Quantification of receptor binding from response data obtained at different receptor levels: a simple individual sigmoid fitting and a unified SABRE approach

Methods that allow quantification of receptor binding (occupancy) by measuring response (effect) data only are of interest as they can be used to allow characterization of binding properties (e.g., dissociation constant, K(d)) without having to perform explicit ligand binding experiments that require different setups (e.g., use of labeled ligands). However, since response depends not just on the binding affinity-determined receptor occupancy, but also on receptor activation, which is affected by ligand efficacy (plus constitutive activity, if present), and downstream pathway amplification, this requires the acquisition and fitting of multiple concentration-response data. Here, two alternative methods, which both are straightforward to implement using nonlinear regression software, are described to fit such multiple responses measured at different receptor levels that can be obtained, for example, by partial irreversible receptor inactivation (i.e., Furchgott method) or different expression levels. One is a simple method via straightforward fitting of each response with sigmoid functions and estimation of K(d) from the obtained E(max) and EC(50) values as K(d) = (E(max)·EC′(50) − E′(max)·EC(50))/(E(max) − E′(max)). This is less error-prone than the original Furchgott method of double-reciprocal fit and simpler than alternatives that require concentration interpolations, thus, should allow more widespread use of this so-far underutilized approach to estimate binding properties. Relative efficacies can then be compared using E(max)·K(d)/EC(50) values. The other is a complex method that uses the SABRE receptor model to obtain a unified fit of the multiple concentration-response curves with a single set of parameters that include binding affinity K(d), efficacy ε, amplification γ, and Hill coefficient n. Illustrations with simulated and experimental data are presented including with activity data of three muscarinic agonists measured in rabbit myocardium.