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 (Kd), Receptor activation Efficacy (ε), and constitutive activity (εR0). 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 Kds). Simpler cases can be fit by using consecutively reduced forms obtained by constraining parameters to specific values, e.g., εR0 = 0: no constitutive activity, γ = 1: no amplification (Emax-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.
Highlights
Well-known important cases where fractional response and occupancy are not aligned and challenging to fit include (a) the presence of “receptor reserve” (“spare receptors”)[7] and/or partial agonism (often in Scientific Reports | (2020) 10:13386
Combination)[8,9], (b) multiple responses assessed at different vantage points along a signaling pathway, (c) responses that are different along distinct divergent downstream pathways originating from the same receptor, and (d) constitutive activity
A set of illustrative examples are included in Fig. 1 showing the concentration-dependency of occupancy and response as well as the corresponding response versus occupancy curves
Summary
Well-known important cases where fractional response and occupancy are not aligned and challenging to fit include (a) the presence of “receptor reserve” (“spare receptors”)[7] and/or partial agonism (often in Scientific Reports | (2020) 10:13386. Note that in some of the more complex cases, the fractional response can be both ahead and behind the fractional occupancy even for the same compound (red and blue arrows indicating deviations from the unity line in E and F). Cannot be used as they assume responses proportional with occupancy; do not allow separation between fractional response, fresp = E/Emax, and occupancy, foccup = [LRoccup]/[LRmax] (Fig. 1A,B) They do not include parametrization for efficacy, only for occupancy via Kd, the classic equilibrium dissociation constant characterizing receptor binding, which is defined in terms of the concentrations of the species involved (see Fig. 2, bottom row) and measured in units of concentrations:
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