Sigmoidal curves, allosteric

As noted previously, in all cases these various functions describe an inverse sigmoidal curve between the displacing ligand and the signal. Therefore, the mechanism of interaction cannot be determined from a single displacement curve. However, observation of a pattern of such curves obtained at different tracer ligand concentrations (range of [A ] values) may indicate whether the displacements are due to a competitive, noncompetitive, or allosteric mechanism. 

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. 

Hyperbolic shape of the enzyme kinetics curve Most enzymes show Michaelis-Menten kinetics (see p. 58), in which the plot of initial reaction velocity, v0, against substrate concentration [S], is hyperbolic (similar in shape to that of the oxygen-dissociation curve of myoglobin, see p. 29). In contrast, allosteric enzymes frequently show a sigmoidal curve (see p. 62) that is similar in shape to the oxygen-dissociation curve of hemoglobin (see p. 29). 

Shapes of the kinetics curves for simple and allosteric enzymes Enzymes following Michaelis-Menten kinetics show hyperbolic curves when the initial reaction velocity (v0) of the reaction is plotted against substrate concentration. In contrast, allosteric enzymes generally show sigmoidal curves. 

Not all enzymes afford a hyperbolic relationship between their rate and substrate concentration. Sigmoidal curves are common and indicate either cooperativity in a multienzyme complex or involvement of an allosteric site on the enzyme (Figure 4.10). These types of curves can be fit by introducing exponents on [S] and Km in Equation 4.11. 

A plot of VQ against [S] for an allosteric enzyme gives a sigmoidal-shaped curve. Allosteric enzymes often have more than one active site which co-operatively bind substrate molecules, such that the binding of substrate at one active site induces a conformational change in the enzyme that alters the affinity of the other active sites for substrate. Allosteric enzymes are often multi-subunit proteins, with an active site on each subunit. In addition, allosteric enzymes may be controlled by effector molecules (activators or inhibitors) that bind to a site other than the active site and alter the rate of enzyme activity. Aspartate transcarbamoylase is an allosteric enzyme that catalyzes the committed step in pyrimidine biosynthesis. This enzyme consists of six catalytic subunits each with an active site and six regulatory subunits to which the allosteric effectors cytosine triphosphate (CTP) and ATP bind. Aspartate transcarbamoylase is feedback-inhibited by the end-product of the pathway, CTP, which acts as an allosteric inhibitor. In contrast, ATP an intermediate earlier in the pathway, acts as an allosteric activator. 

Aspartate transcarbamoylase (aspartate carbamoyltransferase ATCase), a key enzyme in pyrimidine biosynthesis (see Topic FI), provides a good example of allosteric regulation. ATCase catalyzes the formation of N-carbamoylaspar-tate from aspartate and carbamoyl phosphate, and is the committed step in pyrimidine biosynthesis (Fig. 2). The binding of the two substrates aspartate and carbamoyl phosphate is cooperative, as shown by the sigmoidal curve of V0 against substrate concentration (Fig. 3). 

Figure 10.12. Basis for the Sigmoidal Curve. The generation of the sigmoidal curve by the property of cooperativity can be understood by imagining an allosteric enzyme as a mixture of two Michaelis-Menten enzymes, one with a high value of n, that corresponds to the T state and another with a low value of that corresponds to the R state. As the concentration of substrate is increased, the equilibrium shifts from the T state to the R state, which results in a steep rise in activity with respect to substrate concentration.

Displacement experiments yield an inverse sigmoidal curve for nearly all modes of antagonism. Competitive, noncompetitive, and allosteric antagonism can be discerned from the pattern of multiple displacement curves. 

Allosteric enzymes show a sigmoid curve relating initial velocity to substrate concentration (Fig. 8.11). The sigmoid curve starts very slowly because the enzyme has low affinity for substrate. However, binding of one molecule of substrate increases the affinity of the enzyme for subsequent substrate molecules and the curve turns upward and the maximum velocity is soon reached. This is an example of positive cooperativity. 

Cooperative enzymes show sigmoidal curves of reaction rate as a function of substrate concentration. Allosteric regulators may change the Cm ax of such enzymes and/or change the cooperativity. 

Fig. 20.13. Allosteric regulation of isocitrate dehydrogenase (ICDH). Isocitrate dehydrogenase has eight subunits, and two active sites. Isocitrate, NAD, and NADH bind in the active site ADP and Ca are activators and bind to separate allosteric sites. A. A graph of velocity versus isocitrate concentration shows positive cooperativity (sigmoid curve) in the absence of ADP. The allosteric activator ADP changes the curve into one closer to a rectangular h5 perbola, and decreases the (S0.5) for isocitrate. B. The allosteric activation by ADP is not an all-or-nothing response. The extent of activation by ADP depends on its concentration. C. Increases in the concentration of product, NADH, decrease the velocity of the enzyme through effects on the allosteric activation.

When ATGase catalyzes the condensation of aspartate and carbamoyl phosphate to form carbamoyl aspartate, the graphical representation of the rate as a function of increasing substrate concentration (aspartate) is a sigmoidal curve rather than the hyperbola obtained with nonallosteric enzymes (Figure 7.2a). The sigmoidal curve indicates the cooperative behavior of allosteric enzymes. In this two-substrate reaction, aspartate is the substrate for which the concentration is varied, while the concentration of carbamoyl phosphate is kept constant at high levels. 

K and h represent a kind of Michaelis constant and the Hill coefficient, respectively. If Vmax is known, these constants can be calculated from the slope and intercept of the Hill plot (eqn [15]). If the Hill coefficient results equal to one, then there is no coope-rativity and the graph is hyperbolic. An increasing value of h will show an increasingly sigmoidal curve with positive cooperativity for the substrate. A value less than one shows negative cooperativity. The reaction rate of these enzymes is easily controlled by allosteric effectors, activators, or inhibitors, this mechanism being of crucial importance for the control of metabolic pathways. Equally important, this mechanism can also be used for the detection of analytes. 

We have observed a stimulation of ADP-ribosylation by nanomolar concentrations of benzamides both in intact and permeabilized cells. This stimulation is reminiscent of that found with competitive inhibitors of allosteric enzymes. At very low NAD " concentrations, Kun has reported finding a sigmoidal curve of velocity versus NAD concentration for purified nuclear ADP-ribosyl transferase (12). The observed allosteric behavior is likely to arise from the interaction of NAD binding sites either on the same or different enzyme molecules. There is no evidence that nuclear ADP-ribosyl transferase is an oligomeric protein. More than one nuclear ADP-ribosyl transferase molecule is involved however in the... 

Allosteric enzymes show anomalous kinetics. Instead of the usual simple hyperbolic substrate concentration curve a sigmoid curve is obtained, which means that at low [S] values the reaction is slow but as [S] increases so the rate of reaction is greatly increased (Figure 6.9). 

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