Sequential computation of elementary modes and minimal cut sets in genome-scale metabolic networks using alternate integer linear programming

Abstract Background The concept of minimal cut sets (MCS) has become an important mathematical framework for analyzing and (re)designing metabolic networks. However, the calculation of MCS in genome-scale metabolic models is a complex computational problem. The development of duality-based algorithms in the last years allowed the enumeration of thousands of MCS in genome-scale networks by solving mixed-integer linear problems (MILP). A recent advancement in this field was the introduction of the MCS2 approach. In contrast to the Farkas-lemma-based dual system used in earlier studies, the MCS2 approach employs a more condensed representation of the dual system based on the nullspace of the stoichiometric matrix, which, due to its reduced dimension, holds promise to further enhance MCS computations. Results In this work, we introduce several new variants and modifications of duality-based MCS algorithms and benchmark their effects on the overall performance. As one major result, we generalize the original MCS2 approach (which was limited to blocking the operation of certain target reactions) to the most general case of MCS computations with arbitrary target and desired regions. Building upon these developments, we introduce a new MILP variant which allows maximal flexibility in the formulation of MCS problems and fully leverages the reduced size of the nullspace-based dual system. With a comprehensive set of benchmarks, we show that the MILP with the nullspace-based dual system outperforms the MILP with the Farkas-lemma-based dual system speeding up MCS computation with an averaged factor of approximately 2.5. We furthermore present several simplifications in the formulation of constraints, mainly related to binary variables, which further enhance the performance of MCS-related MILP. However, the benchmarks also reveal that some highly condensed formulations of constraints, especially on reversible reactions, may lead to worse behavior when compared to variants with a larger number of (more explicit) constraints and involved variables. Conclusions Our results further enhance the algorithmic toolbox for MCS calculations and are of general importance for theoretical developments as well as for practical applications of the MCS framework.

Download Full-text

On the Computation of Minimal Cut Sets in Genome Scale Metabolic Networks

2007 American Control Conference ◽

10.1109/acc.2007.4282821 ◽

2007 ◽

Cited By ~ 1

Author(s):

Marcin Imielinski ◽

Calin Belta

Keyword(s):

Metabolic Networks ◽

Minimal Cut Sets ◽

Minimal Cut ◽

Genome Scale

Download Full-text

Computing irreversible minimal cut sets in genome-scale metabolic networks via flux cone projection

Bioinformatics ◽

10.1093/bioinformatics/bty1027 ◽

2018 ◽

Vol 35 (15) ◽

pp. 2618-2625 ◽

Cited By ~ 5

Author(s):

Annika Röhl ◽

Tanguy Riou ◽

Alexander Bockmayr

Keyword(s):

Metabolic Networks ◽

Supplementary Information ◽

Oriented Matroid ◽

Matroid Theory ◽

Supplementary Data ◽

Large Genome ◽

Minimal Cut Sets ◽

Minimal Cut ◽

Genome Scale ◽

Target Reaction

Abstract Motivation Minimal cut sets (MCSs) for metabolic networks are sets of reactions which, if they are removed from the network, prevent a target reaction from carrying flux. To compute MCSs different methods exist, which may fail to find sufficiently many MCSs for larger genome-scale networks. Results Here we introduce irreversible minimal cut sets (iMCSs). These are MCSs that consist of irreversible reactions only. The advantage of iMCSs is that they can be computed by projecting the flux cone of the metabolic network on the set of irreversible reactions, which usually leads to a smaller cone. Using oriented matroid theory, we show how the projected cone can be computed efficiently and how this can be applied to find iMCSs even in large genome-scale networks. Availability and implementation Software is freely available at https://sourceforge.net/projects/irreversibleminimalcutsets/. Supplementary information Supplementary data are available at Bioinformatics online.

Download Full-text

Genome-scale strain designs based on regulatory minimal cut sets

Bioinformatics ◽

10.1093/bioinformatics/btv217 ◽

2015 ◽

Vol 31 (17) ◽

pp. 2844-2851 ◽

Cited By ~ 21

Author(s):

Radhakrishnan Mahadevan ◽

Axel von Kamp ◽

Steffen Klamt

Keyword(s):

Minimal Cut Sets ◽

Minimal Cut ◽

Genome Scale

Download Full-text

Minimal Cut Sets and the Use of Failure Modes in Metabolic Networks

Metabolites ◽

10.3390/metabo2030567 ◽

2012 ◽

Vol 2 (3) ◽

pp. 567-595 ◽

Cited By ~ 3

Author(s):

Sangaalofa T. Clark ◽

Wynand S. Verwoerd

Keyword(s):

Metabolic Networks ◽

Failure Modes ◽

Minimal Cut Sets ◽

Minimal Cut

Download Full-text

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

Bioinformatics ◽

10.1093/bioinformatics/btz393 ◽

2019 ◽

Vol 35 (14) ◽

pp. i615-i623 ◽

Cited By ~ 2

Author(s):

Reza Miraskarshahi ◽

Hooman Zabeti ◽

Tamon Stephen ◽

Leonid Chindelevitch

Keyword(s):

Metabolic Networks ◽

Supplementary Information ◽

Intermediate Step ◽

Original Network ◽

Practical Advantage ◽

Minimal Cut Sets ◽

Minimal Cut ◽

Constraint Based Modeling ◽

Target Reaction ◽

Insight Into

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. 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.

