sequencespace

Sequence space is the set of all possible sequences formed from a given alphabet at a specified length. In biological contexts, the alphabet may be nucleotides (A, C, G, T or U) or amino acids, and the length corresponds to the number of positions in the sequence. The total number of sequences is k^L, where k is the alphabet size and L is the sequence length.

Formally, a sequence space can be viewed as the metric space (Sigma^L, d), where Sigma is the alphabet and d is a distance function. The most common metric is the Hamming distance, which counts the number of positions at which two sequences differ. In some settings, edit distance (accounting for insertions and deletions) is used. The sequence space can also be represented as a graph: each node is a sequence, and edges connect sequences that differ by a single substitution; for a binary alphabet this forms a hypercube of dimension L, and for larger alphabets it generalizes to k-ary Hamming graphs.

In evolutionary and computational biology, sequence space is paired with a fitness landscape that assigns a fitness value to each sequence. This enables the study of mutational pathways, robustness, and the accessibility of high-fitness genotypes. Key concepts include mutational steps, local optima, and ruggedness of the landscape, which influence evolutionary trajectories.

Applications include understanding protein evolution and design, RNA/DNA sequence optimization, and exploration of genotype–phenotype mappings. Limitations arise from the combinatorial explosion of possibilities as L grows, necessitating sampling, approximation, or heuristic search methods to study the vast sequence space.