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.
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