Speeding Up the Structural Analysis of Metabolic Network Models Using the Fredman-Khachiyan Algorithm B.

The problem of computing the Elementary Flux Modes (EFMs) and Minimal Cut Sets (MCSs) of metabolic network is a fundamental one in metabolic networks. A key insight is that they can be understood as a dual pair of monotone Boolean functions (MBFs). Using this insight, this computation reduces to the question of generating from an oracle a dual pair of MBFs. If one of the two sets (functions) is known, then the other can be computed through a process known as dualization. Fredman and Khachiyan provided two algorithms, which they called simply A and B that can serve as an engine for oracle-based generation or dualization of MBFs. We look at efficiencies available in implementing their algorithm B, which we will refer to as FK-B. Like their algorithm A, FK-B certifies whether two given MBFs in the form of Conjunctive Normal Form and Disjunctive Normal Form are dual or not, and in case of not being dual it returns a conflicting assignment (CA), that is, an assignment that makes one of the given Boolean functions True and the other one False. The FK-B algorithm is a recursive algorithm that searches through the tree of assignments to find a CA. If it does not find any CA, it means that the given Boolean functions are dual. In this article, we propose six techniques applicable to the FK-B and hence to the dualization process. Although these techniques do not reduce the time complexity, they considerably reduce the running time in practice. We evaluate the proposed improvements by applying them to compute the MCSs from the EFMs in the 19 small- and medium-sized models from the BioModels database along with 4 models of biomass synthesis in Escherichia coli that were used in an earlier computational survey Haus et al. (2008).

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

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. 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, minimal coordinated support (MCS2), and describe how it can be modified to compute the few smallest MCSs for a given target reaction. RESULTS: We compare MCS2 to the method of Ballerstein et al. and two other existing methods. We show that MCS2 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 AND IMPLEMENTATION: MCS2 is freely available at https://github.com/RezaMash/MCS under the GNU 3.0 license. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Minimal conflicting sets for the consecutive ones property in ancestral genome reconstruction.

A binary matrix has the Consecutive Ones Property (C1P) if its columns can be ordered in such a way that all 1's on each row are consecutive. A Minimal Conflicting Set is a set of rows that does not have the C1P, but every proper subset has the C1P. Such submatrices have been considered in comparative genomics applications, but very little is known about their combinatorial structure and efficient algorithms to compute them. We first describe an algorithm that detects rows that belong to Minimal Conflicting Sets. This algorithm has a polynomial time complexity when the number of 1s in each row of the considered matrix is bounded by a constant. Next, we show that the problem of computing all Minimal Conflicting Sets can be reduced to the joint generation of all minimal true clauses and maximal false clauses for some monotone boolean function. We use these methods on simulated data related to ancestral genome reconstruction to show that computing Minimal Conflicting Set is useful in discriminating between true positive and false positive ancestral syntenies. We also study a dataset of yeast genomes and address the reliability of an ancestral genome proposal of the Saccharomycetaceae yeasts.

Computing knock-out strategies in metabolic networks.

Given a metabolic network in terms of its metabolites and reactions, our goal is to efficiently compute the minimal knock-out sets of reactions required to block a given behavior. We describe an algorithm that improves the computation of these knock-out sets when the elementary modes (minimal functional subsystems) of the network are given. We also describe an algorithm that computes both the knock-out sets and the elementary modes containing the blocked reactions directly from the description of the network and whose worst-case computational complexity is better than the algorithms currently in use for these problems. Computational results are included.