FIGURE 3.

Mathematical formulations for metabolic modeling of the gut microbiota. The formulations of the α- and β-problem have been defined. In the α-problem the abundance of each individual species in the community is well-defined and through minimization for substrate/diet, the profile of SCFAs is estimated. In the β-problem the abundances of individuals can be predicted through maximization of the community biomass and by using a well-defined substrate/diet composition. (D: dilution rate, $\frac{\mathrm{K}}{\mathrm{D}}$: ratio of SCFAs absorption, Prod: butyrate, propionate, and acetate).