title: CycleFreeFlux: efficient removal of thermodynamically infeasible loops from flux distributions.
abstract: BACKGROUND
  Constraint-based metabolic modeling methods such as Flux Balance Analysis (FBA) are routinely used to predict metabolic phenotypes, e.g. growth rates, ATP yield or the fitness of gene knockouts. One frequent difficulty of constraint-based solutions is the inclusion of thermodynamically infeasible loops (or internal cycles), which add nonbiological fluxes to the predictions.
  
  
  RESULTS
  We propose a simple postprocessing of constraint-based solutions, which removes internal cycles from any given flux distribution [Formula: see text] without disturbing other fluxes not involved in the loops. This new algorithm, termed CycleFreeFlux, works by minimizing the sum of absolute fluxes [Formula: see text] while (i) conserving the exchange fluxes and (ii) using the fluxes of the original solution to bound the new flux distribution. This strategy reduces internal fluxes until at least one reaction of every possible internal cycle is inactive, a necessary and sufficient condition for the thermodynamic feasibility of a flux distribution. If alternative representations of the input flux distribution in terms of elementary flux modes exist that differ in their inclusion of internal cycles, then CycleFreeFlux is biased towards solutions that maintain the direction given by [Formula: see text] and towards solutions with lower total flux [Formula: see text]. Our method requires only one additional linear optimization, making it computationally very efficient compared to alternative strategies.
  
  
  METHODS
  We provide freely available R implementations for the enumeration of thermodynamically infeasible cycles as well as for cycle-free FBA solutions, flux variability calculations and random sampling of solution spaces.
  
  
  BACKGROUND
  lercher@cs.uni-duesseldorf.de.
authors.affiliation: Institute for Computer Science, Institute for Mathematics, Cluster of Excellence on Plant Sciences, Heinrich Heine University, 40225 Düsseldorf, Germany, Faculty of Computers and Informatics, Suez Canal University, Ismailia, Egypt Institute for Computer Science, Institute for Mathematics, Cluster of Excellence on Plant Sciences, Heinrich Heine University, 40225 Düsseldorf, Germany, Faculty of Computers and Informatics, Suez Canal University, Ismailia, Egypt.
authors.forename: Abdelmoneim Amer
authors.initials: AA
authors.lastname: Desouki
authors.affiliation: Institute for Computer Science, Institute for Mathematics, Cluster of Excellence on Plant Sciences, Heinrich Heine University, 40225 Düsseldorf, Germany, Faculty of Computers and Informatics, Suez Canal University, Ismailia, Egypt.
authors.forename: Florian
authors.initials: F
authors.lastname: Jarre
authors.affiliation: Institute for Computer Science, Institute for Mathematics, Cluster of Excellence on Plant Sciences, Heinrich Heine University, 40225 Düsseldorf, Germany, Faculty of Computers and Informatics, Suez Canal University, Ismailia, Egypt.
authors.forename: Gabriel
authors.initials: G
authors.lastname: Gelius-Dietrich
authors.affiliation: Institute for Computer Science, Institute for Mathematics, Cluster of Excellence on Plant Sciences, Heinrich Heine University, 40225 Düsseldorf, Germany, Faculty of Computers and Informatics, Suez Canal University, Ismailia, Egypt Institute for Computer Science, Institute for Mathematics, Cluster of Excellence on Plant Sciences, Heinrich Heine University, 40225 Düsseldorf, Germany, Faculty of Computers and Informatics, Suez Canal University, Ismailia, Egypt.
authors.forename: Martin J
authors.initials: MJ
authors.lastname: Lercher
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D064688:Metabolic Flux Analysis / Q000379:methods*; D053858:Metabolic Networks and Pathways; D008954:Models, Biological; D013816:Thermodynamics