Enzymes sigmoidal saturation curve

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... 

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. 

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. 

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. 

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... 

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)-... 

Our own work with the enzyme obtained from Salmonella [49] confirms the synergistic inhibition by AMP and GMP. In addition, an intermediate precursor, AICAR, was found to be as effective as AMP and GMP alone and synergistic with either. With a partially purified preparation, sigmoidal PRPP saturation curves were obtained with an interaction coefficient of 1.8 obtained by the Hill plot. This sigmoid... 

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. 

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