Subject: CCL: when to take a logarithm of biological activity in QSAR studies?

From: Stephen Bowlus <chezbowlus!at!goldrush.com>
Date: Mon, 5 Jan 2004 10:15:39 -0800

It certainly makes sense to express the effective concentration as a 
logarithm, for the reasons given by several respondents to this query.  
It must be appreciated, however, that there is an ASSUMPTION here that 
binding affinity is the activity-limiting feature of a given ligand and 
especially across a series of ligands, if one is extracting a 
structure-activity relationship.  This assumption is frequently 
violated if one is using whole-organism data as the endpoint for 
activity. The distribution characteristics of the logarithm are also 
statistics-friendly when extracting the model (I assume one is using 
some sort of regression here).

Use of %-inhibition (at  a given concentration) is a common practice 
noted by J Panek, particularly for whole-organism response.  Just as 
use of the log is good in the above case, there are other 
transformations of this data which give (statistically) better 
distribution, and these should be investigated when developing an SAR 
equation.  The use of the sqrt(arcsin(X)) comes to mind.

Historically, I think use of the logarithm sort of (uncritically) grew 
out of its use in "Hansch-like" QSAR studies, which share theoretical 
underpinnings with the classic Hammett relationship (and other 
free-energy relationships).  In medicinal chemistry, the use of -logX 
arose out of a desire that "bigger numbers are better."

sb