ZODIAC: database-independent molecular formula annotation using Gibbs sampling reveals unknown small molecules

Marcus Ludwig; Louis-Félix Nothias; Kai Dührkop; Irina Koester; Markus Fleischauer; Martin A. Hoffmann; Daniel Petras; Fernando Vargas; Mustafa Morsy; Lihini Aluwihare; Pieter C. Dorrestein; Sebastian Böcker

For each pair of compounds, we have to compare up to 50 times 50 fragmentation trees: For swift computations, we refrain from using fragmentation tree alignments 56 but instead, simply count the number of common fragments and precursor (root) losses in the two trees 56 . Evaluations indicate that this method, while performing worse than fragmentation tree alignments, is still able to detect structural similarity between compounds 56 . When counting common root losses, the empty root . CC-BY-NC-ND 4.0 International license author/funder. It is made available under a The copyright holder for this preprint (which was not peer-reviewed) is the . https://doi.org/10.1101/842740 doi: bioRxiv preprint loss is ignored. We introduce two modications to the score from 56 : Let n 1 , n 2 be size of the two fragmentation trees, dened by the number of fragments and root losses. Instead of normalizing the number of common fragments plus root losses s by the size of the smaller tree min{n 1 , n 2 }, we use s/n 1 + s/n 2 (6) as the normalized score; by this, we slightly penalize large trees, as having common fragments or root losses is more likely against a large than a small tree. But this score favors small trees and, hence, inferior molecular formula candidates. To this end, we use the size of the largest fragmentation tree, among all candidate molecular formulas, for the normalization of each compound; this is the maximum number of explainable peaks in the tandem MS data of the compound. Fragments and root losses can be weighted by importance ι. The weight of two common fragments or root losses m 1 and m 2 is ι(m 1 )ι(m 2 ). The weighted size of a tree is