

Reaction mechanism of 21S dynein ATPase from sea urchin sperm. I. Kinetic properties in the steady state

21S Dynein ATPase [EC 3.6.1.3] from axonemes of a Japanese sea urchin, Pseudocentrotus depressus, and its subunit fractions were studied to determine their kinetic properties in the steady state, using [gamma-32P]ATP at various concentrations, 5 mM divalent cations, and 20 mM imidazole at pH 7.0 and 0 degrees C. The following results were obtained. 1. 21S Dynein had a latent ATPase activity of about 0.63 mumol Pi/(mg . min) in 1 mM ATP, 100 mM KCl, 4 mM MgSO4, 0.5 mM EDTA, and 30 mM Tris-HCl at pH 8.0 and 25 degrees C. Its exposure to 0.1% Triton X-100 for 5 min at 25 degrees C induced an increase in the ATPase activity to about 3.75 mumol Pi/(mg . min) and treatment at 40 degrees C for 5 min also induced a similar activation. 2. The double-reciprocal plot for the ATPase activity of dynein activated by the treatment at 40 degrees C consisted of two straight lines, while that of nonactivated 21S dynein fitted a single straight line. 3. In low ionic strength solution, the Mg- and Mn-ATPase of 21S dynein showed substrate inhibition at ATP concentrations above 0.1 mM; the inhibition decreased with increasing ionic strength. Ca- and Sr-ATPase showed no substrate inhibition. 4. Both the Vmax and Km values of dynein ATPase decreased reversibly upon addition of about 40% (v/v) glycerol. In the presence of glycerol, the dynein ATPase showed an initial burst of Pi liberation. The apparent Pi-burst size was 1.0 mol/(10(6) g protein) and the true size was calculated to be 1.6 mol/1,250 K after correcting for the effect of Pi liberation in the steady state and the purity of our preparation. 5. One of the subunit fractions of 21S dynein which was obtained by the method of Tang et al. showed substrate inhibition and an initial burst of Pi liberation of 1.4 mol/(10(6) g protein) in the presence of 54% (v/v) glycerol.     

A graphical method for determining inhibition constants

A new simple graphical method is described for the determination of inhibition type and inhibition constants of an enzyme reaction without any replot. The method consists of plotting experimental data as (V–v)/v versus the inhibitor concentration at two or more concentrations of substrate, where V and v represent the maximal velocity and the velocity in the absence and presence of inhibitor with given concentrations of the substrate, respectively. Competitive inhibition gives straight lines that converge on the abscissa at a point where [I]?=??K_i. Uncompetitive inhibition gives parallel lines with the slope of 1/K’_i. For mixed type inhibition, the intersection in the plot is given by [I]?=??K_i and (V–v)/v?=??K_i/K’_i in the third quadrant, and in the special case where K_i?=?K’_i (noncompetitive inhibition) the intersections occur at the point where [I]?=??K_i and (V–v)/v?=??1. The present method, the “quotient velocity plot,” provides a simple way of determining the inhibition constants of all types of inhibitors.     

Estimation of kinetic parameters for substrate and inhibitor in a reaction with an enzyme sample containing different types of inhibitor

The method of kinetic analysis is developed to obtain the maximum velocity (V_m), the Michaelis constant (K_m) and the parameters characterizing the inhibitors in an impure enzyme reaction, contaminated with one of four types of inhibitor (competitive, noncompetitive, uncompetitive and mixed-type). Although the reaction rate decreases with the increasing concentration of the enzyme sample containing an inhibitor, the double-reciprocal plot of the rate against the sample concentration becomes linear. The slopes of these linear plots at several different concentrations of substrate provide K_m and the specific enzyme activity, which is proportional to V_m, in the sample. These linear straight lines intersect in a point, of which the coordinates give the unique parameters for the inhibitor. To prove the validity of this kinetic method, the model experiments were carried out with acetylcholinesterase and its inhibitors, phenyltrimethylammonium and trimethylammonium. The present method was applied to the measurement of the specific activity of galactosylceramide galactosidase in the mouse cerebral homogenate. In addition, a kinetic method is indicated for the inhibition of an enzymatic reaction by a contaminant which binds the substrate to reduce the fraction available to the enzyme.     

