The Relationship between Receptor Occupancy and Tissue Response

2 The Relationship between Receptor Occupancy and Tissue Response 

This is the second of the two questions identified at the start of Section 1.2, where it was noted that the earliest pharmacologists had no choice but to use indirect methods in their attempts to account for the relationship between the concentration of a drug and the tissue response that it elicits. In the absence at that time of any means of obtaining direct evidence on the point, A. V. Hill and A. J. Clark explored the consequences of assuming (1) that the law of mass action applies, so that Eq. (1.2), derived above, holds and (2) that the response of the tissue is linearly related to receptor occupancy. Clark went further and made the tentative assumption that the relationship might be one of direct proportionality (though he was well aware that this was almost certainly an oversimplification, as we now know it usually is). 

Should there be direct proportionality, and using y to denote the response of a tissue (expressed as a percentage of the maximum response attainable with a large concentration of the agonist), the relationship between occupancy and response becomes  

Combining this with Eq. (1.2) gives an expression that predicts the relationship between the concentration of the agonist and the response that it elicits  

The applicability of this expression (and by implication Eq. (1.4)) can be tested by measuring a series of responses ( v) to different concentrations of A and then plotting log (y/(100 - y)) against 

---