title: Autocatalytic sets inE. colimetabolism.
abstract: BACKGROUND
  A central unsolved problem in early evolution concerns self-organization towards higher complexity in chemical reaction networks. In theory, autocatalytic sets have useful properties to help model such transitions. Autocatalytic sets are chemical reaction systems in which molecules belonging to the set catalyze the synthesis of other members of the set. Given an external supply of starting molecules - the food set - and the conditions that (i) all reactions are catalyzed by at least one molecule, and (ii) each molecule can be constructed from the food set by a sequence of reactions, the system becomes a reflexively autocatalytic food-generated network (RAF set). Autocatalytic networks and RAFs have been studied extensively as mathematical models for understanding the properties and parameters that influence self-organizational tendencies. However, despite their appeal, the relevance of RAFs for real biochemical networks that exist in nature has, so far, remained virtually unexplored.
  
  
  RESULTS
  Here we investigate the best-studied metabolic network, that ofEscherichia coli, for the existence of RAFs. We find that the largest RAF encompasses almost the entireE. colicytosolic reaction network. We systematically study its structure by considering the impact of removing catalysts or reactions. We show that, without biological knowledge, finding the minimum food set that maintains a given RAF is NP-complete. We apply a randomized algorithm to find (approximately) smallest subsets of the food set that suffice to sustain the original RAF.
  
  
  CONCLUSIONS
  The existence of RAF sets within a microbial metabolic network indicates that RAFs capture properties germane to biological organization at the level of single cells. Moreover, the interdependency between the different metabolic modules, especially concerning cofactor biosynthesis, points to the important role of spontaneous (non-enzymatic) reactions in the context of early evolution. Graphical AbstractE. colimetabolic network in the context of autocatalytic sets.
authors.affiliation: Institute of Molecular Evolution, Heinrich Heine Universität, Düsseldorf, Germany.
authors.forename: Filipa L
authors.initials: FL
authors.lastname: Sousa
authors.affiliation: SmartAnalytiX.com, Lausanne, Switzerland.
authors.forename: Wim
authors.initials: W
authors.lastname: Hordijk
authors.affiliation: Allan Wilson Centre Molecular Ecology and Evolution, University of Canterbury, Christchurch, New Zealand.
authors.forename: Mike
authors.initials: M
authors.lastname: Steel
authors.affiliation: Institute of Molecular Evolution, Heinrich Heine Universität, Düsseldorf, Germany.
authors.forename: William F
authors.initials: WF
authors.lastname: Martin
keywords: Autocatalytic networks; Metabolic network; Origin of life