Replication error rates

Due to autocatalytic reactions, there is a tendency for further increase of the molecules that are in the majority. This leads to competition for replication between molecular types of the same species. Since the total number of Y molecules is small, this competition leads to all-or-none behavior for the survival of molecules. As a result, only a single type of species Y remains, while for species X the numbers of molecules of different types are statistically distributed as guaranteed by the uniform replication error rate. 

The model is simulated as follows At each step, a pair of molecules, say, i and j, is chosen randomly. If there is a reaction path between species i and j, and i (j) catalyzes j (i), one molecule of the species j ( ) is added with probability c, (cj), respectively. The molecule is then changed to another randomly chosen species with the probability of the replication error rate p. When the total number of molecules exceeds a given threshold (denoted as N), the cell divides into two such that each daughter cell inherits half (N/2) of the molecules of the mother cell, chosen randomly [2],... 

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However, complex error corrections (by repair enzymes) permit a great reduction in the error rate. Such repair systems were not available to primitive replicators, so they needed to survive with error rates of more than 1 100 this reduced the size of the genome to around 100 bases (nucleotides). This became obvious in work done by Saul Spiegelmann (1967) and the Eigen group (Biebricher et al 1981). 

As early as 1972, Kuhn described a model in which he assumed that RNA replication with a certain error rate could have occurred without the participation of enzymes. Natural phenomena with cyclic behaviour are an important factor in Kuhn s thinking these drive duplication processes. Examples are summer and winter, day and night, or high and low tide (whereby the latter were probably subject to greater variations on the primeval Earth than they are today). These rhythms were often linked with considerable temperature variations, which, for example, made possible the transition from double to single strand RNA (and vice versa). It can be assumed that the cyclic variations involved reactions in which monomers were linked to form polymers. 

Replication of DNA does not occur with complete precision, but rather has an intrinsic inaccuracy. The error rate for incorporation of nucleotides in DNA replication is of the order of one error per 10 - 10 correctly incorporated nucleotides. 

RNA replicase isolated from Qj8-infected E. coli cells catalyzes the formation of an RNA complementary to the viral RNA, in a reaction equivalent to that catalyzed by DNA-dependent RNA polymerases. New RNA strand synthesis proceeds in the 5 —>3 direction by a chemical mechanism identical to that used in all other nucleic acid synthetic reactions that require a template. RNA replicase requires RNA as its template and will not function with DNA. It lacks a separate proofreading endonuclease activity and has an error rate similar to that of RNA polymerase. Unlike the DNA and RNA polymerases, RNA replicases are specific for the RNA of their own virus the RNAs of the host cell are generally not replicated. This explains how RNA viruses are preferentially replicated in the host cell, which contains many other types of RNA. 

Postreplicational mismatch repair has been found to correct errors in base substitution occurring during DNA replication in prokaryotes.48 This lowers the error rate for the polymerase from 1 in 106 to 107 to the observed range of values of 1 in 108 to 1010 in E. coli. How does the repair system know in this case which base in a mispair is the incorrect one The answer appears to be that the parent strand is tagged by methylation. A small proportion, some 0.2%, of the cytosine residues are methylated at the 5 position, and a similar proportion of the adenine residues are methylated at the 6 position. As methylation is a postreplicative event, the daughter strand is temporarily undermethylated after replication. 

The first replicative units must have possessed considerably less information than the RNA viruses, which work with an optimized RNA-copying machinery. In the absence of efficiently adapted enzymes the accuracy of reproduction depends solely on the stability of the base pairs. Under these conditions the GC pair has a selective advantage over the AU pair of a factor of about 10. Model experiments show that for GC-rich polynucleotides the error rate per nucleotide can hardly be reduced below a value of 10-2. The first genes must accordingly have been polynucleotides with a chain length around 100 bases or less. 

Figure 11. The error threshold of replication and mutation in genotype space. Asexually reproducing populations with sufficiently accurate replication and mutation, approach stationary mutant distributions which cover some region in sequence space. The condition of stationarity leads to a (genotypic) error threshold. In order to sustain a stable population the error rate has to be below an upper limit above which the population starts to drift randomly through sequence space. In case of selective neutrality, i.e. the case of equal replication rate constants, the superiority becomes unity, Om = 1, and then stationarity is bound to zero error rate, pmax = 0. Polynucleotide replication in nature is confined also by a lower physical limit which is the maximum accuracy which can be achieved with the given molecular machinery. As shown in the illustration, the fraction of mutants increases with increasing error rate. More mutants and hence more diversity in the population imply more variability in optimization. The choice of an optimal mutation rate depends on the environment. In constant environments populations with lower mutation rates do better, and hence they will approach the lower limit. In highly variable environments those populations which approach the error threshold as closely as possible have an advantage. This is observed for example with viruses, which have to cope with an immune system or other defence mechanisms of the host.

Figure 12. The error threshold of replication and mutation in phenotype space. The genotypic error threshold approaches zero in the case of selective neutrality. Despite changing genotypes a phenotype may be conserved in evolution whenever it has higher fitness than the other phenotypes in the population. The concept of error threshold can easily be extended to competition between phenotypes. The distribution of phenotypes is stationary provided the error rate does not exceed the maximum value pmax which is a function of the mean fraction of nearest neighbors, X, and the superiority of the master phenotype, a. The illustration shows the position of the phenotypic error threshold in the X, p plane. Selective neutrality allows more errors to be tolerated and pmax increases accordingly with increasing X. If X approaches the inverse superiority, X — a-1, the tolerated error may grow to pmax = 1, and this means the phenotype will never be lost, no matter how many errors are made in replication.

Experimental results from an HTS assay are not the truth but merely an estimate of the true potency of a molecule. Because molecules are only measured one time in the HTS setting, there is a high degree of uncertainty. One thing that can be done is to look for highly similar molecules and treat them as pseudo replicates of the same parent molecule. See Goldberg (1978) for further discussion on estimating the error rate. 

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...

Fig. 2.6. Evolutionary design of biopolymers in selection cycles. Properties of biomolecules, for example binding to a target or catalytic function, are optimized iteratively through selection cycles. Each cycle consists of three phases (i) amplification, (ii) diversification by replication with problem adjusted error rates (or random synthesis), and (iii) selection. Amplification and di-...

A major goal of directed evolution of DNA polymerases has been to elucidate the structural elements that confer high fidelity during DNA replication. If DNA polymerases were to rely solely on the stability of nucleotides that aligned with template for discrimination of correct template-directed polymerization, the error frequency would be in the order of one mispaired nucleotide per 100 incorporated [23], The measured error rate for incorporation and extension of a mismatched nucleotide attributable to DNA polymerases lacking an error correcting exonucleolytic activity range... 

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