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Dynamics of autocatalytic replicator networks based on higher-order ligation reactions

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Abstract

A class of autocatalytic reaction networks based on template-dependent ligation and higher-order catalysis is analysed. Apart from an irreversible ligation reaction we consider only reversible aggregation steps that provide a realistic description of molecular recognition. The overall dynamics can be understood by means of replicator equations with highly non-linear interaction functions. The dynamics depends crucially on the total concentration c 0 of replicating material.

For small c 0, in the hyperbolic growth regime, we recover the familiar dynamics of second-order replicator equations with its wealth of complex dynamics ranging from multi-stability to periodic and strange attractors as well as to heteroclinic orbits. For large c 0, in the parabolic growth regime, product inhibition becomes dominating and we observe a single globally stable equilibrium tantamount to permanent coexistence. In an intermediate parameter range we sometimes observe a behavior that is reminiscent of ’survival of the fittest’. Independently replicating species (Schlögl’s model) and the hypercycle are discussed in detail.

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Authors and Affiliations

  1. Institut für Theoretische Chemie und Molekulare Strukturbiologie, Universität Wien, Vienna, Austria

    Bärbel M. R. Stadler, Peter F. Stadler & Peter Schuster

  2. The Santa Fe Institute, Santa Fe, New Mexico, USA

    Peter F. Stadler & Peter Schuster

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  1. Bärbel M. R. Stadler
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  2. Peter F. Stadler
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  3. Peter Schuster
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Correspondence to Peter F. Stadler.

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Stadler, B.M.R., Stadler, P.F. & Schuster, P. Dynamics of autocatalytic replicator networks based on higher-order ligation reactions. Bull. Math. Biol. 62, 1061–1086 (2000). https://doi.org/10.1006/bulm.2000.0194

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  • DOI: https://doi.org/10.1006/bulm.2000.0194

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