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| |
|from |
|BLAST |
|By Joseph Bedell, |
|Ian Korf, |
|Mark Yandell |
|Publishe|: O'Reilly |
|r | |
|Pub Date|: July 2003|
|ISBN |: |
| |0-596-00299|
| |-8 |
|Pages |: 360 |
| | |









4.3 Scoring Matrices

A two-dimensional matrix containing all possible pair-wise amino acid
scores is called a scoring matrix. Scoring matrices are also called
substitution matrices because the scores represent relative rates of
evolutionary substitutions. Scoring matrices are evolution in a nutshell.
Take a moment now to peruse the scoring matrix in Figure 4-5 and compare it
to the chemical groupings in Figure 4-3.

Figure 4-5. BLOSUM62 scoring matrix

























Lod scores are real numbers but are usually represented as integers in text
files and computer programs. To retain precision, the scores are generally
multiplied by some scaling factor before converting them to integers. For
example, a lod score of -1.609 nats may be scaled by a factor of two and
then rounded off to an integer value of -3. Scores that have been scaled
and converted to integers have a unitless quantity and are called raw
scores.

4.3.1 PAM and BLOSUM Matrices

Two different kinds of amino acid scoring matrices, PAM (Percent Accepted
Mutation) and BLOSUM (BLOcks SUbstitution Matrix), are in wide use. The PAM
matrices were created by Margaret Dayhoff and coworkers and are thus
sometimes referred to as the Dayhoff matrices. These scoring matrices have
a strong theoretical component and make a few evolutionary assumptions. The
BLOSUM matrices, on the other hand, are more empirical and derive from a
larger data set. Most researchers today prefer to use BLOSUM matrices
because in silico experiments indicate that searches employing BLOSUM
matrices have higher sensitivity.
There are several PAM matrices, each one with a numeric suffix. The PAM1
matrix was constructed with a set of proteins that were all 85 percent or
more identical to one another. The other matrices in the PAM set were then
constructed by multiplying the PAM1 matrix by itself: 100 times for the
PAM100; 160 times for the PAM160; and so on, in an attempt to model the
course of sequence evolution. Though highly theoretical (and somewhat
suspect), it is certainly a reasonable approach. There was little protein
sequence data in the 1970s when these matrices were created, so this
approach was a good way to extrapolate to larger distances.
Protein databases contained many more sequences by the 1990s so a more
empirical approach was possible. The BLOSUM matrices were constructed by
extracting ungapped segments, or blocks, from a set of multiply aligned
protein families, and then further clustering these blocks on the basis of
their percent identity. The blocks used to derive the BLOSUM62 matrix, for
example, all have at least 62 percent identity to some other member of the
block.
Why, then, are the BLOSUM matrices better than the PAM matrices with
respect to BLAST? One possible answer is that the extrapolation employed in
PAM matrices magnifies small errors in the mutation probabilities for short
evolutionary time periods. Another possibility is that the forces governing
sequence evolution over short evolutionary times are different from those
shaping sequences over longer intervals, and you can't estimate distant
substitution frequencies without alignments from distantly related
proteins.



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