Summary
By introducing a modified enzyme coupling in Eigen's hypercycle equations we have produced an exactly solvable selfreproductive hypercycle model. The model shows explicitly how collections of different macromolecular information carriers may coexist, through internal couplings, in the presence of constraints. We show how the “selective value” concept is manifested in the model and give simple criteria for selection among competing hypercycles.
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References
Eigen, M.: Selforganization of Matter and the Evolution of Biological Macromolecules. Naturwiss. 55, 465–523 (1971).
Jones, B. L., Enns, R. H., Rangnekar, S. S.: On the Theory of Selection of Coupled Macromolecular Systems. Bull. Math. Biol. 38, 15–28 (1976).
Jones, B. L.: Analysis of Eigen's Equations for Selection of Biological Molecules with Fluctuating Mutation Rates. Bull. Math. Biol. (1976, to be published).
Montroll, E. W.: Some Statistical Aspects of the Theory of Interacting Species, in: Some Mathematical Questions in Biology, Vol. 3, pp. 99–143 (Cowan, J. D., ed.). 1972.
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Jones, B.L. A solvable selfreproductive hypercycle model for the selection of biological molecules. J. Math. Biology 4, 187–193 (1977). https://doi.org/10.1007/BF00275984
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DOI: https://doi.org/10.1007/BF00275984