Lineweaver-Burk,Hanes, Eadie-Hofstee and Dixon plots in non-steady-state situations

Lineweaver-Burk, Hanes, Eadie-Hofstee and Dixon plots can only be used when a true initial rate is measured. Despite the fact that this point has often been stressed, it is far too often ignored in favour of restricting the assay time to one where low amounts of substrate are used. When one or several irreversible and slow steps occur with an inactivator during the incubation of a ternary enzyme-substrate-inactivator mixture, the rate of the enzyme-catalysed reaction progressively decreases. Even under these conditions, the present computer simulations investigations show that apparently linear Lineweaver-Burk, Hanes, Eadie-Hofstee and Dixon graphs can be obtained when the amount of product formed is mistakenly assumed to represent the true initial rate. Moreover, the observed pattern can change with time, going for instance from non-competitive to competitive. “Ki's” measured under these conditions also vary with time and bear little relationship to the true constants involved in the interaction.     

Urethane as an inhibitor of the firefly light reaction

A study has been made to test the hypothesis that general anesthetics such as urethane are able to inhibit light from a firefly reaction mixture. Urethane was found to reduce light emission in a dose-dependent manner, the minimal effective concentration being about 20 mM. Dixon plots gave a Ki value in the range of 175 to 215 mM. Lineweaver-Burk plots showed that urethane increases the apparent Km for ATP and reduces Vmax for the reaction. This is taken to mean that urethane acts as both a competitive and non-competitive inhibitor of the firefly light reaction (mixed-type inhibition).     

Mixed-Type Inhibition of Pulmonary Angiotensin I-Converting Enzyme by Captopril,Enalaprilat and Ramiprilat

Abstract

We have compared at the enzymological level pulmonary angiotensin I-converting enzymes (ACE) purified to electrophoretic homogeneity from four mammalians species: pig, rat, monkey and human. Using both substrates hippuryl-histidyl-Ieucine and furylacryloyi-phenylal-anyl-glycyi-glycine in steady-state conditions, all the ACES exhibited Michaelis kinetics with identical Michaelis constants, maximal velocities, optimal pH and optimal activating chloride-concentrations. The apparent inhibitory constant was higher for Captopril than for Enalaprilat and even more so for Ramiprilat irrespective of the origin of ACE and the substrate used. Although these inhibitors have been described as competitive inhibitors, Lineweaver-Burk plots were not in accordance with a simple competitive model; moreover, Dixon plots were rather characteristic of non-competitive inhibition. These data emphasize the hypothesis that ACE inhibitors act with mixed-type inhibition, which is consistent with their slow-tight binding to the ACE active center, also with binding of chloride on a critical lysine residue leading to a potential conformational change, and finally with the fact that ACE has two domains, each bearing one catalytic site. On the other hand, as identical kinetic parameters were obtained on the different ACE preparations, results from animal models should allow the extrapolation to humans, in particular for investigations on both renin-angiotensin and kallikrein-kinin systems, and on their inhibition.     

Resolution of multiple forms of bovine liver arginase by chromatofocusing

1. Bovine liver arginase could be resolved into three distinct peaks by chromatofocusing in the pH range 7-4. 2. In other experimental systems the enzyme appeared to consist of a single active component. 3. Sodium dodecylsulphate-polyacrylamide gel electrophoresis revealed a single band which could be assigned to arginase, with no indication of inherent or protease-induced multiplicity. 4. Lineweaver-Burk plots for arginine were linear over a wide concentration range, as were Dixon plots for reversible inhibitors. 5. Covalent inhibition by 1-ethyl-3-(3-dimethylaminopropyl)-carbodiimide gave semilogarithmic plots of residual activity vs time which were strictly linear. 6. It was concluded that the enzyme was homogeneous with respect to subunit size and kinetic behaviour, but heterogeneous with respect to molecular charge. 7. The charge heterogeneity may have kinetic and regulatory implications, as previously suggested for mouse liver arginase [Z. Spolarics and J. S. Bond (1988) Archs Biochem. Biophys. 260, 469-479].     

