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Error propagation in the hypercycle

Error propagation in the hypercycle,10.1103/PhysRevE.61.2996,Physical Review E,P. R. A. Campos,J. F. Fontanari,P. F. Stadler

Error propagation in the hypercycle   (Citations: 13)
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We study analytically the steady-state regime of a network of n error-prone self-replicating templates forming an asymmetric hypercycle and its error tail. We show that the existence of a master template with a higher non-catalyzed self-replicative productivity, a, than the error tail ensures the stability of chains in which m<n-1 templates coexist with the master species. The stability of these chains against the error tail is guaranteed for catalytic coupling strengths (K) of order of a. We find that the hypercycle becomes more stable than the chains only for K of order of a2. Furthermore, we show that the minimal replication accuracy per template needed to maintain the hypercycle, the so-called error threshold, vanishes like sqrt(n/K) for large K and n<=4.
Journal: Physical Review E - PHYS REV E , vol. 61, no. 3, pp. 2996-3002, 2000
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    • ...In addition, hypercycles with a large number of different templates are subject to large fluctuations in the concentrations of its members, rendering it susceptible to extinction by stochastic effects (Nu˜no and Tarazona, 1994; Campos et al., 2000)...
    • ...The analysis of the error propagation in the hypercycle (Campos et al., 2000) is not useful here because the error tail (mutant) class considered in that work is not equivalent to the parasite class of the package models, since those mutants do no receive catalytic support from the hypercycle members...

    Daniel A. M. M. Silvestreet al. Package models and the information crisis of prebiotic evolution

    • ...Secondly, the evolution of complexity via the cooperation of several replicator species— e.g., via the hypercycle (Eigen and Schuster 1979)—is hindered by parasitic replicators, which do not contribute to the replication of the other replicators but still benefit from (or exploit) cooperative replicators (Maynard Smith 1979; Bresch et al. 1980)...
    • ...It is natural to conceive that a parasite can be a better template than the catalyst (Maynard Smith 1979; Bresch et al. 1980)...

    Nobuto Takeuchiet al. The Role of Complex Formation and Deleterious Mutations for the Stabil...

    • ...This simplified formulation facilitated greatly the analysis of the error threshold in Eigen’s model (Maynard Smith, 1983; Scheuring, 2000) as well as in the hypercycle (Garcı´ a-Tejedor et al., 1987; Nun˜ o et al., 1993; Campos et al., 2000)...

    Jose F. Fontanaria. Coexistence and error propagation in pre-biotic vesicle models: A grou...

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