Subject: RE: when to take a logarithm of biological activity in QSAR studi es?

From: VITORGE Pierre 094605 <vitorge!at!azurite.cea.fr>
Date: Mon, 5 Jan 2004 09:49:34 +0100

log(copncentration) is used because it is related to (macroscopic)
thermodynamic chemical potential, mu:
mu = mu0 + RT ln(activity)
(this equation is the definition of chemical activity)
and a good approximation of this activity is concentration (typically for
dilute solutions). Chemical potential, mu, is Gibbs energy, G, for 1 mole
(it is its definition). From delta_G of reaction and usual thermodynamics,
mass action law is demonstrated, for reaction
A + B -> C
it is K = [C] / ([A] [B])
where 
[X] is the concentration of chemical species X,
delta_G = -RT lnK = mu0(C) - mu0(A) - mu0(B)

in reaction
A + B -> C

A, B and C can actually be any entity for which a chemical potential can be
defined. It is typically used for "sorption sites", it can very well be used
for binding sites of macromolecules

Pierre Vitorge
CEA DEN Saclay DPC/SECR/LSRM & UMR 8587 (CEA-Universite d'Evry-CNRS)
Bat.391 Pe.40a
91191 Gif sur Yvette cedex
France
tel.(+33) 169-08-32-65, secr.: (+33)169-08-32-50, fax:(+33)169-08-32-42
http://perso.club-internet.fr/vitorgen/pierre

-----Message d'origine-----
De : Jaroslaw Panek [mailto:jarek!at!elrond.chem.uni.wroc.pl]
Envoyi : mardi 30 dicembre 2003 13:02
@ : chemistry!at!ccl.net
Objet : CCL:when to take a logarithm of biological activity in QSAR
studies?

Dear CCLers,

there is an established tradition of taking a LOGARITHM of concentrations
(e.g. -log (IC50), -log(ED50) ) as biological activity parameter in QSAR
studies. As I understand, this comes either from the need to bring widely
different numerical data (like 0.0001 and 0.1) into more balanced scale,
or from generally logarithmic nature of biological response to external
stimuli. Now, my question is: do you think that when applying other,
non-concetration-based types of biological activity, one should also take
their logarithm for QSAR studies? I am thinking specifically about
percentages, as in "inhibition percentage", which are commonly encountered
as results of biological assays.

Happy New Year to everybody!

Jaroslaw Panek
Faculty of Chemistry, University of Wroclaw
ul. F. Joliot-Curie 14, 50-383 Wroclaw, Poland

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From: "Mathias, Paul" <Paul.Mathias.-at-.aspentech.com>
Date: Mon, 5 Jan 2004 15:20:39 -0500

There are other reasons why the logarithm is often used in QSAR models:

1.  Typically, the quantity being modeled can only be positive.  Using the
logarithm ensures this.

2.  Many QSAR correlations are derived from theory.  For example,
correlations for activity coefficients are based upon the excess Gibbs Free
Energy; the logarithm of the activity coefficient of a particular component
in a mixture is related to its partial molar derivative of the mixture
excess Gibbs Free Energy.  Models for the excess Gibbs Free Energy (e.g.,
Hildebrand's Regular-Solution Theory and UNIQUAC) invariably result in a
mathematical expression for the logarithm of the activity coefficient as a
function of composition, temperature and physical quantities representing
the intermolecular interaction.

It's best to have a model for the target property of interest.  If the model
is good, an accurate QSAR model will be obtained with only a few adjustable
parameters.  And, for quantities like activities, the resulting QSAR
relationship will usually be in the form of a logarithm.

I have a related quote in my files from somebody named D. L. Bunker (I don't
know who he is):  "Physical Chemistry is research on everything for which
the negative logarithm is linear with 1/T."

Paul Mathias

-----Original Message-----
From: Stephen Bowlus [mailto:chezbowlus.-at-.goldrush.com]
Sent: Monday, January 05, 2004 1:16 PM
To: CHEMISTRY.-at-.ccl.net
Subject: CCL:when to take a logarithm of biological activity in QSAR
studies?

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

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