Wavelength is a physical measure of light, and the intricate understanding of its link to perceived colour enables the creation of perceptual entities such as metamers—non-overlapping spectral compositions that generate identical colour percepts1. By contrast, scientists have been unable to develop a physical measure linked to perceived smell, even one that merely reflects the extent of perceptual similarity between odorants2. Here, to generate such a measure, we collected perceptual similarity estimates of 49,788 pairwise odorants from 199 participants who smelled 242 different multicomponent odorants and used these data to refine a predictive model that links odorant structure to odorant perception3. The resulting measure combines 21 physicochemical features of the odorants into a single number—expressed in radians—that accurately predicts the extent of perceptual similarity between multicomponent odorant pairs. To assess the usefulness of this measure, we investigated whether we could use it to create olfactory metamers. To this end, we first identified a cut-off in the measure: pairs of multicomponent odorants that were within 0.05 radians of each other or less were very difficult to discriminate. Using this cut-off, we were able to design olfactory metamers—pairs of non-overlapping molecular compositions that generated identical odour percepts. The accurate predictions of perceptual similarity, and the ensuing creation of olfactory metamers, suggest that we have obtained a valid olfactory measure, one that may enable the digitization of smell.
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All data generated during this study are included in the Article and its Supplementary Information. All the odorants used are included in Supplementary Table 1, all behavioural similarity results are included in Supplementary Table 2 and all behavioural discrimination results are included in Supplementary Table 3. An additional external dataset used can be found in the supplementary material of a previously published study15.
The custom code used to process the data collected in this study is available at https://gitlab.com/AharonR/olfaction.
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This work was primarily supported by the Horizon 2020 FET Open project NanoSmell (662629). Additional support from grant 1599/14 from the Israel Science Foundation, by a grant from Unilever, and by the Rob and Cheryl McEwen Fund for Brain Research.
The Office of Technology Licensing at the Weizmann Institute of Science is filing for patents on the algorithms developed in this study. A small portion of this work was supported by a research grant from Unilever, a company with interests in the fragrance industry. Unilever had no input or impact on the design of experiments, or on analysis and presentation of the results. C.L. is the owner of DreamAir LLC, a company with interests in the fragrance industry. DreamAir had no input or impact on the analysis and presentation of the results.
Peer review information Nature thanks Tatyana Sharpee and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.
Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Extended data figures and tables
a, As in the main text, the 148 molecules used across experiments overlaid on 4,046 molecules within the first and second principal components of the 21-descriptor physicochemical space. b, The same molecules within the first and second principal components of perceptual space. Perceptual space data for 470 molecules as background (data from previously published studies4,7), containing 115 of the 148 molecules that we used. c, Histograms showing the experiment odorant distribution on each principal component (PC) in the range of PC1–PC6. The principal components were computed as in a, on the 21-descriptor physicochemical space. There is a large decline in the explained variance from the third principal component onward. d, Histograms showing the distances between all odorant pairs, per experiment. The distances are summed (black line) for the overall distribution. Although monomolecules were not used as a stimulus for discrimination, this is to show that there was no bias in their selection, because for each experiment the distances of the pairs spanned a range of distances.
Ordered depiction of the tasks across the seven reported experiments.