Acetylcholinesterase. I. Kinetic aspects of interaction with reversible effectors]

Interaction of an effector M with acetylcholinesterase (EC 3.1.1.7) according to the model of Krupka and Laidler was analysed. Some usual functions of [M] : 1/VM, [(VO/VM)-1]/[M] (where VO and VM are the steady state rates in the absence and in the presence of modifiers, respectively), vertical intercept 1/VM, slope KM/VM and absolute value of reciprocal horizontal intercept KM of Lineweaver-Burk plots are investigated and corresponding plots described. It is particularly shown that if Dixon plots are curves concave downwards, plots of [VO/VM)-1]/[M] and 1/VM against [M] are hyperbolas concave upwards and downwards respectively. If Dixon plots are curves concave upwards, plots of [(VO/VM)-1]/[M] and 1/VM versus [M] are hyperbolas concave downwards and upwards respectively. Moreover plots of KM/VM against [M] are linear. However, this model does not explain some observations, under conditions of high ionic strength (gamma/2 greater than or equal to 0,1), where Dixon plots are curves concave upwards, plots of [VO/VM)-1]/[M] versus [M] strainght lines, the plot of 1/VM against [M] is a straight line or a curve concave upwards of positives slopes and the plot of KM/VM versus [M] a curve of positive slope concave upwards. These experimental data might be interpreted by an extension of the preceding model to a mechanism with two enzymatic binding sites under kinetic conditions that are determined.     

Isolation and cholinesterase-inhibition studies of sterols from Haloxylon recurvum

Haloxysterols A-D (1-4), new C-24 alkylated sterols, have been isolated from the chloroform soluble fraction of Haloxylon recurvum, along with five known sterols 5-9, which are reported for the first time from this species. Their structures were determined by means of 1D- and 2D-NMR techniques. Compounds 1-9 inhibited cholinesterase enzymes in a concentration-dependent manner with K(i) values ranging between 0.85-25.5 and 1.0-19.0 microM against acetylcholinesterase (AChE; EC 3.1.1.7) and butyrylcholinesterase (BChE; EC 3.1.1.8) enzymes, respectively. Lineweaver-Burk, Dixon plots and their secondary replots indicated that compounds 1-9 are non-competitive inhibitors of both AChE and BChE enzymes.     

Inositolphospholipid-accelerated activation of prekallikrein by activated factor XII and its inhibition by beta 2-glycoprotein I

Inositolphospholipid-accelerated activation of prekallikrein by alpha-factor XIIa was determined by measuring the appearance of kallikrein amidolytic activity towards the chromogenic substrate, D-prolyl-phenylalanyl-arginyl p-nitroanilide (S-2302). The activation reaction did not exhibit normal Michaelis-Menten kinetics. The Hill coefficient was found to be 1.6 indicating that the activation followed an allosteric reaction mechanism. The temperature dependence of the reaction showed a thermal transition at 30 degrees C, which in addition to the allosteric reaction mechanism is indicative of a conformational change of prekallikrein following binding to the inositolphospholipid. The reaction exhibited pH optimum at pH 7.2 and ionic strength optimum at 50 mM NaCl. At optimal conditions the apparent KA value and the kcat/KA value for factor XIIa on prekallikrein were calculated to be 73 nM and 9.3 x 10(6) s-1 M-1, respectively. Kinetic constants could not be calculated at salt concentrations higher than the optimal concentrations, as Lineweaver-Burk plots were curvilinear in agreement with the Hill coefficient greater than unity. The activation was inhibited competitively by beta 2-glycoprotein I with a Ki value of 77 nM as determined by the Dixon plot.     

Kinetics of the two-sited enzyme. II. A method of distinguishing between anticooperative and independent active sites based on competitive inhibition

The presence of two active sites on an enzyme leads to downwardly curving Lineweaver-Burk plots if (A) the sites are independent, but have different Michaelis constants, or (B) if the sites interact anticooperatively to impair binding, but not catalysis, at the second site filled. Cases A and B are kinetically indistinguishable when only enzyme and substrate are present. However, equations derived by the rapid-equilibrium treatment show that the two cases have different patterns of competitive inhibition and become distinguishable in the presence of a suitable inhibitor. The inhibitor may decrease or increase the curvature of Lineweaver-Burk plots, but certain patterns have diagnostic value because they can occur only in case (B).In one type of diagnostic pattern, high concentrations of inhibitor cause the Lineweaver-Burk plots to curve upward, and cause the corresponding saturation curves to become sigmoid. The effect of the inhibitor is thus to make sites which are anticooperative appear to be cooperative. This suggests that the mere occurrence of sigmoid saturation curves is not necessarily evidence of cooperative binding effects, and may have uncertain significance in considerations of enzyme regulation.     

