Metabolic pathways are fundamental maps in biochemistry that detail how molecules are transformed through various reactions. Metabolomics refers to the large-scale study of small molecules. High-throughput, untargeted, mass spectrometry-based metabolomics experiments typically depend on libraries for structural annotation, which is necessary for pathway analysis. However, only a sma fraction of spectra can be matched to know structures in these libraries and only a portion of annotated metabolites can be associated with specific pathways, considering that numerous pathways are yet to be discovered. The complexity of metabolic pathways, where a single compound can play a part in multiple pathways, poses an additional challenge. This study introduces a different concept: mass spectra distribution, which is the empirical distribution of the intensity times their assocated m/z values. Analysis of solarization, COVID-19, and mouse brain datasets shows that by estimating the differences of the point estimations of these.distributions, it becomes possible.to.infer the metabolic directions and magnitutes without requiring knowledge of the exact chemical structures of these compounds and their related pathways. The overall.metabolic map, named as vectome, has the potential to bypass current bottleneck and provide fresh insights into metabolomics studies. This brief report thus provides a mathematical framing for a classic biology concept.

This manuscript was prepared two years ago, it was delayed since the author has been focusing on the estimations of moments (also attached with a response to comments). All these papets are currently under review in PNAS. For more.information, please visit https//github.com/tuobangli. If you are interested, feel free to contact tl@biomathematics.org, for more materials available by request. Please do not use it without the author's approval before publishing.