a, b, Factoring odorant intensity. a, In experiment 1, the overall MC-odorant intensity could have been used to determine similarity, n = 23 participants for intensity ratings and 22 participants for similarity ratings. Correlation coefficient r = −0.61, P < 6 × 10−11, n = 95 (r = −0.57, P < 6 × 10−11, n = 91, for comparisons excluding identical pairs). To check whether intensity similarity and angle-distance similarity account for overlapping information, we built a linear model considering the two factors. We found that this two-factor model could account for larger variability than each of the models alone (adjusted R2 = 0.37 versus adjusted R2 = 0.32 for intensity difference and adjusted R2 = 0.16 for angle distance). Both factors were significant in this model (both P < 0.005). In other words, although intensity differences could explain variance in the results, angle distance was a significant factor as well, and could explain independent variance. b, The same analysis for experiment 2. Here, MC-odorant intensity was weakly, albeit significantly correlated with MC-odorant similarity (n = 30 participants for intensity ratings and 29 participants for similarity ratings, correlation coefficient r = −0.22, P = 0.03, n = 95) and this correlation was entirely explained by comparing odorants to themselves, and once these comparisons were removed, the correlation was lost altogether (r = 0.04, P = 0.68, n = 91 for comparisons excluding identical pairs). Thus, experiment 2 largely negated this overall concern. c–i, Predicting odorant intensity. c, Estimated performance of predicted intensity model as correlation between actual and predicted intensity on k-fold test-set (Supplementary Methods). Expected variance estimated using cross-validation (k varied according to the number of molecules (n) used in each concentration; k = 8, 10, 10 and 5, and n = 134, 422, 346 and 58 for concentrations of 10−1, 10−3, 10−5 and 10−7, respectively). In the violin plot large points are averages of k-folds, vertical lines are quartiles 2–3. All four models have correlations significantly larger than zero, with peak at the 10−3 concentration (average r = 0.67). d–i, We used the 10−3 concentration data (Supplementary Methods) to devise a predictive model for intensity ratings, this time excluding molecules used in experiments 1 and 2 to avoid overfitting. d, g, Intensity predictions generated by this model for monomolecule intensities in experiments 1 (d) and 2 (g). The x axis is actual intensity (averages of n = 23 participants, 2 repetitions each for experiment 1; and n = 29 participants, 3 repetitions each for experiment 2) and the y axis is predicted intensity. We show correlations in black and in red to be compatible with other panels, although no zero intensity odours were included. d, Correlation coefficient r = 0.36, P < 0.02, n = 44 monomolecules. g, Correlation coefficient r = 0.68, P < 7 × 10−7, n = 43 monomolecules. e, h, Angle distance estimation using the intensity factor. The intensity factor was calculated based on predicted intensity (d, g) as in Fig. 1e; these predicted factors were then used to model MC-odorants. Finally, angle distances between pairs of MC-odorants were calculated according to predicted intensity compared to those obtained by rated intensity (as used in the main text). e, Correlation coefficient r = 0.53, P < 3 × 10−8, n = 95 (r = 0.29, P < 6 × 10−3, n = 91 for comparisons excluding identical pairs). h, Correlation coefficient r = 0.73, P < 2 × 10−17, n = 95 (r = 0.56, P < 7 × 10−9, n = 91 for comparisons excluding identical pairs). f, i, Prediction of measured similarity from angle distances calculated using predicted intensity (similar to Figs. 1f, 2c). In the scatter plot, each dot is a pairwise comparison of MC-odorants; the y axis shows their actual similarity as rated by participants (for experiment 1, n = 22, 2 repetitions; for experiment 2, n = 29, 2 repetitions) and the x axis shows their angle distance according to predicted intensity. Red regression lines include comparisons of identical MC-odorants (zero angle distance), black regression lines are with those comparisons removed. f, Correlation coefficient r = −0.50, P < 3 × 10−7, n = 95 (r = −0.29, P < 6 × 10−3, n = 91 for comparisons excluding identical pairs). i, Correlation coefficient r = 0.74, P < 9 × 10−19, n = 95 (r = 0.54, P < 5 × 10−8, n = 91 for comparisons excluding identical pairs). f, i, Correlations between previous and current results were not significantly different. f, Experiment 1, difference between result using rated and predicted monomolecule intensities (r = −0.41 and r = −0.29, respectively) was not significantly different (Z = 0.91, P = 0.36, two-tailed, n = 91 comparisons). i, Experiment 2, same procedure, difference between r = −0.69 and r = −0.54 was not significantly different (Z = −1.62, P = 0.011, two-tailed, n = 91 comparisons). We summarize that this is a promising direction for the future, but beyond the scope of this manuscript.
