Allosteric enzymes kinetics

In contrast with Michaelian enzymes, which have hyperbolic kinetics, allosteric enzymes, thanks to their sigmoidal kinetics, possess an enhanced sensitivity towards variations in the concentration of an effector or of the substrate. This is the reason why many enzymes that play an important role in the control of metabolism are of the allosteric type. 

Allosteric enzymes display sigmoidal kinetics when rates are plotted versus substrate concentration. Michaelis-Menten enzymes exhibit hyperbolic kinetics. Allosteric enzymes usually have multiple subunits, and the binding of substrates or effector molecules to one subunit changes the binding behavior of the other subunits. 

The basic kinetic properties of this allosteric enzyme are clearly explained by combining Monod s theory and these structural results. The tetrameric enzyme exists in equilibrium between a catalytically active R state and an inactive T state. There is a difference in the tertiary structure of the subunits in these two states, which is closely linked to a difference in the quaternary structure of the molecule. The substrate F6P binds preferentially to the R state, thereby shifting the equilibrium to that state. Since the mechanism is concerted, binding of one F6P to the first subunit provides an additional three subunits in the R state, hence the cooperativity of F6P binding and catalysis. ATP binds to both states, so there is no shift in the equilibrium and hence there is no cooperativity of ATP binding. The inhibitor PEP preferentially binds to the effector binding site of molecules in the T state and as a result the equilibrium is shifted to the inactive state. By contrast the activator ADP preferentially binds to the effector site of molecules in the R state and as a result shifts the equilibrium to the R state with its four available, catalytically competent, active sites per molecule. 

If the kinetics of the reaction disobey the Michaelis-Menten equation, the violation is revealed by a departure from linearity in these straight-line graphs. We shall see in the next chapter that such deviations from linearity are characteristic of the kinetics of regulatory enzymes known as allosteric enzymes. Such regulatory enzymes are very important in the overall control of metabolic pathways. 

Because this enzyme catalyzes the committed step in fatty acid biosynthesis, it is carefully regulated. Palmitoyl-CoA, the final product of fatty acid biosynthesis, shifts the equilibrium toward the inactive protomers, whereas citrate, an important allosteric activator of this enzyme, shifts the equilibrium toward the active polymeric form of the enzyme. Acetyl-CoA carboxylase shows the kinetic behavior of a Monod-Wyman-Changeux V-system allosteric enzyme (Chapter 15). 

To refer to the kinetics of allosteric inhibition as competitive or noncompetitive with substrate carries misleading mechanistic implications. We refer instead to two classes of regulated enzymes K-series and V-se-ries enzymes. For K-series allosteric enzymes, the substrate saturation kinetics are competitive in the sense that is raised without an effect on V. For V-series allosteric enzymes, the allosteric inhibitor lowers... 

When binding of a substrate molecule at an enzyme active site promotes substrate binding at other sites, this is called positive homotropic behavior (one of the allosteric interactions). When this co-operative phenomenon is caused by a compound other than the substrate, the behavior is designated as a positive heterotropic response. Equation (6) explains some of the profile of rate constant vs. detergent concentration. Thus, Piszkiewicz claims that micelle-catalyzed reactions can be conceived as models of allosteric enzymes. A major factor which causes the different kinetic behavior [i.e. (4) vs. (5)] will be the hydrophobic nature of substrate. If a substrate molecule does not perturb the micellar structure extensively, the classical formulation of (4) is derived. On the other hand, the allosteric kinetics of (5) will be found if a hydrophobic substrate molecule can induce micellization. 

In addition to the binding of substrate (or in some cases co-substrates) at the active site, many enzymes have the capacity to bind regulatory molecules at sites which are usually spatially far removed from the catalytic site. In fact, allosteric enzymes are invariably multimeric (i.e. have a quaternary structure) and the allosteric (regulatory) sites are on different subunits of the protein to the active site. In all cases, the binding of the regulatory molecules is non covalent and is described in kinetic terms as noncompetitive inhibition. 

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. 

B. i. Kurganov (1982) Allosteric Enzymes Kinetic Behavior, Wiley,... 

Figure 1. Plot of v/V ax versus the millimolar concentration of total substrate for a model enzyme displaying Michaelis-Menten kinetics with respect to its substrate MA (i.e., metal ion M complexed to otherwise inactive ligand A). The concentrations of free A and MA were calculated assuming a stability constant of 10,000 M k The Michaelis constant for MA and the inhibition constant for free A acting as a competitive inhibitor were both assumed to be 0.5 mM. The ratio v/Vmax was calculated from the Michaelis-Menten equation, taking into account the action of a competitive inhibitor (when present). The upper curve represents the case where the substrate is both A and MA. The middle curve deals with the case where MA is the substrate and where A is not inhibitory. The bottom curve describes the case where MA is the substrate and where A is inhibitory. In this example, [Mfotai = [Afotai at each concentration of A plotted on the abscissa. Note that the bottom two curves are reminiscent of allosteric enzymes, but this false cooperativity arises from changes in the fraction of total "substrate A" that has metal ion bound. For a real example of how brain hexokinase cooperatively was debunked, consult D. L. Purich H. J. Fromm (1972) Biochem. J. 130, 63.

Finally, because nucleotides can also act as allosteric effectors, an investigator seeking to characterize the kinetic properties of allosteric enzymes should consider using the methods described above to determine whether the true effector is the free nucleotide or the form com-plexed with metal ion. 

C. Many allosteric enzymes have multiple subunits whose interaction accounts for their unusual kinetic properties. 

The Kinetic Properties of Allosteric Enzymes Diverge from Michaelis-Menten Behavior... 

