Sigmoidal saturation

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). 

In the absence of activators AMP aminohydrolase from brain (149), erythrocytes (143, 150), muscle (145), and liver (128) gave sigmoid curves for velocity vs. AMP concentration which were hyperbolic after the addition of monovalent cations, adenine nucleotides, or a combination of monovalent cations and adenine nucleotides. For the rabbit muscle enzyme (145), addition of K+, ADP, or ATP produced normal hyperbolic saturation curves for AMP as represented by a change in the Hill slope nH from 2.2 to 1.1 Fmax remained the same. The soluble erythrocyte enzyme and the calf brain enzyme required the presence of both monovalent cations and ATP before saturation curves became hyperbolic. In contrast, the bound human erythrocyte membrane enzyme did not exhibit sigmoid saturation curves and K+ activation was not affected by ATP (142). 

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 4 Effect of quinine on the carbamazepine saturation curve. Quinine makes the sigmoidal saturation curve more hyperbolic. Source Courtesy of K. Nandigama and K. Korzekwa (unpublished results).

Two other examples of sigmoidal reactions that are made linear by an activator include a report by Johnson et al. (31), who showed that pregnenolone has a nonlinear double-reciprocal plot that was made linear by the presence of 5 pM 7,8-benzoflavone, and Ueng et al. (23), who showed that aflatoxin B1 has sigmoidal saturation curve that is made more hyperbolic by 7,8-benzoflavone. As with the effect of quinine on carbamazepine metabolism, 7,8-benzoflavone is an activator at low aflatoxin B1 concentrations and an inhibitor at high aflatoxin B1 concentrations. 

In mammalian systems, the initial evidence for feedback control was obtained in in vivo systems by showing that purines were effective inhibitors of the accumulation of an early intermediate, formyl-GAR [51-54]. A purified enzyme preparation has been obtained from cell culture of a mouse tumor [55]. It shows a sigmoidal saturation curve with PRPP (n = 1.9). All nucleotides are inhibitory, the most potent being dGDP. The inhibitory patterns were altered by Mg, diphosphate and triphosphate nucleotides (except GTP) becoming less inhibitory with increase in Mg concentration. 

For hemoglobin, n 2.8 (sigmoidal saturation curve), and for myoglobin, n = 1 (hyperbolic saturation curve). The efficiency of O2 transfer from hemoglobin to myoglobin is further enhanced by a decrease in pH since oxygen binding is pH-dependent (the Bohr effect). 

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