Additional ﬁle 1: Diﬀerent approaches to ﬂux coupling analysis and implementation details Laszlo David, Sayed-Amir Marashi, Abdelhalim Larhlimi, Bettina Mieth and Alexander Bockmayr In this study, we implemented the diﬀerent approaches to compare their time eﬃciency. MMB-FCA, EFP-FCA and FCF are the previous approaches which were (re-)implemented in this study. Additionally, our new method called FFCA, together with three improved versions of the FCF method, namely W-FCF (FCF without splitting reversible reactions), WR-FCF (FCF without splitting reversible reactions and with Reversibility-Type prunings) and WRP-FCF (FCF without splitting reversible reactions, with Reversibility-Type prunings and Prev/Frev-based improvement) were implemented in order to get a better picture about the eﬃciency of the diﬀerent approaches. Some deﬁnitions In this text we will use the following notation: • [k] is used as an abbreviation for the set {1,...,k}. • If S is an m × n matrix, A ⊆ [m] and B ⊆ [n], then S A,B is the submatrix of S formed by the rows in A and the columns in B. Implementation of MMB-FCA In this approach, a convex basis of the ﬂux cone is needed. We use the software cdd [1], a tool based on the double description method, to compute a minimum set of generating vectors. These correspond to the lineality space and the minimal proper faces (or minimal metabolic behaviors, MMBs) of the ﬂux cone (see [2] for more details). Next the reversibility type of the reactions is determined by computing the sets Blk, Irev, P rev, and Frev. The ﬂux coupling relations are then obtained as described in [3]. The following pseudo-code (Algorithm 1) summarizes the procedure. CouplingRelation is a matrix where the entry (i, j ), with i<j , describes the coupling relation between two unblocked reactions i and j . 1