Enzyme kinetics sigmoidal

The answer is c. (Murray, pp 48-73. Scriver, pp 4571-4636. Sack, pp 3-17. Wilson, pp 287-317.) Allosteric enzymes, unlike simpler enzymes, do not obey Michaelis-Menten kinetics. Often, one active site of an allosteric enzyme molecule can positively affect another active site in the same molecule. This leads to cooperativity and sigmoidal enzyme kinetics in a plot of [S] versus V The terms competitive inhibition and noncompetitive inhibition apply to Michaelis-Menten kinetics and not to allosteric enzymes. 

Comparison of hyperbolic and sigmoidal enzyme kinetics. The plot of velocity, rate of reaction, versus concentration of substrate or activator shows the response of a hyperbolic (Michaelis-Menten) reaction in black. The response of a sigmoidal reaction is shown by the purple curve. The shaded area indicates the range of physiological concentrations of substrate or activator. 

FIGURE 15.8 Sigmoid versus [S] plot. The dotted line represents the hyperbolic plot characteristic of normal Michaelis-Men ten-type enzyme kinetics. 

For example, Bachelard used [Mgtotai]/[ATPtotai ] = 1 in his rate studies, and he obtained a slightly sigmoidal plot of initial velocity versus substrate ATP concentration. This culminated in the erroneous proposal that brain hexokinase was allosterically activated by magnesium ions and by magnesium ion-adenosine triphosphate complex. Purich and Fromm demonstrated that failure to achieve adequate experimental control over the free magnesium ion concentration can wreak havoc on the examination of enzyme kinetic behavior. Indeed, these investigators were able to account fully for the effects obtained in the previous hexokinase study. ... 

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). 

The previous section illustrated how allosteric cooperativity can result in a sigmoidal relationship between binding saturation and substrate concentration. In this section, we demonstrate how a sigmoidal relationship between product concentration and time can arise from enzyme kinetics with time lags. 

In quantitative determinations usually the optical density of the product is measured. Absorbance values, obtained for different dilutions of the antibody or antigen of known concentration, mostly yield sigmoidal calibration dose-response curves. Although this procedure seems rather simple and straightforward, it is not. Enzyme kinetics may be influenced by any of the factors discussed in Chapter 9. Correlation of absorbance with sample dilution beyond the linear... 

It is interesting to note that this sigmoidal character of enzyme kinetics plays an essential role in regulation. Most of the regulatory enzymes in the metabolic pathways of amino acid biosyntheses and in carbohydrate metabolism exhibit such behavior, with the result that the kinetics can change in the presence of effectors (intermediary metabolities) from sigmoid to hyperbolic (see glycolysis oscillations. Sect. 5.2.1). 

Hill plot A graphical procedure used to fit experimental enzyme kinetic data to an S-shaped or sigmoidal curve that deviates firom Michaelis-Menten kinetics. It involves plotting log V/(V-v) as a function of the substrate concentration, S, where Vis the maximum velocity, and v is the observed velocity. The straight line has a gradient that indicates the number of interacting sites on the enzyme or enzyme complex. 

In the semilogarithmic plot (Figure 112.1a), the curves have the same sigmoidal shape and differ only by lateral displacement. The symmetrical sigmoidal shape is a property of the hyperbolic saturation function, which is frequently used to fit fluence-response curves and other types of stimulus-response relationships in sensory physiology, - in photochemical kinetics, and in other areas of biophysics and biology, including the well-known MichaeHs-Menten enzyme kinetics (see below). 

Cooperative enzymes show sigmoid or sigmoidal kinetics because the dependence of the initial velocity on the concentration of the substrate is not Michaelis-Menten-like but gives a sigmoid curve (Fig. 8-7). 

If an approximate Km value for the enzyme-substrate combination of interest is known, a full-scale kinetic assay may be done immediately. However, often an approximate value is not known and it is necessary first to do a range finding or suck and see preliminary assay. For such an assay, a concentrated substrate solution is prepared and tenfold serial dilutions of the substrate are made so that a range of substrate concentrations is available within which the experimenter is confident the Km value lies. Initial velocities are determined at each substrate concentration, and data may he plotted either hyperholically (as V versus [S]) or with [S] values expressed as logio values. In the latter case, a sigmoidal curve is fitted to data with a three parameter logistic equation (O Eq. 4) ... 

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. 

In the late 1960s, two groups reported results that indicated the possibility of more than one form of MAO. In 1967, Maitre suggested that tissue (brain vs liver)-dependent potencies of inhibitors could be explained by the presence of different forms of MAO [4]. In 1968, Johnston published an analysis of unusual kinetics observed with the new MAO inhibitors that were being developed. He concluded that the most reasonable hypothesis to explain such results as double sigmoid curves was the existence of at least two forms of the enzyme [5]. By the mid-1980s, differences of substrate and inhibitor specificity of two MAOs, now called MAO A and B, were well understood [6]. 

PFK displays sigmoidal kinetics for the conversion of fructose-6-P, although not for ATP. The enzyme is allosterically activated by ADP and allosterically inhibited by phos-phoenolpyruvate (fig. 2.6). 

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). 

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. 

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