Fig 1. Illustration of the issue of spurious cycles of reversible reactions from the H set appearing in our linear programming formulation.

A) Example reference metabolic network with a 3-level classification of reactions. It involves ten reactions plus the biomass reaction. Reversible fluxes are split into two non-negative steps. Backward reactions are shown in dashed line. Reactions 3, 4, 5, 7 and 9 are classified as H; reactions 2, 8 and 10 as M; and reactions 1 and 6 as L. B) Solution obtained when solving the linear program defined by Eq 6 subject to Eqs 1–5. Thicker arcs represent active reactions, cycles involving the forward and backward steps of a reversible reaction in H are represented with thinner lines and inactive reactions are colored in light grey.