Enzyme fluctuations data improve inference of metabolic interaction networks with an inverse differential Jacobian approach

The development of next-generation sequencing and single-cell technology has generated vast genome-scale multi-omics datasets. Dedicated mathematical algorithms are required to dissect intricate molecular causality within metabolic networks using these datasets. Based on the network analysis, recent research has introduced the inverse differential Jacobian algorithm, which combines metabolic interaction network construction and covariance matrix analysis of genome-scale metabolomics data to elucidate system regulatory factors near steady-state dynamics. Traditionally, these studies assumed metabolomics variations solely resulted from metabolic system fluctuations, acting independently on each metabolite. However, emerging evidence highlights the role of internal network fluctuations, particularly from the gene expression fluctuations, leading to correlated perturbations on metabolites. In this article, we propose a novel approach that exploits these correlations to reconstruct relevant metabolic interactions. Thereby, enzymes exhibiting significant variances in activity values serve as indicators of large fluctuations in their catalyzed reactions. By integrating this information in an inverse Jacobian algorithm, we are able to exploit the underlying reaction network structure to improve the construction of the fluctuation matrix required in the inverse Jacobian algorithm. After a comprehensive assessment of three critical factors affecting the algorithm accuracy, we conclude that using the enzyme fluctuation data significantly enhances the inverse Jacobian algorithm performance. We applied this approach to a breast cancer dataset with two different cell lines, which highlighted metabolic interactions where fluctuations in enzyme gene expression yield a relevant difference between the cell lines. ### Competing Interest Statement The authors have declared no competing interest.