Fig. 1. A comparison of flux balance analysis (FBA, top) and growth balance analysis (GBA, bottom) for a simple schematic model.
A nutrient G is taken up through a transporter t at rate vt and is then converted by an enzyme e with rate ve into a precursor for protein synthesis, AA. In FBA, AA is equated with the biomass, the production of which is maximized while enforcing the stationarity of internal concentrations (blue); this leads to a linear dependence of growth rate on uptake flux. In GBA, AA is converted further into total protein P by a ribosome R, where P represents the sum of the three proteins (t, e, R). GBA maximizes the balanced production of the cellular composition with growth (blue), offsetting the dilution of the cellular components (G, AA, P) with the growth rate μ indicated by the blue arrows. The reaction fluxes are constrained by non-linear reaction kinetics (red) and a limit on cellular density (dry mass per volume, gray); this leads to a non-linear dependence of growth rate on nutrient concentrations.