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

Abstract

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 (γ), Binding affinity (K_d), Receptor activation Efficacy (ε), and constitutive activity (ε_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_ds). Simpler cases can be fit by using consecutively reduced forms obtained by constraining parameters to specific values, e.g., ε_R0 = 0: no constitutive activity, γ = 1: no amplification (E_max-type fitting), and ε = 1: no partial agonism (Clark equation). Here, a Hill-type extension is introduced (n ≠ 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.