A single unified model for fitting simple to complex receptor response data

The fitting of complex receptor-response data where fractional response and occupancy do not match is challenging. They encompass important cases including (a) the presence of receptor reserve and/or partial agonism, (b) multiple responses assessed at different vantage points along a pathway, (c) responses that are different along diverging downstream pathways (biased agonism), and (d) constitutive activity. For these, simple models such as the well-known Clark or Hill equations cannot be used. Those that can, such as the operational (Black&Leff) model, do not provide a unified approach, have multiple nonintuitive parameters that are challenging to fit in well-defined manner, have difficulties incorporating binding data, and cannot be reduced or connected to simpler forms. We have recently introduced a quantitative receptor model (SABRE) that includes parameters for Signal Amplification (gamma), Binding affinity (K-d), Receptor activation Efficacy (epsilon), and constitutive activity (epsilon (R0)). It provides a single equation to fit complex cases within a full two-state framework with the possibility of incorporating receptor occupancy data (i.e., experimental K(d)s). Simpler cases can be fit by using consecutively reduced forms obtained by constraining parameters to specific values, e.g., epsilon (R0)=0: no constitutive activity, gamma =1: no amplification (E-max-type fitting), and epsilon =1: no partial agonism (Clark equation). Here, a Hill-type extension is introduced (n not equal 1), and simulated and experimental receptor-response data from simple to increasingly complex cases are fitted within the unified framework of SABRE with differently constrained parameters.