Menten Equation

Velocity depends on substrate concentration when [S] is low but does not depend on substrate concentration when [S] is high. 

Mathematically, the Michaelis-Menten equation is the equation of a rectangular hyperbola. Sometimes you ll here reference to hyperbolic kinetics, this means it follows the Michaelis-Menten equation. A number of other names also imply that a particular enzyme obeys the Michaelis-Menten equation Michaelis-Menten behavior, saturation kinetics, and hyperbolic kinetics. 

The initial velocity is measured at a series of different substrate concentrations. In all cases the concentration of substrate used is much higher (by thousands of times, usually) than that of the enzyme. Each substrate concentration requires a separate measurement of the initial velocity. At low concentrations of substrate, increasing the substrate concentration increases the velocity of the reaction, but at high substrate concentrations, increasing the initial substrate concentration does not have much of an effect on the velocity (Fig. 8-4). 

The derivation of the equation is found in most texts and for the most part can be ignored. What you want to understand is how and why it works as it does. 

When there is no substrate present ([S] = 0), there is no velocity— so far, so good. As the substrate concentration [S] is increased, the reaction goes faster as the enzyme finds it easier and easier to locate the substrate in solution. At low substrate concentrations ([S] K, dou- 

Note that [A] is assumed to be so large relative to enzyme concentration that it is negligibly decreased by formation of EA. Briggs and Haldane [4] introduced the less restrictive steady-state assumption. Here it is postulated only that the rates of formation and removal of EA through whatever route are equal. This avoids arbitrary assumptions about the relative values of A 2 and A , . Thus now  

Regardless of the assumption adopted in order to obtain the unknown concentrations [E] and [EA] in terms of known quantities, we need a second equation relating [E] and [EA], In fact we know that  

the enzyme conservation equation , simply indicates that the total enzyme concentration in all forms, e, remains constant. If we substitute for E from Eqn. la, we obtain 

We also know that the overall rate of product formation, v, is given by 

If [A] becomes very large, v will approach k-ye, which is therefore defined as the maximum rate. k /k can also be replaced by a single constant, the 

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Since the El complex does not yield product P, and I competes with S for E, there is a state of competitive inhibition. By analogy to the Michaelis-Menten equation ... 

The Michaehs-Menten equation and other similar nonhnear expressions characterize immobihzed enzyme kinetics. Therefore, for a spherical porous carrier particle with enzyme molecules immobilized on its external as well as internal surfaces, material balance of the substrate will result in the following ... 

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 ...

Equation 1-108 can be considered as the Michaelis-Menten equation, where is the Michaelis constant and represented as... 

Equation 11-15 is known as the Michaelis-Menten equation. It represents the kinetics of many simple enzyme-catalyzed reactions, which involve a single substrate. The interpretation of as an equilibrium constant is not universally valid, since the assumption that the reversible reaction as a fast equilibrium process often does not apply. 

The Michaelis-Menten Equation 11-15 is not well suited for estimation of the kinetic parameters and Reananging Equation 11-15 gives various options for plotting and estimating the parameters. 

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]. 

Equation (3-150) is the Michaelis-Menten equation, Vm is the maximum velocity (for the enzyme concentration ,), and is the Michaelis constant. 

The Michaelis-Menten equation is, like Eq. (3-146), a rectangular hyperbola, and it can be cast into three linear plotting forms. The double-reciprocal form, Eq. (3-152), is called the Lineweaver-Burk plot in enzyme kinetics. ... 

Substituting this relationship into the expression for v gives the Michaelis-Menten equation... 

The Michaelis-Menten equation (14.23) describes a curve known from analytical geometry as a rectangular hyperbola. In such curves, as [S] is increased,... 

Linear Plots Can Be Derived from the Michaelis-Menten Equation... 