Extended Data Fig. 4 Variability in predictions of perceptual similarity from structure in olfaction and audition.
a, Recreation of Fig. 2c, which shows our underlying results, with the point of maximal variance highlighted with a blue ellipse. b, Data extracted from figure 22 from a previously published study13, which shows the state-of-the-art predictions from around ad 2000 of sound similarity from sound structure (overlaying points may be missing, as these data were extracted from the graph). Correlation coefficient r = −0.80, P < 2 × 10−103, n = 462. c, Data extracted from figure 3 of a previously published study14, which shows the state-of-the-art predictions from around ad 2014 of sound similarity from sound structure. Note that we formatted the data to compare the datapoints to our data by putting the data into the same graph colour and structure and by reversing the axes. Correlation coefficient r = −0.84, P < 3 × 10−26, n = 96. d, Comparison of points of maximal variance across datasets (blue, olfaction; red and green, audition). In audition technology, the major standard is PEAQ—the ITU standard for objective measurement of perceived audio quality. PEAQ defines the subjective difference grade, which is the equivalent of our ‘perceived similarity’, and the objective difference grade (ODG), which is the equivalent of our ‘angle distance’. The field is tasked with developing different objective difference grades, which can be made of various combined measures such as frequency, timbre, power, and so on. We observe that the overall correlation in audition is not very different from olfaction, and that the variability at a given physical distance is perhaps even greater in audition compared with olfaction.
a, c, Scatter plots om which each dot is a pairwise comparison of two odorants; the y axis shows their actual similarity as rated by participants and the x axis shows their distance according to the model. a, Data from the experiment containing rose, violet, asafoetida and 11 additional MC-odorants. All comparisons containing rose are shown in red, all comparisons containing are shown violet in violet and all comparisons containing asafoetida are shown in mustard (n = 29 participants, 2 repetitions each). Correlation coefficient r = −0.55, P < 3 × 10−5, n = 52 (r = −0.31, P < 0.03, n = 48 for comparisons excluding identical pairs). b, Rated similarity versus angle distance between rose, violet and asafoetida comparisons in this experiment. The rated similarity data (dark blue) are the average of n = 29 participants, mean of 2 repetitions. Data are mean ± s.e.m. Blue circles are individual ratings of similarity. c, Data from experiments 1 and 2 used for model building, taken from Figs. 1f, 2c. Correlation coefficient r = −0.66, P < 3 × 10−25, n = 190 (r = −0.55, P < 2 × 10−15, n = 182 for comparisons excluding identical pairs). d, End result of predicted versus actual similarity of rose, violet and asafoetida, rated similarity (dark blue) is as in b. Data for predicted similarity (light blue) presented as mean prediction using the linear regression model described in c (red line); the error bars show the confidence intervals (P = 0.05) for this model prediction. See Supplementary Methods for transformation from angle distance to predicted similarity.
a, Performance displayed by individual participant rather than by odorant comparison, sorted by performance. The z axis and colour both code participant performance accuracy. White, 41.8% accuracy or d′ = 1; red, d′ < 1; blue, d′ > 1. b, Performance displayed by individual participants rather than by odorant comparison, sorted by performance. Colour codes are shown for the participant d′ as estimated in Fig. 3c. white, d′ = 1; red, d′ < 1; blue, d′ > 1.
