Sequence Comparison.pdf

150 8 Scoring Matrices
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Fig. 8.1 The correspondence between the PAM evolutionary distances and the dissimilarity levels.
There is no general theory on constructing scoring matrices for local alignments
with gaps. One issue in gapped alignment is to select appropriate gap costs. In Section
8.7, we briefly discuss the affine gap cost model and related issues in gapped
alignment.
We conclude the chapter with the bibliographic notes in Section 8.8.
8.1 The PAM Scoring Matrices
The PAM matrices are the first amino acid substitution matrices for protein sequence
comparison. Theses matrices were first constructed by Dayhoff and coworkers based
on a Markov chain model of evolution. A point accepted mutation in a protein is
a substitution of one amino acid by another that is “accepted” by natural selection.
For a mutation to be accepted, the resulting amino acid must have the same function
as the original one. A PAM unit is an evolutionary time period over which 1% of
the amino acids in a sequence are expected to undergo accepted mutations. Because
a mutation might occur several times at a position, two protein sequences that are
100 PAM diverged are not necessarily different in every position; instead, they are
expected to be different in about 52% of positions. Similarly, two protein sequences
that are 250 PAM diverged have only roughly 80% dissimilarity. The correspondence
between the PAM evolutionary distance and the dissimilarity level is shown
in Figure 8.1.
Dayhoff and her coworkers first constructed the amino acid substitution matrix
for one PAM time unit, and then extrapolated it to other PAM distances. The
construction started with 71 blocks of aligned protein sequences. In each of these
blocks, a sequence is no more than 15% different from any other sequence. The high
within-block similarity was imposed to minimize the number of substitutions that
may have resulted from multiple substitutions at the same position.