title: Large-scale computation of elementary flux modes with bit pattern trees.
abstract: BACKGROUND
  Elementary flux modes (EFMs)--non-decomposable minimal pathways--are commonly accepted tools for metabolic network analysis under steady state conditions. Valid states of the network are linear superpositions of elementary modes shaping a polyhedral cone (the flux cone), which is a well-studied convex set in computational geometry. Computing EFMs is thus basically equivalent to extreme ray enumeration of polyhedral cones. This is a combinatorial problem with poorly scaling algorithms, preventing the large-scale analysis of metabolic networks so far.
  
  
  RESULTS
  Here, we introduce new algorithmic concepts that enable large-scale computation of EFMs. Distinguishing extreme rays from normal (composite) vectors is one critical aspect of the algorithm. We present a new recursive enumeration strategy with bit pattern trees for adjacent rays--the ancestors of extreme rays--that is roughly one order of magnitude faster than previous methods. Additionally, we introduce a rank updating method that is particularly well suited for parallel computation and a residue arithmetic method for matrix rank computations, which circumvents potential numerical instability problems. Multi-core architectures of modern CPUs can be exploited for further performance improvements. The methods are applied to a central metabolism network of Escherichia coli, resulting in approximately 26 Mio. EFMs. Within the top 2% modes considering biomass production, most of the gain in flux variability is achieved. In addition, we compute approximately 5 Mio. EFMs for the production of non-essential amino acids for a genome-scale metabolic network of Helicobacter pylori. Only large-scale EFM analysis reveals the >85% of modes that generate several amino acids simultaneously.
  
  
  BACKGROUND
  An implementation in Java, with integration into MATLAB and support of various input formats, including SBML, is available at http://www.csb.ethz.ch in the tools section; sources are available from the authors upon request.
authors.affiliation: Institute of Computational Science and Swiss Institute of Bioinformatics, ETH Zurich, 8092 Zurich, Switzerland.
authors.forename: Marco
authors.initials: M
authors.lastname: Terzer
authors.forename: Jörg
authors.initials: J
authors.lastname: Stelling
mesh_terms: D000465:Algorithms; D002468:Cell Physiological Phenomena; D003198:Computer Simulation; D004926:Escherichia coli / Q000235:genetics / Q000378:metabolism; D008660:Metabolism; D020543:Proteome / Q000032:analysis / Q000378:metabolism; D049490:Systems Biology / Q000379:methods*
chemical_list: D020543:Proteome