Non-Michaelis-Menten kinetics

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... 

Non MM = non Michaelis-Menten kinetics. Note also that the kinetic differences between yl and y2 containing ADH are functionally negligible. Alterations in the (J and y subunits are seen primarily to... 

Substrate A has a hyperbolic saturation curve Enzymes that bind to only one substrate molecule will show hyperbolic saturation kinetics. However, the observation of hyperbolic saturation kinetics does not necessarily mean that only one substrate molecule is interacting with the enzyme (see discussion of non-Michaelis-Menten kinetics in sec. IV). 

If enzyme activation and the other unusual kinetic characteristics result from multiple substrates in the active site, kinetic parameters will be difficult to characterize and drug interactions will be more difficult to predict, since they are a function of the enzyme and of both the substrates. In addition, there are some indications that non-Michaelis-Menten kinetics can be seen in vivo (27-29). 

If non-Michaelis-Menten kinetics for all P450 enzymes are a result of multiple substrates binding to the enzyme, then the reaction kinetics for the binding of two substrates to an active site can be complicated. A number of analyses of... 

Kmi would be the standard Michaelis constant for the binding of the first substrate, if [ESS] = 0. Km2 would be the standard Michaelis constant for the binding of the second substrate, if [E] = 0 (i.e., the first binding site is saturated). In the complete equation, these constants are not true Km values, but their form (i.e., Km] = (k2 + k25)/k 2) and significance are analogous. Likewise, k25 and k35 are Vmi/Et and Vm2/Et terms when the enzyme is saturated with one and two substrate molecules, respectively. Equation (10) describes several non-Michaelis-Menten kinetic profiles. Autoactivation (sigmoidal saturation curve) occurs when k35 > k24 or Km2 < Km 1, substrate inhibition occurs when k24 > 35, and a biphasic saturation... 

For substrates exhibiting non-Michaelis-Menten kinetics (e.g., several CYP3A4 substrates), a wider range of substrate concentrations may be required to accurately determine reaction kinetics. CYP3A4 should be measured with at least two substrates, one exhibiting positive cooperativity (e.g., testosterone) and one exhibiting autoinhibition (e.g., midazolam). 

The regulation of enzymes by metabolites leads to the concept of allostenc regulation. Allosteric means other structure. Allosteric modulators can bind at a site other than the active site in question and cause activation or inhibition. These modulators can include the substrate itself, which binds at another active site in a multi-subunit enzyme. In fact, allosterically modulated enzymes almost always have a complex quaternary structure (multiple subunits) and exhibit non-Michaelis-Menten kinetics. 

Atkins WM. Non-Michaelis-Menten kinetics in cytochrome P450-catalyzed reactions. An Rev Pharmacol Toxicol 2005 45 291-310. 

In some ways CYP3A4 is the most important of the human isoforms. It is certainly responsible for the metabolism of more drugs and other xenobiotics than any other P450. The diversity of its substrates, which include large molecules such as steroids, cyclosporin, and macrolide antibiotics, and its continuing ability to exhibit complex non-Michaelis-Menten kinetics and cooperativity has led many to believe that the active site of this enzyme is very large with the ability to contain several substances at the same time. In 2004 the same two groups as before, at Scripps and Astex, almost simultaneously published... 

Alternatively, another substrate molecule or other nucleophile can react with the covalent intermediate E-X in a transglycosylation reaction ( 4). This can lead to non-Michaelis-Menten kinetics when the apparent F ax continues to increase with increasing substrate concentration caused by an increase in k. ... 

The inactivation is normally a first-order process, provided that the inhibitor is in large excess over the enzyme and is not depleted by spontaneous or enzyme-catalyzed side-reactions. The observed rate-constant for loss of activity in the presence of inhibitor at concentration [I] follows Michaelis-Menten kinetics and is given by kj(obs) = ki(max) [I]/(Ki + [1]), where Kj is the dissociation constant of an initially formed, non-covalent, enzyme-inhibitor complex which is converted into the covalent reaction product with the rate constant kj(max). For rapidly reacting inhibitors, it may not be possible to work at inhibitor concentrations near Kj. In this case, only the second-order rate-constant kj(max)/Kj can be obtained from the experiment. Evidence for a reaction of the inhibitor at the active site can be obtained from protection experiments with substrate [S] or a reversible, competitive inhibitor [I(rev)]. In the presence of these compounds, the inactivation rate Kj(obs) should be diminished by an increase of Kj by the factor (1 + [S]/K, ) or (1 + [I(rev)]/I (rev)). From the dependence of kj(obs) on the inhibitor concentration [I] in the presence of a protecting agent, it may sometimes be possible to determine Kj for inhibitors that react too rapidly in the accessible range of concentration. ... 

The effect of non-participating ligands on the copper catalyzed autoxidation of cysteine was studied in the presence of glycylglycine-phosphate and catecholamines, (2-R-)H2C, (epinephrine, R = CH(OH)-CH2-NHCH3 norepinephrine, R = CH(OH)-CH2-NH2 dopamine, R = CH2-CH2-NH2 dopa, R = CH2-CH(COOH)-NH2) by Hanaki and co-workers (68,69). Typically, these reactions followed Michaelis-Menten kinetics and the autoxidation rate displayed a bell-shaped curve as a function of pH. The catecholamines had no kinetic effects under anaerobic conditions, but catalyzed the autoxidation of cysteine in the following order of efficiency epinephrine = norepinephrine > dopamine > dopa. The concentration and pH dependencies of the reaction rate were interpreted by assuming that the redox active species is the [L Cun(RS-)] ternary complex which is formed in a very fast reaction between CunL and cysteine. Thus, the autoxidation occurs at maximum rate when the conditions are optimal for the formation of this species. At relatively low pH, the ternary complex does not form in sufficient concentration. 