Temperature and pH dependence of mold α-galactosidase

The effect of temperature and pH on kinetic behavior of α-galactosidase of Mortierella vinacea was investigated on the hydrolysis of p-nitrophenyl-α-D -galactopyranoside (PNPG). A very unusual kinetic behavior was observed for the soluble α-galactosidase i.e., substrate inhibition diminished gradually with increasing temperature or near the neutral pH range, and the kinetics approached the ordinary Michaelis-Menten (MM) type. On the other hand, with decreasing temperature or in acidic pH range, substrate inhibition was accelerated. Therefore, Arrhenius plots based on the initial reaction rate did not give straight lines. Furthermore, the slope in the Arrhenius plot changed with substrate concentration, which would make the determination of a characteristic value using conventional methods meaningless. However, the Arrhenius plots of individual kinetic parameters in the rate equation resulted in straight lines in the temperature range 15 to 50°C. From this, the drastic change in kinetic behavior could be explained in connection with the temperature and pH dependence of kinetic parameters in the model. For mold pellets (whole-cell enzyme), however, the influence of temperature and pH was less apparent than that of soluble enzyme because of the limitation in intraparticle diffusion. By using the rate equation that was determined for soluble enzyme and the theoretically derived effectiveness factor, the overall reaction rate for mold pellets at various temperature and pH could be predicted to some extent.     

Action of amyloglucosidase on oxidised amylose

The Michaelis constant and maximal velocity of alpha-amylase-free amylo-glucosidase decrease with increasing periodate oxidation of amylose. These kinetic features have been explained on the basis of competitive inhibition by the oxidised non-reducing end of the (1→4)-α-d-glucan chain with the active centres of the enzyme. A kinetic model is proposed to demonstrate this special kind of inhibition where the concentration of inhibitor is directly proportional to the substrate concentration. The experimental data fitted this model, and the plots of 1/K_m and 1/V against the ratio or oxidised/unoxidised non-reducing end-groups were straight lines.     

Steady-state kinetic analysis for the reaction of ammonium and alkylammonium ions with methylamine dehydrogenase from bacterium W3A1

The steady-state kinetic mechanism for the reaction of n-alkylamines and phenazine ethosulfate (PES) or phenazine methosulfate (PMS) with methylamine dehydrogenase from bacterium W3A1 is found to be of the ping-pong type. This conclusion is based on the observations that 1/v versus 1/[methylamine] or 1/[butylamine] plots, at various constant concentrations of an oxidizing substrate, and 1/v versus 1/[PES] or 1/[PMS] plots, at various constant concentrations of a reducing substrate, are parallel. Additionally, the values of kcat/Km for four n-alkylamines are identical when PES is the oxidizing substrate, as were the kcat/Km values for four reoxidizing substrates when methylamine was the reducing substrate. Last, analysis of steady-state kinetic data obtained when methylamine and propylamine are presented to the enzyme simultaneously and PES and PMS are used simultaneously also supports the involvement of a ping-pong mechanism. The enzymic reaction with either methylamine or PES is dependent on the ionic strength, and the data indicate that each interacts with an anionic site on methylamine dehydrogenase. The presence of ammonium ion at low concentration activates the enzyme, but at high concentration this ion is a competitive inhibitor in the reaction involving methylamine and the enzyme. A complete steady-state mechanism describing these ammonia effects is presented and is discussed in light of the nature of the pyrroloquinoline quinone cofactor covalently bound to the enzyme.     

Phosphatidic acid synthesis in Escherichia coli

The kinetic properties of acyl-coenzyme A (CoA): l-alpha-glycerol-phosphate trans-acylase (EC 2.3.1.15) from Escherichia coli were studied. At 10 C, a temperature at which the reaction was proportional to time and enzyme concentration, the enzyme had an apparent K(m) of 60 mum for l-alpha-glycerol-phosphate. The curve describing the velocity of the reaction as a function of palmitoyl-CoA concentration was sigmoid but the plot of v(-1) versus [S](-3) gave a straight line. A K(m) of about 11 mum was calculated for palmitoyl-CoA. Adenosine triphosphate specifically inhibited the reaction, being a noncompetitive inhibitor in respect to l-alpha-glycerol phosphate. Inhibition only occurred with high concentrations of palmitoyl-CoA, and maximal inhibition was 60%.     

