Michaelis-Menten kinetics inhibition

FIGURE 12.1 Effects of substrate (reactant) concentration on the rate of enzymatic reactions (a) simple Michaelis-Menten kinetics (b) substrate inhibition (c) substrate activation. 

The solid or dashed lines correspond to modified Michaelis-Menten kinetics assuming activation with one and inhibition with two molecules bound according to Eq. (15). Solid symbols represent average value of n = 3-5 parallel measurements made with one single cell preparation. (Adapted from Ref. [58].)... 

In the presence of sucrose alone as the single substrate, initial reaction rates follow Michaelis-Menten kinetics up to 200 mM sucrose concentration, but the enzyme is inhibited by higher concentrations of substrate.30 The inhibitor constant for sucrose is 730 mM. This inhibition can be overcome by the addition of acceptors.31,32 The enzyme activity is significantly enhanced, and stabilized, by the presence of dextran, and by calcium ions. 

Because of the complexity of biological systems, Eq. (1) as the differential form of Michaelis-Menten kinetics is often analyzed using the initial rate method. Due to the restriction of the initial range of conversion, unwanted influences such as reversible product formation, effects due to enzyme inhibition, or side reactions are reduced to a minimum. The major disadvantage of this procedure is that a relatively large number of experiments must be conducted in order to determine the desired rate constants. 

Results have generally been disappointing. It can be difficult to remove the TSA from the polymer, but a more fundamental problem concerns the efficiency of the catalysis observed. The most efficient systems catalyze the hydrolysis of carboxylate and reactive phosphate esters with Michaelis-Menten kinetics and accelerations (koAJKM)/kunoJ approaching 103,1661 but the prospects for useful catalysis of more complex reactions look unpromising. Apart from the usual difficulties the active sites produced are relatively inflexible, and the balance between substrate binding and product inhibition is particularly acute. 

The architecture of various CYPs may accommodate entities of different shapes [139]. Several CYPs, particularly CYP3A4 [140,141] and CYP2C9 [142], may exhibit atypical (non-Michaelis-Menten) kinetics such as heterotropic activation, homotropic activation, substrate inhibition and partial inhibition, all in a substrate-effector-dependent manner [143]. Several hypotheses have been proposed to account for the observation of atypical kinetics, including simultaneous occupancy of the CYP active site by two substrates (or one substrate and one effector simultaneously) [144] and allosteric changes in CYP architecture due to binding of an effector [145,146]. Along... 

Figure 9. Various types of inhibition that occur for Michaelis Menten kinetics. Shown is competitive (A), uncompetitive (B), and noncompetitive inhibition (C). The corresponding rate laws are listed in Table II, (see text for details).

Aiming at a computer-based description of cellular metabolism, we briefly summarize some characteristic rate equations associated with competitive and allosteric regulation. Starting with irreversible Michaelis Menten kinetics, the most common types of feedback inhibition are depicted in Fig. 9. Allowing all possible associations between the enzyme and the inhibitor shown in Fig. 9, the total enzyme concentration Er can be expressed as... 

The overall influence of ATP on the rate V (ATP) is measured by a saturation parameter C (—oo, 1]. Note that, when using Eq. (139) as an explicit rate equation, the saturation parameter implicitly specifies a minimal Hill coefficient min > C necessary to allow for the reverse transformation of the parameters. The interval 6 [0,1] corresponds to conventional Michaelis Menten kinetics. For = 0, ATP has no net influence on the reactions, either due to complete saturation of a Michaelis Menten term or, equivalently, due to an exact compensation of the activation by ATP as a substrate by its simultaneous effect as an inhibitor. For < 0, the inhibition by ATP supersedes the activation of the reaction by its substrate ATP. 

Antibody 15C5 was able to catalyse the hydrolysis of the triester [105] with cat 2.65 x 10 3 min 1 whilst a second antibody from the same immunization programme was later found to hydrolyse the acetylcholinesterase inhibitor Paraoxon [106] with kcat = 1.95 x 10 3min-1 at 25°C (Appendix entry 6.2) (Lavey and Janda, 1996b). Antibody 3H5 showed Michaelis-Menten kinetics and was strongly inhibited by the hapten [104]. It exhibited a linear dependence of the rate of hydrolysis on hydroxide ion concentration, suggesting that 3H5 effects catalysis by transition state stabilization rather than by general acid/base catalysis. 

MS is lower than that of M the system is in the regime of substrate saturation addition of more S does not lead to a rate increase. The behaviour of the reaction rate in case B is typical of enzymes and in biochemistry this is referred to as Michaelis-Menten kinetics. The success of the application of the Michaelis-Menten kinetics in biochemistry is based on the fact that indeed only two reactions are involved the complexation of the substrate in the pocket of the enzyme and the actual conversion of the substrate. Usually the exchange of the substrate in the binding pocket is very fast and thus we can ignore the term k2[H2] in the denominator. Complications arise if the product binds to the binding site of the enzyme, product inhibition, and more complex kinetics result. 

El to E4 are irreversible enzymes that follow Michaelis-Menten kinetics. Ei and E2 are inhibited by the noncompetitive inhibitors li and I2. Concentrations of Xi are held constant. Inputs concentrations of E and E. Output steady-state concentration of A. The concentrations of the species marked with ( ) are fixed. 

Transport of NO3 formed from NH4+ towards the root and its consumption in denitrification and uptake by the root. Denitrification is described with Michaelis-Menten kinetics with an inhibition function related to [O2]. 

