Bulletin of Mathematical Biology

, Volume 76, Issue 1, pp 201–224 | Cite as

Autocatalytic Sets and Biological Specificity

  • Wim Hordijk
  • Peter R. Wills
  • Mike Steel
Original Article


A universal feature of the biochemistry of any living system is that all the molecules and catalysts that are required for reactions of the system can be built up from an available food source by repeated application of reactions from within that system. RAF (reflexively autocatalytic and food-generated) theory provides a formal way to study such processes. Beginning with Kauffman’s notion of “collectively autocatalytic sets,” this theory has been further developed over the last decade with the discovery of efficient algorithms and new mathematical analysis. In this paper, we study how the behaviour of a simple binary polymer model can be extended to models where the pattern of catalysis more precisely reflects the ligation and cleavage reactions involved. We find that certain properties of these models are similar to, and can be accurately predicted from, the simple binary polymer model; however, other properties lead to slightly different estimates. We also establish a number of new results concerning the structure of RAFs in these systems.


Origin of life Autocatalytic sets Template-based catalysis Wills–Henderson model 



We thank the Allan Wilson Centre for Molecular Ecology and Evolution and the Alexander von Humboldt Foundation for helping fund part of this research. We also thank an anonymous reviewer for several helpful suggestions.


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Copyright information

© Society for Mathematical Biology 2013

Authors and Affiliations

  1. 1.SmartAnalytiX.comLausanneSwitzerland
  2. 2.Intergrative TranscriptomicsUniversität TübingenTübingenGermany
  3. 3.Dept. of PhysicsUniversity of AucklandAucklandNew Zealand
  4. 4.Allan Wilson Centre for Molecular Ecology and EvolutionUniversity of CanterburyChristchurchNew Zealand

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