Dose‐response curves. With many full agonists, such as a, occupation of a small fraction of receptors elicits a nearly maximal response. A partial agonist can either be an agent such as b, where higher occupancy is required to elicit a response, or an agent such as c, which does not elicit the maximum response even at very high concentrations. Stephenson 20 would have referred to agonist a as a “strong” agonist.

Schild regression. In the presence of a competitive antagonist (dashed line) the dose‐response curve for an agonist is shifted to the right. The agonist can still elicit the same maximal response, but it takes a higher concentration. A demonstrates the definition of the dose ratio. It is the concentration of agonist required to elicit a response in the presence of antagonist divided by the concentration of agonist needed to elicit that same response in the absence of antagonist. B: a Schild regression. Each circle represents a dose ratio of agonist in the presence of a different concentration of antagonist. If the drug is a competitive antagonist, the slope of the Schild regression line must equal 1.0. The intercept when log (dose ratio — 1) equals zero (that is, when dose ratio = 2) is the K_d of the antagonist. The term pA₂ sometimes is used to refer to the K_d for a competitive antagonist; pA₂ = ‐log K_d for the antagonist.

Saturation binding. A: total and nonspecific binding at equilibrium as a function of increasing concentrations of radioligand. The difference, also shown, is specific binding. B: specific binding only. Note the definition of B_max (the maximal amount of binding extrapolated to infinite radioligand concentration) and K_d (the concentration of radioligand that occupies half the receptors at equilibrium). C: the same data, but plotting the concentration of radioligand on a logarithmic axis. The solid part of the curve in C corresponds to the curve in B; the dotted portion is extrapolated. D: the same data transformed into a Scatchard plot.

Competitive binding experiments. A: definition of the IC₅₀ as the concentration of unlabeled drug that competes for half of specific radioligand binding at equilibrium. B: competition by three different drugs. The IC₅₀ is lowest for drug a, so drug a has the highest affinity. The order of potency is a>b>c. C: an 81‐fold increase in the concentration of unlabeled drug makes the curve descend from 90% to 10% occupancy. If the curve is shallower or steeper than this, then the radioligand and competitor do not compete for binding to a single class of binding sites with unchanging affinity for radioligand and competitor.

Dissociation kinetics. A: before the first time point on the graph, binding was allowed to occur, perhaps to equilibrium. At time zero on the graph, dissociation was initiated by infinite dilution or by addition of an excess of unlabeled drug. Under either condition, the radioligand cannot rebind after dissociating from the receptor; consequently the total amount of binding decreases over time. The half‐life (t_1/2) is the time when half of the specific binding has dissociated. B: the same data on a log plot, which linearizes the dissociation data.

Association kinetics. Radioligand binding was added at time zero, and the graph shows the increase in specific binding thereafter.

Complex competitive binding curves. A: the meaning of the slope factor. A fractional slope factor (such as −0.5) means that the curve is shallow. A normal competitive binding curve (single binding site, no cooperativity) has a slope factor of −1.0, as shown in the solid curve. B: competition for two different binding sites. The radioligand binds identically to both sites, but the competitor has a tenfold difference in affinity. Although the curve is shallow, it is not obviously biphasic.

Saturation binding to two sites. A: binding to two distinct receptor types indicated by dotted and dashed curves. The two sum to the solid curve. Experimental data will follow the solid curve, and computer analysis is needed to find the B_max and K_d of the two components. B: the same data as represented on a Scatchard plot.

Distinguishing between multiple subtypes (A) and negative cooperativity (B) by dissociation kinetic strategies. If the binding sites are independent (no cooperativity, right panel) the rate of dissociation will be identical when dissociation is initiated by infinite dilution (solid curve) or addition of excess unlabeled drug (dashed curve). If the binding sites are cooperative, then the dissociation curve will differ depending on how dissociation was initiated. When monitoring of the dissociation phase is initiated by adding an excess of unlabeled drug, all of the binding sites are always occupied by either labeled or unlabeled drug. With infinite dilution, there is no rebinding and the number of occupied sites decreases over time. After radioligand dissociates from one site, the affinity at another site will increase and the observed rate of dissociation will slow.

Evaluating allosteric regulation. Radioligand is allowed to bind to a site, and then dissociation begins when an excess of unlabeled agent is added. Addition of an allosteric modified can accelerate or slow the rate of dissociation.

The extended ternary complex model. The left panel shows the simple ternary complex model. Receptors can be coupled or uncoupled from G. Agonist or hormone (H) binding facilitates the interaction of R with R. The right panel shows the extended ternary complex model. Receptors exist in interconvertible R and R^* states. Binding of agonist promotes transition to the R^* state. Only the R^* state can interact with G proteins. (see refs. 9, 15.