Hypercycle model

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 It seems possible that the protein enzymes on the primeval Earth could have been replaced by ribozymes.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... 

From the methodological point of view the hypercycle model is the most impressive example of the possibility of unifying detailed biochemical examinations and mathematical models of chemical reactions. Both the prebiotic relevance of the model and its mathematical structure were studied, sometimes critically (e.g. King, 1981 Miiller-Herold, 1983 Szathmary, 1984). It was suggested that the hypercyclic evolution is not as effective as conventional autocatalysis, and the model should be defined by multiple time singular perturbation theory. 

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. 

At the point where amphiphiles were recruited to provide the precursors to cell membranes, stable lipid vesicles could have evolved [141] to enclose autocatalytic chiral hypercycles. Credible models for the subsequent evolution of vesicles containing self-replicating chiral molecules have appeared in the literature. [193,194] These vesicles could then emerge from the feldspar spaces [134,192] as micron-sized self-reproducing, energy-metabolizing vesicular systems protobacteria ready to face the hydrothermal world on their own terms. 

Model focusing on the dynamics of replicating units (e.g., hypercycle). For a cell to grow effectively, there should be some positive feedback process to amplify the number of each molecular species. Such a positive feedback process leads to an autocatalytic process to synthesize each molecular species. For reproduction of a cell, (almost) all molecule species are somehow synthesized. Then, it would be possible to take a replication reaction from the beginning as a model. For example, consider a reaction... 

Recursiveness of Production in an Intermingled Hypercycle Network. Next, a protocell model consisting of a variety of mutually catalyzing molecular species is investigated. When the numbers of molecules in a cell is not too small and the number of possible species is not too large in a cell, recursive production of a cell is achieved. This recursive production state consists of 5-12... 

Destabilization of a recursive state in the present model occurs through the decrease of the population of the minority molecules in the core hypercycle. As this molecular species is taken over by parasitic molecules, the switching starts to occur. In this sense, the process in the switching is not random, but is restricted to specific routes within the phase space of chemical composition, as in the chaotic itinerancy. It is interesting to study the present switching over the recursive state by generalizing the concept of chaotic itinerancy [46], to include stochastic process. 

Universal Statistics and Control of Fluctuations. Statistics of the number fluctuations of each molecular species is studied. We have found (i) power-law distribution of fast switching molecules, (ii) suppression of fluctuation in the core hypercycle species, and (iii) ubiquity of log-normal distribution for most other molecular species. The origin of log-normal distribution is generally due to multiplicative stochastic process in the catalytic reaction dynamics, as is confirmed in several other reaction network models. On the other hand, suppression of the number fluctuations of the core hypercycle is due to high connections in reaction paths with other molecules. In particular, reduced is the number fluctuations of the minority molecular species that has high catalytic connections with others. This suppression of fluctuation further reinforces the... 

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