Catalytic networks of self-replicative species are used as a model for the first steps of prebiotic evolution. Prior to the establishment of living beings separated from the environment with a membrane, macromolecules with the ability of self-reproduction and of catalysis of each other self-reproduction (likely RNAs) were the subject of evolution.
In the hypercycle, proposed by Eigen & Schuster, a set of self-replicative species catalyse the reproduction of one of the others and are catalysed by another one in a cycle. We have studied the properties of such an organisation when the number of species hypercyclically coupled is two, and they produce and compete with species with self-reproductive properties though without catalytic abilities [1].
The catalytic networks are a more general case of hypercycles. In catalytic networks the catalytic relationship between the self-replicative species could be different from a cyclic one. We have studied the selective and evolutive properties of catalytic networks competing with non-catalytic species [2, 3] and characterised the system dynamics focusing on the strange attractor that appears when the number of species of the network is four or higher [4].
We reviewed in a book the current state of the art in prebiotic evolution with an introduction to the prebiotic evolution models [5].
References
[1] Andrade, M.A., A.J. García-Tejedor and F. Montero. 1991. Study of an error-prone hypercycle formed from two kinetically distinguishable species. Biophys. Chem. 40, 43-57
[2] Nuño, J.C., M.A. Andrade, F. Morán and F. Montero. 1993. A model of an auto-catalytic network formed by error-prone self-replicative species. Bull. Math. Biol. 55, 385-415
[3] Nuño, J.C., M.A. Andrade and F. Montero. 1993. Non-uniformities and superimposed competition in a model of auto-catalytic network formed by error-prone self-replicative species. Bull. Math. Biol. 55, 417-449
[4] Andrade, M.A., J.C. Nuño, F. Morán, F. Montero and G.J. Mpitsos. 1993. Complex dynamics of a catalytic network having faulty replication into error-species. Physica D. 63, 21-40
[5] Montero, F., J.C. Nuño and M.A. Andrade. 1993. Evolución Prebiótica: el camino hacia la vida. Colección Eudema Biología. Eudema.