Chem. Senses 27: 95-104,
2002
© Oxford University Press 2002
A Model for Odour Thresholds
Department of Chemistry, University College London, 20 Gordon Street, London WC1H 0AJ, UK 1 Chemosensory Perception Laboratory, Department of Surgery (Otolaryngology), University of California, San Diego, Mail Code 0957, La Jolla, CA 92093-0957, USA
Correspondence to be sent to: Michael H. Abraham, Department of Chemistry, University College London, 20 Gordon Street, London WC1H 0AJ, UK. e-mail: m.h.abraham{at}ucl.ac.uk
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Abstract |
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Odour detection thresholds, that we have previously obtained, have been analysed by a general equation for selective transport. It is shown that such selective transport can account for some 77% of the total effect. The remainder is due to a specific size effect, that might involve odour-binding proteins, and a specific effect for aldehydes and carboxylic acids. Our analysis raises the question of whether selective transport is physically separable from the specific effects of receptor activation. The model predicts a chemical cut-off in odour detection along any homologous series.
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Introduction |
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TopAbstractIntroductionMethodologyResults and discussionReferences |
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There have been a number of correlations of odour detection thresholds (ODT) with various properties of odorants, the study by Laffort and Patte (Laffort and Patte, 1987
)
being one of the first to employ a physicochemical analysis. Chastrette
(Chastrette, 1997) has
reviewed work up to 1996; many studies involved sets of odorants of similar
structure, and none led to any conclusions of mechanistic significance. Two
subsequent studies related ODT to properties of homologous series of odorants.
Yamanaka (Yamanaka, 1995)
showed that odour thresholds of Devos et al.
(Devos et al., 1990)
for several homologous series could be correlated with the odorant activity
coefficient in water, 
w, through a set of equations of the
type:
 | (1) |
) who
used the following representation of a possible mechanism:
 | (2) |
 | (3) |
); the
coefficients a and b vary from one homologous series to
another. The interpretation of equation (3) was that KW is
an approximation for KAM, as both refer to the equilibrium
between the gas phase and an aqueous condensed phase, and that
KMB and KR are both functions of
Poct.
Both equations (1) and (3) suffer from shortcomings as predictive
equations, in that only homologous series can be considered. This excludes
numerous types of important VOCs such as inhalation anaesthetics and terpenes
that do not fall into any homologous series. The model of Hau and Connell
(Hau and Connell, 1998) is
significant, however, because it is the only real attempt to correlate ODT
values on any mechanistic basis.
There have been studies using sets of varied structural types of VOCs,
rather than restriction to homologous series. Dravnieks
(Dravnieks, 1974) correlated
four sets of threshold data of vapours, using various structural features as
the independent variables, but results were not very good, with
r2 ranging from 0.42 to 0.58 with four independent
variables. Such methods may be useful as empirical correlations, but yield
little mechanistic information.
In order to investigate odour thresholds in more detail, it is important to
understand the way in which olfactory perception is processed, via the
relationship between odour stimuli and the receptive surface
(Pearce et al.,
1998). Once in the airspace above the olfactory mucosa, the
molecules must diffuse through a layer of mucus (10-30 µm thick) to gain
final access to the receptors themselves
(Hornung and Mozell, 1981;
Snyder et al., 1988).
Such diffusion, or transport, may involve (at least in part) odorant binding
proteins (OBPs) that can act as carriers
(Bianchet et al.,
1996; Brownlow and Sawyer,
1996; Tegoni et al.,
1996;
Löbel et
al., 2001). The central pocket in the OBP has dimensions of
11 x 10 x 7 
(i.e. 770
3) with an opening size of 6
x 7
(Tegoni et al.,
1996), although a much larger cavity of 1100-1300
3 has been suggested
(Bianchet et al.,
1996). Once transported across the mucosal layer to a receptor
area or biophase, the VOC (or the VOC/OBP complex) can then interact with
odour receptors at the surface of the cilia membrane of the olfactory neuron.
