Olfactory Fingerprints Were Based on Matrices of Perceived Odorant Similarity.

We derived fingerprints using a matrix of perceived odor similarities (21). We used a palette of 28 odors (list of experiment 1A odors in Table S1) that provided for 378 pairwise similarities (28 × 27/2 = 378). Such a 378-dimensional olfactory fingerprint allows for potential characterization of a practically infinite number of individuals. Rather than directly obtaining pairwise similarity estimates, we derived pairwise similarity from 54 different descriptors applied to each odorant alone (list of experiment 1A descriptors in Table S2). We opted for derived over direct similarity ratings because though the two are highly correlated (22), derived similarity is potentially much easier and faster to obtain. For example, direct similarity ratings of the 378 possible odorant pairs in this study would entail 756 individual odorant presentations (A vs. B × 378) each followed by one question: rate similarity. Such a large number of odorant presentations (756) are impractical in an experiment with a human subject. In contrast, 378 derived similarity ratings entail 28 odorant presentations each followed by several questions (e.g., rate how coconut, rate how lemony), and derivation of similarity from the answers; this remains a feasible experiment, and moreover, the number of questions can later be reduced based on the current analysis. Importantly, we acknowledge that the use of odorant descriptors likely entails personal (23) and cultural differences (24), yet this method does not assume or rely on any agreement across individuals in the application of a given descriptor (Fig. 1 contains a schematic of fingerprint acquisition that explains this issue). Thus, we calculated an individual olfactory fingerprint by computing all of the pairwise distances (i.e., derived similarity) between all odorants rated. For a measure of distance between odorant k and odorant m we used the following equation:distancek,m=∑i=1n(Pik−Pim)2n,[1]where Pik is the perceptual rating of odorant k using descriptor i, and Pim is the perceptual rating of odorant m using descriptor i. In words, the distance between odorant k and odorant m is the square root of the mean of the squared difference between all perceptual ratings for those two odorants. Once all of the pairwise distances are computed, we can notate an olfactory fingerprint in the following form:FPk+m−1=distancek,m,[2]where k = 1…N − 1 and m = k + 1…N. In words, each element of the olfactory fingerprint is the distance between pairs of odorants, where each pairwise distance is calculated only once (because distance_k,m = distance_m,k), and the distance between an odorant to itself is omitted (because distance_k,k = 0). Consequently, if we use N odors to construct an olfactory fingerprint, the resulting olfactory fingerprint will have N×(N−1)2 elements. To negate the impact of variance in the number of descriptors used by subjects (e.g., one subject may have used only 50 of the 54 descriptors, and another only 45, leaving all other descriptors unrated, see Figs. S1 and S2 for descriptor use), we normalized each distance between odor pairs by the number of mutual descriptors used for this pair. For example, if odors A and B were rated along 50 descriptors by subject 1, and 45 descriptors by subject 2, dividing the distance between odor pairs by 50 for subject 1 and by 45 for subject 2 enables direct comparison of the perceived distances between odors A and B for subjects 1 and 2.

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Fig. 1.

A schematic for obtaining olfactory fingerprints. Odorant ratings along visual analog scales (VAS) are converted into numbers reflecting location on the VAS line. Pairwise odorant similarity is calculated as the distance across all descriptors used, and pairwise person similarity is calculated as the correlation across individuals. All this ensures that fingerprints are odorant specific but descriptor independent. For example, imagine John who was raised on an island smelling real coconuts, and Jane who knows coconut only from Bounty chocolate bars. Coconut is very different for these two individuals. John may rate odor A as 47% like coconut, odor B as 49% like coconut, and odor C as 4% like coconut. Thus, odors A and B are highly similar, and both are dissimilar from odor C. Jane may rate same odor A as 21% like coconut, odor B as 19% like coconut, and odor C as 100% like coconut. Once again, odors A and B are highly similar, and both are dissimilar from odor C. Thus, John and Jane will have very similar olfactory fingerprints derived from these three odorants and one descriptor, even though they are in total disagreement as to what coconut smell is like.

