Sigmoidal substrate saturation curves

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,... 

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)-... 

In other words, a sigmoidal substrate saturation curve that fits the velocity equation of the former model can be shown to fit the velocity equation of the latter model as weU. 

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. 

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. 

Consequently, substrate saturation curves are sigmoid instead of hyperbolic. CTP exerts its inhibitory effect by increasing the interaction between the four catalytic binding sites, which decreases the affinity of the enzyme for the substrate. 

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). 

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. 

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... 

Irrespective of the interpretative approach, it is now widely recognised that many enzymes do show marked deviations from Michaelis-Menten behaviour, and the deviation is often interpretable in terms of regulatory function in vivo. Thus, for example, a number of enzymes, including threonine deaminase [30] and aspartate transcarbamylase [31] as textbook cases, show a sigmoid, rather than hyperbolic dependence of rate upon substrate concentration. This, like the oxygen saturation curve of haemoglobin, permits a response to changes in substrate concentration... 

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