Open Journal of Physical Chemistry, 2013, 3, 150-156
Published Online November 2013 (
Open Access OJPC
A Slightly Modified Expression of the Polar Surface
Area Applied to an Olfactory Study
Paul Laffort
Centre des Sciences du Goût, Dijon, France
Received August 21, 2013; revised September 20, 2013; accepted September 28, 2013
Copyright © 2013 Paul Laffort. This is an open access article distributed under the Creative Commons Attribution License, which
permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The polar surface area of a molecule is currently defined as the surface sum over all polar atoms, primarily oxygen and
nitrogen, also including their attached hydrogens (named PSA1 in the present study). Some authors also include sulfur
and phosphor (PSA3). The slight modification suggested here is based on the fact that it is difficult to consider, on a
theoretical point of view, hexavalent S and pentavalents N and P as polar atoms. Indeed, in these cases, all their periph-
eral electrons are involved in bondings. We propose to define PSA2 using the initial definition extended to O, S, N, P,
with the exception of hexavalent S and pentavalents N and P. In order to test this hypothesis, the three expressions
PSA1, PSA2 and PSA3 have been applied in a QSAR to a physiological phenomenon called comfort olfactory per-
ceived intensity, for the human responses to 186 odorants (QSAR stands for Quantitative Structure Activity Relation-
ship). The PSA2 expression has been selected as the more suitable, associated with two other molecular properties
(molar refraction and Van der Waals molecular volume).
Keywords: Polar Surface Area; QSAR; Cheminformatics; Olfaction; Honey-Bee; Psychophysics
1. Introduction
The polar surface area PSA is a quite fascinating mole-
cular property on various aspects. On one hand, its defi-
nition is chemically simple and precise, according to
Palm et al. [1]: “the area occupied by nitrogen and oxy-
gen atoms, and hydrogen atoms attached to these het-
eroatoms”. On the other hand, its justification has been
considered, in a first time, as strictly pharmacological, in
the sense that it mainly reflects the molecular transport
properties of drugs, particularly blood-brain barrier (BBB)
penetration and intestinal absorption [1,2]. The consid-
eration that PSA could also be involved in the physico-
chemical field as a general criterion of polarity was un-
expected, since, for example, strongly polar elements
such as halogens, particularly fluorine, have always been
excluded of its definition. We have however recently
shown that PSA, associated with the Van der Waals mo-
lecular volume Vw, is strongly involved in the charac-
terization of the polarity of gas-liquid chromatography
stationary phases [3].
As already pointed out in 2007 by Ertl [4], the number
of publications in which PSA is involved has been
growing exponentially since 1996. One of the more
noteworthy recent ones is due to Muehlbacher et al. [5],
who have obtained a discrimination without misclassifi-
cation between two sets of drugs (87 not BBB permeable
compounds and 133 BBB permeable compounds), using
only four molecular descriptors in which PSA has a key
The aim of the present study is firstly to propose, on
theoretical considerations, a slightly modified definition
of PSA, and then to test if one or another of its expres-
sions reflects, possibly associated with other molecular
characteristics, the biological phenomenon summarized
hereafter in the particular case of human olfactory re-
The Comfort Olfactory Perceived Intensity
This phenomenon can be apprehended in the Figure 1.
The top of the figure is a classical representation in log-
log coordinates of the olfactory perceived intensity (OLPI)
vs. the air concentration for three different odorants. It
visualizes an observation firstly shown in 1973 by Laf-
fort and Dravnieks [6] and always verified since: the
lower the threshold, the lower the slope, as a general
trend with a few exceptions (outliers). It seems that
log conc. in air (molarfraction)
log OLPI
log conc. atthe levelof receptors
log OLPI
R comfort
C comfort
Figure 1. Simplified representation of the comfort model for
the olfactory perceived intensity (OLPI), already verified in
the honey-bee. Concentrations are expressed in molar frac-
tions. See details in text.
odorant concentration has to be considered at the recap-
tors level rather than in air, in order to have a complete
description of the phenomenon. This transformation is
supposed to be obtained using a simple physicochemical
The bottom of the Figure 1 visualizes the results we
have already verified in the honey bee. Firstly, the con-
vergence of the straight lines using electroantenographi-
cal responses vs. fractions of saturated vapor pressures is
high (r = 0.97, N = 59, F = 404, without outliers) [7].
