The number of active metabolic pathways is bounded by the number of cellular constraints at maximal metabolic rates
Fig 4
The cost vector formalism provides insight in how growth rate maximization leads to overflow metabolism.
a) A core model with two EFMs that individually lead to cell synthesis (orange: respiration and blue: acetate overflow). All considered reactions have an associated enzyme, whose activity depends on kinetic parameters and the metabolite concentrations. We varied growth rate by changing the external substrate concentration. Given this external condition, the growth rate was optimized under two enzymatic constraints (limited cytosolic enzyme Σ ei,cyto ≤ 1 and limited membrane area etransport ≤ 0.3). b) The predicted substrate uptake fluxes directed towards respiration and overflow are in qualitative agreement with the experimental data (shown before in Fig 2) of several microorganisms scaled with respect to the growth rate (μcrit) and uptake rate (qcrit) at the onset of overflow [4, 38, 39]. c) The cost vectors (solid arrows) of the two EFMs before (left) and after (right) the respirofermentative switch. The x-coordinate of the cost vectors denote the fraction of the cytosolic volume that is needed to produce one unit objective flux with the corresponding EFM. The y-coordinate shows the necessary fraction of the available mebrane area. The position of the cost vectors are shown for the optimized metabolite concentrations; the shaded regions show alternative positions of the cost vectors at different enzyme and metabolite concentrations. The dashed vectors show the usage of the EFMs in the optimal solution.