Figure 1.
Optimal (A) and non-optimal (B) reaction activity in the reconstructed metabolic network of E. coli in glucose minimal medium (Materials and Methods).
The pie charts show the fractions of active and inactive reactions in the metabolic subsystems defined in the iJR904 database [75]. The color code is as follows: active reactions (red), inactive reactions due to mass balance (black) and environmental constraints (blue), inactive reactions due to the irreversibility (green) and cascading (yellow) mechanisms, and conditionally inactive reactions (orange), which are inactive reactions that can be active for other growth-maximizing states under the same medium condition. The optimal state shown in panel A was obtained by flux balance analysis (FBA, see Materials and Methods). The network is constructed by drawing an arrow from one subsystem to another when there are at least 4 metabolites that can be produced by reactions in the first subsystem and consumed by reactions in the second. Larger pies represent subsystems with more reactions.
Table 1.
Reversibility of metabolic reactions in the reconstructed networks.
Figure 2.
Number of active and inactive reactions in the metabolic networks of H. pylori, S. aureus, E. coli, and S. cerevisiae.
For each organism, the bars correspond to a typical non-optimal state (top), a growth-maximizing state (middle), and a state with the minimum number of active reactions required for growth (bottom), which was estimated using the algorithm described in Materials and Methods. The error bar represents the upper and lower theoretical bounds, given by Eq. (3), on the number of active reactions in any growth-maximizing state. The breakdown of inactive reactions and their color coding are the same as in Figure 1. All results are obtained using glucose minimal media (Materials and Methods) and are further detailed in Tables 2 and 3.
Table 2.
Metabolic reactions in typical non-optimal states of the simulated metabolisms.
Figure 3.
Portions of E. coli metabolic network under maximum growth condition.
(A) P1, P2, and P3 are alternative pathways for glucose transport and utilization. The most efficient pathway, P1, is active under maximum growth in glucose minimal medium. P2 and P3 are inactive, but if P1 is knocked out, P2 becomes active, and if both P1 and P2 are knocked out, P3 becomes active. In both knockout scenarios, the growth is predicted to be suboptimal. (B) Isocitrate lyase reaction in the pathway bypassing the tricarboxylic acid (TCA) cycle is predicted to be inactive under maximum growth due to its irreversibility. If it were to operate in the opposite direction, it would serve as a transverse pathway which redirects metabolic flow to growth-limiting reactions, increasing the maximum biomass production rate slightly. In both panels, single and double arrows are used to indicate irreversible and reversible reactions, respectively, and colors indicate the behavior of the reactions under maximum growth: active (red), inactive due to the irreversibility (green), and inactive due to cascading (yellow).
Figure 4.
Probability distribution of the number of active reactions in nonzero-growth states that optimize typical objective functions.
The red solid lines indicate the corresponding number in the growth-maximizing state of Figure 2 (middle bar, red), and the red dashed lines indicate our estimates of the minimum number of reactions required for the organism to grow (Materials and Methods). [When the nonzero growth requirement is relaxed, a second sharp peak (not shown) arises, corresponding to a drop of ∼250 in the number of active reactions caused by the inactivation of the biomass reaction.]
Table 3.
Metabolic reactions in maximum growth states of the simulated metabolisms.a
Table 4.
Experimentally determined fluxes of intracellular reactions involved in the glycolysis, pentose phosphate pathway, TCA cycle, and amino acid biosynthesis of E. coli K12 MG1655 under aerobic and anaerobic conditions [50].
Table 5.
Experimentally determined fluxes of intracellular reactions involved in the glycolysis, metabolic steps around pyruvate, TCA cycle, glyoxylate cycle, gluconeogenesis, and pentose phosphate pathway of S. cerevisiae strain CEN.PK1137D grown under glucose, maltose, ethanol, and acetate limitation [51].
Table 6.
Fraction of inactive reactions in the simulated metabolism of E. coli and S. cerevisiae under maximum growth condition.a
Table 7.
Experimentally determined fluxes of reversible and irreversible reactions of wild-type E. coli JM101 versus its pyruvate kinase-deficient mutant PB25 [53].
Figure 5.
Distribution of the number of active reactions in the E. coli metabolic network after a single-reaction knockout.
(A) The initial response is predicted by the minimization of metabolic adjustment (MOMA) and the endpoint of adaptive evolution by the maximization of the growth rate (FBA), using the medium defined in Materials and Methods and a commercial optimization software package [79]. We consider all 77 nonlethal single-reaction knockouts that change the flux distribution. (B) Schematic illustration of the network reaction activity during the adaptive evolution after a small perturbation, indicating the temporary activation of many latent pathways.