As noted, such derivations of similarity do not assume that people agree with each other along any given descriptor (e.g., how coconut?), they only assume that a person agrees with him/herself (Fig. 1). In other words, such similarity matrices are odor dependent but descriptor independent, which is here verified in experiments where fingerprints for the same individual obtained with the same odorants but different descriptors remained highly correlated. Finally, for fingerprint visualization purposes alone, we first generated a rectangular image by interpolating the 378 fingerprint values to 500 values. We then projected these values onto a 25 × 20 matrix, and conducted a 2D interpolation providing a 2 × 2 K matrix, which we then projected onto a semicircle (Fig. 2 A–D). We applied these methods in 89 subjects (40 women, mean age = 25.7 ± 3.1 y).

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Fig. 2.

Olfactory fingerprints were consistent within individuals and different across individuals. To visualize fingerprints, we interpolated the 378 pairwise similarities (Methods). (A) An example olfactory fingerprint of one individual. (B) The olfactory fingerprint of the same individual from A, but here derived using a different set of nonoverlapping descriptors. (C) The olfactory fingerprint of the same individual from A and B, but here obtained separately 16 d later. (D) The olfactory fingerprint of a different individual. Correlations: A ⇔ B, r = 0.89; A ⇔ C, r = 0.61; A ⇔ D, r = 0.25. (E) The best-correlated descriptors across all odors. (F) Heat-map matrix of distances between all subject pairs. (G) Histogram of correlation coefficients of all non-self–self pairs.

Olfactory Fingerprints Were Individually Specific.

Previous studies implied that gross olfactory perception is similar across individuals (25), and to test whether this was true here as well, we calculated the mean rating along each descriptor for each odorant, and then calculated the correlation of each individual with the mean. Note that here we are not comparing fingerprints, but rather ratings along specific descriptors; this revealed that individuals are indeed similar to each other in their gross perception. For example, in all top 10 correlated descriptors the mean perception was a very good predictor of individual perception (all r > 0.68; Fig. 2E). Moreover, the primary perceptual dimension of odor, namely pleasantness (2, 26) was particularly highly correlated across individuals and odors, at r = 0.73 ± 0.1 (Fig. 2E). In other words, the average description of an odorant using common descriptors is a pretty good estimation of what any given individual will say about that odor.

We next set out to determine whether despite this gross agreement on odor perception, our sensitive perceptual test will uncover a unique olfactory perceptual fingerprint. Consistent with our hypothesis, we found that across the 89 subjects we tested, no two subjects had the same fingerprint (e.g., Fig. 2A vs. Fig. 2 D, F, and G). We calculated all pairwise distances between olfactory fingerprints (using Pearson’s correlation) and found that the average correlation across individuals (omitting self–self) was r = 0.3 ± 0.13 (Fig. 2G). In other words, whereas gross perception was similar across individuals, a fine measure of perception revealed individual perception for each of the 89 subjects we tested.

Olfactory Fingerprints Were Independent of Descriptor Identity.

