Michaelis-Menten rate constants

Ludferin/ludferase fed to each side of jimction determination of Michaelis-Menten rate constants... 

Continuous flow in microfluidic system was also used for the bioluminescent reaction between ATP and luciferin, which was promoted by the enzyme ludferase to ultimately yield oxyluciferin and AMP [149]. The microfluidic technique allowed for the determination of Michaelis-Menten rate constants with a single experiment. 

The MichaeUs-Menten-Henri model is one of the simplest for enzymatic action, and considers the velocity of enzymatic conversion at steady state, where there is a constant concentration of the enzyme-substrate complex, which itself can either dissociate or proceed to final product formation. The measured velocity is related to substrate concentration c, and the Michaelis-Menten rate constant M y ... 

This ratio is of fundamental importance in the relationship between enzyme kinetics and catalysis. In the analysis of the Michaelis-Menten rate law (equation 5.8), the ratio cat/Km is an apparent second-order rate constant and, at low substrate concentrations, only a small fraction of the total enzyme is bound to the substrate and the rate of reaction is proportional to the free enzyme concentration ... 

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.

In the same vein and under dimensionally restricted conditions, the description of the Michaelis-Menten mechanism can be governed by power-law kinetics with kinetic orders with respect to substrate and enzyme given by noninteger powers. Under quasi-steady-state conditions, Savageau [25] defined a fractal Michaelis constant and introduced the fractal rate law. The behavior of this fractal rate law is decidedly different from the traditional Michaelis-Menten rate law ... 

Figure 2.4 A typical conceptual representation of a PBTK model for a volatile organic chemical A. Each box represents a tissue compartment and arrows depict arterial and venous blood circulation. RAM refers to the rate of the amount metabolized. Vmax and Km refer to the maximal rate of metabolism and the Michaelis-Menten affinity constant, respectively. C is concentration in blood (V ), fat (FA), richly perfused tissues (RA), poorly perfused tissues (PA), liver (LA), and arterial blood (aA). Ql is the blood flow.

Often the key entity one is interested in obtaining in modeling enzyme kinetics is the analytical expression for the turnover flux in quasi-steady state. Equations (4.12) and (4.38) are examples. These expressions are sometimes called Michaelis-Menten rate laws. Such expressions can be used in simulation of cellular biochemical systems, as is the subject of Chapters 5, 6, and 7 of this book. However, one must keep in mind that, as we have seen, these rates represent approximations that result from simplifications of the kinetic mechanisms. We typically use the approximate Michaelis-Menten-type flux expressions rather than the full system of equations in simulations for several reasons. First, often the quasi-steady rate constants (such as Ks and K in Equation (4.38)) are available from experimental data while the mass-action rate constants (k+i, k-i, etc.) are not. In fact, it is possible for different enzymes with different detailed mechanisms to yield the same Michaelis-Menten rate expression, as we shall see below. Second, in metabolic reaction networks (for example), reactions operate near steady state in vivo. Kinetic transitions from one in vivo steady state to another may not involve the sort of extreme shifts in enzyme binding that have been illustrated in Figure 4.7. Therefore the quasi-steady approximation (or equivalently the approximation of rapid enzyme turnover) tends to be reasonable for the simulation of in vivo systems. 

The amount of verapamil presented to the liver, and its effective concentration in the region of the hepatic er zymes soon after oral dosing, are related to the rate at which verapamO is absorbed from the gastrointestinal tract into the portal vein and to the flow rate of blood in the portal vein to the liver. For instance, by hypothesizing a Michaelis-Menten metabolic process, when the absorption rate is slow and concentrations in the portal vein and liver are low, the hepatic metabolism of both enantiomers will be approximately first-order. Under these conditions, the K S ratio of the umnetabolized enantiomers leaving the liver will be closely related to the ratio of the Michaelis-Menten saturation constants (K ) for the enantiomers. The observed more rapid metabolism of S-verapamil than R-verapamil (i.e., S-verapamil has the lower systemic concentrations) is consistent with the lower reported for S-verapamil (16). 

