PAM matrices (Percent Accepted Mutation, Accepted Point Mutation( APM -> PAM))

Those matrices, estimated using 1572 changes in 71 groups of protein sequences in which over 85% similar, indicate the likelihood of change from one amino to another in homologous protein sequences during short-term evolution. The change of an amino acid at particular site is assumed to be independent of previous mutation; i.e. the probability of amino acid A to B is the same in any sequences, regardless of the previous changes at the site. Thus the substitutions in a protein sequence are concerned as Markov Model – the change state in a system does not depend on the previous state. This is the reason why PAM matrices cover longer periods of evolutionary time. Using closely related protein groups, the amino acid substitutions will be gaccepted mutationsh by natural selection.

PAM-N matrix means that PAM-1 matrix, each amino acid changing to another is ~1%, or 99% identical, is multiplied by itself N times; PAM250 represents 250% change expected in 2500 million years.

 

Calculation

Step 1. Organizing given protein sequences into a phylogenetic tree

Step 2. Count each amino acid change into every other amino acid

Step 3. Calculate mutabilities for normalizing biased sequence characteristics; counted the number of changes in each amino acid is divided by a factor, derived from the frequency of occurrence of the amino acid in that sequence group and total number of amino acid changing in that group per 100 sites

Step 4. Multiply counted exchanges and the mutabilities.

Step 5. The fraction of amino pair(i,j) changes over all changes of i to any other amino acid to get mutation probability score. Thus 20x20 matrix (PAM1) is created.

Step 6. Multiply PAM1 and itself by N times.

Step 7. Calculate the log odds values; in the case of amino acid pair (I,J), I changes to J, the score Sij is divided by the frequency Fij, X=Sij / Fij, then  X is converted to a logarithm to the base 10 ( log10 X = Xf). Xf is multiplied by 10 for discarding fractional values (Xf * 10 = Yij). Similarly, Yji is calculated. The PAM250 score in pair(ij) (= pair(ji) is the average of Yij and Yji.

 

The log odds values in PAM250 lie within the range of –8 to 17. zero means that the frequency of the substitution between a matched pair of amino acids is as expected by chance. Negative or positive values indicate that the frequency is less than or greater than that expected by chance.

 

Ref. [17]
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