Sigmoidal saturation kinetics

Figure 8-6. Representation of sigmoid substrate saturation kinetics.

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). 

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... 

Biphasic Kinetics (Nonasymptotic) For the purposes of this discussion, a biphasic kinetic profile is defined as one in which the kinetic profile does not follow saturation kinetics and has two distinct phases (Fig. 4.6). Note that sigmoidal kinetics may also be biphasic but exhibits saturation. 

Many regulatory enzymes are allosterically controlled by a product or products of the reaction sequence that is to say they are subject to feedback control. The binding of an effector to the enzyme causes a conformational change which is transmitted to the active site and causes either an increase or a decrease in activity over a range of substrate concentrations. Frequently, in the absence of an activator or in the presence of an inhibitor, the enzyme exhibits sigmoidal kinetics with respect to substrate concentration. Addition of the activator or removal of the inhibitor restores normal saturation kinetics. 

In contrast to the kinetics of isosteric (normal) enzymes, allosteric enzymes such as ACTase have sigmoidal (S-shaped) substrate saturation curves (see p. 92). In allosteric systems, the enzyme s af nity to the substrate is not constant, but depends on the substrate concentration [A]. Instead of the Michaelis constant Km (see p. 92), the substrate concentration at half-maximal rate ([AJo.s) is given. The sigmoidal character of the curve is described by the Hill coef cient h. In isosteric systems, h = 1, and h increases with increasing sigmoid icity. 

The first product of nitrosyl transfer to nitrite in Eq. (2), E N203, contains N-N bonded N2O3 which is itself a well-known and powerful nitrosyl donor. It is reasonable to suppose therefore that nitrosyl transfer reactions with N- and O-nucleophiles could involve both E NO (or E HONO) and E N205. In addition, the involvement of a second molecule of nitrite for denitrification would require that the substrate saturation curve should be sigmoidal to reflect a term second-order in nitrite concentration. No such effect has been reported to our knowledge. The use of bimolecular substrate kinetics in dilute solutions to generate an intermediate subject to solvolysis seems metabolically unwise hut not impossible. 

The previous section illustrated how allosteric cooperativity can result in a sigmoidal relationship between binding saturation and substrate concentration. In this section, we demonstrate how a sigmoidal relationship between product concentration and time can arise from enzyme kinetics with time lags. 

In contrast to competitive immunoassays, the number of theoretical models describing the kinetics and thermodynamics of non-competitive immunoassays is considerably lower and most of them are derived from double-site immunometric configurations. The dose-response curve for such assays is sigmoid the signal increasing with the analyte concentration with a plateau value reached when the capture antibody becomes saturated. 

Fig. 9.3. A comparison between hexokinase I and glucokinase. The initial velocity (vj) as a fraction of is graphed as a function of glucose concentration. The plot for glucokinase (heavy blue line) is slightly sigmoidal (S-shaped), possibly because the rate of an intermediate step in the reaction is so slow that the enzyme does not follow Michaelis-Menten kinetics. The dashed blue line has been derived from the Michaelis-Menten equation fitted to the data for concentrations of glucose above 5 mM. For S-shaped curves, the concentration of substrate required to reach half or half-saturation, is sometimes called the Sq 5 or Kq 5, rather than K. At = 0.5, the is 5 mM, and...

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)-... 

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