Metabolic graphs, LIFE method and the modeling of drug action on Mycobacterium tuberculosis

This paper serves as a framework for designing advanced models for drug action on metabolism. Drug treatment may affect metabolism by either enhancing or inhibiting metabolic reactions comprising a metabolic network. We introduce the concept of $\mathit{\text{metabolic}}\mathit{\text{graphs}}$, a generalization of hypergraphs having specialized features common to metabolic networks. Linear-in-flux-expression (briefly LIFE) is a methodology for analyzing metabolic networks and simulating virtual patients. We extend LIFE dynamics to be compatible with metabolic graphs, including the more complex interactions of enhancer and inhibitor molecules that affect biochemical reactions. We discuss results considering network structure required for existence and uniqueness of equilibria on metabolic graphs and show simulations of drug action on $\mathit{\text{Mycobacterium}}\mathit{\text{tuberculosis}}$ (briefly MTB)