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). 

The activity of allosteric enzymes is adjusted by reversible binding of a specific modulator to a regulatory site. Modulators may be the substrate itself or some other metabolite, and the effect of the modulator may be inhibitory or stimulatory. The kinetic behavior of allosteric enzymes reflects cooperative interactions among enzyme subunits. 

For an enzyme with typical Michaelis-Menten kinetics, the value of e ranges from about 1 at substrate concentrations far below Km to near 0 as Vmax is approached. Allosteric enzymes can have elasticities greater than 1.0, but not larger than their Hill coefficients (p. 167). 

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. 

Allosteric enzymes do not follow the Michaelis-Menten kinetic relationships between substrate concentration Fmax and Km because their kinetic behaviour is greatly altered by variations in the concentration of the allosteric modulator. Generally, homotrophic enzymes show sigmoidal behaviour with reference to the substrate concentration, rather than the rectangular hyperbolae shown in classical Michaelis-Menten kinetics. Thus, to increase the rate of reaction from 10 per cent to 90 per cent of maximum requires an 81-fold increase in substrate concentration, as shown in Fig. 5.34a. Positive cooperativity is the term used to describe the substrate concentration-activity curve which is sigmoidal an increase in the rate from 10 to 90 per cent requires only a nine-fold increase in substrate concentration (Fig. 5.346). Negative cooperativity is used to describe the flattening of the plot (Fig. 5.34c) and requires requires over 6000-fold increase to increase the rate from 10 to 90 per cent of maximum rate. 

Some allosteric enzymes are also classified by the way in which they are affected by the binding of a modulator some affect the value of Km without affecting that of Vmtx- They are classed as K-series enzymes while others, which affect Fmax without affecting Km, are called M-series enzymes. Figure 5.35 shows the characteristic kinetic patterns observed for K-series and M-series enzymes. There are, of course, exceptions to these two extremes of kinetic behaviour. 

One indication of the importance of intersubunit interactions in allosteric enzymes is that many such enzymes do not obey the classical Michaelis-Menten kinetic equation. A... 

Although the Michaelis-Menten model provides a very good model of the experimental data for many enzymes, a few enzymes do not conform to Michaelis-Menten kinetics. These enzymes, such as aspartate transcarbamoylase (ATCase), are called allosteric enzymes (see Topic C5). 

Figure 22 Examples of enzyme kinetic plots used for determination of Km and Vmax for a normal and an allosteric enzyme Direct plot [(substrate) vs. initial rate of product formation] and various transformations of the direct plot (i.e., Eadie-Hofstee, Lineweaver-Burk, and/or Hill plots) are depicted for an enzyme exhibiting traditional Michaelis-Menten kinetics (coumarin 7-hydroxylation by CYP2A6) and one exhibiting allosteric substrate activation (testosterone 6(3-hydroxylation by CYP3A4/5). The latter exhibits an S-shaped direct plot and a hook -shaped Eadie-Hofstee plot such plots are frequently observed with CYP3A4 substrates. Km and Vmax are Michaelis-Menten kinetic constants for enzymes. K is a constant that incorporates the interaction with the two (or more) binding sites but that is not equal to the substrate concentration that results in half-maximal velocity, and the symbol n (the Hill coefficient) theoretically refers to the number of binding sites. See the sec. III.C.3 for additional details.

It was noted earlier that Michaelis-Menten kinetics and its linear transformations are not valid for allosteric enzymes. Instead, the Hill equation, an equation originally empirically developed to describe the cooperative binding of Oz to hemoglobin (Chapter 7), is used. The expression describing such a straight-line plot is... 

The Hill equation is used to estimate Km for allosteric enzymes. Equations based on classic Michaelis-Menten kinetics are not applicable. 

Allosteric Effectors. Many enzymes are subject to metabolic regulation through interaction with metabolites that often act at allosteric sites, which are distinct from the active site. The kinetic behavior of such enzymes is often more complex than the behavior we have discussed above, and such complex kinetics may serve as an indication that you are dealing with an allosteric enzyme. Further discussion of this subject is found in Experiments 9 and 15. 

Gardiol, A., and Preiss, J. 1990. Escherichia coli E-39 ADPglucose synthetase has different activation kinetics from the wild type allosteric enzyme. Arch. Biochem. Biophys. 280, 175-180. 

Kinetic experiments may be used for revealing the type of inhibition in enzymes. By inserting experimental data to the inverted Michaelis-Menten equation this gives straight-line plots (Lineweaver-Burk), which can be extrapolated to yield the characterizing constants of the enzyme. However, the Michaelis-Menten model cannot account properly for the kinetic properties of allosteric enzymes [34]. 

Allosteric Enzymes Do Not Obey Michaelis-Menten Kinetics... 

The Michaelis-Menten model has greatly assisted the development of enzyme chemistry. Its virtues are simplicity and broad applicability. However, the Michaelis-Menten model cannot account for the kinetic properties of many enzymes. An important group of enzymes that do not obey Michaelis-Menten kinetics comprises the allosteric enzymes. These enzymes consist of multiple subunits and multiple active sites. 

Figure 8.14. Kinetics for an Allosteric Enzyme. Allosteric enzymes display a sigmoidal dependence of reaction velocity on substrate concentration. 

Allosteric enzymes constitute an important class of enzymes whose catalytic activity can be regulated. These enzymes, which do not conform to Michaelis-Menton kinetics, have multiple active sites. These active sites display cooperativity, as evidenced by a sigmoidal depen-dence of reaction velocity on substrate concentration. 

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