Origins of Life and Evolution of Biospheres

, Volume 44, Issue 2, pp 111–124 | Cite as

Conditions for Evolvability of Autocatalytic Sets: A Formal Example and Analysis

  • Wim Hordijk
  • Mike Steel
Theoretical Modeling


We provide a formal but visually clear example of how a set of minimal necessary conditions for evolvability of autocatalytic sets is satisfied in a simple model of chemical reaction systems. Furthermore, we show how these conditions can be captured and analyzed with RAF theory, and how the results can be generalized with a somewhat more elaborate example. Finally, we argue that our results clearly support the hypothesis that autocatalytic sets can be evolvable, and that this might even be an expected property of such sets.


Origin of life Autocatalytic sets Evolvability 



We thank the Allan Wilson Centre, New Zealand, for helping fund this work, and two anonymous reviewers for helpful suggestions to improve the manuscript.


  1. Ashkenasy G, Jegasia R, Yadav M, Ghadiri MR (2004) Design of a directed molecular network. PNAS 101(30):10872–10877PubMedCentralPubMedCrossRefGoogle Scholar
  2. Dyson FJ (1982) A model for the origin of life. J Mol Evol 18:344–350PubMedCrossRefGoogle Scholar
  3. Dyson FJ (1985) Origins of Life. Cambridge University PressGoogle Scholar
  4. Gillespie DT (1976) A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. J Comput Phys 22:403–434CrossRefGoogle Scholar
  5. Gillespie DT (1977) Exact stochastic simulation of coupled chemical reactions. J Phys Chem 81(25):2340–2361CrossRefGoogle Scholar
  6. Hordijk W (2013) Autocatalytic sets. From the origin of life to the economy. BioScience 63(11):877–881CrossRefGoogle Scholar
  7. Hordijk W, Steel M (2004) Detecting autocatalytic, self-sustaining sets in chemical reaction systems. J Theor Biol 227(4):451–461PubMedCrossRefGoogle Scholar
  8. Hordijk W, Steel M (2013) A formal model of autocatalytic sets emerging in an RNA replicator system. J Syst Chem 4:3CrossRefGoogle Scholar
  9. Hordijk W, Steel M (2014) Autocatalytic sets and boundaries. J Syst Chem. In revisionGoogle Scholar
  10. Hordijk W, Hein J, Steel M (2010) Autocatalytic sets and the origin of life. Entropy 12(7):1733–1742CrossRefGoogle Scholar
  11. Hordijk W, Kauffman SA, Steel M (2011) Required levels of catalysis for emergence of autocatalytic sets in models of chemical reaction systems. Int J Mol Sci 12(5):3085–3101PubMedCentralPubMedCrossRefGoogle Scholar
  12. Hordijk W, Steel M, Kauffman S (2012) The structure of autocatalytic sets: Evolvability, enablement, and emergence. Acta Biotheoretica 60(4):379–392PubMedCrossRefGoogle Scholar
  13. Hordijk W, Hasenclever L, Gao J, Mincheva D, Hein J (2014a) An investigation into irreducible autocatalytic sets and power law distributed catalysis. Natural Computing 13(3):287–296CrossRefGoogle Scholar
  14. Hordijk W, Smith JI, Steel M (2014b) Algorithms for detecting and analysing autocatalytic sets. Algorithms for Molecular Biology. In revisionGoogle Scholar
  15. Hordijk W, Wills P, Steel M (2014c) Autocatalytic sets and biological specificity. Bull Math Biol 761:201–224CrossRefGoogle Scholar
  16. Kauffman SA (1971) Cellular homeostasis, epigenesis and replication in randomly aggregated macromolecular systems. J Cybern 1(1):71–96CrossRefGoogle Scholar
  17. Kauffman SA (1986) Autocatalytic sets of proteins. J Theoretical Biol 119:1–24CrossRefGoogle Scholar
  18. Kauffman SA (1993) The Origins of Order. Oxford University PressGoogle Scholar
  19. Lifson S (1997) On the crucial stages in the origin of animate matter. J Mol Evol 44:1–8PubMedCrossRefGoogle Scholar
  20. Martin W, Russel MJ (2007) On the origin of biochemistry at an alkaline hydrothermal vent. Philos Trans R Soc B 362:1887–1925CrossRefGoogle Scholar
  21. Mossel E, Steel M (2005) Random biochemical networks. The probability of self-sustaining autocatalysis. J Theor Biol 233(3):327–336PubMedCrossRefGoogle Scholar
  22. Orgel L E (2008) The implausibility of metabolic cycles on the prebiotic earth. PLoS Biol 6(1):5–13CrossRefGoogle Scholar
  23. Segré D, Ben-Eli D, Deamer DW, Lancet D (2001) The lipid world. Orig Life Evol Biosph 31(1-2):119–145PubMedCrossRefGoogle Scholar
  24. Sievers D, von Kiedrowski G (1994) Self-replication of complementary nucleotide-based oligomers. Nature 369:221–224PubMedCrossRefGoogle Scholar
  25. Smith J, Steel M, Hordijk W (2014) Autocatalytic sets in a partitioned biochemical network. J Syst Chem 5:2PubMedCentralPubMedCrossRefGoogle Scholar
  26. Sousa FL, Hordijk W, Steel M, Martin W (2014) Autocatalytic sets in the metabolic network of E. coli. J Syst Chem. In revisionGoogle Scholar
  27. Steel M (2000) The emergence of a self-catalysing structure in abstract origin-of-life models. Appl Math Lett 3:91–95CrossRefGoogle Scholar
  28. Steel M, Hordijk W, Smith J (2013) Minimal autocatalytic networks. J Theor Biol 332:96–107PubMedCrossRefGoogle Scholar
  29. Taran O, Thoennessen O, Achilles K, von Kiedrowski G (2010) Synthesis of information-carrying polymers of mixed sequences from double stranded short deoxynucleotides. J Syst Chem 1(9)Google Scholar
  30. Vaidya N, Manapat ML, Chen IA, Xulvi-Brunet R, Hayden EJ, Lehman N (2012) Spontaneous network formation among cooperative RNA replicators. Nature 491:72–77PubMedCrossRefGoogle Scholar
  31. Vasas V, Szathmáry E, Santos M (2010) Lack of evolvability in self-sustaining autocatalytic networks constraints metabolism-first scenarios for the origin of life. PNAS 107(4):1470–1475PubMedCentralPubMedCrossRefGoogle Scholar
  32. Vasas V, Fernando C, Santos M, Kauffman S, Sathmáry E (2012) Evolution before genes. Biol Direct 7(1)Google Scholar
  33. Wächtershäuser G (2007) On the chemistry and evolution of the pioneer organism. Chem Biodivers 4:584–602PubMedCrossRefGoogle Scholar
  34. Wills PR, Henderson L (2000) Self-organisation and information-carrying capacity of collectively autocatalytic sets of polymers: ligation systems. In: Bar-Yam Y (ed) In Unifying Themes in Complex Systems: Proceedings of the First International Conference on Complex Systems. Perseus Books, pp 613–623Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.SmartAnalytiX.comLausanneSwitzerland
  2. 2.Allan Wilson CentreUniversity of CanterburyChristchurchNew Zealand

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