Quantitative Relationship between Intracellular Metabolic Responses against Nutrient Conditions and Metabolic Inhibitions

Many previous studies have attempted to predict the metabolic states of cells assuming metabolic regulation is optimized through (sometimes artificial) evolution for some objective, e.g., growth rate or production of some metabolites. Conventional approaches, however, require identifying the microscopic details of individual metabolic reactions and the objective functions of cells, and their predictions sensitively depend on such details. In this study, we focus on the responses of metabolic systems to environmental perturbations, rather than their metabolic states themselves, and theoretically demonstrate a universal property of the responses independent of the systems details. With the help of a microeconomic theory, we show a simple relationship between intracellular metabolic responses against nutrient abundance and metabolic inhibition due to manipulation such as drug administration: these two experimentally measurable quantities show a proportional relationship with a negative coefficient. This quantitative relationship should hold in arbitrary metabolic systems as long as the law of mass conservation holds and cells are optimized for some objectives, but the true objective functions need not be known. Through numerical calculations using large-scale metabolic networks such as the E. coli core model, we confirmed that the relationship is valid from abstract to detailed models. Because the relationship provides quantitative predictions regarding metabolic responses without prior knowledge of systems, our findings have implications for experimental applications in microbiology, systems biology, metabolic engineering, and medicine, particularly for unexplored organisms or cells.