Fig. 1: Constraint-based metabolic model.
From: Metabolic coordination and phase transitions in spatially distributed multi-cellular systems
a Sketch of the single-cell metabolic network representing the central carbon pathways (uG glucose uptake, uL lactate flux, uO oxygen uptake). b Feasible single-cell flux space (\({{{\mathcal{F}}}}_{1}\)) in the (uO, uG) plane, bounded by Eqs (3) (glucose intake), (4) (oxygen intake), and (5) (ATP maintenance). For a single cell (as well as for the average bulk behavior) the purple region (uL > 0 or lactate import) is unfeasible unless lactate is exogenously provided. Points A-G are those where the cell would maximize rate of ATP production (A), maximize rate of ATP production with zero net lactate exchange (B), maximize rate of ATP production while using lactate as the only carbon source (C), minimize rate of ATP production while using lactate as the only carbon source (D), minimize rate of ATP production with zero net lactate exchange (E), minimize rate of ATP production anaerobically (F), or maximize rate of lactate excretion (G). c The possibility for cells to exchange lactate defines an extended metabolic flux space for a system of N cells (\({{{\mathcal{F}}}}_{N}\)) whose configurations can be projected into single-cell flux space. In turn, the corresponding lactate fluxes define a spatial concentration gradient in the medium via (8). d Case N = 2, feasible space in the plane \(({u}_{{{\rm{L}}}}^{(1)},{u}_{{{\rm{L}}}}^{(2)})\). In cases A and E cells are coupled via lactate exchange, one cell acting as a donor (red) for the other (blue). This makes the uL > 0 (purple) region of panel (b) viable for the acceptor cell even in absence of an external lactate source.
