Michaelis-Menten kinetics constants

Dowd, J.E. and Riggs, D.S. (1965) A comparison of estimates of Michaelis—Menten kinetic constants from various linear transformations. /. Biol. Chem., 240, 863. 

Figure 22 Examples of enzyme kinetic plots used for determination of Km and Vmax for a normal and an allosteric enzyme Direct plot [(substrate) vs. initial rate of product formation] and various transformations of the direct plot (i.e., Eadie-Hofstee, Lineweaver-Burk, and/or Hill plots) are depicted for an enzyme exhibiting traditional Michaelis-Menten kinetics (coumarin 7-hydroxylation by CYP2A6) and one exhibiting allosteric substrate activation (testosterone 6(3-hydroxylation by CYP3A4/5). The latter exhibits an S-shaped direct plot and a hook -shaped Eadie-Hofstee plot such plots are frequently observed with CYP3A4 substrates. Km and Vmax are Michaelis-Menten kinetic constants for enzymes. K is a constant that incorporates the interaction with the two (or more) binding sites but that is not equal to the substrate concentration that results in half-maximal velocity, and the symbol n (the Hill coefficient) theoretically refers to the number of binding sites. See the sec. III.C.3 for additional details.

Fig. 3. Operational equation of radioactive deoxyglucose method in comparison to the general equation for measurement of the reaction rates with tracers. T represents the time at the termination of the experimental period X equals the ratio of the distribution space of deoxyglucose in the tissue to that of glucose equals the fraction of glucose which, once phosphorylated, continues down the glycolytic pathway Km, Vm and Km, Vm represent the familiar Michaelis-Menten kinetic constants of hexokinase for deoxyglucose and glucose, respectively. These six constants collectively constitute the lumped constant (equivalent to the isotope-effect correction factor of the general equation). The other symbols are the same as those defined in Fig. 2. (Reproduced with permission from Sokoloff, 1978.)...

Dowd JE, Riggs DS. A comparison of estimates of Michaelis-Menten kinetic constants from various linear transforms. J Biol Chem 240 863-869, 1965. 

The Michaelis constant is equal to substrate concentration at which the rate of reaction is equal to one-half the maximum rate. The parameters and characterize the enzymatic reactions that are described by Michaelis-Menten kinetics. is dependent on total... 

Saturation kinetics are also called zero-order kinetics or Michaelis-Menten kinetics. The Michaelis-Menten equation is mainly used to characterize the interactions of enzymes and substrates, but it is also widely applied to characterize the elimination of chemical compounds from the body. The substrate concentration that produces half-maximal velocity of an enzymatic reaction, termed value or Michaelis constant, can be determined experimentally by graphing r/, as a function of substrate concentration, [S]. 

Solution Most enzyme reactors use such high concentrations of water that the fluid density is constant. Applying Michaelis-Menten kinetics to the component balance for a steady-state CSTR gives... 

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. ... 

Sato et al. (1991) expanded their earlier PBPK model to account for differences in body weight, body fat content, and sex and applied it to predicting the effect of these factors on trichloroethylene metabolism and excretion. Their model consisted of seven compartments (lung, vessel rich tissue, vessel poor tissue, muscle, fat tissue, gastrointestinal system, and hepatic system) and made various assumptions about the metabolic pathways considered. First-order Michaelis-Menten kinetics were assumed for simplicity, and the first metabolic product was assumed to be chloral hydrate, which was then converted to TCA and trichloroethanol. Further assumptions were that metabolism was limited to the hepatic compartment and that tissue and organ volumes were related to body weight. The metabolic parameters, (the scaling constant for the maximum rate of metabolism) and (the Michaelis constant), were those determined for trichloroethylene in a study by Koizumi (1989) and are presented in Table 2-3. 

The reaction was monitored by UV/Vis spectroscopy by following the product formation at 420 mn. The initial rates were used for analysis of the catalyzed oxidation of 8 into 9 that follows Michaelis-Menten kinetics. Control experiments show a linear increase of the reaction rates with the catalyst concentration at constant substrate concentration. 