Secondly, the ordinate of this point corresponds to an
OLPI value associated with an optimal learning of olfac-
tory recognition using an associating conditioning of the
proboscical reflex [8-10]. For this reason we consider the
ordinate of this convergence point as reflecting an opti-
mal comfort. The abscissa of the convergence point, iden-
tical for all odorants, is the logarithmic value of 1/250 of
the maximal possible concentration at the receptor levels
(expressed in molar fraction, i.e. 2.4).
Unfortunately, if the saturated vapor pressure at room
temperature appears to be a suitable property to trans-
form the top into the bottom of Figure 1 for honey-bees,
it is not the case for humans [11,12]. The explanation
seems to be that the odorants reach the olfactory den-
drites via a humid way in vertebrates, and through a dry
route into pores-tubules in insects.
It should be noted that a synthesis of the experimenta-
tions on honey-bees summarized above has not yet been
published except in a shortened form [13], but has been
orally presented in Dijon [13] and at the Monell Chemi-
cal Senses Center [14].
2. Methods
2.1. Molecular Properties
Three groups of physicochemical properties have been
tested, all derived from the molecular structure.
Properties more or less associated with the mo-
lecular size, namely molar mass (M), Van der Waals
molecular volume (Vw), Van der Waals molecular sur-
face (Sw), Molar refractivity (MR), molecular polariza-
bility (PIZ), partition coefficient octanol-water (ClogP).
All these properties have been got from the Chemaxon
calculator-plugins [15]. A seventh expression has been
considered, the solvation parameter of dispersion (δ) ac-
cording to Laffort and Héricourt [16].
Properties of polar nature, rather independent of
the molecular size, namely three different expressions
of the polar surface area (PSA).
In a first time, PSA values have been established by
Palm et al. [1,2] using sophisticated programs taking into
account the molecular three-dimensional shape and its
flexibility. Later, a very simple topological method using
summation of surface contributions of polar fragments
(termed TPSA) has been applied by Ertl et al. [17], ex-
hibiting an excellent correlation with theoretical PSA
values (r = 0.991, N = 34 810 substances).
The slightly polar atoms sulfur and phosphor have
sometimes been taken into consideration [4,18]. We have
called PSA1 the version with only O and N and PSA3 the
version with O, N, S and P.
We have added a supplementary version, named PSA2,
which includes O, S except when it is hexavalent, and N
and P only when they are trivalent. That implies, among
others, the exclusion of N in nitrates, S in sulfates, P in
phosphates. This alternative choice is in agreement with
the fact, according to the Lewis theory [19], that the pe-
ripheral electrons involved in dative (or semi-polar)
bonding should totally attributed to the more polar of the
two concerned polar atoms. For example, four out five
peripheral electrons of N in organic nitrates should to-
tally be attributed to the two O, whereas the fifth electron
is shared in a covalent bonding with one C. Therefore,
this type of pentavalent nitrogen should totally be non
polar, as it is visualized in Figure 2, and on the contrary
to that admitted in the PSA1 and PSA3 versions.
The orientation solvation parameter ω according to
Laffort and Héricourt [16] has been discarded because
not predicted with enough accuracy from the 2D mo-
lecular structure.
Open Access OJPC
Figure 2. Graphical representation of the four dative (or
semi-polar) bonds and the four covalent bonds of nitro-
methane, according to the Lewis theory [19], clearly show-
ing that the pentavalent nitrogen is not polar (absence of
pairs of peripheral electrons not included in the bonding,
whereas each oxygen has two pairs).
One induction/polarizability index, also independ-
ent of the molecular size. This property is the ε solva-
tion parameter according to Laffort and Héricourt [16]. It
is very similar to the descriptor named R2 or E according
to Abraham and co-authors [20,21].
