Abstract
BackgroundA 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.ResultsHere we investigate the best-studied metabolic network, that of Escherichia coli, for the existence of RAFs. We find that the largest RAF encompasses almost the entire E. coli cytosolic 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.ConclusionsThe 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 E. coli metabolic network in the context of autocatalytic sets.Electronic supplementary materialThe online version of this article (doi:10.1186/s13322-015-0009-7) contains supplementary material, which is available to authorized users.
Highlights
A central unsolved problem in early evolution concerns self-organization towards higher complexity in chemical reaction networks
RAF sets in the metabolic network of E. coli Applying the RAF algorithm to the E. coli metabolic network results in a maximal RAF set consisting of 1787 reactions
An outline of the number of reactions per functional category in the maximal RAF (maxRAF) is presented in Table 2, where it can be seen that all the major functional categories, such as amino acid biosynthesis, carbon metabolism, and cofactor and prosthetic group biosynthesis, are represented within the RAF set
Summary
We investigate the best-studied metabolic network, that of Escherichia coli, for the existence of RAFs. We find that the largest RAF encompasses almost the entire E. coli cytosolic reaction network. We systematically study its structure by considering the impact of removing catalysts or reactions. 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
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