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
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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.
Bonchev, D., & Mekenyan, O. (1994). Graph theoretical approaches to chemical reactivity. Dordrecht: Kluwer.
Crick, F. H. C. (1958). On protein synthesis. Symp. Soc. Exp. Biol., 12, 138–163.
Garey, M. R., & Johnson, D. S. (1979). Computers and intractability: a guide to the theory of NP-completeness. New York: Freeman.
Hordijk, W., & Steel, M. (2004). Detecting autocatalytic, self-sustaining sets in chemical reaction systems. J. Theor. Biol., 227(4), 451–461.
Hordijk, W., & Steel, M. (2012a). Autocatalytic sets extended: dynamics, inhibition, and a generalization. J. Syst. Chem., 3, 5.
Hordijk, W., & Steel, M. (2012b). Predicting template-based catalysis rates in a simple catalytic reaction model. J. Theor. Biol., 295, 132–138.
Hordijk, W., & Steel, M. (2013). A formal model of autocatalytic sets emerging in an RNA replicator system. J. Syst. Chem., 4, 3.
Hordijk, W., Kauffman, S. A., & Steel, M. (2011). Required levels of catalysis for emergence of autocatalytic sets in models of chemical reaction systems. Int. J. Mol. Sci., 12(5), 3085–3101.
Hordijk, W., Steel, M., & Kauffman, S. (2012). The structure of autocatalytic sets: evolvability, enablement, and emergence. Acta Biotheor., 60(4), 379–392.
Kauffman, S. A. (1971). Cellular homeostasis, epigenesis and replication in randomly aggregated macromolecular systems. J. Cybern., 1(1), 71–96.
Kauffman, S. A. (1993). The origins of order. Oxford: Oxford University Press.
Mincheva, M., & Roussel, M. R. (2007). Graph-theoretic methods for the analysis of chemical and biochemical networks, I: multistability and oscillations in ordinary differential equation models. J. Math. Biol., 55, 61–86.
Mossel, E., & Steel, M. (2005). Random biochemical networks: the probability of self-sustaining autocatalysis. J. Theor. Biol., 233(3), 327–336.
Schrödinger, E. (1944). What is life? Cambridge: Cambridge University Press.
Vaidya, N., Manapat, M. L., Chen, I. A., Xulvi-Brunet, R., Hayden, E. J., & Lehman, N. (2012). Spontaneous network formation among cooperative RNA replicators. Nature, 491, 72–77.
Vasas, V., Fernando, C., Santos, M., Kauffman, S., & Sathmáry, E. (2012). Evolution before genes. Biol. Direct, 7, 1.
Watson, J. D., & Crick, F. H. C. (1953). Genetical implications of the structure of deoxyribonucleic acid. Nature, 171, 964–967.
Wills, P., & Henderson, L. (2000). Self-organisation and information-carrying capacity of collectively autocatalytic sets of polymers: ligation systems. In Y. Bar-Yam (Ed.), Unifying themes in complex systems: proceedings of the first international conference on complex systems (pp. 613–623). Jackson: Perseus.