The emergence of 89 individual fingerprints alone does not necessarily imply that we captured individual olfactory perception because one can potentially obtain such a result (89 different fingerprints) with random odor similarity ratings. To verify that olfactory fingerprints captured individual olfactory perception, for each of the 89 participants we next generated two alternative fingerprints, A and B, each using a random independent half of the descriptors used to derive similarity. We computed a matrix of all of the pairwise distances between olfactory fingerprints A and B (89 × 89) and tested whether the distance of a subject from him/herself (using different descriptors) was smaller than the distance of a subject to anyone else. In other words, whether, despite the use of different descriptors each time, a subject remained more similar to him/herself than to anyone else (distance between fingerprints was estimated by correlation, see SI Text and Figs. S3–S5 for impact of alternative methods); we repeated this 1,000 times, each time selecting a different set of nonoverlapping descriptors for fingerprints A and B, and assessed the distances between fingerprints. We again plotted the heat-map correlation matrix of each individual with all other individuals, this time, however, each pairwise distance is computed as the correlation between olfactory fingerprints A and B (Fig. 3A). We found that the distance between an individual’s two fingerprints based on the same odors but different descriptors (the diagonal in Fig. 3A, and Fig. 2A vs. Fig. 2B) was overwhelmingly smaller than the average distance between two different individuals [nondiagonal values in Fig. 3A and Fig. 2A vs. Fig. 2D; mean difference between an individual’s two fingerprints r = 0.75 ± 0.025, mean difference between two different individuals’ fingerprints r = 0.25 ± 0.008, paired t test, t(999) = 885.7, P < 10⁻¹⁰; Fig. 3B]. We also found that the maximum of the heat-map correlation matrix lies on the diagonal (i.e., self–self correlation). In other words, olfactory fingerprints A and B of the same individual were always more similar than olfactory fingerprints of different individuals. We repeated the analysis of this data using a permutational multivariate ANOVA (PERMANOVA) to compare the distance between an individual’s two fingerprints based on the same odors but different descriptors (e.g., Fig. 2A vs. Fig. 2B) to the distance between two different individuals (e.g., Fig. 2A vs. Fig. 2D). PERMANOVA implements a flexible nonparametric distance-based analog of analysis of variance for multivariate data that provides a distribution-free means of testing differences between treatments in their multivariate profile (27). Again, the mean difference between an individual’s two fingerprints was r = 0.75 ± 0.025, whereas the mean difference between two different individuals’ fingerprints was r = 0.25 ± 0.008 (PERMNOV test, pseudo F = 8.16, P < 10⁻⁶; Fig. S3C). Thus, the fingerprint genuinely captured personal identity, and a subject’s odorant-specific olfactory fingerprint remains unique even when different descriptors are used to construct it. Once we established the main effect using PERMANOVA, we set out to extrapolate the ability of the olfactory fingerprint to identify an individual beyond our sample; for this, one needs to calculate whether a subject’s correlation to him/herself (calculated between fingerprints A and B) is within the distribution of correlations of a subject to all other subjects (between fingerprint A of a subject to fingerprint A of all other subjects). In other words, to conclude that a subject has a unique fingerprint, the intersubject correlation should not belong (low probability) to the distribution of intrasubject correlations. We fitted a Gaussian to the intrasubject distances distribution, then calculated how many SDs a intersubject’s score lies from the mean of the distribution of intrasubject scores (i.e., z value); from this, we determined the probability of a subject’s correlations to him/herself to be within the distribution of correlations of a subject to all other subjects (i.e., P value). Finally, we averaged all of the individual z-value scores and calculated the overall P value. The distribution of correlations of a subject to all other subjects is not Gaussian, and the subject’s correlation to him/herself is limited by 1 (or −1), hence other metrics for distance between subjects may yield modestly different results (see SI Text for caveats of the Z value and for impact of alternative methods). We repeated this procedure 1,000 times, each time randomly halving the descriptors used to derive similarity (with one half used to generate fingerprint A and the other half used to generate fingerprint B), and averaged across all iterations and all subjects. We obtained an average Z value of 4.9 that corresponds to an ability to use the 28-odor olfactory fingerprint to identify one person of ∼2 million individuals.

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Fig. 3.

Olfactory fingerprints are independent of descriptor identity. (A) Heat-map matrix of distances between fingerprints A and B for 89 subjects, where A and B were derived using the same odorants but different descriptors. The diagonal represents the correlation of a subject to him/herself. (B) Violin plots comparing correlation coefficients of all self–self pairs (using different descriptors) to all self–other pairs, the distribution of correlation coefficients of self–self and self–others are shown in orange; the mean and median of the distribution are depicted in black and red, respectively.

Fingerprint Specificity Depended on Number of Descriptors and Odors Used.

In our initial experiment we used as many as 54 descriptors and 28 odors because we wanted to explore the impact of these parameters. To estimate the dependence of fingerprint discriminability on the number of descriptors and odorants used, we again generated two alternative fingerprints for each subject, A and B, each using a random independent half of the descriptors used to derive similarity. Here, however, we successively reduced the number of odorants and descriptors used. We repeated each analysis 1,000 times, each time shuffling the particular odorants and descriptors omitted. We plotted the averaged fingerprint specificity (averaging the Z score across subjects and iterations) as a function of the number of descriptors and odorants used to generate it (Fig. 4 A and B). We observed a monotonic decrease in the specificity of the fingerprint, yet even with only 7 odors and 11 descriptors, the correlation between an individual’s two fingerprints based on the same odors but different descriptors was significantly above the correlation between two different individuals: z = 1.65, P < 0.05. Thus, potentially meaningful olfactory fingerprints can be obtained in under 10 min. In turn, we extrapolated to estimate how many odors and descriptors we would need to use to obtain an individual fingerprint for each of the ∼7 billion people on earth, and concluded at 34 odors and 35 descriptors. We estimate that obtaining such a detailed fingerprint would take ∼5 h.

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Fig. 4.