The actual binding pocket in the rat OR5 receptor, however, is no less than 12
from the extracellular surface of the
receptor (Singer and Shepherd,
1994). A general model that we suggest is shown in
Figure 1. It is useful to
consider two types of interaction. Simple transport processes are selective,
in that different VOCs will have different equilibrium constants, depending on
their structure. However, small changes in structure or small positional
changes of functional groups have rather small effects on such processes. On
the other hand, in processes such as ligand/receptor interactions, small
changes in structure can have very large effects; we refer to these processes
as having specific effects. In Figure
1 we indicate which processes may be selective and those that may
be specific in nature.
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Whether the VOC/OBP interactions and the VOC/R interactions are general
interactions that can be modelled by a physicochemical transport process, or
whether they are more specific interactions, is a crucial point. The analysis
of Hau and Connell (Hau and Connell,
1998) certainly supposes that the VOC/R interaction is a general
interaction that can be modelled by a simple physicochemical descriptor, such
as log Poct.
Our approach is first to use a model that simply reflects a passive physicochemical transport property. Comparison with physicochemical transport to various solvents or to various biophases will then indicate whether or not such passive transport can model all or part of the odour detection process.
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Methodology |
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TopAbstractIntroductionMethodologyResults and discussionReferences |
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We have devised a very general equation for the correlation of a variety of processes in which VOCs are transferred from the gas phase to some condensed phase (Abraham et al., 1991
; Abraham,
1993):
 | (4) |
) properties of
the VOCs. We use a simplified nomenclature, with the original nomenclature in
parentheses: E (R2) is an excess molar refraction,
S (
2H) is the dipolarity/polarizability,
A (
2H) and B
(ß2H) are the overall or effective
hydrogen-bond acidity and basicity, and L (log L16) is
defined through L16, the solute Ostwald solubility coefficient on
hexadecane at 298K. The L-descriptor is itself a combination of two
solute properties: (i) a general measure of solute size, and (ii) the ability
of a solute to interact with a solvent phase through dispersion forces. The
units of E are cm3/10; the other descriptors have no units
because they are all derived from the logarithm of an equilibrium constant.
The coefficients c, e, s, a, b and l are found by multiple
linear regression analysis. They reflect the complementary properties of the
receptor phase. The e-coefficient gives the tendency of the phase to
interact with VOCs through polarizability-type interactions, mostly via
electron pairs. The s-coefficient is a measure of the phase
dipolarity/polarizability. The a-coefficient represents the
complementary property to VOC hydrogen-bond acidity and so is a measure of the
phase hydrogen-bond basicity. Likewise, the b-coefficient is a
measure of the phase hydrogen-bond acidity. Finally, the
l-coefficient is a measure of the hydrophobicity of the phase.
Equation (4) has been applied to numerous gas—solvent partitions
(Abraham et al.,
1994b,
1998b,
1999a,b),
to gas—biophase partitions (Abraham
and Weathersby, 1994), and to a very large number of gas
chromatographic systems (Abraham et
al., 1999c), so it is a well tried and tested equation.
We have previously used equation (4) to correlate nasal pungency threshold
values (NPT, in p.p.m.) for 43 varied compounds
(Abraham et al.,
1998a), resulting in equation (5):
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The coefficients in equation (5) can be compared with those for various
gas-condensed phase partitions that take place by simple transfer mechanisms,
as shown in Table 1 (Abraham
et al., 1994b,
1998b,
1999a,b).
There is considerable similarity between the NPT equation and equations for
the solubility of gaseous VOCs in solvents such as wet l-octanol and methanol.
There is also some similarity with equations for the solubility of gaseous
VOCs in a number of biophases (Abraham and
Weathersby, 1994). There is therefore nothing extraordinary about
equation (5), which can be regarded as an equation for simple transfer of VOCs
from the gas phase to a biophase. It is noteworthy that equation (5)
encompasses a wide variety of VOCs, including carboxylic acids, aldehydes,
ketones, alcohols, etc., with but one outlier—acetic acid. Following the
analysis of Abraham et al.
