Sigmoidal saturation curve

The converse situation applies in the presence of I, which binds only to T. T binding will lead to an increase in the population of T conformers, at the expense of Rq (Figure 15.11). The decline in [Rq] means that it is less likely for S (or A) to bind. Consequently, the presence of I increases the cooperativity (that is, the sigmoidicity) of the substrate saturation curve, as evidenced by the shift of this curve to the right (Figure 15.11). The presence of I raises the apparent value of L. 

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. 

Binding of O2 to one of the subunits of the T form leads to a local conformational change that weakens the association between the subunits. Increasing O2 partial pressure thus means that more and more molecules convert to the higher-af nity R form. This cooperative interaction between the subunits increases the O2 af nity of Hb with increasing O2 concentrations—i. e., the O2 saturation curve is sigmoidal (see p. 282). 

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. 

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). 

Other heterotropic allosteric enzymes respond to an activator by an increase in Fmax with little change in if0i5 (Fig. 6-29c). A negative modulator (an inhibitor) may produce a more sigmoid substrate-saturation curve,... 

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 Zmax. The central curve shows the substrate-activity relationship without a modulator, (c) A less common type of modulation, in which Vmax is altered and /C0.sis nearly constant. 

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. 

Binding of 02 to one heme group in hemoglobin increases the affinity for 02 of its other heme groups. This effect produces the sigmoidal oxygen saturation curve. 

Figure 2-13. Oxygen saturation curves for myoglobin and adult hemoglobin (HbA). Myoglobin has a hyperbolic saturation curve. HbA has a sigmoidal curve. The HbA curve shifts to the right at lower pH, with higher concentrations of 2,3-bisphosphoglycerate (BPG), or as C02 binds in the tissues. Thus, 02 is released more readily. P50 ( ) is the partial pressure of 02 at which HbA is half-saturated with 02.

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