Minimal cut sets (MCSs) have been introduced to define perturbations in a metabolic network needed to repress the activity of a given target reaction. While this approach gives interesting insight into the structure of metabolic networks, it suffers from two major drawbacks that are limiting in practice. First, using MCSs becomes inadequate when we are interested in inhibiting only one direction of a reversible target reaction. Second, and more importantly, the computation of MCSs by currently available methods is limited by the combinatorial explosion of the number of elementary modes and hence is not practical for genomescale networks. To overcome these problems, we introduce the concept of minimal direction cuts. A minimal forward (resp. backward) direction cut (MFC) (resp. MBC) is a minimal set of reactions whose removal prevents the target reaction from carrying a flux in the forward (resp. backward) direction. Computing MFCs and MBCs does not require to determine beforehand the elementary modes of the network. Instead it can be based on the Farkas lemma for equality and inequality constraints. This leads to a new algorithm to identify minimal direction cuts, which can also be used for a direct computation of MCSs.
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