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

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

On porcine pancreatic alpha-amylase action: kinetic evidence for the binding of two maltooligosaccharide molecules (maltose, maltotriose and o-nitrophenylmaltoside) by inhibition studies. Correlation with the five-subsite energy profile

Hydrolysis of small substrates (maltose, maltotriose and o-nitrophenylmaltoside) catalysed by porcine pancreatic alpha-amylase was studied from a kinetic viewpoint over a wide range of substrate concentrations. Non-linear double-reciprocal plots are obtained at high maltose, maltotriose and o-nitrophenylmaltoside concentrations indicating typical substrate inhibition. These results are consistent with the successive binding of two molecules of substrate per enzyme molecule with dissociation constants Ks1 and Ks2. The Hill plot, log [v/(V-v)] versus log [S], is clearly biphasic and allows the dissociation constants of the ES1 and ES2 complexes to be calculated. Maltose and maltotriose are inhibitors of the amylase-catalysed amylose and o-nitrophenylmaltoside hydrolysis. The inhibition is of the competitive type. The (apparent) inhibition constant Kiapp varies with the inhibitor concentration. These results are also consistent with the successive binding of at least two molecules of maltose or maltotriose per amylase molecule with the dissociation constants Ki1 and Ki2. These inhibition studies show that small substrates and large polymeric ones are hydrolysed at the same catalytic site(s). The values of the dissociation constants Ks1 and Ki1 of the maltose-amylase complexes are identical. According to the five-subsite energy profile previously determined, at low concentration, maltose (as substrate and as inhibitor) binds to the same two sites (4,5) or (3,4), maltotriose (as substrate and as inhibitor) and o-nitrophenyl-maltoside (as substrate) bind to the same three subsites (3,4,5). The dissociation constants Ks2 and Ki2 determined at high substrate and inhibitor concentration are consistent with the binding of the second ligand molecule at a single subsite. The binding mode of the second molecule of maltose (substrate) and o-nitrophenylmaltoside remains uncertain, very likely because of the inaccuracy due to simplifications in the calculations of the subsite binding energies. No binding site(s) outside the catalytic one has been taken into account in this model.     

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.     

Kinetic analysis of LY320236: competitive inhibitor of type I and non-competitive inhibitor of type II human steroid 5alpha-reductase

Type I and type II steroid 5alpha-reductases (5alpha-R) catalyze the conversion of testosterone (T) to dihydrotestosterone (DHT). LY320236 is a benzoquinolinone (BQ) that inhibits 5alpha-R activity in human scalp skin (Ki(typeI)=28.7+/-1.87 nM) and prostatic homogenates (Ki(typeII)=10.6+/-4.5 nM). Lineweaver-Burk, Dixon, and non-linear analysis methods were used to evaluate the kinetics of 5alpha-R inhibition by LY320236. Non-linear modeling of experimental data evaluated V(max) in the presence or absence of LY320236. Experimental data modeled to the following equation 1v=+ fixing the In0c value equal to 1.0 or 0 are consistent with non-competitive or competitive inhibition, respectively. LY320236 is a competitive inhibitor of type I 5alpha-R (In0c=0, Ki=3.39+/-0.38, RMSE = 1.300) and a non-competitive inhibitor of type II 5alpha-R (In0c=1, Ki=29. 7+/-3.4, RMSE = 0.0592). These data are in agreement with linear transformation of the data using Lineweaver-Burk and Dixon analyses. These enzyme kinetic data support the contention that the BQ LY320236 is a potent dual inhibitor with differing modes of activity against the two known human 5alpha-reductase isozymes. LY320236 represents a class of non-steroidal 5alpha-R inhibitors with potential therapeutic utility in treating a variety of androgen dependent disorders.     

Inhibition of beta-lactamase of Bacillus licheniformis 749/C by compound PS-5, a new beta-lactam antibiotic.