2.2. Olfactory Properties
Two experimental olfactory properties are needed to
draw the top of the Figure 1 for humans:
Olfactory thresholds, which are, in some way, the in-
tercept of the straight lines with the X axis,
The slopes of the straight lines, currently named pow-
er law exponents.
Presently, the most complete and sure compilation of
human olfactory thresholds in air has been established in
2011 by Van Gemert [22] and concerns 1150 odorants.
However, an issue encountered with this type of compi-
lation is that different authors obtain widely different
values for the same substance. We have shown since
1963 [23] that these differences, mainly due to differ-
ences in experimental protocols, can be considerably re-
duced by assigning a specific weighting coefficient to
each author’s results. Applying this method, Devos et al.
[24] have established in 1990 the most recent published
collection of standardized thresholds, which concerns
529 odorants. An updated version of this compilation,
unpublished, has been established in 1995 for 117 sup-
plementary compounds [25].
It is also well established since 1969 that the exponent
values differ, for a given odorant, with the experimental
procedure [26]. Applying a similar method as for thresh-
olds, Devos et al. [27] have published in 2002 the most
recent and complete collection of standardized human
power law exponents in air.
The updated compilation of olfactory thresholds and
that of power law exponents according to Devos et al.
[25,27], concern in common 194 odorants. Eight com-
pounds have been discarded of this overlapping set:
Two selenium compounds for which part of the tested
molecular properties have not been found (ethanese-
nelol and diethyl selenide).
Four charged compounds for which part of the tested
molecular properties have not been found (ozone,
2-propenyl isocyanide, phenyl isocyanide and ammo-
nia, i.e. NH4OH in aqueous solution).
Two alcohols presenting very small values of power
law exponents (0.11 and 0.08 for 1-nonanol and 1-
decanol respectively). Indeed, in the explored regres-
sions of log of thresholds vs. other characteristics, the
exponents being expressed in inverse values, they could
present an excessive influence in the statistical proc-
essing (expressed in inverse values, the 186 kept val-
ues represent 1/3 of the total range when these two
alcohols are included).
2.3. Statistical Tools
In addition to the Microsoft Excel Windows facilities for
drawing diagrams and handling data sets, the SYSTAT®
10.2 for Windows has been applied for stepwise MLRA
(Multidimensional Linear Regression Analysis).
3. Results
3.1. QSAR (Quantitative Structure/Activity
Relationship) for 186 Odorants
We have compared all together the olfactory properties
and the molecular parameters for the 186 compounds
described in the Methods section, in order to embrace the
larger possible of molecular features. The eleven mo-
lecular parameters have been tested in multiple cross
combinations using the SYSTAT stepwise MLRA. The
best obtained regression is given by Equation (1):
 
0.81777.406 MRPSA2
.ol3.604 2.3
100 Vw
66 14272
 
n (1)
in which p.ol stands for the negative log of concentration
at threshold level (1995 version) expressed in molar frac-
tion, n stands for standardized power function exponent
according to Devos et al. [25], MR stands for molar re-
fraction and Vw for Van der Waals molar volume (the
two later according to the Chemaxon calculator-plugins
[15]), and at last PSA2 stands for the new proposed ex-
pression of the polar surface area, as defined in the
Methods section. The numbers situated below the three
independent variables of Equation (1) stand for the par-
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tial F ratios corresponding to each term.
The global characteristics of the regression are:
r = 0.77, N = 186, F = 89, without outliers
Equation (1) means that the stepwise regression analy-
has confirmed the selection of 1/n,
has selected one of the terms more or less related to
the molecular size, with a preference for molar refrac-
has selected an expression of the polarity expressed
by the ratio PSA2/Vw (preference of the new expres-
sion of PSA and preference of Vw over Sw, among
has not selected the proposed induction/ polarizability
expression (δ),
has not selected ClogP (partition coefficient octanol-
water), very popular in pharmacology.
