Fig 3. Impact of a heterogeneous ancestral population on the evolutionary outcome.

(A) Explanation of the RooM and RooM-het methods. The figure shows a hypothetical flux space where the fluxes through reaction i (J_i) and j (J_j) are shown. Different carbon source consumption and production rates impose different constraints that affect the allowable solution space of ancestor, producer and consumer strains differently. The allowable solution space corresponds to the space of flux distributions that fulfill a set of constraints, here shown as grey, blue and red areas for the ancestor, producer and consumer respectively. To perform RooM we first identified an ancestral flux distribution with pFBA (here represented as the grey circle labeled A_pFBA). We used this flux distribution as a reference to identify the producer (blue circle labeled P_ROOM) and consumer (red circle labeled C_ROOM) flux distributions that would require the minimal number of flux changes. In contrast, RooM-het requires no ancestral reference flux distribution. When using this method to identify a producer flux distribution, the method returns two flux distributions, one that satisfies all the constraints of being a producer, and another that satisfies all the constraints of being an ancestor. The same holds when predicting a consumer flux distribution. In the figure, the resulting producer and consumer flux distributions are shown as blue and red circles labeled P_ROOM−het and C_ROOM−het. The two distinct ancestral flux distributions that result when identifying the producer and consumer distribution are labeled A_ROOM−het. (B) Sum of the ancestor-producer and ancestor-consumer distances (vertical axis) as a function of the glucose consumed by the ancestral population (horizontal axis). Predictions for acetate and glycerol are shown in orange and green, respectively. Grey circles correspond to predictions for one of the twenty metabolites with a predicted likelihood of being subject to evolved cross-feeding greater than that observed for acetate when either RooM or RooM-het are performed at the minimal glucose consumption rate of 2.14 mmol gDW^-1 h^-1.