Sequence space (evolution)

Although such overwhelming multidimensionality cannot be visualised or represented diagrammatically, it provides a useful abstract model to think about the range of proteins and evolution from one sequence to another.

[9] Enzyme superfamilies, therefore, exist as tiny clusters of active proteins in a vast empty space of non-functional sequence.

[14][15] In the Library of Babel, finding any book that made sense was impossible due to the sheer number and lack of order.

For example, in an extremely simplified view, all amino acids can be sorted into two classes (hydrophobic/polar) by hydrophobicity and still allow many common structures to show up.

Early life on Earth may have only four or five types of amino acids to work with,[16] and researches have shown that functional proteins can be created from wild-type ones by a similar alphabet-reduction process.

Protein sequence space can be represented as a space with n dimensions , where n is the number of amino acids in the protein. Each axis has 20 positions representing the 20 amino acids. There are 400 possible 2 amino acid proteins ( dipeptide ) which can be arranged in a 2D grid. the 8000 tripeptides can be arranged in a 3D cube. Most proteins are longer than 100 amino acids and so occupy large, multidimensional spaces containing an astronomical number protein sequences.
How directed evolution climbs fitness landscapes. Performing multiple rounds of directed evolution is useful not only because a new library of mutants is created in each round, but also because each new library uses better mutants as templates than the previous. The experiment is analogous to climbing a hill on a 'fitness landscape,' where elevation represents the desired property. The goal is to reach the summit, which represents the best achievable mutant. Each round of selection samples mutants on all sides of the starting template (1) and selects the mutant with the highest elevation, thereby climbing the hill. This is repeated until a local summit is reached (2).
How DNA libraries generated by random mutagenesis sample sequence space. The amino acid substituted into a given position is shown. Each dot or set of connected dots is one member of the library. Error-prone PCR randomly mutates some residues to other amino acids. Alanine scanning replaces each reside of the protein with alanine, one-by-one. Site saturation substitutes each of the 20 possible amino acids (or some subset of them) at a single position, one-by-one.