Allosteric equilibrium constant

Symmetry model for allosteric transitions of a dimeric enzyme. The model assumes that the enzyme can exist in either of two different conformations (T and R), which have different dissociation constants for the substrate (KT and Kk). Structural transitions of the two subunits are assumed to be tightly coupled, so that both subunits must be in the same state. L is the equilibrium constant (T)/(R) in the absence of substrate. If the substrate binds much more tightly to R than to T (AfR [Pg.183]

Phosphofructokinase was one of the first enzymes to which Monod and his colleagues applied the symmetry model of allosteric transitions. It contains four identical subunits, each of which has both an active site and an allosteric site. The cooperativity of the kinetics suggests that the enzyme can adopt two different conformations (T and R) that have similar affinities for ATP but differ in their affinity for fructose-6-phosphate. The binding for fructose-6-phosphate is calculated to be about 2,000 times tighter in the R conformation than in T. When fructose-6-phosphate binds to any one of the subunits, it appears to cause all four subunits to flip from the T conformation to the R conformation, just as the symmetry model specifies. The allosteric effectors ADP, GDP, and phosphoenolpyruvate do not alter the maximum rate of the reaction but change the dependence of the rate on the fructose-6-phosphate concentration in a manner suggesting that they change the equilibrium constant (L) between the T and R conformations. 

The main effect of AMP on either phosphorylase b or phosphorylase a is to decrease the Km for P,. This change can be interpreted as we have interpreted the actions of allosteric effectors on phosphofructokinase and aspartate carbamoyl transferase, on the model that the enzyme can exist in two conformational states (R and T) with different affinities for the substrate. However, phosphorylase presents the additional complexity that the equilibrium constant (L) between the two conformational states can be altered by a covalent modification of the enzyme. In the absence of substrates, [T]/[R] appears to be greater than 3,000 in phosphorylase b but to decrease to about 10 in phosphorylase a. 

Enzyme Coenzymes and Cofactors Allosteric Modulators Positive Negative Equilibrium Constant atpH7.0(K ) AG° kcal/mol (kj/mole)... 

Li allosteric constant equilibrium constant for conformational change of protein with i ligands bound... 

Fig. 28.11 The allosteric model of drug-recepto interaction where the receptor exists (minimally) in twc states R and T. /Car and /Cat are the equilibrium constant for drug binding to states R and T. L is the equilibriunr constant for the R to T transition.

The reservoirs affect the concentration of the cycle species in two ways. The first is through the direct influx represented by the first term in each of eqs. (10.2). The second and more interesting way is through control of the enzyme activities, where the reservoir species F and T are allowed to become effectors of the enzymes. The type of control modeled is noncompetitive allosteric binding of the effectors, where each effector binds to the enzyme independently, as shown in fig. 10.2. In this scheme, the enzyme with effector bound is assumed to have altered catalytic activity toward its substrate compared to that of the enzyme without effector bound. The scheme as shown also relies on the simplifying assumptions that (1) the association and dissociation between enzyme and substrate are unaffected by the binding of the effector, and (2) the binding of substrate to enzyme is much faster than the conversion of bound substrate to product. Under these assumptions, the Michaelis constant Km represents the equilibrium constant for... 

Note The equilibrium constants for allosteric transitions for phospho- and dephospho-GP are ... 

Figure 13 The allosteric cooperativity factor a is the equilibrium constant for the conversion of the hypothetical noncooperative complex into the cooperative complex. The figure depicts the case of a saturated divalent receptor.

The real situation is, of course, much more complex, but the same principles are applicable. An important additional property of the system is that the binding of nucleotides to a second binding site, probably on an adjacent P subunit of the ATPase, causes a dramatic increase of ca. 10 in the rate and equilibrium constants for dissociation of nucleotides from the active site [24]. This cannot occur during ATP synthesis because the synthesis of ATP requires that it binds very strongly (Fig. 2). The proton may act as a key to regulate this allosteric action of nucleotides. It is not unreasonable that the binding and dissociation of nucleotides should require the protonated state of the enzyme for the allosteric effect as well as for catalysis. Thus, the proton may act as a key that permits other nucleotides to provide a driving force that facilitates the dissociation of ATP. 

The equilibrium constant or dissociation constant of the enzyme-inhibitor complex, Ki, also known as the inhibitor constant, is a measure of the extent of inhibition. The lower the value of Ki, the higher the affinity of the inhibitor for the enzyme. Kinetically, three kinds of reversible inhibition can be distinguished competitive, non-competitive and uncompetitive inhibition (examples in Table 2.10). Other possible cases, such as allosteric inhibition and partial competitive or partial non-competitive inhibition, are omitted in this treatise. 

Thermodynamically it would be expected that a ligand may not have identical affinity for both receptor conformations. This was an assumption in early formulations of conformational selection. For example, differential affinity for protein conformations was proposed for oxygen binding to hemoglobin [17] and for choline derivatives and nicotinic receptors [18]. Furthermore, assume that these conformations exist in an equilibrium defined by an allosteric constant L (defined as [Ra]/[R-i]) and that a ligand [A] has affinity for both conformations defined by equilibrium association constants Ka and aKa, respectively, for the inactive and active states ... 

AR] complex) interacts with an equilibrium association constant Ke (to yield an efficacy term x) and the allosterically altered agonist-bound receptor complex ([ABR] complex) interacts with the cell with equilibrium association constant K e (to yield an altered efficacy x7). It is useful to define a ratio of efficacies for the native and allosterically modulated receptor of x /x (denoted , where = x//x). 

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 describe the all-or-none transition between distinct conformational states of enzymes or receptors — an allosteric transition. In keeping with this usage, the constant that describes the position of the equilibrium between the states (e.g., E0 in the schemes of Figures 1.11 and 1.28) is sometimes described as the allosteric constant. 

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