Infer metabolic velocities from moment differences of molecular weight distributions

Metabolic pathways are fundamental maps in biochemistry that detail how molecules are transformed through various reactions. The complexity of metabolic network, where a single compound can play a part in multiple pathways, poses a challenge in inferring metabolic balance changes over time or after different treatments. Isotopic labeling experiment is the standard method to infer metabolic flux, which is currently defined as the flow of a single metabolite through a given pathway over time. However, there is still no way to accurately infer the metabolic balance changes after different treatments in an experiment. This study introduces a different concept: molecular weight distribution, which is the empirical distribution of the molecular weights of all metabolites of interest. By estimating the differences of the location and scale estimates of these distributions, it becomes possible to quantitatively infer the metabolic balance changes even without requiring knowledge of the exact chemical structures of these compounds and their related pathways. This research article provides a mathematical framing for a classic biological concept.