Generation of ranked list of metabolic pathways based on their representation in the active, variable and inactive non-core

We computed a score, ranging between 0 and 1, to quantify the ambiguity found in individual metabolic pathways (subsystems in the GEM) across the space of alternative optimal networks. Concretely, the score of a pathway, M, represents the fraction of the reactions in the (total) non-core set, P, belonging to the pathway that are assigned to the active, variable or inactive non-core (thus producing a score value for each case). That is, in general,

where X_M ∈ {A_M, V_M, I_M} represents the number of reactions assigned to M that are included in the active, variable or inactive non-core, respectively.