Quasi-replication

This then is the solution of the ribotype theory in order to avoid the error catastrophes in the journey toward exact replication, it was necessary to have high molecular weight protoribosomes, and the production of these ribosomes for an indefinite number of generations was possible, before exact replication, because ribosoids could achieve it with processes of self-assembly and quasi-replication. The development of high-molecular-weight protoribosomes took place during postchemical evolution, simply because all necessary conditions existed in that period, and the development could be realised with processes that were both natural and primitive. 

The origin-of-life scenario was instrumental for the new theory of the cell, because it led to the the conclusion that the ribotype had an evolutionary priority over genotype and phenotype. More precisely, the scenario described a precellular ribotype world (not to be confused with the RNA world) where some ribosoids could act as templates (ribogenotype), others as enzymes (ribophenotype), and others as polymerising ribosoids (ribotype) that were responsible for the growth and the quasi-replication of the ribonucleoprotein systems. 

A hypercycle is a more complex organisation form. Its precondition is the presence of several RNA quasi-species which are able to amalgamate chemically with certain proteins (enzymes or their precursors). If such a protein is linked to a quasi-species, the resulting duo favours the replication of a second quasispecies. According to Dyson, the linked populations get stuck in a stable equilibrium. Problems occur at this level Any theory on the origin of replication has the central problem that the replication process must occur perfectly in order to ensure survival . If there are replication errors, these will increase from generation to generation, until the system collapses the error catastrophe has then occurred ... 

Most origins have quasi-palindromic nucleotide sequences, perhaps so that DNA can be looped out from the main duplex as is shown in Fig. 27-18A and B. The lengths of ori sequences vary, as does the complexity of their possible folding patterns. Plasmids have been constructed which not only contain the E. coli origin, but are dependent upon that origin for their own replication.3823 Study of those plasmids indicate... 

CTP), which are the building blocks for polynucleotide synthesis. The rate of RNA synthesis (lower part) is measured through incorporation of radioactive GTP into the newly produced RNA molecules. The rate of replication shows stepwise increase. An early decrease is observed, because first a quasi-species is formed by the master sequence through production of mutants of lower fitness. The figure is redrawn from the data in [12]. 

Fig. 2.5. A quasi-species-type mutant distribution around a master sequence. The quasi-species is an ordered distribution of polynucleotide sequences (RNA or DNA) in sequence space. A fittest genotype or master sequence /m, which is commonly present at highest frequency, is surrounded in sequence space by a cloud of closely related sequences. Relatedness of sequences is expressed (in terms of error classes) by the number of mutations which are required to produce them as mutants of the master sequence. In case of point mutations the distance between sequences is the Hamming distance. In precise terms, the quasi-species is defined as the stable stationary solution of Eq. (2) [16,19, 20], In reality, such a stationary solution exists only if the error rate of replication lies below a maximal value called the error threshold. In this region, i.e. below...

An interesting detail of the quasi-species concept was predicted more than twelve years ago [24] and has been observed recently with virus populations [25] and computer simulations [26] We assume two genotypes of high fitness, each one surrounded by a specific mutant doud (Fig. 2.5). Genotype Iml has higher fitness compared to Im2 but less efficient mutants in the sense of a mutant cloud with lower mean fitness. The quasi-species considered as a function of the mutation rate p may show a rearrangement reminiscent of a phase transition at some critical replication accuracy qa = 1 - pCT. At low mutation rates, p>pCI, the difference in fitness values determines selection and hence, the master sequence with higher fitness, fml, dominates. Above the critical mutation rate, p>pCI, however, mutational backflow to the master is decisive and then fm2 is selected. 

Equation (III.2) may be rewritten to isolate the dependence on the copying fidelity q in order to demonstrate that for a given set of replication parameters there is an error-rate-dependent threshold sequence length for quasi-species instability. To this end the selective advantage or superiority parameter a was introduced ... 

It should be briefly pointed out that simply decreasing the replication rates of other sequences to increase the superiority of the master does not indefinitely postpone the error threshold. Once the replication rates for mutant sequences fall below the destruction rate for the master sequence, the domain of viable existence for the quasi-species is limited by A Q > D . In Section III.3 a more fundamental statistical argument restricts the effective superiority to a finite value of order 1. 

