Fig. 2

A PD microbial consortium [17]. The network is shown as a bipartite graph with metabolites (rectangles; red means extracellular) and reactions (diamonds). For turnover of a reaction, all its adjacent metabolites (indicated by edges) are used / produced jointly. Numbers next to edges are stoichiometric coefficients. The directionality of a reaction is determined by the arrows on the edges: arrows indicate products, and consequently arrows on both sides of a reaction denote bidirectionality. For example, \(t_{A,1}\), the transport reaction of A in organism 1, is bidirectional. Likewise, the representation of \(\mu _1\), the growth reaction of organism 1, specifies that the reaction is uni-directional and uses one unit of \(A_{c,1}\) and one unit of \(B_{c,1}\) to produce biomass. The subscripts c and e denote intra- and extracellular compounds, respectively. Species 1 and 2 (blue and brown symbols) can choose to crossfeed the compounds A and B to increase their yields by activating the reactions with the red dashed lines