Figure 2.

Schemes used to describe the interaction between an agonist and its receptor. Scheme 1 describes Clark's occupancy theory (8). In Clark's theory, an agonist (A) will combine with the receptor (R) to form an agonist–receptor complex (AR). The level of the AR complex present at thermodynamic equilibrium can be defined by the equilibrium dissociation constant (K_A). A physiological response (Q) will result only when the AR complex is formed, and a maximal response (Q_max) will occur when the agonist occupies all receptor sites. Scheme 2 describes the Stephenson–Furchgott model of efficacy (10). Stephenson postulated that the activity of the agonist is determined by the affinity of the drug for the receptor (K_A) and efficacy (e). Since the occupancy of receptors by the agonist did not appear to be linearly proportional to the response (Q), a dimensionless quantity called the stimulus (S) was introduced. The stimulus would lead to a response in a relationship that was not apparent at the time and was therefore left undefined [i.e., Q = f(S)]. The stimulus is defined explicitly as the product of efficacy and the fraction of receptors occupied by the agonist (i.e., S = e[AR]/[R]_t). This model was refined later by Furchgott, who defined efficacy as the product of the concentration of the total active receptor ([R]_t) and a quantity specific to the agonist–receptor complex designated as the intrinsic efficacy (ε) [i.e., e = ε[R]_t, S = ε[AR] = e[A]/(K_A + [A])] (9). An explicit expression for the response is given for the simple case in which the dose–response relationship is in the form of a rectangular hyperbola. Scheme 3 describes the multisite model (154), where an agonist (A) can bind to multiple classes of sites (R_j, j = 1, 2, 3, …, n) that are mutually independent and non-interconverting. The agonist can bind to each of the sites with distinct affinities (K_Aj). An equation for the binding isotherm is provided where Y is the fractional occupancy of the receptor by the agonist (i.e., $Y={\sum }_{j=1}^n\left[{\mathrm{AR}}_j\right]∕{\left[\mathrm{R}\right]}_{\mathrm{t}}$) and f_j is the fraction of total receptor that is of type j (i.e., f_j = [R_j]_t/[R]_t, where ${\left[\mathrm{R}\right]}_{\mathrm{t}}={\sum }_{j=1}^n{\left[{\mathrm{R}}_j\right]}_{\mathrm{t}}$. Scheme 4 describes the ternary complex model (138, 151), where the receptor (R) and G protein (G) are freely mobile within the plane of the membrane and interact through random collisions. Agonists bind to the free receptor (R) or receptor coupled to the G protein (RG) with dissociation constants K_A and K_AG, respectively. The G protein binds to the free receptor or receptor occupied by agonist (AR) with dissocation constants K_G and K_GA, respectively. Agonists promote coupling (K_AG < K_A) and therefore favor a ternary complex (ARG) (K_A/K_AG = K_G/K_GA). There are three conditions that need to be met for the ternary complex model to account for the dispersion of affinities observed in the binding of agonists. First, the agonist must differ in its affinity for the coupled and uncoupled states of the receptor (i.e., K_A ≠ K_AG). Second, the total concentration of the receptor must be bracketed by the affinity of the receptor for the G protein in the absence and presence of the agonist (i.e., K_GA < [R]_t < K_G). Third, the total number of G proteins must be equal to or less than the total number of receptors (i.e., [G]_t ≤ [R]_t). If these conditions are not met, then the ternary complex model predicts that agonist binding curves will have the form of a rectangular hyperbola (i.e., n_H = 1) (139, 142, 151, 153, 210). Scheme 5 describes cooperativity within a tetravalent receptor (n = 4) that interconverts spontaneously between two states (R and T) (101). The distribution of sites in the absence of agonist is defined by the constant K_RT. Binding occurs in a sequential manner where the first equivalent of agonist binds the vacant oligomer with the microscopic dissociation constant K_AR or K_AT (a_R1 = 1 and a_T1 = 1; A₀R ≡ R and A₀T ≡ T). The degree of cooperativity exerted on the binding of subsequent equivalents of the agonist will be reflected in cooperativity factors (a_Rj and a_Tj, j = 2, 3, or 4). Positive cooperativity occurs when a_Rj or a_Tj is less than 1; negative cooperativity occurs when a_Rj or a_Tj is greater than 1, and no cooperativity occurs when a_Rj or a_Tj is equal to 1. The oligomer is assumed to be symmetric, in that two or more vacant sites within either R or T are indistinguishable (1 ≤ j ≤ 3).