Effect of temperature and pH on phosphate transport through brush border membrane vesicles in rats

The kinetics of sodium gradient dependent phosphate uptake by the renal brush border membrane vesicles of the rat have ben studied under various conditions of temperature and pH. From 7 to 30 degrees C the Lineweaver-Burk plots are linear, and the apparent Km progressively increases from 54 to 91 microM. Above 30 degrees C, the apparent Km continues to increase to reach 135 microM at 40 degrees C, but a break is observed in the Lineweaver-Burk plots at the substrate concentration of 300 microM. The existence of this break, confirmed by the Eadie-Hofstee plot supports the hypothesis of a dual mechanism of phosphate transport, one for low concentrations of substrate with a Km of 100 microM and the other for high concentrations with a Km of approximately 240 microM. When the two components of the Eadie-Hofstee plot are analyzed according to a nonlinear regression program, these two values of Km become 70 microM and 1.18 mM, respectively. The Vmax continuously increases with temperature. However, the Arrhenius plot (In Vmax vs. 1/TK) shows an abrupt discontinuity at 23 degrees C. pH experiments were performed at 35 degrees C. In the absence of a proton gradient, increasing the pH from 6.5 to 7.5 and 8.5 decreases the apparent Km from 341 to 167 and 94 microM, respectively. When only the divalent form of phosphate is considered as the substrate, the apparent Km does not vary anymore with the pH and remains around the mean value of 105 microM. The uniformity of the apparent Km for the total phosphate uptake, when only the divalent phosphate is considered as being the substrate, suggests that this divalent form is the only one which is transported. Whatever the substrate considered, total phosphate or divalent phosphate, the highest Vmax is obtained at pH 7.5 which probably approximates the optimum pH inside the vesicles for the phosphate uptake.     

Modification of sarcoplasmic reticulum adenosine triphosphatase by adenosine triphosphate magnesium

Lineweaver-Burk plots of Ca²⁺-activated adenosine triphosphatase from rabbit muscle sarcoplasmic reticulum have been determined for a wide range of substrate concentrations. The plots measured at constant Mg²⁺ concentrations are normally nonlinear, but approach linearity either as the sarcoplasmic reticulum ages, or when small quantities of Triton-X100 are added. Titration with N-ethylmaleimide has the same effect on the activity of the ATPase measured either at high or low substrate concentrations. Lineweaver-Burk plots measured under conditions where the Mg²⁺ concentration is varied so as to be always equal to the ATP concentration are linear. These results have been interpreted as evidence that the adenosine triphosphatase has a single active site which uses MgATP as its substrate and which can be modified by free Mg²⁺.     

The effects of hydrogen ion concentration on the simplest steady-state enzyme systems

Laidler (1955) showed that consideration of the effect of pH on enzymic mechanisms that obey steady-state kinetics leads to the inclusion in the equations of a ;perturbation term' that can introduce curvature into the Lineweaver-Burk plots. He also stated conditions in which this term vanishes. This term can lead to apparent activation by substrate. Further, several cases are shown in which simplification, but not disappearance, of the perturbation term can lead to linearity of Lineweaver-Burk plots. These cases arise when the ionization of groups at the active site either is unaffected or is completely prevented when the enzyme-substrate complex is formed. It is also shown that V((app.)) can vary with pH without a concomitant change in K(m(app.)) in certain cases that obey steady-state kinetics without implying that K(m)=K(s). When the perturbation term is significant, Dixon's (1953) rules for the calculation of pK values will not always apply.     

Renin inhibition activity by chitooligosaccharides

Six kinds of chitooligosaccharides (COSs) with different molecular weight (MW) and degree of deacetylation (DD) were prepared using ultrafiltration membrane reactor, and their renin inhibition modes were evaluated. All the COSs showed the renin-inhibitory activities with dose-dependent manner, and 90-COSs had the potent renin-inhibitory activity than that of 50-COSs. Among them, 90-MMWCOS (1000-5000Da) exhibits the highest activity with IC(50) value of 0.51mg/mL and acts as competitive inhibitor with K(i) value of 0.28mg/mL by Lineweaver-Burk and Dixon plots. These results indicated that DD value and MW of COSs are important factors affecting renin-inhibitory activity.     

