Sequence space

The set of candidate solutions considered by a search procedure is often called the search space of the problem. For molecular design problems, there are several possible search spaces, the most common being sequence space, the space of all molecules being considered [4,37-39], The concept of a sequence space is important because it provides a framework for formal theory and it has heuristic value in developing intuition for searches and communicating ideas. Sequence spaces are discrete, though search spaces in general may be discrete, continuous, or discrete on some axes and continuous on others. 

Sequence spaces may also be defined based on encoded libraries. In such libraries, different molecular species are labeled with readable tags that record the sequence of 

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The sequence space of proteins is extremely dense. The number of possible protein sequences is 20. It is clear that even by the fastest combinatorial procedure only a very small fraction of such sequences could have been synthesized. Of course, not all of these sequences will encode protein stmctures which for functional purjDoses are constrained to have certain characteristics. A natural question that arises is how do viable protein stmctures emerge from the vast sea of sequence space The two physical features of folded stmctures are (l)in general native proteins are compact but not maximally so. (2) The dense interior of proteins is largely made up of hydrophobic residues and the hydrophilic residues are better accommodated on the surface. These characteristics give the folded stmctures a lower free energy in comparison to all other confonnations. 

Figure C2.5.4. Schematic illustration of the stages in the drastic reduction of sequence space in tire process of evolution to functionally competent protein stmctures.

The reason(s) for the success of ISM has to do with the fact that sequence space has been confined to defined locations in the protein that are most likely to respond positively in an additive or cooperative manner. In sharp contrast, when performing several rounds of epPCR (4—8 are typical ), the whole protein is addressed repeatedly although only a fraction of the amino acid positions are important. Owing to statistical reasons, a given improved mutant (hit) evolved by ISM is not... 

Finally, the region of accessible protein sequence space was extended by developing a modified version of Stemmer s combinatorial multiple-cassette mutagenesis (CMCM)... 

These initial systematic studies regarding the directed evolution of PAL allowed several conclusions to be made. Protein sequence space can be explored successfully by applying the following strategies [8c,33j ... 

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. 

Robertson DE et al. (2004) Exploring nitrilase sequence space for enantioselective catalysis. Appl Environ Microbiol 70 2429-2436. 

Reetz MT, Wang LW, Bocola M (2006) Directed evolution of enantioselective enzymes iterative cycles of CASTing for probing protein-sequence space. Angew Chem Int Ed 45 1236-1241... 

Evaluation of protein sequence analysis methods based on the use of PSSMs in benchmarking experiments and in a number of test cases shows that these methods are capable of systematically detecting relationships between proteins that previously have been deemed tractable only at the structure-comparison level. Clearly, however, there is still a lot of room for improvement, as many automated procedures missed subtle connections that subsequendy have been revealed on a case-by-case basis, in part thanks to a careful choice of starting points for the PSSM construction. An exhaustive exploration of the sequence space by recursive iterative searching is likely to yield additional, on many occasions unexpected, links between proteins and, in particular, is expected to increase the rate of structure prediction. 

Clearly, all of these strategies for navigating in protein sequence space are successful, but it is not obvious which ones are optimal. 

The results of these and other experiments are summarized in Fig. 17. A total of only 40 000 mutants was screened, which is actually a small number in our context. It is likely that upon exploration of larger portions of protein sequence space efficiently, even better lipase-variants can be identified. The assumption that millions of potential variants in the vast protein sequence space are highly enan-tioselective is not unfounded. 

Dynamic combinatorial libraries (DCLs) are continuously interconverting libraries that evenmally evolve to an equilibrium distribution [61-65]. This approach has been used successfully in the discovery of stable supramolecular assemblies from mixtures. Due to the nearly endless possible peptide sequences that can potentially be synthesised, the DCL approach is attractive for the identification of supramolecular peptide interactions. Indeed, disulfide exchange between cysteine residues has been explored for this purpose [66, 67] as has peptide-metal binding [68]. We have recently demonstrated protease-catalysed amide exchange in this context, which allows for the evolution of the self-assembled peptide structures, and will therefore allow exploration of peptide sequence space for biomaterials design. 

In chemistry, one area that has received outstanding attention is that of RNA folding, shape, and evolution. Peter Schuster, Walter Fontana, Peter Stadler and their colleagues have made major contributions. Among the concepts here are energy landscapes for computer-folded models of RNA molecules, the evolution of model RNA sequences over these landscapes in sequence space, the folded shapes of model RNA sequences, and the existence of connected neutral pathways across sequence space among model RNA molecules that fold to the same shape. 

Jirholt, P., Ohlin, M., Borrebaeck, C.A.K., Soderlind, E. (1998). Exploiting sequence space Shuffling in vivo rearranged CDR into a master framework. Gene, 215, 471 -76. 

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