PAM matrix

The PAM matrix (Point Accepted Mutation matrix) is a family of scoring matrices used in protein sequence alignment to quantify the likelihood that one amino acid will be substituted for another during evolutionary divergence. Developed by Margaret Dayhoff in 1978, the PAM matrices were the first attempt to encode biochemical and evolutionary knowledge into the scoring functions of sequence alignment algorithms like the Needleman-Wunsch algorithm.

Dayhoff derived the PAM1 matrix by analyzing 1,572 observed mutations across 71 groups of closely related protein sequences. A PAM1 matrix represents an evolutionary distance of 1 accepted point mutation per 100 amino acids. Higher-numbered PAM matrices (PAM100, PAM250) are computed by extrapolating PAM1 through matrix multiplication, modeling greater evolutionary divergence. The underlying assumption is that amino acid substitutions follow a Markov chain — the probability of a future substitution depends only on the current state, not on the path taken to reach it.

The PAM matrices encode a subtle but crucial insight: amino acids with similar biochemical properties — similar size, charge, hydrophobicity — exchange more frequently than dissimilar ones. A leucine-to-isoleucine substitution, both small hydrophobic residues, scores positively. A cysteine-to-tryptophan substitution, wildly different in chemistry and structure, scores negatively. The matrix thus transforms the abstract string-matching problem of alignment into a physical inference problem about protein chemistry and evolutionary plausibility.

The PAM matrices have been largely superseded by BLOSUM matrices in modern bioinformatics, but Dayhoff's conceptual framework — that alignment scoring should reflect evolutionary and chemical reality, not arbitrary string distance — remains the foundation of all statistical approaches to sequence comparison.