Selection sequence space

The choice of the particular upward pathway in the kinetic resolution of rac-19, that is, the specific order of choosing the sites in ISM, appeared arbitrary. Indeed, the pathway B C D F E, without utilizing A, was the first one that was chosen, and it led to a spectacular increase in enantioselectivity (Figure 2.15). The final mutant, characterized by nine mutations, displays a selectivity factor of E=115 in the model reaction [23]. This result is all the more remarkable in that only 20000 clones were screened, which means that no attempt was made to fully cover the defined protein sequence space. Indeed, relatively small libraries were screened. The results indicate the efficiency of iterative CASTing and its superiority over other strategies such as repeating cycles of epPCR. 

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.

Effect of initial copy number For large sequence spaces, a library can only include a small fraction of all possible sequences. The maximally diverse library, the most likely type of library to result from random sampling of a large sequence space, has only one copy of each sequence. Having only one copy is a major source of noise and error in the selection. For example, in all our simulations, increasing the initial copy number of all species from 1 drastically increases both the mole fraction of the best phage and the library s average affinity in all rounds. 

Fig. 3. Neutral networks in sequence space. Depending on the fraction of nearest neighbors that are selectively neutral (X), the network is either partitioned into a largest component, the so-called giant component, and many small components (A X< Xcr) or it consists of a single component, usually spanning the whole sequence space (B X >Xcr). In case of RNA secondary structures, common structures form connected networks of type B.

Third, we have selected aptamers that can bind to the 3II isozyme of protein kinase C from an RNA pool that spanned 120 random positions [5], The aptamers fell into several families, and individuals from two of the most prominent families were assayed for their ability to inhibit the enzymatic activity ofPKC. While these aptamers efficiently inhibited the enzymatic activity of the 3II isozyme, they had a 10-fold lower K, for the 3I isozyme (96% similar) and showed no activity against the a isozyme (80% similar). These specificities rival those seen with monoclonal antibodies. We have now selected aptamers that can bind to the a isozyme ofPKC from the same RNA pool. Sequence comparisons of the anti-pil and anti-a aptamers (Fig. 13) suggest that the map that relates target space and sequence space is convoluted. For example, while one family of aptamers was returned from both selections, other families were unique for one or the other isozyme. 

Fig. 18. Generalized diffusion constants for diffusion in sequence space (solid line) and diffusion in structure space (dotted line) as a function of the fitness cutoff Fciit. As / increases, the selection strength increases. Diffusion in structure space is more dependent on Fcnt than diffusion in sequence space. Reprinted from Govindarajan and Goldstein (1997b) with permission.

Variation and selection turns out to be an enormously potent tool for improvement also in vitro. Why this is so, does not trivially follow from the nature of random searches. The efficiency of Monte-Carlo methods may work very poorly as we know from other optimization problems. The intrinsic regularities of genotype-phenotype mappings with high degrees of neutrality and very wide scatter of the points in sequence space, which lead to the same or very similar solutions, are the clues to evolutionary success. 

It is in the realm of very large combinatorial libraries that selection rather than screening gains crucial importance. As the focus shifts from randomizing an eight-residue peptide to a 100 amino acid protein (the typical size of a small functional domain, for example a chorismate mutase domain), the number of sequence permutations rises to an astronomical 20100. The ability to assay even a tiny fraction of this sequence space in directed molecular evolution experiments demands selection, even though initial development of an appropriate system may be considerably more involved than the setup of a screening procedure. 

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