The classical form of the TCM suggests that the probe dependence of the G protein defines the ability of the orthosteric ligand to promote the formation of the ternary complex and as such, the efficacy of an orthosteric ligand (Fig. 2.1b, middle). Within this model, the G protein has positive cooperativity with an orthosteric agonist, negative cooperativity with an orthosteric inverse agonist, and neutral cooperativity with an orthosteric antagonist. The TCM can also be used as a more general model to describe any allosteric interaction between two binding sites on a receptor. The allosteric ternary complex model (ATCM) is the simplest mechanistic framework that can quantify the binding properties of an allosteric modulator (Fig. 2.1c, right). The difference underlying the two models is that in contrast to the classical TCM, the ATCM makes no assumptions with regards to the efficacy of either ligand, purely modeling ligand binding. At the level of binding, allosteric modulators are described by two parameters, affinity and cooperativity. In contrast to affinity, which is a system-independent property of an allosteric modulator, cooperativity is dependent on the orthosteric ligand present, and is described as the ratio of the affinity of the free receptor to that of the occupied receptor. The coopera-tivity between an orthosteric and allosteric ligand is always reciprocal, and therefore, a single cooperativity factor can be used to describe the effect of an orthosteric ligand on allosteric binding and vice versa [68-71] . According to the ATCM, the fractional occupancy of the orthosteric ligand is governed by the following equation:
Within this model, KA and KB denote the equilibrium dissociation constants of the orthosteric ligand (A) and the allosteric ligand (B), respectively, and a denotes the binding cooperativity. A value of a greater than one describes positive cooperativity, less than one describes negative cooperativity, and equal to one describes neutral cooperativity. Highly negative cooperative interactions occur when a approaches zero. In these instances, the allosteric interaction between the allosteric modulator and orthosteric ligand can become indistinguishable from those of a competitive nature .
The ATCM is useful when describing allosteric interactions at the binding level; however, when assessing receptor function, a number of allosteric modulators have been identified whose properties do not follow the predictions of the ATCM. For example, at the human cannabinoid CB1 receptors, Org27569 displays positive cooperativity in terms of binding of the orthosteric agonist CP55940, but negative cooperativity in terms of efficacy . Under such circumstances, a more complex model is required. The allosteric two- s tate model (ATSM) is an extension of the ATCM that allows for allosteric effects on orthosteric ligand efficacy and allosteric agonism (Fig. 2.1c, right) . The ATSM describes orthosteric (A) and allosteric (B) ligand binding in terms of their affinity for the free and bound active (R*) and inactive form (R) of the receptor. Within this model, a is analogous to that in the ATCM; ß and y describe the preference of A and B, respectively, for R* over R, and as such, their intrinsic efficacy and 8 describes the activation cooperativity between the two ligands when they are simultaneously bound, forming the ternary complex. The ATSM separates the modulation of an allosteric ligand into independent effects on orthosteric ligand binding (a) and efficacy (8 ). Another important property of this model is that it allows allosteric ligands to possess efficacy in their own right. Allosteric ligands have been identified that can modulate receptor activity in the absence of orthosteric ligand. For example, the well-characterized allosteric modulator, alcuronium, has been shown to decrease the constitutive activity of the M2 mAChR . In contrast, the highly selective 2-amino-3-benzoylthiophene compounds that act as allosteric enhancers of agonist binding to the adenosine A1 receptor have been shown to enhance constitutive receptor activity from an allosteric binding site . Similar to the effects that increasing the constitutive activity has on agonist affinity (reviewed in Reference 16), the efficacy of an allosteric modulator will alter the equilibrium between the different receptor states and, as a result, alter the affinity of the orthosteric agonists and inverse agonists. Allosteric agonists will enrich the active form of the receptor, enhancing the affinity of orthosteric agonists but decreasing the affinity of orthosteric inverse agonists. Allosteric inverse agonists will drive the equilibrium toward the inactive receptor and mediate the reciprocal effect to that of an allosteric agonist. This modulation of orthosteric affinity is driven by - and therefore is independent to that defined by the cooperativity factors a and 8. The overall modulation mediated by the allosteric ligand will be a combination of all three cooperativity factors. While remain ing a useful tool to explain qualitative effects of an allosteric modulator on receptor and/or orthosteric ligand efficacy, the complex nature of the ATSM has meant that it remains elusive in terms of obtaining parameter estimates from experimental data.
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