Michaelis-Menten -

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

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 biodegradation rate R is characterized by the Monod (or Michaelis-Menten) following relationship ... 

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 ...

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

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... 

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. 

LINEARIZED FORM OF THE INTEGRATED MICHAELIS-MENTEN (MM) EQUATION... 

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]. 

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,... 

The turnover number of an enzyme, is a measure of its maximal catalytic activity, is defined as the number of substrate molecules converted into product per enzyme molecule per unit time when the enzyme is saturated with substrate. The turnover number is also referred to as the molecular activity of the enzyme. For the simple Michaelis-Menten reaction (14.9) under conditions of initial velocity measurements, Provided the concentration of... 

Under physiological conditions, [S] is seldom saturating, and itself is not particularly informative. That is, the in vivo ratio of [S]/A , usually falls in the range of 0.01 to 1.0, so active sites often are not filled with substrate. Nevertheless, we can derive a meaningful index of the efficiency of Michaelis-Menten-type enzymes under these conditions by employing the following equations. As presented in Equation (14.23), if... 

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. 

The Effect of Various Types of Inhibitors on the Michaelis-Menten Rate Equation and on Apparent K, and Apparent F ,ax ... 

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]... 

For a Michaelis-Menten reaction, ki = 7X10VAf- sec, /f i = 1 X lOVsec, and fe = 2 X lOVsec. What are the values of Ks and Does substrate binding approach equilibrium or does it behave more like a steady-state system ... 

Smith, W. G., 1992. In kinetics and the reversible Michaelis-Menten model. Journal of Chemical Education 12 981 — 984. 

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.)... 

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. 

Each of the processes shown in Figure 2.8 can be described by a Michaelis-Menten type of biochemical reaction, a standard generalized mathematical equation describing the interaction of a substrate with an enzyme. Michaelis and Men ten realized in 1913 that the kinetics of enzyme reactions differed from the kinetics of conventional... 

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