(Abraham et al.,
1994a), equation (5) could be interpreted as arising from
transport of VOCs to a biophase, followed by activation of a receptor through
an `on—off' mechanism that was independent of the structure of the
VOC.
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Our strategy is to apply the general equation (4) to ODT values, in the hope that we might deduce whether or not the resulting equation is consistent with simple transfer of VOCs from the gas phase to a biophase.
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Results and discussion |
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TopAbstractIntroductionMethodologyResults and discussionReferences |
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General analysis
ODTs for a series of 64 compounds, including esters, aldehydes, ketones,
alcohols, carboxylic acids, aromatic hydrocarbons, terpenes and a number of
other VOCs, have been determined previously (Cometto-Muniz and Cain,
1990,
1991,
1993,
1994,
1995) and by Cometto-Muniz
et al. (Cometto-Muniz et al.,
1998a,b),
using a standardized protocol. This protocol entails direct measurement of
vapour phase concentration of the VOCs for as many steps on the dilution
series of each VOC as the sensitivity of an FID gas chromatographic detector
(or sometimes a PID detector) allows; this is a rarity in olfactory research.
The average standard deviation for all odour thresholds, expressed as
log(1/ODT) is 0.63 log unit. The VOCs used in these studies are listed in
Table 2, together with
log(1/ODT) values, where ODT is in p.p.m. The corresponding VOC descriptors
are given in Table 3. As a
first step we applied equation (4) to all the VOCs except the carboxylic acids
and aliphatic aldehydes that were clearly out of line. The VOCs, propanone,
l-octanol, methylacetate and t-butylacetate were then also revealed to be
outliers, and were removed to yield the correlation equation,
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The closeness of equation (6) to equation (5), shows also that values of
log(1/NPT) and log(1/ODT), except for the aldehydes and carboxylic acids, will
be reasonably well correlated, which is indeed the case. Inspection of
Table 1 also leads to the
conclusion that the aqueous mucus layer that covers the olfactory epithelium
does not influence the transport process, because the equation for gas/water
transfer (Abraham et al.,
1994b) is completely different to equation (6). The latter
equation is also in agreement with the finding that the odour receptor binding
pocket, at least for the OR5 receptor, is a considerable distance away from
the extracellular surface of the receptor
(Singer and Shepherd,
1994).
In order to ascertain what other factors, as well as simple transport,
influence the ODT values, it is instructive to plot the residuals in equation
(6), i.e. [log(1/ODT)obs — log(1/ODT)calc] against the `size' parameter,
L. The residuals are not random, and both small VOCs and large VOCs are
less potent than expected. An even more informative plot, shown in
Figure 2, is of the residuals
versus the maximum length, D, of the VOC. The latter was obtained by
means of a computer-assisted molecular-modelling program
(Molecular Modeling Pro,
1992). The maximum value for D in a VOC was obtained after
geometry optimization. In Figure
2, only the residuals for some homologous series are given, for
clarity. It can then be seen that the residuals follow a `parabolic-like'
curve: as molecular size increases, the residual value increases to a maximum
value and then decreases.
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We suggest that the pattern of residuals in
Figure 2 is due to an extra
effect, in addition to simple transfer. The effect can be quantified and
incorporated into an equation for log(1/ODT) through addition of a parabolic
term in (D — D2):
 |
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0.6 log units (see later), of the order of
experimental error. Four compounds are again outliers to equation (8), namely,
propanone, methylacetate, t-butylacetate and 1-octanol. We shall use equation
(8) as the basis of our model of odour detection, but suggest that an
alternative predictive equation can be constructed by using a parabolic term
in L, rather than in D:
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The necessity for the use of an indicator variable for aldehydes and
carboxylic acids arises because these two sets of compounds are more potent
than predicted by equation (7). There is precedent for the extra potency of
aldehydes and carboxylic acids. Alarie et al.
