Mixed-Integer Optimization for Loopless Flux Distributions in Metabolic Networks
Abstract
Constraint-based metabolic models can be used to investigate the intracellular physiology of microorganisms. These models couple genes to reactions, and typically seek to predict metabolite fluxes that optimize some biologically important metric. Classical techniques, like Flux Balance Analysis (FBA), formulate the metabolism of a microbe as an optimization problem where growth rate is maximized. While FBA has found widespread use, it often leads to thermodynamically infeasible solutions that contain internal cycles (loops). To address this shortcoming, Loopless-Flux Balance Analysis (ll-FBA) seeks to predict flux distributions that do not contain these loops. ll-FBA is a disjunctive program, usually reformulated as a mixed-integer program, and is challenging to solve for biological models that often contain thousands of reactions and metabolites. In this paper, we compare various reformulations of ll-FBA and different solution approaches. Overall, the combinatorial Benders' decomposition is the most promising of the tested approaches with which we could solve most instances. However, the model size and numerical instability pose a challenge to the combinatorial Benders' method.
Authors 15
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Affiliation as printed
ZIB - Zuse Institute Berlin (Konrad-Zuse-Zentrum für Informationstechnik Berlin (ZIB Takustraße 7 D-14195 Berlin-Dahlem - Germany)
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Universidade do Porto · RWTH Aachen University
Affiliation as printed
RWTH Aachen University , Lehrstuhl für Operations Research , Kackertstr. 7 , 52072 Aachen , Germany
Universidade do Porto = University of Porto (Praça de Gomes Teixeira, 4099-002 Porto - Portugal)
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Affiliation as printed
Zuse Institute Berlin , Department A 2 IM , Takustr. 7 , 14195 Berlin , Germany
COPT GmbH (Germany)
ZIB - Zuse Institute Berlin (Konrad-Zuse-Zentrum für Informationstechnik Berlin (ZIB Takustraße 7 D-14195 Berlin-Dahlem - Germany)
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Affiliation as printed
DAGOPT Optimization Technologies GmbH
ZIB - Optimization Department (Konrad-Zuse-Zentrum für Informationstechnik Berlin Takustrasse 7 D-14195 Berlin-Dahlem Germany - Germany)
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Zuse Institute Berlin · RWTH Aachen University
Affiliation as printed
RWTH Aachen University , Lehrstuhl für Operations Research , Kackertstr. 7 , 52072 Aachen , Germany
ZIB - Zuse Institute Berlin (Konrad-Zuse-Zentrum für Informationstechnik Berlin (ZIB Takustraße 7 D-14195 Berlin-Dahlem - Germany)
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Affiliation as printed
DAGOPT Optimization Technologies GmbH
ZIB - Zuse Institute Berlin (Konrad-Zuse-Zentrum für Informationstechnik Berlin (ZIB Takustraße 7 D-14195 Berlin-Dahlem - Germany)
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Affiliation as printed
Zuse Institute Berlin , Department AIS 2 T , Takustr. 7 , 14195 Berlin , Germany
Dagopt Optimization Technologies Gmbh [Leonding] (Im Bäckerfeld 19, 4060 Leonding - Austria)
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Affiliation as printed
RWTH Aachen University , Lehrstuhl für Operations Research , Kackertstr. 7 , 52072 Aachen , Germany
RWTH Aachen - RWTH Aachen University = Rheinisch-Westfälische Technische Hochschule Aachen (RWTH Aachen – Templergraben 55 – 52062 Aachen (Hausanschrift) – 52056 Aachen (Postanschrift) – Deutschland - Germany)
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Zuse Institute Berlin · RWTH Aachen University
Affiliation as printed
RWTH Aachen University , Lehrstuhl für Operations Research , Kackertstr. 7 , 52072 Aachen , Germany
ZIB - Zuse Institute Berlin (Konrad-Zuse-Zentrum für Informationstechnik Berlin (ZIB Takustraße 7 D-14195 Berlin-Dahlem - Germany)
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Zuse Institute Berlin · RWTH Aachen University
Affiliation as printed
RWTH Aachen University , Lehrstuhl für Operations Research , Kackertstr. 7 , 52072 Aachen , Germany
ZIB - Zuse Institute Berlin (Konrad-Zuse-Zentrum für Informationstechnik Berlin (ZIB Takustraße 7 D-14195 Berlin-Dahlem - Germany)
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Erik Mühmer Aachen
Affiliation as printed
RWTH Aachen - RWTH Aachen University = Rheinisch-Westfälische Technische Hochschule Aachen (RWTH Aachen – Templergraben 55 – 52062 Aachen (Hausanschrift) – 52056 Aachen (Postanschrift) – Deutschland - Germany)
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Zuse Institute Berlin · Technische Universität Berlin
Affiliation as printed
Zuse Institute Berlin , Department AIS 2 T , Takustr. 7 , 14195 Berlin , Germany
TUB - Technical University of Berlin / Technische Universität Berlin (Straße des 17. Juni 135 10623 Berlin - Germany)
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Affiliation as printed
COPT GmbH , Berlin , Germany
DAGOPT Optimization Technologies GmbH
COPT GmbH (Germany)
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Affiliation as printed
ZIB - Zuse Institute Berlin (Konrad-Zuse-Zentrum für Informationstechnik Berlin (ZIB Takustraße 7 D-14195 Berlin-Dahlem - Germany)
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Zuse Institute Berlin · RWTH Aachen University
Affiliation as printed
RWTH Aachen University , Lehrstuhl für Operations Research , Kackertstr. 7 , 52072 Aachen , Germany
ZIB - Zuse Institute Berlin (Konrad-Zuse-Zentrum für Informationstechnik Berlin (ZIB Takustraße 7 D-14195 Berlin-Dahlem - Germany)
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