Enzyme kinetics sigmoidal binding curve

Kmi would be the standard Michaelis constant for the binding of the first substrate, if [ESS] = 0. Km2 would be the standard Michaelis constant for the binding of the second substrate, if [E] = 0 (i.e., the first binding site is saturated). In the complete equation, these constants are not true Km values, but their form (i.e., Km] = (k2 + k25)/k 2) and significance are analogous. Likewise, k25 and k35 are Vmi/Et and Vm2/Et terms when the enzyme is saturated with one and two substrate molecules, respectively. Equation (10) describes several non-Michaelis-Menten kinetic profiles. Autoactivation (sigmoidal saturation curve) occurs when k35 > k24 or Km2 < Km 1, substrate inhibition occurs when k24 > 35, and a biphasic saturation... 

Figure 10.3 ATCase displays sigmoidal kinetics. A plot of product formation as a function of substrate concentration produces a sigmoidal curve because the binding of substrate to one active site increases the activity at the other active sites. Thus, the enzyme shows cooperativity.

Why do chymotrypsin and ATCase have different velocity curves Chymotrypsin and aspartate transcar-bamoylase exhibit different types of kinetics. Chymotrypsin is a nonallosteric enzyme and exhibits hyperbolic kinetics. ATCase is an allosteric enzyme. It has multiple subunits, and the binding of one molecule of substrate affects the binding of the next molecule of substrate. It exhibits sigmoidal kinetics. 

In the case of the oligomeric enzymes the kinetic cooperativity is more complex. The interactions between the subunits can influence the rate (speed) of the transition or even alter the three-dimensional structure of the subunits themselves. Weakly coupled subunits generate no sigmoidal substrate saturation curve and in this instance the kinetic cooperativity can be greater or smaller than the corresponding substrate binding cooperativity. This is the case for V2, as it can be seen from the values of h exf(13)-... 

A large family of enzymes that deviate from hyperbolic kinetics (Michaelis) is the allosteric enzymes. These enzymes contain two or more topologically distinct binding sites that interact functionally with each other. Most commonly, sigmoidal or S-shaped curves are obtained, being indicative of positive substrate cooperativity. The reaction rate for these enzymes can be calculated by the Hill equation ... 

Cooperative substrate binding results in sigmoidal v versus [S] curves (Fig. 8.1). The Michaelis-Menten model is therefore not appMcable to cooperative enzymes. Two major equihbrium models have evolved to describe the catalytic behavior of cooperative enzymes the sequential interaction and concerted transition models. The reader should be aware that other models have also been developed, such as equilibrium association-dissociation models, as well as several kinetic models. These are not discussed in this chapter. 

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