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. 

Non Michaelis-Menten behavior (i.e., no saturation kinetics in presence of excess HC03) was observed and the second-order rate constants for the catalyzed decarboxylation (/ = k k<>j(k i / 2) for... 

Allosteric enzymes show relationships between V0 and [S] that differ from Michaelis-Menten kinetics. They do exhibit saturation with the substrate when [S] is sufficiently high, but for some allosteric enzymes, plots of V0 versus [S] (Fig. 6-29) produce a sigmoid saturation curve, rather than the hyperbolic curve typical of non-regulatory enzymes. On the sigmoid saturation curve we can find a value of [S] at which V0 is half-maximal, but we cannot refer to it with the designation Km, because the enzyme does not follow the hyperbolic Michaelis-Menten relationship. Instead, the symbol [S]0 e or K0,5 is often used to represent the substrate concentration giving half-maximal velocity of the reaction catalyzed by an allosteric enzyme (Fig. 6-29). 

Evaluate the Michaelis-Menten kinetic parameters by employing (a) the Langmuir plot, (b) the Lineweaver-Burk plot, (c) the Eadie-Hofstee plot, and (d) non-linear regression procedure. 

The turnover frequency allows performance comparison between different catalyst systems, biological and/or non-biological. Its threshold is at 1 event per second per active site. According to the definition, a turnover frequency can be determined only if the number of active sites is known (Chapter 9, Section 9.2.3). For an enzyme reaction obeying Michaelis-Menten kinetics, Eq. (2.15) holds. 

Kemp elimination was used as a probe of catalytic efficiency in antibodies, in non-specific catalysis by other proteins, and in catalysis by enzymes. Several simple reactions were found to be catalyzed by the serum albumins with Michaelis-Menten kinetics and could be shown to involve substrate binding and catalysis by local functional groups (Kirby, 2000). Known binding sites on the protein surface were found to be involved. In fact, formal general base catalysis seems to contribute only modestly to the efficiency of both the antibody and the non-specific albumin system, whereas antibody catalysis seems to be boosted by a non-specific medium effect. 

Mean clearance (CL) values for cetuximab are displayed as a function of dose in Fig. 14.3. Mean CL values decreased from 0.079 to 0.018 L/h/m2 after single cetuximab doses of 20 to 500 mg/m2, respectively. In the dose range 20 to 200 mg/m2, CL values decreased with dose. At doses of 200 mg/m2 and greater, CL values leveled off at a value of approximately 0.02 L/h/m2. This biphasic behavior suggests the existence of two elimination pathways. The elimination of cetuximab apparently involves a specific, capacity-limited elimination process that is saturable at therapeutic concentrations, in parallel with a nonspecific first-order elimination process that is non-saturable at therapeutic concentrations. Increasing doses of cetuximab will therefore ultimately lead to the saturation of the elimination process that is capacity-limited and that follows Michaelis-Menten kinetics, whereas the first-order process will become the dominant mechanism of elimination beyond a particular dose range. 

Shaw and Bell (1991) examined this effect in the case of competition between radiocaesium and the K+ and NH4+ ions during root uptake by wheat (Triticum aestivum). These authors formalised the observed relationships in terms of classical Michaelis-Menten kinetics which necessitates the assumption that each of these ions is taken up by identical sites associated with the root plasmalemma. Lembrechts et al. (1990) found a similar negative and non-linear relationship between the concentration of Ca either in soil or in solution culture and the degree of radiostrontium uptake by lettuce Lactuca saliva). The principle of competitive exclusion of a radionuclide by an ion analogue may be exploited, with varying degrees of success, as a post-con-... 

Due to the formation of an intermediate complex, this type of reaction mechanism was described as being analogous to Michaelis-Menten kinetics [39]. A common error made when examining the behaviour of systems of this type is to use the Koutecky-Levich equation to analyse the rotation speed-dependence of the current. This is incorrect because the Koutecky-Levich analysis is only applicable to surface reactions obeying strictly first-order kinetics. Applying the Koutecky-Levich analysis to situations where the surface kinetics are non-linear, as in this case, leads to erroneous values for the rate constants. Below, we present the correct treatment for this problem based on an extension of a model originally developed by Albery et al. [42]... 

The ALS isolated as described in Table III displayed typical Michaelis-Menten kinetics with respect to pyruvate with a Km of 2.44 mM. Substrate concentrations as high as 50x Km had no effect on the rate of the reaction. Thiamine pyrophosphate, FAD and Mg(2+) were an absolute requirement for catalysis by the purified enzyme. These properties are consistent with observations made by others (30). Optimum activity was obtained at pH 7.1 and 37C, which were also the best conditions for inhibition by TP. There was no significant difference in the 1(50) value of TP whether ALS was taken after step 2 or 5, indicating low potential for non-specific binding of the herbicide to other proteins. 

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