A substitution matrix is a collection of scores for aligning nucleotides or amino acids with one another. These scores generally represent the relative ease with which one nucleotide or amino acid may mutate into or substitute for another, and they are used to measure similarity in sequence alignments. Substitution matrices are used in conjunction with gap costs to construct local or global alignments. A local alignment substitution matrix implicitly corresponds to a set of target frequencies for aligned letters, which characterise the alignments the matrix may most easily distinguish from chance. Thus different substitution matrices are optimal for comparing related sequences that have diverged to differing degrees. The point accepted mutation and blocks substitution matrix (BLOSUM) series of matrices for protein sequence comparison have been derived from collections of related sequences. Special-purpose matrices may be appropriate for comparing sequences with biased nucleotide or amino acid composition.

Key Concepts:

• Match/mismatch scores generally are suboptimal for comparing protein sequences.
  
• A log-odds substitution matrix is characterised by its target frequencies and scale.
  
• All local-alignment substitution matrices are implicitly log-odds matrices.
  
• Different substitution matrices are tailored to different degrees of evolutionary divergence.
  
• Amino acid substitution matrices are constructed from curated sets of alignments.
  
• The sequence divergence for which a substitution matrix is tailored may be measured by relative entropy.
  
• Special matrices may be preferred for comparing sequences with nonstandard nucleotide or amino acid composition.
  
• For gapped local alignments, statistical parameters must be estimated by random simulation.
  
• For protein-coding DNA, distant relationships are more easily detected at the protein than at the DNA level.
  
• For global alignments, an equivalent scoring system results from adding 2x to all substitution scores, and x to the score for each letter aligned with a null.