Interplay between Constraints, Objectives, and Optimality for Genome-Scale Stoichiometric Models
Fig 4
Reversible-reaction splitting guarantees finding all non-decomposable flux pathways in the optimum.
Metabolites (capital letters) are converted by irreversible reactions to achieve the conversion of X to Y (underlined metabolites are boundary species). Split reversible reactions are denoted as R3f and R3b. We maximized the flux through R18 with FBA, subject to the steady-state constraint and J1 ≤ 2. The optimal solution space is now characterized by seven rays (A) and twelve vertices which originate from three CoPE-FBA subnetworks (B). (A) the five split reversible reactions and {R2–R4} in forward and backward direction form together seven rays. (B) three subnetworks give rise to twelve vertices (2×2×3). The third subnetwork (red) now has a third alternative flux distribution {R12, R15} which was without reversible-reaction splitting a convex combination of the other two flux distributions, {R12, R13f, R14f} and {R15, R13b, R14b}.