Regulatory Enzymes:- The Kinetic Properties of Allosteric Enzymes Diverge from Michaelis-Menten Behavior
Allosteric enzymes show relationships between V0 and [S] that differ from Michaelis-Menten kinetics. They do exhibit saturation with the substrate when [S] is sufficiently high, but for some allosteric enzymes, plots of V0 versus [S] (Fig. 6–29) produce a sigmoid saturation curve, rather than the hyperbolic curve typical of nonregulatory enzymes. On the sigmoid saturation curve we can find a value of [S] at which V0 is half-maximal, but we cannot refer to it with the designation Km, because the enzyme does not follow the hyperbolic Michaelis Menten relationship. Instead, the symbol [S]0.5 or K0.5 is often used to represent the substrate concentration giving half-maximal velocity of the reaction catalyzed by an allosteric enzyme (Fig. 6–29). Sigmoid kinetic behavior generally reflects cooperative interactions between protein subunits. In other words, changes in the structure of one subunit are translated into structural changes in adjacent subunits, an effect mediated by noncovalent interactions at the interface between subunits. The principles are particularly well illustrated by a nonenzyme: O2 binding to hemoglobin. Sigmoid kinetic behavior is explained by the concerted and sequential models for subunit inter actions (see Fig. 5–15). Homotropic allosteric enzymes generally are multi subunit proteins and, as noted earlier, the same binding site on each subunit functions as both the active site and the regulatory site. Most commonly, the substrate acts as a positive modulator (an activator), because the subunits act cooperatively: the binding of one molecule of substrate to one binding site alters the enzyme’s con formation and enhances the binding of subsequent substrate molecules. This accounts for the sigmoid rather than hyperbolic change in V0 with increasing [S]. One characteristic of sigmoid kinetics is that small changes in the concentration of a modulator can be associated with large changes in activity. As is evident in Figure 6–29a, a relatively small increase in [S] in the steep part of the curve causes a comparatively large increase in V0. For heterotropic allosteric enzymes, those whose modulators are metabolites other than the normal substrate, it is difficult to generalize about the shape of the substrate-saturation curve. An activator may cause the curve to become more nearly hyperbolic, with a decrease in K0.5 but no change in Vmax, resulting in an increased reaction velocity at a fixed substrate concentration (V0 is higher for any value of [S]; Fig. 6–29b, upper curve).
Other heterotropic allosteric enzymes respond to an activator by an increase in Vmax with little change in K0.5 (Fig. 6–29c). A negative modulator (an inhibitor) may produce a more sigmoid substrate-saturation curve, with an increase in K0.5 (Fig. 6–29b, lower curve). Heterotropic allosteric enzymes therefore show different kinds of responses in their substrate-activity curves, because some have inhibitory modulators, some have activating modulators, and some have both.
FIGURE 6–29 Substrate-activity curves for representative allosteric enzymes. Three examples of complex responses of allosteric enzymes to their modulators. (a) The sigmoid curve of a homotropic enzyme, in which the substrate also serves as a positive (stimulatory) modulator, or activator. Note the resemblance to the oxygen-saturation curve of hemoglobin (see Fig. 5–12). (b) The effects of a positive modulator (+) and a negative modulator ( ) on an allosteric enzyme in which K0.5 is altered without a change in Vmax. The central curve shows the substrate-activity relationship without a modulator. (c) A less common type of modulation, in which Vmax is altered and K0.5 is nearly constant.