Fingerprints depend on the number of odors and descriptors and the passing of time. (A) Heat map of fingerprint ability to distinguish self–self from self–other pairs (represented in Z-score values) as a function of number of odors and descriptors used. Dashed line represents Z-score value of 1.65 (P = 0.05). (B) 3D plot of Z-score values as a function of number of odors and descriptors used to generate a fingerprint. (C) First test–retest. Violin plot comparing correlation coefficients of 23 subjects refingerprinted across time. (Left) Correlation coefficients distribution of a subject to him/herself over time. (Right) Correlation coefficients distribution of a subject to other subjects over time. The mean and median of the distribution are depicted in black and red, respectively. (D) Second test–retest with five repetitions. Right y axis is correlation across retests (r) shown in yellow. Left y axis is the ability of the fingerprint to discriminate self from others in Z-score values when comparing the first to ensuing retests (black bars) or each two consecutive retests (red line).

Olfactory Fingerprints Remained Specific Despite Fluctuation Over Time.

Olfactory perception is not only variable across individuals, it is also highly variable within individuals over time (28). This variability may reflect in part that odor perception is the combination of a given receptor activation pattern with the fluctuating homeostatic state in which it is perceived (hunger/satiety, mood, arousal, etc.) (2). To test the persistence of the olfactory fingerprint at retest, we refingerprinted 23 participants at a time ranging between 10 and 30 d following their initial fingerprinting (e.g., Fig. 2A vs. Fig. 2C). We found that the average distance of a person from him/herself remained significantly lower than the average distance between different individuals [mean difference between an individual’s two fingerprints over time: r = 0.58 ± 0.15; mean difference between two different individuals’ fingerprints, r = 0.31 ± 0.076, paired t test, t(44) = 7.69, P < 10⁻⁸; Fig. 4C]. In other words, despite the passage of time, a person remained significantly more correlated with him/herself than with others.

Despite the above result, the slight reduction in self–self correlation over retests raises the concern that given additional retests, the self–self correlation advantage may disappear altogether. To address this concern, we refingerprinted an additional group of 18 subjects across five fingerprinting sessions that spanned 14–30 d (list of odorants and descriptors for experiment 1B in Tables S3 and S4). A repeated-measures ANOVA revealed that at each repetition (II, III, IV, and V) the average distance of a person from his/her first fingerprint remained unchanged [F(17, 3) = 2.24, P = 0.09, mean difference between an individual’s two fingerprints across retests r first–second = 0.58 ± 0.21, r first–third = 0.54 ± 0.18, r first–fourth = 0.54 ± 0.2, r first–fifth = 0.49 ± 0.19; Fig. 4D, yellow]. Moreover, the fingerprint stability in fact improved after the first retest [F(17, 3) = 6.08, P < 0.001] such that the second to third (r = 0.66 ± 0.19), third to fourth (r = 0.68 ± 0.20), and fourth to fifth (r = 0.69 ± 0.16) repetitions were all significantly better than the first to second [r = 0.58 ± 0.21, all t(17) > 2.67, all P < 0.02; Fig. 4D]. Taken together, we conclude that despite the passage of time and repeated testing, a person remained significantly more correlated with him/herself than with others. We recalculated the ability of the olfactory fingerprint to identify an individual beyond our sample, this time comparing the initial and the later (a few weeks later) fingerprints with all of the other subjects, and observed a decreased yet significant discriminability (z_1–2 = 2.67, P < 0.01, z_1–3 = 2.67, P < 0.01, z_1–4 = 2.67, P < 0.01, z_1–5 = 2.67, P < 0.01; Fig. 4D, black and red); this amounts to an ability to use the current olfactory fingerprint to identify 1 subject of ∼300 individuals. Moreover, given this variability over time, to effectively obtain long-lasting olfactory fingerprints for the entire world population we find by extrapolation that rather than 34 odors with 35 descriptors we would now need 160 odors with 35 descriptors. Note that this reduced discriminability is not only because of the extent of shift in fingerprint over time; self-correlation over time decreased from r = 0.75 to r = 0.58, which remains significantly higher than the correlation across individuals. However, because on average all subjects shifted in this way, the ability to identify one person out of a crowd is significantly reduced.

Similar Olfactory Fingerprints Imply High HLA Matching.

