title: Estimating biological elementary flux modes that decompose a flux distribution by the minimal branching property.
abstract: BACKGROUND
  Elementary flux mode (EFM) is a useful tool in constraint-based modeling of metabolic networks. The property that every flux distribution can be decomposed as a weighted sum of EFMs allows certain applications of EFMs to studying flux distributions. The existence of biologically infeasible EFMs and the non-uniqueness of the decomposition, however, undermine the applicability of such methods. Efforts have been made to find biologically feasible EFMs by incorporating information from transcriptional regulation and thermodynamics. Yet, no attempt has been made to distinguish biologically feasible EFMs by considering their graphical properties. A previous study on the transcriptional regulation of metabolic genes found that distinct branches at a branch point metabolite usually belong to distinct metabolic pathways. This suggests an intuitive property of biologically feasible EFMs, i.e. minimal branching.
  
  
  RESULTS
  We developed the concept of minimal branching EFM and derived the minimal branching decomposition (MBD) to decompose flux distributions. Testing in the core Escherichia coli metabolic network indicated that MBD can distinguish branches at branch points and greatly reduced the solution space in which the decomposition is often unique. An experimental flux distribution from a previous study on mouse cardiomyocyte was decomposed using MBD. Comparison with decomposition by a minimum number of EFMs showed that MBD found EFMs more consistent with established biological knowledge, which facilitates interpretation. Comparison of the methods applied to a complex flux distribution in Lactococcus lactis similarly showed the advantages of MBD. The minimal branching EFM concept underlying MBD should be useful in other applications.
  
  
  BACKGROUND
  sinhu@bio.dtu.dk or p.ji@polyu.edu.hk
  
  
  BACKGROUND
  Supplementary data are available at Bioinformatics online.
authors.affiliation: Systems Biotechnology and Biorefining, National Food Institute, Technical University of Denmark, 2800 Kgs. Lyngby, Denmark and Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hung Hom, Hong Kong.
authors.forename: Siu Hung Joshua
authors.initials: SH
authors.lastname: Chan
authors.affiliation: Systems Biotechnology and Biorefining, National Food Institute, Technical University of Denmark, 2800 Kgs. Lyngby, Denmark and Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hung Hom, Hong Kong.
authors.forename: Christian
authors.initials: C
authors.lastname: Solem
authors.affiliation: Systems Biotechnology and Biorefining, National Food Institute, Technical University of Denmark, 2800 Kgs. Lyngby, Denmark and Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hung Hom, Hong Kong.
authors.forename: Peter Ruhdal
authors.initials: PR
authors.lastname: Jensen
authors.affiliation: Systems Biotechnology and Biorefining, National Food Institute, Technical University of Denmark, 2800 Kgs. Lyngby, Denmark and Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hung Hom, Hong Kong.
authors.forename: Ping
authors.initials: P
authors.lastname: Ji
mesh_terms: D000085:Acetates / Q000378:metabolism; D000818:Animals; D004926:Escherichia coli / Q000378:metabolism; D006038:Glyoxylates / Q000378:metabolism; D013294:Lactococcus lactis / Q000235:genetics / Q000378:metabolism; D064688:Metabolic Flux Analysis / Q000379:methods*; D053858:Metabolic Networks and Pathways / Q000235:genetics; D051379:Mice; D009206:Myocardium / Q000378:metabolism
chemical_list: D000085:Acetates; D006038:Glyoxylates; C031150:glyoxylic acid