Double inhibition of L-threonine dehydratase by aminothiols

The inhibition of highly purified rat liver L-threonine dehydratase (L-threonine hydro-lyase (deaminating), EC 4.2.1.16) by aminothiols (L-cysteine, D-cysteine, cysteamine) has been studied. Single inhibition experiments evaluated by Lineweaver-Burk and Dixon plots showed, in a given concentration range, partially (parabolic) competitive inhibitions, indicating two binding sites for each inhibitor. Double inhibition experiments revealed that the inhibition was antagonistic, the two inhibitors weakening each other's effect. Formation of EI1 and EI2 binary complexes, and ESI1, ESI2 and EI1I2 ternary complexes was demonstrated, while formation of the quaternary complex ESI1I2 was ruled out. It is assumed that one inhibitor-binding site coincides with the substrate-binding center while the second inhibitor-binding (allosteric, regulatory) site may comprise the pyridoxal-phosphate-binding SH group(s). The comparison between Km and Ki values and the evaluation of intracellular concentrations of L-threonine, L-cysteine and cysteamine suggest a possible physiological role of the inhibition.     

Biologically active polymer supports based on cellulosic derivatives: synthesis and kinetic study

Bioactive cellulose derivatives have been synthesised by coupling enzymes/antibiotics on carboxymethyl cellulose acid chloride and cellulose carbonate. The effect of pH and temperature on the enzymatic activity of amyloglucosidase immobilised on cellulose carbonate was studied. Michaelis-Menten kinetics have been obeyed to the first degree of approximation despite the restricted mobility of the attached enzyme on the polymer support. Lineweaver-Burk plots for the amyloglucosidase immobilized on carboxymethyl cellulose acid chloride at ambient pH with cellulose carbonate at pH 8 have also been plotted. The Michaelis-Menten constant for the immobilized amyloglucosidase on cellulose carbonate at pH 8 was 9.1 mM, and the activation energy for starch hydrolysis was 21.8 kcals/mole.     

Mechanism of inhibition of purified leaping mullet (Liza saliens) NADPH-cytochrome P450 reductase by toxic metals: aluminum and thallium

Aluminum and thallium may reach life-threatening levels in aquatic systems in the near future because of their extensive use in various industrial fields. It is therefore important to study the mechanism of toxicity of aluminum and thallium on fish enzymes. To this aim, the effects of aluminum and thallium on the activity of purified leaping mullet (Liza saliens) cytochrome P450 reductase, an essential component of the important cytochrome P450 system, have been studied. Results indicated that both metal ions strongly inhibited the NADPH-cytochrome P450 reductase. The IC50 values of AlCl3 and TlCl3 were estimated to be 34 microM and 3 microM, respectively. The Lineweaver-Burk plot and Dixon plot revealed that both metal ions noncompetitively inhibited the purified mullet cytochrome P450 reductase. The K(i) values of Al3+ and Tl3+ were calculated from Dixon plots as 8.9 and 5.6 microM, respectively. The inhibitory effects of Al3+ and Tl3+ on purified cytochrome P450 reductase were partially recovered by 1 mM EDTA. Additionally, tin and magnesium were shown to have no apparent effect on purified mullet cytochrome P450 reductase.     

Estimating Kinetic Parameters when the Amount of Enzyme Added to an Assay Is Not a Controlled Variable: NITROGENASE ACTIVITY OF INTACT LEGUMES

Reliable estimates of Michaelis constants (K_m) and inhibitor constants may be obtained, in the absence of control over the amount of enzyme being added to any assay system, provided the following constraints are met. Michaelis-Menten kinetics are obeyed. Two rate measurements must be made with the same sample of enzyme: at low and high substrate concentration for determining K_m or minus and plus an inhibitor for determining inhibitor constants. The Michaelis constant may be calculated from the equation [Formula: see text] Inhibitor constants are derived graphically from Lineweaver-Burk or Dixon plots, once the K_m has been calculated. The above technique has been applied to study of the acetylene-reducing ability of intact legume plants. The apparent K_m for acetylene reduction by nitrogenase in legume nodules is ~1/100 atmosphere in the absence of nitrogen and ~1/40 atmosphere in its presence.     