By use of a new computer-assisted u.v.-spectrophotometric assay method, the kinetic parameters of the reaction catalysed by Bacillus licheniformis 749/C beta-lactamase were re-examined and the mode of inhibition of the enzyme by compound PS-5, a novel beta-lactam antibiotic, was studied with benzylpenicillin as substrate. (1) The fundamental assay conditions for the determination of Km and V were examined in detail with benzylpenicillin as substrate. In 0.1 M-sodium/potassium phosphate buffer, pH 6.8, at 30 degrees C, initial substrate concentrations of benzylpenicillin above 0.7 mM were very likely to lead to substrate inhibition. The Km value of the enzyme for benzylpenicillin at initial concentrations from 1.96 to 0.07 mM was calculated to be 97-108 microM. (2) The Km values of the enzyme for 6-aminopenicillanic acid, ampicillin and cephaloridine were found to be 25, 154-161 and 144-161 microM respectively. (3) Compound PS-5 was virtually unattacked by Bacillus licheniformis 749/C beta-lactamase. (4) The activity of the enzyme was diminished by compound PS-5, to extents depending on the duration of incubation and the concentration of the inhibitor. The rate of inactivation of the enzyme by compound PS-5 followed first-order kinetics. (5) In an Appendix, a new computer-assisted u.v.-spectrophotometric enzyme assay method, in which a single reaction progress curve of time-absorbance was analysed by the integrated Michaelis-Menten equation, was devised for the accurate and precise determination of the kinetic constants of beta-lactamase. For conversion of absorbance readings into molar substrate concentrations, the initial or final absorbance reading that was independent of the reaction time was used as the basis of calculation. In calculation of Km and V three systematic methods of data combination were employed for finer analysis of the reaction progress curve. A list of the computer program named YF6TAIM is obtainable from the author on request or as Supplementary Publication SUP 50100 (12 pages) from the British Library Lending Division, Boston Spa, Wetherby, West Yorkshire LS23 7BQ, U.K., on the terms indicated in Biochem. J. (1978) 169, 5.     

Kinetic analysis of enzyme systems with suicide substrate in the presence of a reversible competitive inhibitor, tested by simulated progress curves

The use of suicide substrates remains a very important and useful method in enzymology for studying enzyme mechanisms and designing potential drugs. Suicide substrates act as modified substrates for the target enzymes and bind to the active site. Therefore the presence of a competitive reversible inhibitor decreases the rate of substrate-induced inactivation and protects the enzyme from this inactivation. This lowering on the inactivation rate has evident physiological advantages, since it allows the easy acquisition of experimental data and facilitates kinetic data analysis by providing another variable (inhibitor concentration). However despite the importance of the simultaneous action of a suicide substrate and a competitive reversible inhibition, to date no corresponding kinetic analysis has been carried out. Therefore we present a general kinetic analysis of a Michaelis-Menten reaction mechanism with double inhibition caused by both, a suicide substrate and a competitive reversible inhibitor. We assume rapid equilibrium of the reversible reaction steps involved, while the time course equations for the reaction product have been derived with the assumption of a limiting enzyme. The goodness of the analytical solutions has been tested by comparison with the simulated curves obtained by numerical integration. A kinetic data analysis to determine the corresponding kinetic parameters from the time progress curve of the product is suggested. In conclusion, we present a complete kinetic analysis of an enzyme reaction mechanism as described above in an attempt to fill a gap in the theoretical treatment of this type of system.     

The method of Hill's coefficient calculation for the region of inhibition of an enzyme by excess of the substrate. Inhibition of phosphofructokinase by excess of ATP]

The new method for Hill's coefficient (nH) calculation in the region of substrate concentrations where the latter acts as an inhibitor has been developed. The method does not need preliminary determination of maximum value of enzyme reaction rate (V) for ascending branch of the plot of enzyme reaction rate versus substrate concentration and allows to avoid over-estimation of value of nH when the magnitude of optimal reaction rate is less than value of V. The literature data for inhibition of phosphofructokinase by excess of ATP are used for illustration of applicability of the suggested method of Hill's coefficient calculation.