Because of the hyperbolic shape of versus [S] plots, Vmax only be determined from an extrapolation of the asymptotic approach of v to some limiting value as [S] increases indefinitely (Figure 14.7) and is derived from that value of [S] giving v= V(nax/2. However, several rearrangements of the Michaelis-Menten equation transform it into a straight-line equation. The best known of these is the Lineweaver-Burk double-reciprocal plot ... 

Taking the reciprocal of both sides of the Michaelis-Menten equation. Equation (14.23), yields the equality... 

The Hanes-Woolf plot is another rearrangement of the Michaelis-Menten equation that yields a straight line ... 

FIGURE 14.10 A Hanes-Wolff plot of [S]/l/versus [S], another straight-line rearrangement of the Michaelis-Menten equation. 

If the kinetics of the reaction disobey the Michaelis-Menten equation, the violation is revealed by a departure from linearity in these straight-line graphs. We shall see in the next chapter that such deviations from linearity are characteristic of the kinetics of regulatory enzymes known as allosteric enzymes. Such regulatory enzymes are very important in the overall control of metabolic pathways. 

It is revealing to compare the equation for the uninhibited case. Equation (14.23) (the Michaelis-Menten equation) with Equation (14.43) for the rate of the enzymatic reaction in the presence of a fixed concentration of the competitive inhibitor, [I]... 

If the three-parameter Michaelis-Menten equation is divided by C i, it becomes the same as the three-parameter Langmuir-I linshelwood equation where 1/Cm = Ka. Both these rate equations can become quite complex when more than one species is competing with the reactant(s) for the enzyme or active sites on the solid catalyst. 

In evaluation of kinetic parameters, the double reciprocal method is used for linearisation of the Michaelis-Menten equation (5.7.3). 

The above equation can be transformed into the Michaelis-Menten equation by multiplying the numerator and denominator by Km ... 

Membrane module, 369-373 Methylophilus methylotrophus, 338 Michaelis-Menten equation, 109, 137 Microfiltration, 357... 

With the Michaelis-Menten equation, there is no integrated solution for the concentration, but only for the time... 

Kinetic data fitting the rate equation for catalytic reactions that follow the Michaelis-Menten equation, v = k A]/(x + [A]), with[A]0 = 1.00 X 10 J M, k = 1.00 x 10 6 s 1, and k = 2.00 X 10-J molL1. The left panel displays the concentration-time profile on the right is the time lag approach. 

The rates of many catalyzed reactions depend upon substrate concentrations, as shown in Fig. 4-7. The rate at high substrate concentrations is zeroth-order with respect to [S], falling until it shows a first-order dependence in the limit of low [S], This pattern is that of a rectangular hyperbola, defined by an empirical relation known as the Michaelis-Menten equation. 

A noncompetitive inhibitor is one that binds to both E and E S. If both dissociation constants are the same, the Michaelis-Menten equation is... 

Enzyme kinetics. Data for reactions that follow the Michaelis-Menten equation are sometimes analyzed by a plot of v,/tA]o versus l/[A]o. This treatment is known as an Eadie-Hofstee plot. Following the style of Fig. 4-7b, sketch this function and label its features. 

Michaelis-Menten equation, 35, 90-94 Microscopic reversibility, principle of, 172-175... 

A sink flux that has a weaker than proportional dependence on the content M of the emitting reservoir is often described by the Michaelis-Menten equation ... 

Coe and Bessell and coworkers studied the metabolic fates of 2-deoxy-2-fluoro-D-glucose (2DFG) and related compounds by using yeast hexokinase (as a model for mammalian hexokinase), and determined the kinetic constants K and V ) of the Michaelis-Menten equation D-glucose 0.17 (K in mAf)> 1 00 (relative value, D-glucose taken as 1) 2DG 0.59 0.11, 0.85 2DFG 0.19 0.03, 0.50 2-deoxy-2-fluoro-D-mannose (2DFM) 0.41 0.05, 0.85 2-deoxy-2,2-difluoro-D-nraZ>//Jo-hexose... 

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