Del Castillo-Katz model

We assume here that the del Castillo-Katz model applies. Using the Gaddum equation, based on the simpler scheme explored by Hill and by Clark, leads to exactly the same conclusion, as the reader can easily show by following the same steps but starting with Eq. (1.48). 

Analysis based on the del Castillo-Katz model of receptor activation (see Sections 1.2.3 and 1.4.4) The fraction of receptors in the active state is defined by ... 

The term state rather than condition is often used in this context. However, the latter seems preferable in an introductory account. This is because the del Castillo-Katz mechanism is often described as a two-state model of receptor action, meaning here that the occupied receptor exists in two distinct (albeit interconvertible) forms, AR and AR, whereas three conditions of the receptor (R, AR, and AR ) have to be identified when applying the law of mass action to the binding of the ligand, A. 

In the del Castillo and Katz model it is important to notice that the fraction of receptors occupied is the sum of both active (AR ) and occupied, but inactive (AR) receptors ... 

Just a year after Stephenson s classical paper of 1956, J. del Castillo and B. Katz published an electrophysiological study of the interactions that occurred when pairs of agonists with related structures were applied simultaneously to the nicotinic receptors at the endplate region of skeletal muscle. Their findings could be best explained in terms of a model for receptor activation that has already been briefly introduced in Section 1.2.3 (see particularly Eq. (1.7)). In this scheme, the occupied receptor can isomerize between an active and an inactive state. This is very different from the classical model of Hill, Clark, and Gaddum in which no clear distinction was made between the occupation and activation of a receptor by an agonist. 

The next question to consider is the interpretation of efficacy (both in the particular sense introduced by Stephenson and in more general terms) in the context of the model proposed by del Castillo and Katz. 

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