Sequence space (evolution)

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.

In evolutionary biology, sequence space is a way of representing all possible sequences (for a protein, gene or genome).^[1] The sequence space has one dimension per amino acid or nucleotide in the sequence leading to highly dimensional spaces.^[2][3] Most sequences in sequence space have no function, leaving relatively small regions that are populated by naturally occurring genes. Evolution can be visualised as moving along these axes from one sequence to another by mutation.^[4]

Representation

A sequence space is usually laid out as a grid. For protein sequence spaces, each residue in the protein is represented by a dimension with 20 possible positions along that axis corresponding to the possible amino acids.^[5][6] Hence there are 400 possible dipeptides arranged in a 20x20 space but that expands to 10¹³⁰ for even a small protein of 100 amino acids arranges in a space with 100 dimensions. 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.

These highly multidimensional spaces can be compressed to 2 or 3 dimensions using principle component analysis. A fitness landscape is simply a sequence space with an extra vertical axis of fitness is added for each sequence.^[7]

Functional sequences in sequence space

Despite the diversity of protein superfamilies, sequence space is extremely sparsely populated by functional proteins. Most random protein sequences have no fold or function.^[8] Enzyme superfamilies, therefore, exist as tiny clusters of active proteins in a vast empty space of non-functional sequence.^[9][10]

The density of functional proteins in sequence space, and the proximity of different functions to one another is a key determinant in understanding evolvability.^[11] The degree of interpenetration of two neutral networks of different activities in sequence space will determine how easy it is to evolve from one activity to another. The more overlap between different activities in sequence space, the more cryptic variation for promiscuous activity will be.^[12]

References