Hill-Langmuir equation expressing

One way to reduce the risk of confusion is to express ligand concentrations in terms of KA. This normalized concentration is defined as [A IKA and will be denoted here by the symbol eA. We can therefore write the Hill-Langmuir equation in three different though equivalent ways ... 

This is the expression we require. Although it has the same general form as the Hill-Langmuir equation, two important differences are to be noted ... 

With these reservations in mind, we will next consider three approaches that have been used in the past to measure the efficacy of a partial agonist acting on an intact tissue. Each will be analyzed in two ways with the details given in Appendix 1.4C (Section 1.4.9.3). The first is of historical interest only and is based on Stephenson s original formulation, as expressed in Eq. (1.27) (Section 1.4.2) and with receptor occupancy given by the Hill-Langmuir equation in its simplest form, which we have already seen to be inadequate for agonists. The second analysis defines receptor occupancy as all the receptors that are occupied, active plus inactive. 

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