Let us consider the determination of two parameters, the maximum reaction rate (rITOIX) and the saturation constant (Km) in an enzyme-catalyzed reaction following Michaelis-Menten kinetics. The Michaelis-Menten kinetic rate equation relates the reaction rate (r) to the substrate concentrations (S) by... 

Carrier-mediated transport is linear with mucosal solute concentration until this concentration exceeds the number of available carriers. At this point the maximal solute flux (7max) is independent of further increases in mucosal solute concentration. In the linear range of solute flux versus mucosal concentration (C), the proportionality constant is the ratio of / to the solute-carrier affinity constant (Km). This description of Michaelis-Menten kinetics is directly analogous to time changes in mass per unit volume (velocity of concentration change) found in enzyme kinetics, while here the appropriate description is the time change in solute mass per unit surface area of membrane supporting the carrier. 

Lactone3 Dipole moment (P) Rate constant Michaelis-Menten kinetics 1 ... 

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. 

There are two limiting cases of Michaelis-Menten kinetics. Beginning from Eq. (1) at high substrate excesses (or very small Michaelis constants) Eq. (4 a) results. This corresponds to a zero-order reaction with respect to the substrate, the rate of product formation being independent of the substrate concentration. In contrast, very low substrate concentrations [26] (or large Michaelis constants) give the limiting case of first-order reactions with respect to the substrate, Eq. (4b) ... 

This relationship corresponds to the simplest Michaelis-Menten kinetics (Eq. (3)). In addition to the equation derived earlier by Halpern et al. for the simplest model case of a C2-symmetric ligand without intramolecular exchange [21b], every other possibility of reaction sequence corresponding to Scheme 10.3 can be reduced to Eq. (13). Only the physical content of the values of kobs and Km, which must be determined macroscopically, differs depending upon the approach (see [59] for details). Nonetheless, the constants k0bs and KM allow conclusions to be made about the catalyses ... 

A more detailed analysis, however, shows that such comparisons of activity can be completely misleading, because Michaelis-Menten kinetics are principally described by two constants. The Michaelis constant contains information regarding the pre-equilibria, the rate constants quantify the product formation from the intermediates. 

Figure 3. Schematic view of the substrate uptake rate versus concentration relationship as described by the whole-cell Michaelis-Menten kinetics. Q is the substrate uptake rate, <2max the biologically determined maximum uptake rate per biomass, c the substrate concentration, and Kj the whole-cell Michaelis constant, i.e. the concentration resulting in 2max/2 (mass of substrate per volume). At c

Michaelis-Arbusov reaction, 19 29, 53, 54 Michaelis constant, 10 255 14 626-627 Michaelis-Menten equation, in kinetic studies, 14 625-627 Michaelis-Menten kinetics, 10 254-255 Michael reaction, 14 570 Michaels addition, of PVA, 25 602 Michelson interferometer, 14 221, 225 Micrinite, 6 707t... 

Equation (4) corresponds to saturation-type (Michaelis-Menten) kinetics and rate constants obtained over a suitable range of [CD], sufficient to reflect the hyperbolic curvature, can be analysed to provide the limiting rate constant, kc, and the dissociation constant, Ks (VanEtten et al., 1967a Bender and Komiyama, 1978 Szejtli, 1982 Sirlin, 1984 Tee and Takasaki, 1985). The rate constant ku is normally determined directly (at zero [CD]), and sometimes Ks can be corroborated by other means (Connors, 1987). 

In chymotrypsin and other serine proteases the imidazole moiety of histidine acts as a general base not as a nucleophile as is probably the case in the catalysis of activated phenyl ester hydrolysis by (26). With this idea in mind, Kiefer et al. 40) studied the hydrolysis of 4-nitrocatechol sulfate in the presence of (26) since aryl sulfatase, the corresponding enzyme, has imidazole at the active center. Dramatic results were obtained. The substrate, nitrocatechol sulfate, is very stable in water at room temperature. Even the presence of 2M imidazole does not produce detectable hydrolysis. In contrast (26) cleaves the substrate at 20°C. Michaelis-Menten kinetics were obtained the second-order rate constant for catalysis by (26) is 10 times... 

A B —> P The concentrations of A and P are held constant. The conversion of B to P follows Michaelis-Menten kinetics. 

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. 

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