(Alarie et al., 1998)
have shown that these compounds are more potent than expected in sensory
irritation in mice, and suggest that they undergo some actual chemical
reaction. However, aldehydes and carboxylic acids (except acetic acid) fit our
equation for nasal pungency thresholds
(Abraham et al. 1998a)
without use of any indicator variable, see equation (5). There is also the
problem of the four outliers, propanone, methylacetate, t-butylacetate and
1-octanol. There may be extra experimental error with the first three
compounds. Loss of propanone and methylacetate due to their high volatility
would result in the compounds appearing to be of lower potency. In the case of
t-butylacetate, the compound seemed to form an emulsion in some experiments,
and this would result in an erroneous estimation of the ODT value. However, we
have no explanation for the increased potency of 1-octanol.
Very recently, the EVA spectral descriptor has been applied to a selection
of ODT values (Turner and Willett,
2000). No details were given other than for 52 ODT values,
q2 was 0.57 and for 44 log ODT values
q2 was 0.71; unfortunately EVA results cannot be
interpreted in any chemical way and so cannot lead to any mechanistic
conclusions.
Predictive capability
The statistics given for the various equations in log(1/ODT) do not lead to any assessment of their predictive capability, but only of their correlative ability. One method of estimating the predictive power of an equation is to divide total set of data into a training set and a test set. The training set is used to develop a correlation equation that in turn is used to predict the values for the test set. As the latter values have not been used to set up the correlation equation, a comparison of predicted and observed values for the test set is a very useful guide to the predictive power of the training equation. Equations (7), (8) and (9) cannot be studied in this way, because the parabolic terms have been imposed and are not the result of a straightforward correlation. However, equation (6) is an example of a multiple correlation, and so we have used this equation as an example. In order to have sufficient data points to construct a correlation equation for the training set, we used 38 points for the training set and 12 for a test set. It is important that the test set is a representative sample of the entire set. We listed the 50 compounds in order of increasing values of log(1/ODT) and then selected every fourth compound as a member of the test set, leaving 38 compounds as the training set; we refer to this training/test set as 1(ODT). We then listed the 50 compounds in order of the dependent variable E, and chose every fourth compound as a member of a new test set, again leaving 38 compounds as a training set; the new training/test set is denoted as 2(E). A similar process was used to obtain training/test sets by ordering compounds by the other independent variables. This gave six different training/test sets.
A summary of the statistics for the six 38-compound training sets is in
Table 4, and a comparison of
the predicted (pred) and observed (obs) values of log(1/ODT) for the
12-compound test sets is given in Table
5. We give the usual standard deviation as
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As mentioned above, we cannot apply the training/test set method to
estimate the predictive capability of equations (7), (8) and (9), but we think
it reasonable to assign estimates as 0.03 log units higher than the
correlation SD values.
A model of odour detection
Equation (8) is not only a predictive equation, but can be considered to be
compatible with the model shown in Figure
1. A large part of the variation in log(1/ODT) values with the
structure of the VOCs is due to simple transport of the VOC from the gas phase
to a biophase. In addition, there is an effect that we suggest is due to the
size of the VOC, specifically to the maximum length [two recent papers have
stressed the importance of molecular length as a factor in odour recognition
(Araneda et al.,
2000; Johnson and Leon,
2000)]. The potency of VOCs in an homologous series has a maximum
deviation from the simple transport equation (6) when the VOC has a maximum
length of 11-12 . Now this length is
almost the same as the maximum dimension of the central pocket in OBPs,
namely, 11
(Tegoni et al.,
1996); the alternative volume of Bianchet et al.
(Bianchet et al.,
1996) suggests a maximum length of the central pocket of 12-13
. Thus one possible mechanism includes simple
transfer from the gas phase to a biophase mediated by transport by OBPs. The
exceptions are aldehydes and carboxylic acids that are more potent than
calculated by about a factor of 100. We do not suggest that there is only one
OBP or even one type of OBP; there may be several types with maximum
dimensions 10-15 .
Of course, the above is not the only mechanism that fits our data analysis. It is possible that the OBPs have no discrimination at all, and that the `maximum length' effect takes place on activation of the receptor. In any event, we do suggest that at least two types of interaction contribute to the overall threshold effect.
