Scoring matrices are used to determine the relative score made by matching two characters in a sequence alignment. There are many flavors of scoring matrices for amino acid sequences, nucleotide sequences, and codon sequences, and each is derived from the alignment of “known” homologous sequences. These are used to assign scores for comparison of pairs of characters. There are different types of scoring matrices like:

Amino acid substitution matrices, which are 20×20 matrices, have been devised to reﬂect the likelihood of residue substitutions. The substitution matrices apply logarithmic conversions to describe the probability of amino acid substitutions. The converted values are the so-called log-odds scores (or log-odds ratios), which are logarithmic ratios of the observed mutation frequency divided by the probability of substitution expected by random chance.

Construction of the PAM1 matrix involves alignment of full-length sequences and subsequent construction of phylogenetic trees using the parsimony principle. Ancestral sequence information is used to count the number of substitutions along each branch of a tree. The PAM score for a particular residue pair is derived from a multistep procedure involving calculations of relative mutability, normalization of the expected residue substitution frequencies by random chance, and logarithmic transformation to the base of 10 of the normalized mutability value divided by the frequency of a particular residue. The resulting value is rounded to the nearest integer and entered into the substitution matrix, which reﬂects the likelihood of amino acid substitutions. This completes the log-odds score computation. After compiling all substitution probabilities of possible amino acid mutations, a 20×20 PAM matrix is established. Positive scores in the matrix denote substitutions occurring more frequently than expected among evolutionarily conserved replacements. Negative scores correspond to substitutions that occur less frequently than expected.

BLOSUM is the series of blocks of amino acid substitution matrices, all of which are derived based on direct observation for every possible amino acid substitution in multiple sequence alignments. These were constructed based on more than 2,000 conserved amino acid patterns representing 500 groups of protein sequences. The sequence patterns, also called blocks, are ungapped alignments of less than sixty amino acid residues in length. The frequencies of amino acid substitutions of the residues in these blocks are calculated to produce a numerical table, or block substitution matrix. Instead of using the extrapolation function, the BLOSUM matrices are actual percentage identity values of sequences selected for construction of the matrices. For example, BLOSUM 62 shows that the sequences selected for constructing the matrix share an average identity value of 62%. Other BLOSUM matrices based on sequence groups of various identity levels have also been constructed.

The BLOSUM score for a particular residue pair is derived from the log ratio of observed residue substitution frequency versus the expected probability of a particular residue. The log odds are taken to the base of 2 instead of 10 as in the PAM matrices. The resulting value is rounded to the nearest integer and entered into the substitution matrix.

Identity Matrices: In this type of matrix, the score would either be 1’s or 0’s. 1’s will lie along the diagonal. Basically the scoring scheme is based on matches and mismatches.

Unitary scoring matrices: this matrix also has either 0’s or 1’s as their scores. The difference is that it takes into the idea of transitions (change among purines or pyrimidines) and transversions (change between purine and a pyrimidine).