  While visual and auditory information conveyed by wavelength of light and
frequency of sound have been decoded, predicting olfactory information encoded
by the combination of odorants remains challenging due to the unknown and
potentially discontinuous perceptual space of smells and odorants. Herein, we
develop a deep learning model called Mol-PECO (Molecular Representation by
Positional Encoding of Coulomb Matrix) to predict olfactory perception from
molecular structures. Mol-PECO updates the learned atom embedding by
directional graph convolutional networks (GCN), which model the Laplacian
eigenfunctions as positional encoding, and Coulomb matrix, which encodes atomic
coordinates and charges. With a comprehensive dataset of 8,503 molecules,
Mol-PECO directly achieves an area-under-the-receiver-operating-characteristic
(AUROC) of 0.813 in 118 odor descriptors, superior to the machine learning of
molecular fingerprints (AUROC of 0.761) and GCN of adjacency matrix (AUROC of
0.678). The learned embeddings by Mol-PECO also capture a meaningful odor space
with global clustering of descriptors and local retrieval of similar odorants.
Our work may promote the understanding and decoding of the olfactory sense and
mechanisms.
