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

2020 ◽  
Vol 21 (1) ◽  
Author(s):  
Steffen Klamt ◽  
Radhakrishnan Mahadevan ◽  
Axel von Kamp
Keyword(s):  
Metabolic Networks ◽  
Dual System ◽  
Mixed Integer ◽  
Mathematical Framework ◽  
Stoichiometric Matrix ◽  
Farkas Lemma ◽  
Minimal Cut Sets ◽  
Minimal Cut ◽  
General Importance ◽  
Genome Scale

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.

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

2018 ◽  
Vol 35 (15) ◽  
pp. 2618-2625 ◽  
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.

scholarly journals Genome-scale strain designs based on regulatory minimal cut sets

2015 ◽  
Vol 31 (17) ◽  
pp. 2844-2851 ◽  
Author(s):  
Radhakrishnan Mahadevan ◽  
Axel von Kamp ◽  
Steffen Klamt
Keyword(s):  
Minimal Cut Sets ◽  
Minimal Cut ◽  
Genome Scale

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

Metabolites ◽  
2012 ◽  
Vol 2 (3) ◽  
pp. 567-595 ◽  
Author(s):  
Sangaalofa T. Clark ◽  
Wynand S. Verwoerd
Keyword(s):  
Metabolic Networks ◽  
Failure Modes ◽  
Minimal Cut Sets ◽  
Minimal Cut

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

2019 ◽  
Vol 35 (14) ◽  
pp. i615-i623 ◽  
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.

CoBAMP: a Python framework for metabolic pathway analysis in constraint-based models

2019 ◽  
Vol 35 (24) ◽  
pp. 5361-5362 ◽  
Author(s):  
Vítor Vieira ◽  
Miguel Rocha
Keyword(s):  
Operating Systems ◽  
Pathway Analysis ◽  
Mixed Integer Linear Programming ◽  
Source Code ◽  
Mixed Integer ◽  
Metabolic Pathway Analysis ◽  
Minimal Cut Sets ◽  
Genome Scale ◽  
Modular Framework ◽  
Constraint Based Models

Abstract Summary CoBAMP is a modular framework for the enumeration of pathway analysis concepts, such as elementary flux modes (EFM) and minimal cut sets in genome-scale constraint-based models (CBMs) of metabolism. It currently includes the K-shortest EFM algorithm and facilitates integration with other frameworks involving reading, manipulation and analysis of CBMs. Availability and implementation The software is implemented in Python 3, supported on most operating systems and requires a mixed-integer linear programming optimizer supported by the optlang framework. Source-code is available at https://github.com/BioSystemsUM/cobamp.

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

2018 ◽  
Author(s):  
Reza Miraskarshahi ◽  
Hooman Zabeti ◽  
Tamon Stephen ◽  
Leonid Chindelevitch
Keyword(s):  
Metabolic Network ◽  
Metabolic Networks ◽  
Intermediate Step ◽  
Original Network ◽  
Practical Advantage ◽  
Minimal Cut Sets ◽  
Minimal Cut ◽  
Constraint Based Modeling ◽  
Target Reaction ◽  
Insight Into

AbstractMotivationConstraint-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, MCS2, and describe how it can be modified to compute the few smallest MCSs for a given target reaction.ResultsWe 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.AvailabilityMCS2 is freely available at https://github.com/RezaMash/MCS under the GNU 3.0 license.

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