Hyperbolic curve, enzyme catalyzed reaction

Figure Cl. 1.2 shows a typical time course resulting from a continuous assay of product formation in an enzyme-catalyzed reaction. The hyperbolic nature of the curve illustrates that the reaction rate decreases as the reaction nears completion. The reaction rate, at any given time, is the slope of the line tangent to the curve at the point corresponding to the time of interest. Reaction rates decrease as reactions progress for several reasons, including substrate depletion, reactant concentrations approaching equilibrium values (i.e., the reverse reaction becomes relevant), product inhibition, enzyme inactivation, and/or a change in reaction conditions (e.g., pH as the reaction proceeds). With respect to each of these reasons, their effects will be at a minimum in the initial phase of the reaction—i.e., under conditions corresponding to initial velocity measurements. Hence, the interpretation of initial velocity data is relatively simple and thus widely used in enzyme-related assays.

Sigmoid rate curve. The purple line shows how the reaction rate, for a reaction catalyzed by a cooperative enzyme, varies with the substrate concentration. For comparison, the black line shows the shape of the hyperbolic curve seen with reactions catalyzed by enzymes that obey the Michaelis-Menten equation. 

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 non-regulatory 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 e 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). 

---