Download Full-text

Boosting the extraction of elementary flux modes in genome-scale metabolic networks using the linear programming approach

Bioinformatics ◽

10.1093/bioinformatics/btaa280 ◽

2020 ◽

Vol 36 (14) ◽

pp. 4163-4170

Author(s):

Francisco Guil ◽

José F Hidalgo ◽

José M García

Keyword(s):

Linear Programming ◽

Metabolic Networks ◽

Supplementary Information ◽

Programming Approach ◽

Supplementary Data ◽

Main Interest ◽

Elementary Flux Modes ◽

Order Of Magnitude ◽

Genome Scale ◽

Efficiency Rate

Abstract Motivation Elementary flux modes (EFMs) are a key tool for analyzing genome-scale metabolic networks, and several methods have been proposed to compute them. Among them, those based on solving linear programming (LP) problems are known to be very efficient if the main interest lies in computing large enough sets of EFMs. Results Here, we propose a new method called EFM-Ta that boosts the efficiency rate by analyzing the information provided by the LP solver. We base our method on a further study of the final tableau of the simplex method. By performing additional elementary steps and avoiding trivial solutions consisting of two cycles, we obtain many more EFMs for each LP problem posed, improving the efficiency rate of previously proposed methods by more than one order of magnitude. Availability and implementation Software is freely available at https://github.com/biogacop/Boost_LP_EFM. Contact [email protected] Supplementary information Supplementary data are available at Bioinformatics online.

Download Full-text

Predicting novel pathways in genome-scale metabolic networks

Biochemical Society Transactions ◽

10.1042/bst0381202 ◽

2010 ◽

Vol 38 (5) ◽

pp. 1202-1205 ◽

Cited By ~ 3

Author(s):

Stefan Schuster ◽

Luís F. de Figueiredo ◽

Christoph Kaleta

Keyword(s):

Metabolic Networks ◽

Glyoxylate Cycle ◽

System Size ◽

Medium Size ◽

Metabolic Pathway Analysis ◽

Combinatorial Explosion ◽

Novel Approach ◽

Genome Wide ◽

Elementary Modes ◽

Genome Scale

Elementary-modes analysis has become a well-established theoretical tool in metabolic pathway analysis. It allows one to decompose complex metabolic networks into the smallest functional entities, which can be interpreted as biochemical pathways. This analysis has, in medium-size metabolic networks, led to the successful theoretical prediction of hitherto unknown pathways. For illustration, we discuss the example of the phosphoenolpyruvate-glyoxylate cycle in Escherichia coli. Elementary-modes analysis meets with the problem of combinatorial explosion in the number of pathways with increasing system size, which has hampered scaling it up to genome-wide models. We present a novel approach to overcoming this obstacle. That approach is based on elementary flux patterns, which are defined as sets of reactions representing the basic routes through a particular subsystem that are compatible with admissible fluxes in a (possibly) much larger metabolic network. The subsystem can be made up by reactions in which we are interested in, for example, reactions producing a certain metabolite. This allows one to predict novel metabolic pathways in genome-scale networks.

Download Full-text

SAFEPPP: a Simple And Fast method to Find and analyze Extreme Points of a metabolic Phenotypic Phase Plane

10.1101/642363 ◽

2019 ◽

Author(s):

Mohammad Hossein Moteallehi-Ardakani ◽

Sayed-Amir Marashi

Keyword(s):

Linear Programming ◽

Metabolic Networks ◽

Phase Plane ◽

Extreme Points ◽

Solution Space ◽

Fast Method ◽

Optimal Solutions ◽

Long Run ◽

Constraint Based Modeling ◽

Genome Scale

AbstractThere are many algorithms that help us understand how genome-scale metabolic networks work and what are their capabilities. But unfortunately, the majority of these methods are based on integer linear programming suffer from long run times and high instrumental demand. Optimal solutions in any constraint-based modeling as genome-scale metabolic networks models are on the extreme points of the solution space. We introduce a fast and simple toolbox that reveals extreme characters of metabolic networks in desired situations which can unmask the hidden potentials of metabolic networks. Determining the possibility of coupling between two desired reaction and the capability of synergic substrate consuming are examples of the applications of this method. Fast enumeration of elementary flux modes that exist in extreme points of phase plane of any two reactions is another achievement of this study.

Download Full-text