Mutants, sequence space, Hamming

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...

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-...

---