Multiple receptor populations: binding isotherms and their numerical analysis

Abstract

This paper reviews present models and methods of parameter estimation in relationships describing receptor-ligand interactions in equilibrium, as used in the author's laboratory. The state-of-the-art and the present experience can be summarized as follows: 1) Binding isotherms (relationships of bound and free/total ligand concentrations) are superpositions of several elementary terms describing the ligand binding to individual binding sites (receptors) present in the biological material investigated. The "nonspecific binding" is usually represented by a linear term. 2) The elementary terms are most frequently described by a rectangular hyperbola, Hill (power) function, or a rational function (binding of several ligand molecules to one molecule of receptor). Heterologous displacement requires specific functions which, however, can be transformed into one of the elementary terms. 3) Parameters (binding capacities, dissociation constants, Hill coefficients, etc.) can most reliably be estimated by nonlinear regression methods. However, these methods frequently fail to yield physically relevant values if initial estimates are far from "real" values, or if the data are strongly scattered. Some of the available routines (e.g., LIGAND) offer manifold tools to solve these difficulties. 4) The "affinity spectrum", a relationship between binding capacities and equilibrium constants, shows the presence of individual binding sites in the binding system in question. The spectrum can be constructed either by Fourier analysis, or by a stepwise procedure (computation of binding capacity for several dissociation constants). The former way of analysis is demanding; software tools are rare. 5) The "STEP" routine based on Hill/Scatchard linearization routines yields profiles similar to affinity spectra, but offers, in addition, values of Hill coefficients of individual binding populations. Values obtained can be used as initial estimates for nonlinear regression. 6) Selection of a suitable model, its testing, numerical procedures, statistical estimates, etc. frequently entail severe difficulties which are approached in the available software packages in different ways, none of them is usually optimal.