12-Error mutants

One approach to calculating the stationary mutant distributions for longer sequences is to form classes of sequences within the quasi-species. These classes are defined by means of the Hamming distance between the master sequence and the sequence under consideration. Class 0 contains the master sequence exclusively, class 1 the v different one-error mutants, class 2 all v(v —1)/2 two-error mutants, and so on. In general we have all (JJ) fe-error mutants in class k. In order to be able to reduce the 2 -dimensional eigenvalue problem to dimension v 1, we make the assumption that all formation rate constants are equal within a given class. We write Aq for the master sequence in class 0, Ai for all one-error mutants in class 1, 4 2 for all two-error mutants in class 2, and in general A for all k error mutants in class k. 

New variables are introduced for the relative concentrations of the sum of all k-error mutants ... 

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.

At large values of the accuracy of replication (g 1) we observe a quasispecies characteristic for direct replication, /n 2/ predominantly. The master sequence Iq is most frequent, followed by some one-error mutants, two-error mutants, and so on. 

The second example (Figure 15) considers two distant degenerate sequences Iq and /30, with d(0, 30) = 4. Accordingly, we observe selection in the limit q->l. The sequence with more efficient one-error mutants (/30) is selected. In the domain of complementary replication we are dealing with two... 

In order to characterize the distributions of selective values in the second and the third model, we explored the value landscape by a Monte Carlo search. We created three random samples of 38,000 different sequences each (one repeat with 76,000 sequences gave essentially the same results) with predetermined ratios of probabilities for (0/1) digits, Pi = 0.2857, p2 = 0.5, and p3 = 0.7143, which led to mutant distributions centered at the 20-, 35-, and 50-error mutants of the all-zero sequence Iq. Three different parts of the value landscapes determined by Eqs. (IV.9)-(IV.ll) were explored in that way. The results are shown in Figure 22. 

Figure 22. Distribution of selective values in sequence space. Here 38,000 different sequences of length V = 70 generated by introducing digits 1 at random with probabiiity p i = 0.2857, P2 = 0.5, or P3 = 0.7143 into all-zero sequence /q- This produces Gaussian shape samples centered around 20-, 35-, and 50-error mutants of all-zero sequence. Distributions of free energy AG(. k) and excess productions — shown for regions located at mean Ham-...

Figure 23. Partitioning of excess productions E t) into replication (Aj) and degradation (Dj) rate constants. Upper and lower plots show distributions sampled from neighborhoods of 35- and 20-error mutants, respectively, as explained in the caption to Figure 22. Fraction of lethal variants in replication landscape A (this is the fraction of sequences with = 0) it amounts to 0.18 in this particular case has been cut off in order to show details of distribution at positive rate constants.

The results of classical neutral theory are valid only for systems of relatively low population numbers and large genomes. If the genome is large enough that even the 3v one-error mutants cannot be populated because the population number n is smaller than 3v, one may expect the results of so-called neutral theory to be representative. Otherwise, modifications due to the reproducible population of (nearly) neutral mutants, as indicated by the deterministic quasi-species model, pertain and finally destroy the basic assumption of the blind production of mutants at the periphery of the mutant spectrum. 

Figure 26. In serial dilution experiment, Spiegelman [73, 74] and co-workers obtained three successive mutants with increased adaptation to presence of ethidium bromide, a drug that interferes with replication. Experiment starts with population of 10 MDV strands (variant of Q -RNA comprising about 220 nucleotides that is well-adapted to Q -RNA-replicase). Population is amplified to about 10 copies and subsequently diluted to initial concentration. Iteration of this procedure led to final product, three-error mutant that was obtained after about 40 iterations. As replication rate data show, mutant is slightly inferior to wild type in absence of ethidium bromide but twice as efficient as wild type at final concentration of ethidium bromide.

Pseudomonas aeruginosa lipase-catalyzed hydrolysis of racemic ester 23 proceeds with very low enantioselectivity E = 1.1). Sequential use of error-prone PCR, saturation mutagenesis at chosen spots and DNA shuffling resulted in the formation of a mutant whose enantioselectivity was over 50. 

Figure 3.4 Improvement of the activity of chimeric NRPSs using directed evolution. (1) A heterologous A domain is swapped into an NRPS, typically resulting in a significant loss of synthetase activity. (2) A library of chimeric synthetase mutants is constructed in which the heterologous A domain has been diversified (for example, by error-prone PCR). (3) The library is subjected to an in vivo screen for production of the unnatural nonribosomal peptide derivative. (4) Clones showing improved production are characterized and subjected to further rounds of diversification and screening...

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. 

Fig. 7.11. The rate of ubiquitination by the SCF - is dependent on the lysine-destruction motif spacing. (A) Sequences of the wild type and mutant / -catenin and kBa peptides, with the destruction motif and ubiquitinated lysine(s) highlighted. (B) Time courses of ubiquitination of the wild-type and mutant peptides, visualized by Coomassie staining. (C) The reaction yields plotted with error bars from four experiments. (D) The...

The observation that bile acids cause DNA damage (Table 3.4) suggests that bile acids should increase the frequency of mutation since unrepaired DNA damage causes replication errors. Table 3.5 lists the studies showing that bile acids cause an increase in mutant cells in the GI tract. In vitro, DOC treatment... 

The WT lipase leads to an ee value of only 38% in favor of the (If ,45) enantiomer. The application of low-error epPCR increased the enantioselectivity slightly, but high-error rate epPCR turned out to be more successful, with several mutants showing ee values of 54-58% (45,137). The results are in line with the experience gained in the Pseudomonas aeruginosa lipase project (Section IV.A. 1). Of course, a library produced by high mutation rate can also contain hits that have only one amino acid exchange, and this was indeed observed in several cases. 

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