Hypercycle model, Eigen

This dilemma could be overcome by the hypercycle model hypercycles are in fact not theoretical concepts, but can be observed (in a simple form) in today s organisms, where an RNA virus transfers the information for an enzyme in the host cell, which is able to carry out the preferred synthesis of new virus RNA. This RNA synthesis is supported by host factors, and an RNA minus-strand is formed. The following RNA replication affords a plus-strand. The process corresponds to a double feedback loop and involves the enzyme coded by the RNA matrix and the information present in the matrix in the form of a nucleotide sequence. Both factors contribute to the replication of the matrix, so that there is second-order autocatalysis (Eigen et al., 1982). 

The hypercycle models developed later by Eigen were much more complex. Since both protein enzymes and nucleic acids contribute to hypercycles, the latter could only have come into operation at a later stage of the (hypothetical) RNA world. It seems possible that the protein enzymes on the primeval Earth could have been replaced by ribozymes. 

Genuine self-organisation, i.e., self-organisation as a property of the system. Here, a system with a high degree of complexity organises itself under certain conditions. A typical example is Eigen s hypercycle model (see Sect. 8.3). 

We consider a simple test model which has the advantage that it can be studied analytically even for very large numbers of intermediates, which makes it suitable for the analysis of the interference between experimental errors with the errors due to linearization. This type of model, which is somewhat similar to Eigen s hypercycle model [26], has recently been introduced in connection with a population genetic problem [12]. The model used here is essentially a space-independent, homogeneous version of the model from [12]. We assume that there are two types of chemical species in the system, stable chemicals, A , v = 1,2,..., and active intermediates X , u = 1,2,..., and that there is a very large supply of stable species Ay, v = 1,2,..., and their concentrations ay, v = 1, 2,..., are assumed to be constant and only the concentrations Xu,u = 1,2,..., of the active intermediates are variable. We consider that the active intermediates replicate, transform into each other, and disappear through auto-catalytic processes moreover we assume that all active intermediates have the same... 

As expected, a response to the hypercycle criticisms appeared, in fact in the same issue of the Journal of Theoretical Biology (Eigen et al., 1980). According to this, the Freiburg investigations refer to one particular evolution model, in which the occurrence of mutants with different, selective values is ignored. In such realistic models, the error threshold loses its importance for the stability of the wild type. If the latter reaches a finite fitness value, it can always be the subject of selection, as no rivals are present. 

One scenario discussed in the literature is the formation, by chance, of mutually catalyzing polymers. Manfred Eigen of Max Planck Institute in Gottingen (Germany) and his co-workers worked out a model, called hypercycle, which represents a sort of evolution on the level of polymers [25]. The model is dressed up in a beautiful mathematical clothes of differential equations, but its essence is simple. 

Computer modeling of hypercycles (Kiippers, 1975 Eigen and Schuster, 1977, 1978) demonstrates the development of oscillatory behavior around a steady state which, through feedback and coupling of the members of the hypercycle, minimizes the effect of mistakes in reproduction and thus allows for selection and optimization of the dynamic structures. So viewed, hypercycles represent the minimum structural organization for a system to accumulate, maintain, and process the information in the genome. 

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