A Discrete Mathematical Model Applied to Genetic Regulation and Metabolic Networks

This paper describes the use of a discrete mathematical model to represent the basic mechanisms of regulation of the bacteria E. coli in batch fermentation. The specific phenomena studied were the changes in metabolism and genetic regulation when the bacteria use three different carbon substrates (glucose, glycerol, and acetate). The model correctly predicts the behavior of E. coli vis-a-vis substrate mixtures. In a mixture of glucose, glycerol, and acetate, it prefers glucose, then glycerol, and finally acetate. The model included 67 nodes; 28 were genes, 20 enzymes, and 19 regulators/biochemical compounds. The model represents both the genetic regulation and metabolic networks in an integrated form, which is how they function biologically. This is one of the first attempts to include both of these networks in one model. Previously, discrete mathematical models were used only to describe genetic regulation networks. The study of the network dynamics generated 8 $(2^3)$ fixed points, one for each nutrient configuration (substrate mixture) in the medium. The fixed points of the discrete model reflect the phenotypes described. Gene expression and the patterns of the metabolic fluxes generated are described accurately. The activation of the gene regulation network depends basically on the presence of glucose and glycerol. The model predicts the behavior when mixed carbon sources are utilized as well as when there is no carbon source present. Fictitious jokers (Joker1, Joker2, and Repressor SdhC) had to be created to control 12 genes whose regulation mechanism is unknown, since glycerol and glucose do not act directly on the genes. The approach presented in this paper is particularly useful to investigate potential unknown gene regulation mechanisms; such a novel approach can also be used to describe other gene regulation situations such as the comparison between non-recombinant and recombinant yeast strain, producing recombinant proteins, presently under investigation in our group.