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The PAM matrices (also called Dayhoff PAM matrices) were first constructed by Margaret Dayhoff, who compiled alignments of seventy-one groups of very closely related protein sequences. PAM stands for “point accepted mutation”. Because of the use of very closely related homologs, the observed mutations were not expected to significantly change the common function of the proteins. Thus, the observed amino acid mutations are considered to be accepted by natural selection. These protein sequences were clustered based on phylogenetic reconstruction using maximum parsimony. The PAM matrices were subsequently derived based on the evolutionary divergence between sequences of the same cluster. One PAM unit is defined as 1% of the amino acid positions that have been changed. To construct a PAM1 substitution table, a group of closely related sequences with mutation frequencies corresponding to one PAM unit is chosen. Based on the collected mutational data from this group of sequences, a substitution matrix can be derived. Construction of the PAM1 matrix involves alignment of full-length sequences and subsequent construction of phylogenetic trees using the parsimony principle. This allows computation of ancestral sequences for each internal node of the trees. 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. Other PAM matrices with increasing numbers for more divergent sequences are extrapolated from PAM1 through matrix multiplication. For example, PAM80 is produced by values of the PAM1 matrix multiplied by itself eighty times. The mathematical transformation accounts for multiple substitutions having occurred in an amino acid position during evolution. For example, when a mutation is observed as F replaced by I, the evolutionary changes may have actually undergone a number of intermediate steps before becoming I, such as in a scenario of F → M → L → I. For that reason, a PAM80 matrix only corresponds to 50% of observed mutational rates. A PAM unit is defined as 1% amino acid change or one mutation per 100 residues. The increasing PAM numbers correlate with increasing PAM units and thus evolutionary distances of protein sequences. For example, PAM250, which corresponds to 20% amino acid identity, represents 250 mutations per 100 residues. In theory, the number of evolutionary changes approximately corresponds to an expected evolutionary span of 2,500 million years. Thus, the PAM250 matrix is normally used for divergent sequences. Accordingly, PAM matrices with lower serial numbers are more suitable for aligning more closely related sequences.

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