MCS²: Minimal coordinated supports for fast enumeration of minimal cut sets in metabolic networks

Abstract

Motivation: Constraint-based modeling of metabolic networks helps researchers gain insight into the metabolic processes of many organisms, both prokaryotic and eukaryotic. Minimal Cut Sets (MCSs) are minimal sets of reactions whose inhibition blocks a target reaction in a metabolic network. Most approaches for finding the MCSs in constrained-based models require, either as an intermediate step or as a byproduct of the calculation, the computation of the set of elementary flux modes (EFMs), a convex basis for the valid flux vectors in the network. Recently, Ballerstein et al.[BvKKH11] proposed a method for computing the MCSs of a network without first computing its EFMs, by creating a dual network whose EFMs are a superset of the MCSs of the original network. However, their dual network is always larger than the original network and depends on the target reaction. Here we propose the construction of a different dual network, which is typically smaller than the original network and is independent of the target reaction, for the same purpose. We prove the correctness of our approach, MCS 2 , and describe how it can be modified to compute the few smallest MCSs for a given target reaction. Results: We compare MCS 2 to the method of Ballerstein et al. and two other existing methods. We show that MCS 2 succeeds in calculating the full set of MCSs in many models where other approaches cannot finish within a reasonable amount of time. Thus, in addition to its theoretical novelty, our approach provides a practical advantage over existing methods. Availability: MCS 2 is freely available at https://github.com/RezaMash/MCS under the GNU 3.0 license.

Speeding up the core algorithm for the dual calculation of minimal cut sets in large metabolic networks

“…In this study we present new theoretical and algorithmic developments that, on the one hand, extend and generalize the results of Miraskarshahi et al [ 21 ], and, on the other hand, may further speed up duality-based MCS algorithms in general. First of all, we noticed that the mentioned new duality approach in [ 21 ] may only handle single or multiple target reactions but not the more general approach of phenotypes specified by target region(s). Likewise, desired phenotypes cannot be protected which is crucial for applications in metabolic engineering.…”

“…The fact that the MILP-based algorithm delivers in genome-scale networks only a subset of the MCS with smallest (increasing) cardinality was not limiting since in most applications (especially for strain design) the MCS with the fewest interventions are typically most relevant. Several subsequent studies presented variants and extensions of the duality-based MILP approach [ 18 – 21 ].…”

“…A major modification for the duality-based MCS computation was recently proposed by Miraskarshahi et al [ 21 ]. They suggested the use of a more compact dual network based on the nullspace of the stoichiometric matrix reducing the dimension of the problem compared to the Farkas-lemma based dual network derived by Ballerstein et al [ 15 ].…”

“…The authors proved the correctness of their dual network approach for MCS calculation (which they named minimal coordinated support MCS = MCS 2 ), presented several useful properties of this method and showed that it may speed up the full enumeration of MCS in (smaller) networks whenever this enumeration is feasible. Moreover, motivated by their findings, they also proposed another variant of a duality-based MILP algorithm for the computation of shortest MCS in large networks [ 21 ].…”

“…We therefore generalize the MCS 2 approach to allow integration of those specifications. Second, we found that the duality-based MILP algorithm presented by Miraskarshahi et al [ 21 ] did not fully leverage the smaller dual network introduced by the authors and mainly represented a small modification of the traditional MILP formulation [ 7 ], which is based on the duality approach of Ballerstein et al [ 15 ]. We therefore develop a new MILP formulation that fully exploits the dimension reduction implied by the nullspace-based dual network representation.…”