Derivations and numerical examples of the equations discussed in Sections 2 and 3 from The affinity-efficacy problem: an essential part of pharmacology education

This file contains three parts: (1) contains a derivation of the equations for the occupancy of each state in the del Castillo-Katz mechanism; (2) contains two numerical examples of the matrix approach, one for the del Castillo-Katz mechanism and one for the 1985 nAChR mechanism which is used as an example in section 3 of the main text (we also show the derivation of equations for the occupancy of each state in this mechanism, as was done for the del Castillo-Katz mechanism); (3) contains a discussion of constitutive receptor activity and inverse agonism, demonstrating the relationship between these phenomena and the affinity-efficacy problem.