In order to simplify the Equation (1) handling, we pro-
pose to name vertolf (as VERtebrates Olfactory Filter),
the sum of its second and third terms:
7.406 MRPSA2
vertolf 3.604
100 Vw
 (2)
Because of the definition of p.ol, all the terms of Equa-
tion (1) can be multiplied by (1) if the dependent vari-
able is preferred as the log of threshold (also expressed in
molar fraction):
log thresholdvertolf2.3 
n (3)
Equation (3) can be compared to that obtained by Patte
et al. [7] for the honey-bees:
log log
loglog SVP2.4
 
Cn (4)
A comparison between Equations (3) and (4) clearly
shows an almost identical value of the constant, corre-
sponding to the convergence point abscissa in the bottom
of Figure 1 (i.e. approximately the log value of 1/200 the
supposed maximal concentration at the level of recap-
In addition, [- vertolf] expression takes the place of log
SVP, and we can interpret the numerator of the first term
in Equation (3) as follows:
log log 0.8177
RR (5)
3.2. Nature of the Convergence Point Ordinate
The challenge is, as we saw, to check if the ratio RC/R0
equal to 6.57 corresponds or not to an easily noticeable
level, not too faint, not too strong.
The oldest attempt of a standardized scale of OLPI is
credited to Allison and Katz in 1919 [28]. According to
this method, named category scaling, when subjects are
asked to classify odor intensities in, for example, one of
these categories: odorless, very weak, weak, medium,
strong, very strong, by attributing a such value as 0, 1, 2,
3, 4 or 5 to each of these categories, a linearity between
these numbers and the logarithm of the concentration is
observed. In some ways, these categories are directly pro-
portional to a logarithmic expression of the true OLPI.
In a more accurate method, named olfactory matching,
odorous stimuli under study may be compared with a se-
ries of calibrated concentrations of a reference odor, gene-
rally 1-butanol. Initiated in 1971 by Dravnieks [29], this
procedure has been adopted as a standard method by the
ASTM [30] and by AFNOR [31]. In the latter standard,
correspondences between the two scales are indicated.
We have displayed in Figure 3 the corresponding val-
ues between the suprathreshold categories and the 1-but-
anol concentration equivalences according to the AF-
NOR standard X 43-103 [31]. Figure 3 also includes the
corresponding standardized values of the OLPI according
to the equation proposed by Devos et al. [27]:
OLPI 2C (6)
in which C stands for a given odorous intensity expressed
in terms of ppm of 1-butanol. From this equation, 10
units of OLPI2002 correspond to 50 ppm of 1-butanol.
Equation (6) applied to the threshold value of 1-bu-
tanol according to Devos et al. [25] (0.39 ppm vol) gives
Category log ppmppm OLPI Particular cases
Very strong3.0100044.70
2.5316 25.10
1.531.6 7.90
1.2216.75.78 Convergence
Easily noticeable1.010.04.50 point ordinate
(present study)
0.53.16 2.50
-0.410.390.88 Std. threshold
-0.50.3160.80 (1995)
Very faint-1.00.1000.50
-1.50.032 0.25
Figure 3. Some corresponding values of three expressions of
suprathreshold olfactory perceived intensities (OLPI). See
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an OLPI2002 value of 0.88, and therefore the RC value of
fort OLPI Here Proposed
f the convergence point in the bottom
nt in the same
tical tests obtained between ex-
Equation (5) becomes equal to 5.78 (0.88 × 6.57).
It clearly appears in Figure 3 that the conve
int ordinate takes the upper place in the easily notice-
able category and it should therefore be suitable to at-
tribute it the label of comfort point. It should however be
specified that this assertion implies the procedures taken
as a benchmark in the two compilations of Devos et al.
and in the AFNOR standard as well, i.e. the natural sniff-
fing. Using other procedures, as for example a relatively
low flow rate of stimulation (e.g. 160 ml/min, as recom-
mended by ASTM E544-99), leads to a reaching easily
noticeable category for higher concentrations of 1-bu-
tanol (around 87 ppm according to Dravnieks [32]). It
can be seen in Figure 3 that this concentration using na-
tural sniffing corresponds to a strong category.
