Research ArticleNEUROSCIENCE

Hyperbolic geometry of the olfactory space

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Science Advances  29 Aug 2018:
Vol. 4, no. 8, eaaq1458
DOI: 10.1126/sciadv.aaq1458


In the natural environment, the sense of smell, or olfaction, serves to detect toxins and judge nutritional content by taking advantage of the associations between compounds as they are created in biochemical reactions. This suggests that the nervous system can classify odors based on statistics of their co-occurrence within natural mixtures rather than from the chemical structures of the ligands themselves. We show that this statistical perspective makes it possible to map odors to points in a hyperbolic space. Hyperbolic coordinates have a long but often underappreciated history of relevance to biology. For example, these coordinates approximate the distance between species computed along dendrograms and, more generally, between points within hierarchical tree–like networks. We find that both natural odors and human perceptual descriptions of smells can be described using a three-dimensional hyperbolic space. This match in geometries can avoid distortions that would otherwise arise when mapping odors to perception.

This is an open-access article distributed under the terms of the Creative Commons Attribution-NonCommercial license, which permits use, distribution, and reproduction in any medium, so long as the resultant use is not for commercial advantage and provided the original work is properly cited.

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