Allosterism kinetics

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. 

FIGURE 22. The active site of alkaline phosphatase (above) and an allosteric kinetic switch mechanism (below) for the regulatory function of the Mg + ions in controlling the conformation of the nonequivalent subunits (square and circle). Reprinted with permission from Reference 214. Copyright 2005 American Chemical Society... 

Rice endosperm ADPGlc PPase has been purified to apparent homogeneity (43 U/ mg).153 However, electrophoretic analyses detected multiple isoforms, and no kinetic characterization was reported. However another report shows that the purified endosperm ADPGlc PPase is activated by 3PGA (40-fold) and inhibited by Pi.81 The allosteric kinetic constants are given in Table 4.1. 

The value of the substrate concentration corresponding to half-maximal velocity is designated as A o.5 and not since the allosteric kinetics do not follow the hyperbolic Michaelis-Menten relationship. 

The allosteric kinetic effects of ATCase are shown in Figure 7-6. The interaction of substrates with the enzyme is cooperative (an example of homotropic cooperativity), as indicated by the sigmoidal shapes of the v versus [S] plots, CTP being an inhibitor and ATP an activator. These modulators compete for the same regulatory site and modulate the affinity of the enzyme for its... 

Table 3 Allosteric kinetic constants of wild-type coli and S. typhimurium LT-2 and their mutant ADP-GIc PPases affected in their allosteric constants...

Markus et al. (1984) have pursued the experimental analysis of the effect of an external periodicity on glycolytic oscillations. Their study confirmed the results obtained for entrainment and showed, moreover, the possibility of chaotic behaviour (see chapter 4). The same authors (Markus Hess, 1984 Markus et al., 1985) also conducted a parallel study of a four-variable model for glycolytic oscillations, centred around the allosteric kinetics of PFK in the presence of a periodic soiuce of substrate, that model predicted the appearance of aperiodic oscillations and of multiple rhythms in the forced glycolytic system (see also Tomita Daido, 1980). 

As indicated by the experiments on the reconstitution of a minimum system oscillating in vitro (Eschrich et al., 1983), the allosteric kinetics of PFK and its autocatalytic nature represent the core of the mechanism of glycolytic oscillations these elements are central to the two-variable model presented above. 

Phosphofructokinase allosteric kinetics, 41,500 and glycolytic oscillations, 15,37 0 effect of activator and inhibitor, 71,72 periodic variation of activity, 53,55,67 role of cooperativity, 67-73 Phosphoinositidase C, 355,356 Phosphorylation of p-adrenergic receptor, 193 of Ca -dependent K channel, 346 of cAMP receptor in Dictyostelium, 19, 192-5,317... 

See Atkins, W.M. Implications of the allosteric kinetics of cytochrome P450s. Drug Discovery Today 2004, 9, 478-484. 

The properties of the biosynthetic enzymes isolated from multicellular plants are at least qualitatively similar to those of the analogous microbial threonine dehydratases. Measurements of the for threonine are complicated by allosteric kinetics in the presence of trace amounts of isoleucine (this amino acid is often required to stabilize the enzyme) and by a strong dependence of enzyme activity on pH (Section The enzymes are... 

Figure 5.14. Hill plot of allosteric kinetics according to Equ. 5.30.

NMD A receptors are selectively activated by A/-methyl-D-aspartate (NMD A) (182). NMD A receptor activation also requires glycine or other co-agonist occupation of an allosteric site. NMDAR-1, -2A, -2B, -2C, and -2D are the five NMD A receptor subunits known. Two forms of NMDAR-1 are generated by alternative splicing. NMDAR-1 proteins form homomeric ionotropic receptors in expression systems and may do so m situ in the CNS. Functional responses, however, are markedly augmented by co-expression of a NMDAR-2 and NMDAR-1 subunits. The kinetic and pharmacological properties of the NMD A receptor are influenced by the particular subunit composition. 

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. 

First draw both Lineweaver-Burk plots and Hanes-Woolf plots for the following a Monod-Wyman-Changeux allosteric K enzyme system, showing separate curves for the kinetic response in (1) the absence of any effectors (2) the presence of allosteric activator A and (3) the presence of allosteric inhibitor I. Then draw a similar set of curves for a Monod-Wyman-Changeux allosteric Uenzyme system. 

