Figure 1.
Evolution of metabolic fluxes and measures of optimality and predictability.
We consider three ways to analyze changes in metabolism that relate an ancestor (Anc, blue) to an evolved isolate (Ei, green) in regard to an FBA-predicted optimum (Opt, red). A) Evolution of metabolic fluxes can be evaluated from the perspective of changes in proximity to the theoretical maximum for a given optimality criterion (Δ% Optimality). B) A vector of flux ratios defines a position in multi-dimensional flux space. One can then consider the relative Euclidian distance of a given evolved population in this space from its optimum (DEO) compared to that of an ancestor from its optimum (DAO; plotted as log(DEO/DAO)). C) At the most detailed level, one can compare the FBA-predicted value for a given flux ratio versus that observed via 13C labeling.
Table 1.
Major approaches to test of FBA predictions depending upon whether there was known selection under experimental conditions and whether there was direct measurement of internal fluxes.
Figure 2.
Evolved changes in central carbon metabolism for the LTEE populations after 50,000 generations of adaptation on glucose.
A) The flux pathways measured for the LTEE lines are denoted with numbers and red arrows. The genes knocked out in the knockout data set and the entry point of lactate into the network are both indicated. B) A heat map of the difference between evolved and ancestral flux ratios from the LTEE populations. The right side indicates flux ratios predicted for the ancestral line according to each optimality criterion. The number of the flux ratio corresponds to the numbered pathways in A. Single asterisks denote significant changes as calculated by ANOVA, double asterisks are also significant by Tukey-HD.
Figure 3.
Measures of optimality and predictability after adaptation of LTEE populations to glucose for 50,000 generations.
A,D) The % optimality of the ancestor (black) and evolved isolates (grey, same order as Fig. 2); B,E) distance to optimal flux distribution (plotted as log(DEO/DAO)); and C, F) comparison of predicted to observed flux ratios for FBA-predictions based upon BM/S (A–C) or ATP/S (D–F). Error bars represent standard errors of three biological replicates.
Figure 4.
Measures of optimality and predictability after adaptation to lactate for ∼900 generations.
A,D) The % optimality of the ancestor (black) and evolved isolates (grey); B,E) distance to optimal flux distribution (plotted as log(DEO/DAO)); and C, F) comparison of predicted to observed flux ratios for FBA-predictions based upon BM/S (A–C) or ATP/S (D–F).
Figure 5.
Measures of optimality and predictability after adaptation of gene knockouts on glucose for ∼600–800 generations.
A,B) The % optimality of the ancestor (black) and evolved isolates (grey); C,D) distance to optimal flux distribution for FBA-predictions based upon BM/S (A,C) or ATP/S (B,D).
Figure 6.
Evolutionary change in % optimality versus initial % optimality of the ancestor across data sets for BM/S.
Error bars represent standard errors between evolved populations.