Rules, hypergraphs, and probabilities: The three-level analysis of chemical reaction systems and other stochastic stoichiometric population processes
Fig 10
Lattice diagrams for a sequence of complexes that carry one autocatalytic An backbone through the sequence of its conversions in one full turn of the CBB cycle.
To simplify the diagrams, the inputs are taken to be 3A3 + 2K3 (corresponding to 3 GAP + 2 DHAP). First panel, starting with A2, is f14 from Fig 8 of S1 File C 2. Second panel, starting with A3 is f13 from the left panel of Fig 3. Third panel, starting with A4 and representative of An for any n ≥ 4, is f194. The links in each path are to be read in the order that makes a closed cycle. The starting aldose is a 1-complex An, on the lower axis (black dot). Additions of DHAP are red up arrows, forming the 2-complex input to PHL ∘ AL edges (orange), producing 1-complexes (ketoses) on the vertical axis. Additions of GAP are black right arrows, forming the 2-complex inputs to TKL edges (green). Extractions of Ru5P are blue down arrows, converting 2-complexes back to single aldoses on the horizontal axis, from which new complexes are created by DHAP addition. The sub-flow Ru5P_out ∘ TKL ∘ GAP_in ∘ PHL ∘ AL ∘ DHAP_in, shown in the fourth panel, forms one turn of an “algorithmic” loop incrementing the value n for the starting aldose 1-complex An. AlKe conversions (cyan), followed by Ru5P_out ∘ TKL ∘ GAP_in in each of the first three panels, reset two iterations of this algorithmic loop to its starting complex. Also shown in the fourth panel is a 3-cycle of A3 → K3 which, added to the previous graphs, would permit a starting configuration of 5A3 + 0K3, at the cost of slightly greater complexity in plots.