Title: Infer metabolic directions and magnitudes from moment differences of mass-weighted intensity distributions

Abstract: 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 small fraction of spectra can be matched to known 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-weighted intensity distribution, which is the empirical distribution of the intensities times their associated m/z values. Analysis of 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 magnitudes without requiring knowledge of the exact chemical structures of these compounds and their related pathways. The overall metabolic momentum map, named as momentome, has the potential to bypass the current bottleneck and provide fresh insights into metabolomics studies. This brief report thus provides a mathematical framing for a classic biological concept.