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). 

Further, for studying the role of pH and salt concentrations on bulk-electrostatic and non-bulk electrostatic contributions the same approach was made to experiments on the influence of the alcohols mentioned above on the oxygen affinity at various KC1 concentrations and pH-values 144,146). The results obtained indicate that at a low alcohol concentration the bulk-electrostatic contributions are dominant and that with increasing size of the alkyl group, alcohol and KC1 concentration, the nonbulk electrostatic, hydrophobic contributions increase. Recent results of kinetic measurements of 02 release show that cosolvents such as alcohols and formamide influence mainly the allosteric parameter L, i.e. -the equilibrium between T and R conformation and that the separation of the alcohol effects into bulk-electrostatic and hydrophobic (non-bulk electrostatic) contributions is justified. 

A more sensitive and rigorous method of detecting and quantifying allosteric effects is through observation of the kinetics of binding. 

In general, the kinetics of most allosteric modulators have been shown to be faster than the kinetics of binding of the tracer ligand. This is an initial assumption for this experimental approach. Under these circumstances, the rate of dissociation of the tracer ligand (pA t) n the presence of the allosteric ligand is given by [11, 12]... 

FIGURE 4.13 Effect of the allosteric modulator 5-(N-ethyl-N-isopropyl)-amyloride (EPA) on the kinetics dissociation of [3H] yohimbine from c/j-adrenoceptors, (a) Receptor occupancy of [3H] yohimbine with time in the absence (filled circles) and presence (open circles) of EPA 0.03 mM, 0.1 mM (filled triangles), 0.3 mM (open squares), 1 mM (filled squares), and 3 mM (open triangles), (b) Regression of observed rate constant for offset of concentration of [3H] yohimbine in the presence of various concentrations of EPA on concentrations of EPA (abscissae in mM on a logarithmic scale). Data redrawn from [13]. 

Allosteric antagonism is characterized by the fact that it attains a maximal value. A sensitive method for the detection of allosteric effects is through studying the kinetics of binding. 

The fact that the aliosterically preferred conformation may be relatively rare in the library of conformations available to the receptor may have kinetic implications. Specifically, if the binding site for the modulator appears only when the preferred conformation is formed spontaneously, then complete conversion to alios terically modified receptor may require a relatively long period of equilibration. For example, the allosteric p38 MAP kinase inhibitor BIRB 796 binds to a conformation of MAP kinase requiring movement of a Phe residue by 10 angstroms (so-called out conformation). The association rate for this modulator is 8.5 x 105 M-1 s-1, 50 times slower than that required for other inhibitors (4.3 x 107 M 1 s-1). The result is that while other inhibitors reach equilibrium within 30 minutes, BIRB 376 requires 2 full hours of equilibration time [8],... 

Uncompetitive antagonism, form of inhibition (originally defined for enzyme kinetics) in which both the maximal asymptotic value of the response and the equilibrium dissociation constant of the activator (i.e., agonist) are reduced by the antagonist. This differs from noncompetitive antagonism where the affinity of the receptor for the activating drug is not altered. Uncompetitive effects can occur due to allosteric modulation of receptor activity by an allosteric modulator (see Chapter 6.4). 

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... 

Primarily using isolated plasma membrane vesicles as an experimental preparation, the functional properties of Na /H exchangers have been elucidated. The important kinetic properties include (1) stoichiometry (one-for-one) (2) reversibility (3) substrate specificity (monovalent cations Na, H, Li, NH4, but not K, Rb, Cs, choline) (4) modes of operation (Na -for-H, Na -for-Na Li " -for-Na, Na -for-NH4 ) (5) existence of an internal site for allosteric activation by (6) reversible inhibition by amiloride (Af-amidino-5-amino-6-chloropyr-azine carboxamide) and its 5-amino-substituted analogs and (7) competitive nature... 

Clarke RJ, Apell H-J, Kong BY (2007) Allosteric effect of ATP on Na+,K+-ATPase conformational kinetics. Biochemistry 46 7034-7044... 

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