Quantification of signal amplification for receptors: the Kd/EC50 ratio of full agonists as a gain parameter

Concentration-response relationships connecting the concentration of ligands to the responses they produce are central to pharmacology in general and form the core of quantitative pharmacology. While typically they can be well-described by hyperbolic functions (sigmoid on commonly used semi-log scales) and characterized by half-maximal concentrations values (EC₅₀), their connection to receptor occupancy, characterized in a similar manner by the equilibrium dissociation constant <i>K</i> _d, can be complex due to the intermixing of the effects from occupancy-induced activation with those from partial agonism, constitutive activity, and pathway-specific signal amplification. Here, it is proposed that, as long as both occupancy and response follow such typical concentration-dependencies, signal amplification can be quantified using the gain parameter <i>g</i> _<i>K</i> = <i>κ</i> = <i>K</i> _d/EC₅₀ measured for full agonists. This is similar to the gain parameter used in electronics (e.g., <i>g</i> _<i>V</i> = <i>V</i> _out/<i>V</i> _in for voltage). On customarily used semi-log representations, log <i>g</i> _<i>K</i> corresponds to the horizontal shift between the response and occupancy curves, log<i>K</i> _d-logEC₅₀, the presence of which (i.e., <i>K</i> _d > EC₅₀) is generally considered as evidence for the existence of "<i>receptor reserve</i>" or "<i>spare receptors</i>". The latter is a misnomer that should be avoided since even if there are excess receptors, there is no special pool of receptors "not required for ordinary use" as <i>spare</i> would imply. For partial agonists, the <i>κ</i> = <i>K</i> _d/EC₅₀ shift is smaller than for full agonists as not all occupied receptors are active. The <i>g</i> _<i>K</i> gain parameter (full agonist <i>K</i> _d/EC₅₀) corresponds to the <i>γ</i> gain parameter of the SABRE receptor model, which includes parameters for Signal Amplification (<i>γ</i>), Binding affinity (<i>K</i> _d), and Receptor-activation Efficacy (<i>ε</i>); for partial agonists (<i>ε</i> < 1), SABRE predicts a corresponding shift of <i>κ</i> = <i>εγ</i>-<i>ε</i>+1.