We randomly shuffled performance outcome in the previously published dataset15, and in experiments 4–6. For each MC-odorant pair, we assigned performance (means of the participants) randomly 10,000 times, and then computed the correlation between angle distance and ‘shuffled’ performance. a, A copy of Fig. 3b. b, A set of 100 traces (randomly picked for visualization purposes) of a moving average of shuffled data, similar to the black line in a. Red dashed line in a and b is performance of d′ = 1 (41.8% correct) c–f, Histogram of correlations between angle distance and shuffled performance. Red line is the correlation of the observed data. c, The previously published data15. The correlation of observed data (r = 0.50, n = 310 comparisons) outperforms the correlation of shuffled data (P < 10−4, n = 10,000 repetitions). d–f, Angle distance is shown on a log scale. d, Experiment 4, the correlation of observed data (r = 0.51, n = 50 comparisons) outperforms the correlation of shuffled data (P < 10−4, n = 10,000 repetitions). e, Experiment 5, the correlation of observed data (r = 0.42, n = 50 comparisons) is significantly stronger than the correlation of shuffled data (P = 0.0009, n = 10,000 repetitions). f, Experiment 6, the correlation of observed data (r = 0.53, n = 40 comparisons) is significantly stronger than the correlation of shuffled data (P = 0.0013, n = 10,000 repetitions). g–i, Same as d–f, only here angle distance was analysed using a linear rather than logarithmic scale. g, Experiment 4, the correlation of observed data (r = 0.61, n = 50 comparisons) outperforms the correlation of shuffled data (P < 10−4, n = 10,000 repetitions). h, Experiment 5, the correlation of observed data (r = 0.43, n = 50 comparisons) is significantly stronger than the correlation of shuffled data (P = 0.0015, n = 10,000 repetitions). i, Experiment 6, the correlation of observed data (r = 0.45, n = 40 comparisons) outperforms the correlation of shuffled data (P < 10−4, n = 10,000 repetitions). j–l, Here we verify the validity of the choice of performance threshold, namely d′ = 1, in our data. For this verification, we calculate the null distribution for d′ for the discrimination tasks in experiments 4–6. To generate a meaningful distribution, we carefully choose the shuffling in this analysis. For our data, we shuffled the correct responses for each participant in each session, and assigned the responses to different MC-odorant pairs. For each participant, we used a different label assignment; this way we disentangle the difficulty of the task, and produce a statistic on the frequency at which one would expect each d′ by chance. The histograms of performance in the different experiments are shown in the case in which the data of the participants have been shuffled participants. the red areas show the bottom and top 5%; the grey line is d′ = 1. j, Experiment 4. k, Experiment 5. l, Experiment 6.
We wondered whether metamers are simply instances of ‘olfactory white’. This would imply that the difference between (not within) the 3 metamer pairs would be under 0.05 radians. To address this question, we measured the distances between the 3 metamer pairs, which are as follows: pair 1 and pair 2, 0.11 radians; pair 1 and pair 3, 0.13 radians; pair 2 and pair 3, 0.07 radians. In other words, each metamer is a distinct odour. Moreover, we next compared the metamers to ‘olfactory white’. We selected the ‘best’ white from a previously published study8 and measured its distance from each of the metamers. The obtained minimal distances were 0.25, 0.24 and 0.24, all of which are much higher than 0.05 radians. One may note that the white in the previous study8 may not have been ‘true White’, as indeed that study did not have the underlying computational framework developed here. Moreover, that study was restricted to about 30 components. To address this, we generated 1,000 virtual versions of white odours, by combining different sets of 100 components. We observe that all mean distances between the metamers and these whites are above 0.1 radians, and that the minimal distance of any pair to any white is larger than 0.05 radians. a–c, Histograms show distances between current metamer pairs to the 1,000 different white odours that we generated. Distance between one odour (of the metamer pair) to the whites is shown in blue, and distance between the other odour (of the metamer pair) to the whites is shown in red. Circular points show distances of each odour in the pair to the three previously described white odours8. Each panel shows one of the three metamer pairs reported in this paper.
Supplementary Information document containing Supplementary Discussion and Supplementary Methods.
Supplementary Table 1: containing all manuscript odorants and their intensities.
Supplementary Table 2: containing all manuscript similarity ratings.
Supplementary Table 3: containing all manuscript discrimination results.
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Ravia, A., Snitz, K., Honigstein, D. et al. A measure of smell enables the creation of olfactory metamers. Nature 588, 118–123 (2020). https://doi.org/10.1038/s41586-020-2891-7
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