Kinetic experiments with synthetic iron oxyhydroxides have shown that the initial microbial reduction rate increases with increasing initial ferric iron concentration up to a given maximum reduction rate (Bonneville et al. 2004). This observation was explained by a saturation of active membrane sites with Fe(III) centers. The respective reaction was best described with a Michaelis-Menten rate expression with the maximum reduction rate per cell positively correlating with the solubility of the iron oxyhydroxides (Bonneville et al. 2004). Kinetic studies involving iron are not only inherently important to describe reaction pathways and to derive rate constants, which can be used in models. Kinetic studies also increasingly focus on iron isotopic fractionation to better understand the iron isotopic composition of ancient sediments, which may assist in the reconstruction of paleo-environments. Importantly, iron isotope fractionation occurs in abiotic and biotic processes the degree of isotopic fractionation depends on individual reaction rates and the environmental conditions, e.g. whether reactions take place within an open or closed system (Johnson et al. 2004). 

The Michaelis-Menten rate equation shows the relationship between v (rate of reaction), (maximal rate when enzyme is saturated with substrate), and S (substrate concentration) v = V S/(A + S). When S the reaction is first order, and v = (V /AJ5.WhenA S, the reaction is zero order, and v = V = constant. V and are enzyme kinetic parameters. The Michaelis-Menten equation is often valid for other cases, where the derivation of the kinetic parameters from the rate constants is more complicated. 

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.)...

It can be seen that if the concentration of one substrate is much larger than the other and remains essentially constant, then equation 9.19 will behave as a Michaelis-Menten rate law. The partieipation of a cofactor in a singlesubstrate enzymatic reaction (or a dual-substrate enzymatic reaction with [5]. STjg) can be modeled via the sequence given in steps 9.4-9.9. If the substrate concentration is considered to be essentially constant, then equation 9.19 exhibits a Michaelis-Menten dependence on cofactor concentration. 

Figure 1. PBPK model for dX -trans-veimoic acid and its metabolites. Abbreviations are Dy intravenous dose (mg) Q or P or C, flow rate or partition coefficient or concentration (mg/1) subscripts c (cardiac), f (fat), g (gut), 1 (liver), pi (placenta), r (richly perfused tissues muscle, bone), s (slowly perfused tissues mammary gland, uterus), sk (skin) Dsc diffusivity in stratum comeum (cm%r) k rate constant subscripts b (biliary clearance), CO2 (side chain oxidation to carbon dioxide/hr), ct (cis/trans isomerization), tc (trans/cis isomerization) e (diffusion limited transfer between placenta and embryo, 1/hr) f (fecal excretion/hr) h (hydrolysis of glucuronide/hr) o (oral absorption) r (intestinal absorption) v (intravenous injection) K or V (affinity constant or maximum velocity where mg = apparent Michaelis-Menten glucuronidation constant and mx = apparent Michaelis-Menten oxidation constant). Rounded box indicates the submodels as diagrammed in Figures 2-5. (Reproduced with permission of Mosby-Year Book, Inc. from the American Academy of Dermatology. Clewell, [29].)...

The estimated standard errors in both k and Kja are small compared with the values of these constants, consistent with the excellent fit of the Michaelis-Menten rate equation shown in Figure 6-9d. 

The Michaelis-Menten scheme nicely explains why a maximum rate, V"max, is always observed when the substrate concentration is much higher than the enzyme concentration (Figure 11.1). Vmax is obtained when the enzyme is saturated with substrate. There are then no free enzyme molecules available to turn over additional substrate. Hence, the rate is constant, Vmax, and is independent of further increase in the substrate concentration. 

Figure 11.1 A plot of the reaction rate as a function of the substrate concentration for an enzyme catalyzed reaction. Vmax is the maximal velocity. The Michaelis constant. Km, is the substrate concentration at half Vmax- The rate v is related to the substrate concentration, [S], by the Michaelis-Menten equation ...

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... 

Comparison of the ordinary Michaelis-Menten relation with (5.108) shows that the inhibitor did not influence specific growth rate, vmgx, but the Michaelis-Menten constant was affected by the inhibitor and resulted in a constant, known as the apparent Michaelis constant. 

The parameters of the Monod cell growth model are needed i.e. the maximum specific growth rate and the Michaelis-Menten constant are required for a suitable rate equation. Based on the data presented in Tables 10.1 and 10.2, obtain kinetic parameters for... 

A special case for reduced bioavailabilty results from first-pass extraction that sometimes might be subjected to saturable Michaelis-Menten absorption kinetics. The lower the hepatic drug clearance is (Clhep) in relation to liver blood flow (Ql), or the faster the drug absorption rate constant (Ka), and the higher the dose (D) are, the more bioavailable is the drug (F). 

Michaelis constant (KM) A constant in the rate law for the Michaelis—Menten mechanism. 

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