Allosteric constant

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 ... 

Consider a system containing two receptor conformations R, and Ra that coexist in the system according to an allosteric constant denoted L ... 

The resulting modification is called the extended ternary complex model [3], which describes the spontaneous formation of active state receptor ([Ra]) from an inactive state receptor ([RJ) according to an allosteric constant (L = [Ra]/[RJ). The active state receptor can form a complex with G-protein ([G]) spontaneously to form RaG, or agonist activation can induce formation of a ternary complex ARaG ... 

It can be seen from Equation 3.23 that the magnitude of the allosteric constant L and/or the magnitude of the receptor/G-protein ratio determines the amount of... 

The extended ternary complex model [23] was conceived after it was clear that receptors could spontaneously activate G-proteins in the absence of agonist. It is an amalgam of the ternary complex model [12] and two-state theory that allows proteins to spontaneously exist in two conformations, each having different properties with respect to other proteins and to ligands. Thus, two receptor species are described [Ra] (active state receptor able to activate G-proteins) and [RJ (inactive state receptors). These coexist according to an allosteric constant (L = [Ra]/[Ri]) ... 

Measurement of the Affinity and Maximal Allosteric Constant for Allosteric Modulators Producing Surmountable Effects... 

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. 

A simplified scheme, in which only one desensitized and one open-channel state of the receptor exist, is represented in scheme 2, where R is the resting (activat-able) state, R the active (open channel) state and R the desensitized state of the receptor M is an allosteric constant defined by R7R, and K and fC are equilibrium dissociation constants for the ligand. 

Figure 2. Top Effect of the magnitude of the allosteric constant on ligand saturation behavior of a dimer obeying the MWC model. Bottom Fraction of total dimeric protein present in various T- and R-species.

According to the MWC model, in the presence of inhibitor and activator at normalized concentrations P and y an enzyme will still follow Eq. 9-65, but the allosteric constant L will be replaced by an apparent allosteric constant L (Eq. 9-70).86 Figure 9-14 shows plots of Y vs. log a for two different values of L for a tetramer with a specific value assumed for c. In both... 

Figure 9-14 Fractional saturation Y and "function of state" R for hypothetical tetrameric enzymes following the MWC model. Curves are calculated for two different values of the apparent allosteric constant L (Eq. 9-70) and for c = 0.1 (Eq. 9-66). After Rubin and Changeux.86...

The R state with x ligand molecules bound is termed Rx, and the equivalent T state, Tx. The allosteric constant L is then defined by... 

The sigmoid binding curve of any allosteric protein can be calculated by using just three parameters L, the allosteric constant, which is equal to the ratio [T]/[R] for the unligated states and KT and KR, the dissociation constants for each site in the T and R states, respectively. 

The discovery of partial agonists led to further refinement of the ternary complex model by introducing the allosteric constant, a. For full agonists a = 1, while partial agonists have a values <1. 

In this model measurable constitutive activity (elevated levels of [R G]) can be achieved by increasing the concentration of R and/or G. Another way in which constitutive activity can be produced is through alteration of the J or M allosteric constants—for example, by the removal of sodium ions or by introducing different point mutations into the receptor protein. 

Formally, the extended ternary complex model is a two-state model different agonists apparently produce cellular response by causing (quantitatively different) enrichment of the (qualitatively identical) R active receptor conformation. However, upon more careful examination it becomes clear that the allosteric constants a and/or (3 can theoretically be specific for each ligand [42], Under these circumstances the ternary complex... 

Here, L is the allosteric constant which is given (for a dimer) by Eq. 7-36. The constant c is the ratio of dissociation constants and for the two conformers ... 

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