Lung microsomal p-nitrophenol hydroxylase -- characterization and reconstitution of its activity

1. Formation of catechols from benzene and nitrobenzene have been implicated in the carcinogenic activity of these chemicals. In liver, p-nitrophenol, an intermediate of p-nitrobenzene is enzymatically converted to 4-nitrocatechol. 2. For the first time in this study, the presence of a highly active enzyme catalyzing the formation of 4-nitrocatechol from p-nitrophenol was detected in lung microsomes. The average specific activity of lung p-nitrophenol hydroxylase was found to be 0.494 nmol 4-nitrocatechol formed mg prot-1 min-1. 3. The optimum conditions for sheep lung microsomal p-nitrophenol hydroxylase were established. The maximal activity was noted at pH 6.8. The rate of p-nitrophenol hydroxylation was linear up to 2 mg prot/ml of incubation mixture. The maximal rate of 4-nitrocatechol formation was observed with 0.25 mM p-nitrophenol. 4. The Lineweaver-Burk and Eadie-Hofstee plots were found to be curve-linear. Two different Km values were calculated as 11.6 and 71.4 microM from the Lineweaver-Burk plot and as 10.7 and 74.5 microM from the Eadie-Hofstee plot. This suggested that there were either two forms of enzyme or two different enzymes participating in ortho hydroxylation of p-nitrophenol in lung microsomes. 5. Lung microsomal p-nitrophenol hydroxylase activity of sheep was reconstituted in the presence of purified lung microsomal cytochrome P-450, NADPH dependent cytochrome P-450 reductase and synthetic lipid, phosphatidylcholine dilauroyl.     

Purification of mitochondrial NADH dehydrogenase from Drosophila hydei and comparison with the 'heat-shock' polypeptides.

Mitochondrial NADH dehydrogenase (NADH:(acceptor) oxidoreductase, EC .6.99.3) from either Drosophila hydei larvae or embryos has been purified 150- and 120-fold, respectively. The purified enzyme appeared homogeneous and showed a molecular weight of 57 000. The molecular weight of the nondenatured enzyme was 79 000. On isoelectro-focussing of the preparation, two fractions were observed, a major one with an isoelectric point of 6.2 and a minor fraction with an isoelectric point of 4.9. Straight-line kinetics in Lineweaver-Burk plots were observed for the purified enzyme with a Km of 0.040 mM. The Km was not changed during the purification procedure, suggesting that the enzyme was not denatured or inactivated. The pH optimum of the purified enzyme was 5.6. The molecular weight of the purified mitochondrial NADH dehydrogenase does not correspond to that of one of the 'heat-shock' polypeptides.     

Purine nucleoside phosphorylase from bovine liver.

1. Purine nucleoside phosphorylase (purine nucleoside:orthophosphate ribosyltransferase, E.C. 2.4.2.1) from liver of cattle, Bos taurus, was purified to homogeneity. Some properties of the enzymes from three different bovine tissues were compared and discussed. 2. The enzyme has a molecular weight of 83,000, a sedimentation coefficient of 5.3 S, a Stokes' radius of 3.71 nm, a frictional ratio of 1.30 and a subunit molecular weight of 30,000. 3. Optimal pH for xanthosine degradation is around 5.5, whereas a broad pH activity profile for inosine degradation was observed between 5.0 and 7.5. Lineweaver-Burk plots curved downward at high concentrations of substrates, inosine, phosphate and arsenate.     

The inhibitory effect of choline and other quaternary ammonium compounds on thiamine transport in isolated rat hepatocytes

Quaternary ammonium compounds, such as choline and acetylcholine significantly inhibited thiamine uptake in isolated rat hepatocytes. Kinetic analysis using Lineweaver-Burk and Dixon plots of inhibition experiments revealed that choline and acetylcholine were purely competitive inhibitors for thiamine uptake with Ki values of 0.61 mM and 0.31 mM, respectively. Among quaternary ammonium compounds, hemicholinium-3 and curare were the strongest inhibitors, and kinetic studies showed that these compounds were also purely competitive inhibitors with Ki values of 12.5 microM and 4.3 microM, respectively. These results indicate that choline, acetylcholine and their structural analogs share a common binding site with thiamine in isolated rat hepatocytes. On the other hand, choline uptake by isolated rat hepatocytes occurred by a saturable mechanism with a Kt of 162 +/- 3.85 microM and Vmax of 80.1 +/- 1.30 pmol/10(5) cells per min as well as by a nonsaturable mechanism. Thiamine, pyrithiamine, oxythiamine, chloroethylthiamine and dimethialium inhibited choline uptake, while thiamine phosphates such as thiamine monophosphate and thiamine pyrophosphate insignificantly inhibited uptake. Although a Lineweaver-Burk plot of choline uptake in the presence of thiamine showed that thiamine also competitively inhibited choline uptake, a Dixon plot of the inhibition experiment was hyperbolic and indicated that the inhibition of choline uptake by thiamine was 'pseudo-competitive'. On the basis of these results, it is suggested that in isolated rat hepatocytes thiamine and choline do not share common transport sites.