Eigen’s hypercycle model

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... 

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). 

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