Kinetic Michaelis-Menten

Fig. 1. Free-energy profile for a kinetic resolution depicted by equation 1 that follows Michaelis-Menten kinetics.

Figure 11-1a. Simple Michaelis-Menten kinetics. At low substrate concentration...

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... 

Michaelis-Menten kinetics Kineties of eonversion of substrates in enzyme-eatalyzed reaetions. 

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]. 

On the other hand, for an enzyme that obeys Michaelis-Menten kinetics, the reaction is viewed as being first-order in S at low S and zero-order in S at high S. (See Chapter 14, where this distinction is discussed.)... 

Michaelis-Menten kinetics, in 1913 L. Michaelis and M. Men ten realized that the rate of an enzymatic reaction... 

Most enzymes catalyse reactions and follow Michaelis-Menten kinetics. The rate can be described on the basis of the concentration of the substrate and the enzymes. For a single enzyme and single substrate, the rate equation is ... 

The values of the Michaelis-Menten kinetic parameters, Vj3 and C,PP characterise the kinetic expression for the micro-environment within the porous structure. Kinetic analyses of the immobilised lipase in the membrane reactor were performed because the kinetic parameters cannot be assumed to be the same values as for die native enzymes. 

The initial reaction rate (v0) obtained from each substrate concentration was fitted to Michaelis-Menten kinetics using enzyme kinetics. Pro (EKP) Software (ChemSW product,... 

Continnons Infnsion, Zero Order, and Michaelis-Menten Kinetics... 

Membrane, 141, 178 Mercury electrodes, 62, 108 Mercury film electrode, 76, 110 Metals, 75, 81 Metal complexes, 64 Methyl viologen, 43 Michaelis-Menten kinetics, 175 Microbalance, 52, 53 Microcells, 102 Microchip, 194, 195... 

One reaction scheme that leads to Michaelis-Menten kinetics is known as the Briggs-Haldane scheme. It consists of these reactions ... 

Almost every reaction scheme that gives rise to Michaelis-Menten kinetics will proceed at a rate directly proportional to [E]j. It is customary to express Emax as... 

Michaelis-Menten kinetics. Consider the hydrolysis of phenyl acetate catalyzed by acetyl cholinesterase,... 

Runge-Kutta. Consider the disappearance of substrate in an enzyme-catalyzed reaction that follows Michaelis-Menten kinetics ... 

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. 

Example 12.3 Suppose S P according to first-order, Michaelis-Menten kinetics. Find Sout for a CSTR. 

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... 

If the enzyme charged to a batch reactor is pristine, some time will be required before equihbrium is reached. This time is usually short compared with the batch reaction time and can be ignored. Furthermore, 5o Eq is usually true so that the depletion of substrate to establish the equilibrium is negligible. This means that Michaelis-Menten kinetics can be applied throughout the reaction cycle, and that the kinetic behavior of a batch reactor will be similar to that of a packed-bed PFR, as illustrated in Example 12.4. Simply replace t with thatch to obtain the approximate result for a batch reactor. 

The initial condition for [SE] assumes that the enzyme was charged to the reactor in pristine condition. It makes no difference whether the enzyme is free or immobilized provided the reaction follows Michaelis-Menten kinetics. 

Hehre and coworkers showed that beta amylase from sweet potatoes, an inverting, a-specific exo-(l 4)-glucanase, catalyzes the hydrolysis of jS-maltosyl fluoride with complex kinetics which indicated the participation of two substrate molecules in the release of fluoride ion. Furthermore, the reaction was strongly accelerated by the addition of methyl ) -maltoside. Hydrolysis of a-maltosyl fluoride, on the other hand, obeyed Michaelis-Menten kinetics. The main product with both a- and yj-maltosyl fluoride was )S-maltose. The results with )3-maltosyl fluoride were interpreted by the assumption of a glycosylation reaction preceding hydrolysis by which a malto-tetraoside is formed by the replacement of fluoride ion by a second substrate molecule or added methyl -maltoside (see Scheme 5). 

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. 

Kemp and Waters also found the oxidations of cyclohexanone and of mandelic, malonic and a-hydroxyisobutyric acids by Cr(VI) to be Mn(II)-catalysed. In these cases, as with oxalic acid, the [Cr(VI)] versus time plots are almost linear and the reaction becomes first order in substrate (or involves Michaelis-Menten kinetics), and, except at lowest catalyst concentrations, approximately first order in [Mn(II)]. Detailed examination of the initial rate of oxidation of a-hydroxyrobutyric acid as a function of oxidant concentration revealed, however, that the dependence is... 

All the oxidants convert primary and secondary alcohols to aldehydes and ketones respectively, albeit with a great range of velocities. Co(III) attacks even tertiary alcohols readily but the other oxidants generally require the presence of a hydrogen atom on the hydroxylated carbon atom. Spectroscopic evidence indicates the formation of complexes between oxidant and substrate in some instances and this is supported by the frequence occurrence of Michaelis-Menten kinetics. Carbon-carbon bond fission occurs in certain cases. 

On the other hand, the macrolides showed unusual enzymatic reactivity. Lipase PF-catalyzed polymerization of the macrolides proceeded much faster than that of 8-CL. The lipase-catalyzed polymerizability of lactones was quantitatively evaluated by Michaelis-Menten kinetics. For all monomers, linearity was observed in the Hanes-Woolf plot, indicating that the polymerization followed Michaehs-Menten kinetics. The V, (iaotone) and K,ax(iaotone)/ m(iaotone) values increased with the ring size of lactone, whereas the A (iactone) values scarcely changed. These data imply that the enzymatic polymerizability increased as a function of the ring size, and the large enzymatic polymerizability is governed mainly by the reachon rate hut not to the binding abilities, i.e., the reaction process of... 

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