Enzyme kinetics Michaelis-Menten relation

The Michaelis - Menten relation is also obeyed in the processes involving the immobilized ADH (K =44.2 mM). The diffusion effect does not explain in a satisfactory way the increase of Kj, so that conformational modifications of the active center must be considered to affect the enzyme kinetic behaviour. It is known that the ADH molecule consists of 4 protomers bound through a Zn atom to 4 molecules of coenzyme In the coupling processes the carrier - enzyme chemical bond is formed at one protomer only, and the quaternary structure is destroyed. In fact, at lower coupling pH values (pH=8) the ADH activity is strongly diminished probably due to the structure splitting in non-bound protomers, the ADH being active as a complete structural composition only. 

For the sake of completeness, let us start by recalling some basic equations governing enzyme kinetics. A simple mechanism consistent with experimentally observed kinetic data is the Michaelis-Menten relation ° ... 

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... 

Now we can see the types of biochemical factors that determine the rate constant, fcbio for Michaelis-Menten cases the ability of the enzyme to catalyze the transformation as reflected by the quotient, kE/KiMM, and the presence of enzyme in the microorganism population involved, as quantified by [Enz]tot/[B], In the following section, we develop some detailed kinetic expressions for one case of enzyme-mediated transformations. Examination of these results will help us to see how structural features of xenobiotic compounds may affect rates. Finally, we will improve our ability to understand the relative rates for structurally related chemicals that are transformed by the same mechanism and are limited at the same biodegradation step. 

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... 

Many aqueous solution cellular automata models discussed earlier were created for systems in which there have been no changes in the states of any cells that model ingredients. Of great interest are the reactions catalyzed by enzymes, the engines of biochemical function. Some studies relating to this have been reported,89 90 but more attention to this area of modeling would be of value. A recent study on the kinetics of an enzyme reaction93 considered the Michaelis-Menten model shown in Eq. [16]. 

The mathematical expressions relating reaction rate and inhibitor concentration are often rather complicated, but there are four simple equations that are extensions of the Michaelis-Menten formula. These merit special consideration because the kinetics of many enzymes can be satisfactorily described by them. In the equations in Table 9.1, [I] denotes the inhibitor concentration and K and K are inhibition constants, the units of which are those of a dissociation equilibrium constant (mmolL-1). Mechanisms that are consistent with these equations are described in Sect. 9.10. 

If we consider the back reaction Fj Fq + P. where k4 is not zero in the reactions of the enzyme-substrate system, modify the Michaelis-Menten kinetics. Show that when equilibrium is established, after a very long time, equilibrium concentrations of substrate and product are related by the following Haldane s relation... 

Under typical experimental conditions, the enzyme system is saturated with O2 and H+. Thus this enzyme system includes four substrates and four products. However, the initial steady state kinetics of this enzyme system obeys a simple Michaelis-Menten equation (a rectangular hyperbolic relation) for each kinetic phase of the two phases at low and high ferrocytochrome c concentrations as described above. This result indicates that the four ferrocytochromes c react with the enzyme in a ping-pong fashion in each substrate concentration range. That is, each ferroferrocytochrome c reacts with the enzyme after the previous cytochrome c in the oxidized state is released from the enzyme. Cytochrome c... 

Another parameter often referred to when discussing Michaelis-Menten kinetics is kcaJ Ky. This is an apparent second-order rate constant that relates the reaction rate to the free (not total) enzyme concentration. As described above, at very low substrate concentrations when the enzyme is predominantly unbound, the velocity (f) is equal to [El Ky. The value of Is JKy sets a lower limit on the rate constant for the association of enzyme and substrate. It is sometimes referred to as the specificity constant because it determines the specificity of the enzyme for competing substrates. 

A model for enzyme kinetics that has found wide applicability was proposed by Michaelis and Menten in 1913 and later modified by Briggs and Haldane. The Michaelis-Menten equation relates the initial rate of an enzyme-catalyzed reaction to the substrate concentration and to a ratio of rate constants. This equation is a rate equation,... 

Fig. 9.1. Relation of reaction speed (v) to substrate concentration ([S]) in the absence (A, B, C) and presence of enzyme (D, E). The Michaelis constant, K , is the substrate concentration at which half the maximum reaction speed is obtained. To saturate the enzyme completely with substrate, close to lOOxAmis required (D). When the dependence of the rate of enzyme-catalyzed reaction on the substrate concentration can be described by a rectangular hyperbola (E), the reaction is said to obey classical or Michaelis-Menten kinetics.

When interfacial electron exchange rate(s) are sufficiently high and the response is free from mass transport hmitations, the catalytic current will be determined by the inherent activity of the enzyme. Variation of current (activity) with potential can be explained by an extension of the Michaelis-Menten description of enzyme kinetics that relates activity to oxidation state through incorporation of the Nemst equation." " The resulting expressions describe the catalytic cycle, and include rates of intramolecular electron exchange, chemical events, substrate binding and product release, together with the reduction potentials of centres in the enzyme, and the influence of... 

The movement of organic anions such as BSP from blood to bile involves transfer across the sinusoidal and bile canalicular regions of the membrane of hepatic parenchymal cells. The initial rate of removal of BSP from the blood is not related directly to the dose injected (G15) there is a systematic decrease in this rate with increasing doses of the dye. It was proposed (G15) that the transfer of the dye from blood into liver can be described in a manner similar to that of Michaelis-Menten (M22) for enzyme kinetics, i.e.. 

The equations of enzyme kinetics provide a quantitative way of desaibing the dependence of enzyme rate on substrate concentration. The simplest of these equations, the Michaelis-Menten equation, relates the initial velocity (Vj) to the concentration of substrate [S] and the two parametCTS and (Equation 9.1) The of the enzyme is the maximal velocity that can be achieved at an infinite concentration of substrate, and the of the enzyme for a substrate is the concentration of substrate required to reach Vz V iax- The Michaelis-Menten model of enzyme kinetics applies to a simple reaction in which the enzyme and substrate form an enzyme-substrate complex (ES) that can dissociate back to the free enzyme and substrate. The initial velocity of product formation, Vj, is proportionate to the concentration of enzyme-substrate complexes [ES]. As substrate concentration is increased, the concentration of enzyme-substrate complexes increases, and the reaction rate inaeases proportionately. 

Although computer software is now readily available to fit enzyme kinetic data to the Michaelis-Menten and related equations, it can be instructive to use simple graphical methods in some cases. The most convenient of these (though not necessarily the most accurate) are based on doublereciprocal methods that convert the hyperbolic rate equations into much simpler linear forms for plotting. 

This relation, often referred to as Langmuir-Hinshelwood kinetics, is similar to Michaelis-Menten kinetics used to define enzyme-catalyzed processes (p. 303), and a comparable linear form... 

---