The Cubic Ternary Complex Receptor–Occupancy Model II. Understanding Apparent Affinity

Abstract

In part I of this series of papers, we described the cubic ternary complex (CTC) model. In part II, we examine the pharmacological notion of apparent ligand affinity in the light of this model. The high degree of symmetry that characterizes the CTC model makes it possible to use simple geometrical devices to visualize chemical transitions. This geometric point of view provides a motivation for the development of a biological interpretation for apparent affinity. Using this geometrical point of view, an analytical expression for apparent ligand affinity is derived that can be applied to any receptor-occupancy model. When unbound receptors are distributed among a number of states, apparent affinity is a composite measure, a weighted average of the affinities that a ligand has for each of the receptor states. In general, apparent affinity can be interpreted as the mathematical expectation of the simple affinities of members of a native receptor ensemble. The “expectation” method of computing affinity is algebraically equivalent to an even simpler computational method, here called the “diagonalization” method. The use of each method is demonstrated. The CTC model corroborates what other models and some experimental work have previously suggested. Affinity, as it is calculated experimentally for G-protein-coupled receptors, is not purely a receptor property but is a function both of the receptor and of the suite of transitional proteins with which the receptor interacts