Problems associated with the application of the Cheng-Prusoff relationship to estimate atropine affinity constants using functional tissue responses.

We have studied problems associated with the application of the Cheng-Prusoff relationship to the estimation of atropine dissociation constants from isolated guinea-pig tracheal responses. The values obtained have been compared to dissociation constants derived using Schild analysis. It was observed that when either carbachol (an agonist of high efficacy) or pilocarpine (an agonist of low efficacy) was used the dissociation constants estimated for atropine using the Schild analysis were very similar to those estimated using the Cheng-Prusoff relationship. In these latter experiments the agonist concentration used was the EC80. When the agonist concentration used was increased to supramaximal concentrations (3-fold greater than the EC100) the dissociation constants derived were overestimations by approximately 10-fold. It is concluded that in certain circumstances the results obtained using both the Cheng-Prusoff relationship and Schild analysis are comparable. However, it is unlikely that the Cheng-Prusoff relationship is generally applicable and that Schild analysis is clearly preferable in determining antagonist dissociation constants.