Models For Understanding The Effects Of Allosteric Modulators

The recognition that GPCRs can possess binding sites in addition to the orthosteric site has necessitated the development of mathematical models to facilitate descriptions and understanding of allosteric drug-receptor interactions. The binding of an allosteric ligand to its site will change the conformation of the receptor, which means that the "geography" of the orthosteric binding pocket and any other potential receptor-ligand/protein interfaces, may also change. As a consequence, the binding affinity and/or signaling efficacy of the orthosteric ligand can be modulated, either in a positive or negative manner— hence the common use of the term "allosteric modulator" to encompass different types of allosteric ligands. The simplest allosteric GPCR model is one in which the binding of an allosteric ligand modulates only the affinity of the orthosteric ligand; this simple model is referred to herein as the allosteric ternary complex model (ATCM; Fig. 3.1a). Within the framework of the ATCM, the interaction is governed by the concentration of each ligand, the equilibrium dissociation constants of the orthosteric and allosteric ligands (KA and Kb, respectively) for their binding to their sites on the unoccupied receptor, and the "cooperativity factor", a, which is a measure of the magnitude and direction of the allosteric interaction between the two conformationally linked sites. A value of a < 1 (but greater than 0) indicates negative cooperativity, such that the binding of an allosteric ligand inhibits the binding of the orthosteric ligand. Values of a > 1 indicate positive cooperativity, such that the







Figure 3.1 Allosteric models of GPCR-ligand interactions. (a) The allosteric ternary complex model (ATCM), which describes the interaction between an orthosteric ligand, A, and allosteric modulator, B, in terms of their respective equilibrium dissociation constants (KA, KB) and a cooperativity factor, a, which denotes the magnitude and direction of the allosteric effect on ligand binding affinity. (b) The allosteric two state model (ATSM), which describes allosteric modulator effects on affinity, efficacy, and the distribution of the receptor between active (R*) and inactive (R) states, in terms of distinct conformations selected by ligands according to their cooperativity factors for the different states.

allosteric ligand promotes the binding of orthosteric ligand, whereas values of a = 1 indicate neutral cooperativity, that is, no net change in binding affinity at equilibrium. Because the two sites are conformationally linked, the allosteric interaction is reciprocal at equilibrium, in that the orthosteric ligand will modulate the binding of the allosteric ligand in the same manner and to the same extent.

The simple ATCM describes the effect of the modulator only in terms of changes in orthosteric ligand affinity, and vice versa. However, there is no a priori reason why the conformational change engendered by an allosteric modulator in the GPCR does not perturb signaling efficacy in addition to, or independently of, any effects on orthosteric ligand binding affinity. In order to incorporate allosteric modulation of efficacy as well as affinity, the simple ATCM has been extended into an allosteric two -state model (ATSM) [ 18] . This model (Fig. 3.1b) describes GPCR function in terms of: (a) the ability of the receptor to constitutively isomerize between active (R*) and inactive (R)

states, as determined by the isomerization constant, L; (b) the ability of orthosteric and allosteric ligands to modify this transition between states, that is, to act as either agonists or inverse agonists, which is governed by the parameters a and p . (c) the ability of each ligand to allosterically modulate the binding affinity of the other, governed by the "binding cooperativity" parameter, y; and (d) the ability of either ligand to modulate the transition to an active receptor state when both ligands are bound, governed by the "activation cooperativity" parameter, 8. Although the model is more complex due to the increased number of parameters, it has proven very useful in conceptualizing divergent allosteric modulator effects on ligand affinity versus efficacy, which are being recognized with increasing prevalence in many studies [19].

More recently, it has become accepted that GPCRs can adopt multiple active and inactive conformations beyond the simple "R and R*" paradigm. This realization has a number of significant consequences, including the discovery that different ligands can preferentially stabilize unique GPCR conformations, each associated with its own profile of receptor behaviors, to the relative exclusion of other states. The phenomenon has been variously termed "stimulus-trafficking," "biased agonism," "collateral efficacy," "ligand-directed signaling," and "functional selectivity," among others [20]. Because allosteric ligands can themselves stabilize GPCR conformations that change the reactivity of the receptor toward orthosteric ligands and/or its host cellular environment, there is a significant potential for allosteric modulators to engender stimulus-bias and functional selectivity [21]. This is likely to have a significant impact on drug discovery programs in the coming years.

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