We can obtain some information as to the role of OBPs from recent work
(Vincent et al.,
2000) in which complexation constants for a number of VOCs with
porcine OBP were obtained. Details are in
Table 6, with the complexation
constants given as log(1/IC50). Over the seven VOCs
studied, values of log(1/IC50) vary by 0.75 log unit,
whereas log(1/ODT) varies by no less than 3.99 log units. It is therefore
possible that the effect of OBPs is not the prime reason for the variation of
log(1/OTD), but that complexation to OBPs (or possibly the rate of
complexation to OBPs) just mediates the effect of transport to, and
interactions with, the receptor.
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Equation (8) has other consequences, including the effect of homologues.
Descriptors for the higher homologues are given in
Table 7. The linear dependence
of log(1/ODT) on L, as in equation (6), would lead to a regular
increase in log(1/ODT) along an homologous series, as shown in
Figure 3. However, the
parabolic dependence on (D — D2) considerably
modifies the linear increase and results in the prediction shown in
Figure 3. The values of
log(1/ODT) gradually become smaller than expected from the linear
relationship, and eventually even begin to decrease, see
Figure 3. This corresponds to a
chemical cut-off in potency, a prediction that is completely outside the scope
of previous analyses (Yamanaka,
1995; Hau and Connell,
1998). This predicted cut-off effect has a very important
consequence. Hau et al. (Hau
et al., 2000) have used their partition model
(Hau and Connell, 1998) to
predict odour thresholds for VOCs found in the indoor environment. As pointed
out above, these partition models do not include any cut-off effect at all,
and hence higher homologues will be predicted to be more potent than on our
model.
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Another, very important, consequence follows from the initial equation (6).
The dependent variable, log(1/ODT), conceptually takes the place of the
dependent variable, log K, where K is a gas/biophase
equilibrium constant given by:
 | (10) |
The ODT value itself represents the number of molecules in the gas phase,
so that the only way that 1/ODT can take the place of an equilibrium constant,
K, is if the number of molecules of a VOC in the biophase in
equilibrium with the gas phase threshold value of the VOC, is the same for
each VOC. This is a more general conclusion than the supposition of Hau and
Connell (Hau and Connell,
1998) that the minimum proportion of available receptors necessary
for the detection of odours is the same for all members of a homologous
series, but differs from series to series.
The odour perception of enantiomers is well known, but invariably in terms
of odour quality (Rossiter,
1996; Pybus and Sell,
1999). Rossiter (Rossiter,
1996) and Laska et al.
(Laska et al., 1999)
list pairs of enantiomers that elicit different sensations of odour quality.
The latter workers tested odour discrimination of 10 pairs of enantiomers and
concluded that within their experimental procedure, differences in odour
intensity played little or no part in discrimination of the two enantiomeric
forms. Other workers have shown that ODTs for R(+)- and
S(-)-nicotine are essentially the same
(Thuerauf et al.,
1999). This again suggests selective, rather than specific,
transport of VOCs to the biophase.
Regarding the potential implications of our results for the interpretation
of olfactory receptor expression studies, we have shown that an equation set
for selective transport of VOCs to the olfactory biophase is able to account
for 77% of the total effect, measured as ODT. In order to account for the
remaining effect, `specific processes' need to be considered. The addition of
a parabolic term in D (a maximum length parameter) or in L (a size parameter)
raises the explained effect to 85%. Thus, our data indicate that
additional specific parameters, for example those derived from receptor-ligand
studies, might be needed to account completely for the ODT measured. The
question of whether selective transport is physically separable from the
effects of receptor activation remains to be explored: If transport is not an
intrinsic part of the stimulation of the receptors, but merely a filter, then
research on receptors may well need to look at the residual after the
transport aspects are subtracted.
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Acknowledgments |
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We are very grateful to the Center for Indoor Air Research for support of this work. J.E.C.-M. also acknowledges support from grant number R 29 DC 02741 and R 01 DC 02741 from the National Institute on Deafness and other Communication Disorders, NIH.
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Accepted September 25, 2001
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