4. Discussion
4.1. The Model of Com
We have observed some satisfactory results in the previ-
ous section, when compared to those previously obtained
in the honey-bee:
the abscissas o
of Figure 1 are very similar in both cases [values of
constants in Equations (3) an (4)]
the ordinate of the convergence poi
bottom of Figure 1 corresponds in both cases to an
OLPI not too strong, not too faint, optimal for odorant
recognition by the honey-bees (Introduction), and
characterized as easily noticeable from human re-
sponses (Figure 3).
By contrast, the statis
rimental and predicted human olfactory thresholds
using Equation (1) are appreciably lower than in the
honey-bee experimentation (r = 0.77 instead of 0.97, F =
89 instead of 404). One argument seems to indicate that
this observation is rather due to a lack of accuracy of the
biological data than the weakness of the model:
We have compared our above results using
) with the predicted human olfactory thresholds in the
three most recent publications on this QSAR topic, even
not at all involved in the comfort concept here developed
[33-35]. From the comparison of statistical tests, the F
ratio values are moderate in all cases, and incidentally
the best one is observed with the present study, as sum-
marized in Table 1. As a reminder, F ratio value can be
obtained from the correlation coefficient r, the number of
observations N (here the number of odorants) and the
number of independent variables, according to Abdi [36]:
rN NbIndepVar
r (7)
Table 1. Comparative statistical tests SEE, r an
for six QSAR models in three recent publ
and in the present study.
d F observed
ications [33-35]
Authors Indep. Var. N SEErF
Physiol Chem
Equation (6)0.80 5 50 0.58829
Abraham et al.
(2002) Equation (9)60 0.600.9244
present wor
0 7
Equation (5)0 9 193 0.830.8660
Abraham et al.
(2012) Equation (6)6 9 353 0.820.8771
Zarzo (2012)
Equation (4)18 2 114 - 0.9542
Equation (1)1 2 186 0.950.7789
of the pretio
g to the considered statistical test, r or F. The statisti-
The finding that the ratio of the polar surface area over
olume (PSA/Vw) has
The cross validation on the comfort OLPI from honey-
sponses in one hand, and on the ex-
pression PSA/Vw from chromatographic phenomena and
Obviously, the qualitydicn differs accord-
cans appear to favor the second criterion, particularly
when the number of independent variables increases in
large proportion relatively to the number of observations
(here the odorants under study).
One of the possible applications of the model of OLPI
comfort proposed here is the prediction of power law
exponents from experimental data sets of olfactory thresh-
olds, which are known for much more odorants. That
could be useful, for example, in the study of synergy and
inhibition of olfactory mixtures, where it has be shown
for a long time the role played by the power law expo-
nents [37,38]. More generally speaking, the suprathresh-
old OLPI using ASTM or AFNOR standard procedures
should be applied more frequently in place or in com-
plement of thresholds measurements.
4.2. The Polar Surface Area
the Van der Waals molecular v
been selected by the MLRA processing in the present
study may be related to the involving of this expression
in gas-liquid chromatographic phenomena, where it es-
timates well the polarity of stationary phases (Laffort
[3] ). At this stage, only the classical polar surface area,
i.e. PSA1, has been tested in chromatographic phenom-
The PSA2 version, apparently more rational on a theo-
retical point of view than the PSA1 and PSA3 versions,
has been always, in the present study, preferred by the
MLRA processing to the two other versions.
5. Conclusion
bee and human re
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the present psychophysical study in the other hand, pro-
vides strong arguments in favor of a robustness of the
6. Supporting Information
Supporting information associated with this article (nume-
lfactory properties for
equest to the author:
s David Laffort for his
sincerely thanks the C
ly interactive calculator. He
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7. Acknowledgements
The author warmly acknowledge
editing assistance, and also
mAxon Company for its free
is strongly indebted to the co-authors involved in the
previous studies making possible the present synthesis,
more particularly: Gérard Arnold, Isabelle Canard, Mi-
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Héricourt, Pierrette Marfaing, François Patte, Yves
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