The hypothesis underlying our effort was that fingerprints would provide a unique perceptual counterpart of an individual’s unique olfactory receptor subtype genome. Potentially consistent with this notion, 28-odor-based fingerprints were special to the tune of 1 in 2 million. However, whereas olfactory receptor genomes are likely stable over 10–30 d (but see refs. 29⇓⇓–32), fingerprints were less so. Given this temporal fluctuation, we set out to test whether olfactory fingerprints can nevertheless remain informative of genetic traits linked to olfaction, in this case HLA; to test this, we studied an additional 130 subjects (65 women, mean age = 29.93 ± 8.44 y) who provided blood samples for HLA typing (Methods), and olfactory fingerprints using 11 odors (Table S5). Combinatorially, 130 subjects provide for 16,770 possible donor–recipient pairs, because HLA match is not symmetric, i.e., in a given pair, a subject can have a high HLA match as a donor but poor HLA match as a recipient (note that we use the terms “donor” and “recipient” to describe the directionality of HLA matching). Therefore, 130 subjects resulted in 16,770 possible pairs (130 × 129) and not in 8,385 (130 × 129/2). For each pair we calculated an olfactory fingerprint match using Euclidean distance (see SI Text for impact of alternative methods) and an HLA match along a 7-point scale (0–6, 0 = no match) previously described (16). Only 65 of 16,770 possible pairs of individuals had a high HLA match of 5 or 6 (Fig. 5A). We found that the olfactory fingerprint match of these individuals was significantly better than the olfactory fingerprint match for poorly HLA-matched individuals [HLA 5–6: mean olfactory fingerprint match in arbitrary units (AU) of Euclidean distance = 12.7 ± 4.1 AU, HLA 1–4: mean olfactory fingerprint match = 14.6 ± 5.3 AU, Wilcoxon rank-sum test: Z = 3.2, P < 0.0015]. In other words, the olfactory perceptual fingerprint similarity was significantly informative on HLA matching, implying that it captured meaningful genetic information.

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Fig. 5.

Similar olfactory fingerprints imply high HLA matching. (A) A total of 16,770 pairwise comparisons of olfactory fingerprint distance vs. HLA match. The dotted red line reflects the cutoff for saved tests. (B) ROC curves of HLA comparisons saved vs. HLA matches missed. The diagonal identity line reflects no gain or loss. ROCs: red, using all 11 odors; gray, 200 testing curves using 4 odorants; black and blue, median and mean of the 4 best odorants, respectively.

To further assess the strength of the link between olfactory fingerprint match and HLA match, we asked what would happen if one used olfactory fingerprints to screen for potentially high HLA matches in the population. We calculated the percentage of high HLA matches one would potentially miss (incurred cost) vs. the percentage of matches one could identify (gain), and present this using a receiver operating characteristic (ROC) curve (Fig. 5B, red line). We found that all points in the ROC curve fall above the identity line; hence, olfactory fingerprints can potentially identify pairs of individuals likely to have a high HLA match. Given the extended time needed to test 11 odorants as we did in data collection, we next asked if we could optimize this test. We halved the data into training (8,387 subject pairs) and testing sets (8,385 subject pairs), each maintaining the original fractions of each level of HLA match. In the training set, we calculated olfactory fingerprints using all possible combinations of 3–11 odorants, and selected the four best-performing odorants, which we then tested in the testing set. We repeated this 200 times (Fig. 5B, grey lines). Taking the median score (Fig. 5B, black line), we found that a selection of four odors (isoamyl acetate, isovaleric acid, 2-ethyl pyrazine, and 1-hexanol) decreased the average olfactory fingerprint distances of high-HLA matched individuals to 10.8 ± 3.7 AU compared with an olfactory fingerprint distance for poorly HLA matched individuals of 13.8 ± 5.8 AU (Z = 4.35, P < 0.000015). Finally, we calculated the actual savings implicated by this: the 65 high-HLA matches in our data comprised of 45 individuals (some individuals were matched with more than one). We iteratively selected one individual from these 45 as recipient, and randomly drew donors until we encountered a high HLA match. We repeated this 10,000 times. Consistent with the expectation from chance, we had to test an average of 65.35 ± 37.5 donors to identify a match. We then repeated these exact procedures again, but rather than randomly drawing donors, we drew them in rank order in accordance with their rapidly obtainable optimized olfactory fingerprint distance, starting with the closest. We found that the average number of individuals we had to test to identify a match was 44 ± 29, implying a 32% savings [t(64) = 5.5, P < 10⁻⁶]. In other words, using this brief perceptual test, one could rank order the population to save more than 30% of HLA tests.