One possible option is to adopt a statistical description of the kinetic parameters and to ask how likely it is for the quasi-species to be localized about the wild type. This undertaking requires an analysis beyond the second order in perturbation theory since a distant mutant with a selective value very close to that of the wild type may jeopardize the stability of the latter in the population. We were however encouraged by the progress that had been made with a problem of similar difficulty in the very different area of electron or spin localization in disordered solids. Indeed, it turns out that an expression of the form of Eqn. (III.5) may be obtained, with an explicit expression for the superiority parameter Oq, dependent on the distribution of replication rates but not on any average involving population variables. 

In order to answer this question, a significant source of statistical correlation arising from mutation paths that visit a particularly advantageous mutant more than once must be considered. In the perturbation theory these paths are represented by products of factors involving the mutant replication rates, and it is necessary to remove the strong correlation that arises between these factors where repeated indices are present in order to obtain a tractable statistical analysis of convergence. The Watson renormalization procedure [29], the application of which to the steady-state quasi-species is summarized in Appendix 7, accomplishes just this [30]. The cost is a consecutive modification of the denominator, which may however be simplified to good approximation, as in Eqn. (A7.5). 

Figure 10. Quasi-species as function of single-digit accuracy of replication (q) for chain v = 5. We plot relative stationary concentration of master sequence ( (,),fum of relative stationary concentrations of alt one-error mutants ((i), of all two-error mutants ( j), etc. Note that we have only one five-error mutant 7,5, = /s, in this particular example. We observe selection of master sequence at g = 1. Then relative concentration of master sequence decreases with decreasing q. At value q = 0.5 all sequences are present in equal concentrations. Hence, sums of concentrations of two- and three-error mutants are largest—they have statistical weight of 10—those of the one-and four-error mutants are half as large—they have statistical weight of 5—and finally master sequence 7q and its complementary sequence, the five-error mutant /ji, are present in relative concentration ofonly. At q = 0 we have selection o( master pair", which consists of/o and /31 in our example. Thus we have direct replication with errors in range 1 > g > 0.5 and complementary replication with errors in range 0 < q < 0.5. Rate constants chosen as Aq = 10[U ] and A = 1 [t ] for all mutants Ic 0. Here we denote arbitrary reciprocal time unit by [t" ]. All degradation rate constants were put equal 7>o = D, = Dj = = D31 = 0.

Figure 11. Quasi-species as function of single-digit accuracy of replication (q) for chain length V = 10. Computations were performed in complete analogy to those shown in Figure 10. Note that range of "random replication" has increased substantially compared to case v = 5. We observe fairly sharp transitions between direct and random replication at critical value q = and between random and complementary replication aX q =...

Figure 14. Degenerate quasi-species with v = 5. We plot relative concentrations (x,) as functions of single-digit accuracy of replication (g). Two degenerate master sequences /q and are of Hamming distance d(l, 5) = 2 in this example—for numbering of sequences see Figure 13. Rate constant Aq 10, Ai = A2 = = A5 = 5, = 10, A, = = A31 = 1. In limit q -> I...

Several attempts to describe replication-mutation networks by stochastic techniques were made in the past. We cannot discuss them in detail here, but we shall brieffy review some general ideas that are relevant for the quasispecies model. The approach that is related closest to our model has been mentioned already [51] the evolutionary process is viewed as a sequence of stepwise increases in the populations mean fitness. Fairly long, quasi-stationary phases are interrupted by short periods of active selection during which the mean fitness increases. The approach towards optimal adaptation to the environment is resolved in a manner that is hierarchical in time. Evolution taking place on the slow time scale represents optimization in the whole of the sequence space. It is broken up into short periods of time within which the quasi-species model applies only locally. During a single evolutionary step only a small part of sequence space is explored by the population. There, the actual distributions of sequences resemble local quasispecies confined to well-defined regions. Error thresholds can be defined locally as well. 

Figure 30. Error threshold as function of population size. Stochastic replication-mutation dynamics in ensemble of polynucleotide sequences with chain length v = 20 simulated by Gillespie s algorithm [95]. Critical single-digit accuracy of replication (q in) at which ordered quasi-species is converted into changing population of sequences with finite lifetimes is plotted as function of 1/N, reciprocal population size (lower curve). For further details see ref. 96. Upper curve is theoretical prediction of Eqn. (V.l) based on ref. 51.

The notion of catalysis is important. There are many ways to catalyze any reaction. Catalysts are subject to evolution with a tendency to progress towards those that become more sophisticated. An especially relevant case is autocatalysis in which the reaction product catalyzes its own synthesis. In a similar vein, distinct RNA molecules can act as quasi enzymes called ribozymes. Two crucial features of life are replication and metabolism in liquid water. 

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