Figure 1. Plot of v/V ax versus the millimolar concentration of total substrate for a model enzyme displaying Michaelis-Menten kinetics with respect to its substrate MA (i.e., metal ion M complexed to otherwise inactive ligand A). The concentrations of free A and MA were calculated assuming a stability constant of 10,000 M k The Michaelis constant for MA and the inhibition constant for free A acting as a competitive inhibitor were both assumed to be 0.5 mM. The ratio v/Vmax was calculated from the Michaelis-Menten equation, taking into account the action of a competitive inhibitor (when present). The upper curve represents the case where the substrate is both A and MA. The middle curve deals with the case where MA is the substrate and where A is not inhibitory. The bottom curve describes the case where MA is the substrate and where A is inhibitory. In this example, [Mfotai = [Afotai at each concentration of A plotted on the abscissa. Note that the bottom two curves are reminiscent of allosteric enzymes, but this false cooperativity arises from changes in the fraction of total "substrate A" that has metal ion bound. For a real example of how brain hexokinase cooperatively was debunked, consult D. L. Purich H. J. Fromm (1972) Biochem. J. 130, 63.

Crude and three diethyl ether extracted, acetone treated, fractions were isolated from large-scale cultures of Gambierdiscus toxicus. Crude extracts at. 04 mg/ml inhibited the histamine contraction response in smooth muscle of the guinea pig ileum. Three semi-purified fractions at 5 ng/ml, effectively inhibited the guinea pig ileum preparation. Two of these fractions followed Michaelis-Menten kinetics for a competitive inhibition. The third fraction inhibited in a non-reversible manner. This study has established the presence of three lipid extracted toxins in toxicus, outlined a method for their assay in small quantities, and identified at least two of the effects of these toxic extracts in animals. 

Obviously, extrapolation procedures are impractical for routine determination of enzyme activities. When substrate saturation-curves conform to rectangular hyperbolas, reasonable concentrations of substrates should equal 10 to 20 times the respective Km values. As outlined above, application of this rule to assays of bilirubin UDP-glycosyltransferase activities is hampered by substrate inhibition and by occasional deviation from Michaelis-Menten kinetics. The best alternative in such cases may be to choose the concentrations at optimal enzyme activity. However, great care should be exercised in interpreting the results. When a bio-... 

Also characteristic of enzymes that obey Michaelis-Menten kinetics is that suitable inhibitors can compete with the substrate for the enzyme active site, thus impeding the reaction. If the inhibitor binds reversibly to the enzyme active site, then the substrate can compete for the active site leading to competitive inhibition. To test for... 

In binding experiments, the affinity of magnesium ADP to native membranes and to the isolated calcium dependent ATPase was found to be considerably lower than that of magnesium ATP173. On the other hand, from the inhibition of the calcium-dependent ATPase or the activation of calcium release and ATP synthesis apparent affinities for ADP are obtained that are very similar to those of ATP (Fig. 12). The affinity of ADP for the enzyme apparently depends on its functional state. The affinity of ADP for the membranes under conditions of calcium release depends markedly on the pH of the medium. When the medium pH is reduced from 7.0 to 6.0, the affinity drops by a factor of 10. At pH 7.0 the affinity of the membrane for ADP corresponds to the affinity for ATP to the high affinity binding sites in the forward running mode of the pump. In contrast to the complex dependence of the forward reaction on the concentration of ATP, the dependence of the reverse reaction on ADP seems to follow simple Michaelis-Menten kinetics. 

The enzymatic activity of the L-19 IVS ribozyme results from a cycle of transesterification reactions mechanistically similar to self-splicing. Each ribozyme molecule can process about 100 substrate molecules per hour and is not altered in the reaction therefore the intron acts as a catalyst. It follows Michaelis-Menten kinetics, is specific for RNA oligonucleotide substrates, and can be competitively inhibited. The kcat/Km (specificity constant) is 10s m- 1 s lower than that of many enzymes, but the ribozyme accelerates hydrolysis by a factor of 1010 relative to the uncatalyzed reaction. It makes use of substrate orientation, covalent catalysis, and metalion catalysis—strategies used by protein enzymes. 

In the absence of the other ligands, the binding of [14C]-AMP followed simple Michaelis-Menten kinetics at both pH 7.5 and pH 9.2 (35, 57). At saturation 4 equivalents of AMP were bound with an association constant of 0.5 X 105 M l. The lack of AMP inhibition at pH 9.2 (see above) is therefore not related to an inability of the enzyme to bind the inhibitor at this pH. Below pH 7.5, however, the degree of inhibition could be correlated with the extent of binding (35). 

In relation to enzymic cytochrome P-450 oxidations, catalysis by iron porphyrins has inspired many recent studies.659 663 The use of C6F5IO as oxidant and Fe(TDCPP)Cl as catalyst has resulted in a major improvement in both the yields and the turnover numbers of the epoxidation of alkenes. 59 The Michaelis-Menten kinetic rate, the higher reactivity of alkyl-substituted alkenes compared to that of aryl-substituted alkenes, and the strong inhibition by norbornene in competitive epoxidations suggested that the mechanism shown in Scheme 13 is heterolytic and presumably involves the reversible formation of a four-mernbered Fev-oxametallacyclobutane intermediate.660 Picket-fence porphyrin (TPiVPP)FeCl-imidazole, 02 and [H2+colloidal Pt supported on polyvinylpyrrolidone)] act as an artificial P-450 system in the epoxidation of alkenes.663... 

Figure 3.28 shows the consumption functions C(S) for both nonmonotonic and Michaelis-Menten kinetics together with the removal function R(S) = —D S in a line. The intersection ) of C(S) and S(S) are the steady states. It is clear that for Michaelis-Menten3 kinetics, i.e., for nonlinearity with saturation, see Figure 2.2, there is only one steady state for the whole range of D. This is the simplest case of a CSTR without bifurcation. However, for substrate-inhibited nonmonotonic kinetics as depicted by the nonmonotonic curve in Figure 3.28, more than one steady state may occur over a certain range of D values. 

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