1572 observed mutations in the phylogenetic trees of 71 families of closely related proteins. The proteins to be studied were selected on the basis of having high similarity with their predecessors. The protein alignments included were required to display at least 85% identity. As a result, it is reasonable to assume that any aligned mismatches were the result of a single mutation event, rather than several at the same location. Each PAM matrix has twenty rows and twenty columns — one representing each of the twenty amino acids translated by the genetic code. The value in each cell of a PAM matrix is related to the probability of a row amino acid before the mutation being aligned with a column amino acid afterwards. From this definition, PAM matrices are an example of a substitution matrix. Collection of data from phylogenetic trees For each branch in the phylogenetic trees of the protein families, the number of mismatches that were observed were recorded and a record kept of the two amino acids involved. These counts were used as entries below the main diagonal of the matrix . Since the vast majority of protein samples come from organisms that are alive today (extant species), the 'direction' of a mutation cannot be determined. That is, the amino acid present before the mutation cannot be distinguished from the amino acid that replaced it after the mutation. Because of this, the matrix is assumed to be symmetric, and the entries of above the main diagonal are computed on this basis. The entries along the diagonal of do not correspond to mutations and can be left unfilled. In addition to these counts, data on the mutability and the frequency of the amino acids was obtained. The mutability of an amino acid is the ratio of the number of mutations it is involved in and the number of times it occurs in an alignment. Mutability measures how likely an amino acid is to mutate acceptably. Asparagine, an amino acid with a small polar side chain, was found to be the most mutable of the amino acids. Cysteine and tryptophan were found to be the least mutable amino acids. The side chains for cysteine and tryptophan have less common structures: cysteine's side chain contains sulfur which participates in disulfide bonds with other cysteine molecules, and tryptophan's side chain is large and aromatic. Since there are several small polar amino