Biomedical Engineering Reference
In-Depth Information
6.4.4 Log(
P
)
When an organic solute is in equilibrium with water and a polar solvent such as octan-1-ol,
it is observed that the ratio of the concentrations
[Solute in octan-1-ol]
[Solute in water]
is roughly constant.
P
is called the
partition coefficient
, and
P
can be used in predicting
transmembrane transport properties, protein binding, receptor affinity and pharmacological
activity. It is easy to determine
P
experimentally, but in the process of molecular design
we have to deal with a high throughput of possible molecular structures and so numbers of
attempts have been made to give simple models for predicting
P
.
In studying the effect of structural variations on
P
, it was suggested that it had an additive-
constitutive character. In the case of a π -substituent, people made use of Hammett's ideas
and wrote
P
=
π
X
=
log
10
(
P
X
)
−
log
10
(
P
H
)
(6.7)
where
P
H
is the partition coefficient for the parent compound and
P
X
the partition coefficient
for a molecule where X has been substituted for H. Workers in the field refer to 'log(
P
)'
rather than '
P
'.
It was originally envisaged that specific substituents would have the same contribution
in different molecules. It has been demonstrated, however, that this hoped-for additivity
does not even hold for many disubstituted benzenes. There are two classical methods for
estimating log(
P
), both based on the assumed additivity: the
f
-constant method of Rekker
(1976) and the fragment approach of Leo
et al.
(1975).
Rekker defined an arbitrary set of terminal fragments using a database of some 1000
compounds with known log(
P
). Linear regression was performed, and the regression coef-
ficients designated
group contributions
. Deviations from the straight lines were corrected by
the introduction of multiples of a so-called 'magic factor' that described special structural
effects such as polar groups, etc. Log(
P
) is calculated from the fragmental contributions
and the correction factors.
Leo
et al.
derived their own set of terminal fragments, together with a great number of
correction factors.
Klopman and Iroff (1981) seem to be the first authors tomake use of quantummechanical
molecular structure calculations. They performed calculations at the quantum mechanical
MINDO/3 level of theory (to be discussed in Chapter 18) in order to calculate the atomic
charge densities of a set of 61 simple organic molecules. They then developed a linear
regression model that included the number of C, N, H and O atoms in the given molecule,
the atomic charges on C, N and O, and certain 'indicator' variables
n
A
,
n
T
and
n
M
designed
to allow for the presence of acid/ester, nitrile and amide functionalities. They found
log
10
(
P
)
=
0.344
+
0.2078
n
H
+
0.093
n
C
−
2.119
n
N
−
1.937
n
O
−
1.389
q
C
−
17.28
q
N
+
0.7316
q
O
+
2.844
n
A
+
0.910
n
T
+
1.709
n
M
(6.8)
The terms involving
q
2
represent the interaction of the solute and solvent.
The method of Klopman and Iroff was a great step forward; there are many fewer
parameters, it does not produce ambiguous results depending on an arbitrary choice of
fragment scheme and it does not have a complicated correction scheme, apart from the
