BLOSUM substitution matrices

Fig. 4. Substitution matrix based on disordered protein families. Below the diagonal are the scores for each amino acid substitution. Above the diagonal are the differences between BLOSUM 62 and the disorder matrix. On the diagonal are the scores/differences. (From Radivojac et al., 2002, PSB 2002 7, 589-600, with permission of World Scientific Publishing Co. Pte Ltd.)...

Fig. 2. The BLOSUM 50 substitution matrix (Henikoff and Henikoff, 1992) lower) and the difference matrix upper) obtained by subtracting it from the Gonnet matrix (Gonnet et al., 1992) position by position.

From the examination of appropriately aligned sequences, substitution matrices can be deduced. In these matrices, a large positive score corresponds to a substitution that occurs relatively frequently, whereas a large negative score corresponds to a substitution that occurs only rarely. The Blosum-62 substitution matrix illustrated in Figure 7 9 is an example. The highest scores in this substitution matrix indicate that amino acids such as cysteine (C) and tryptophan (W) tend to be conserved more than those such as serine (S) and alanine (A). Furthermore, structurally conservative... 

Figure 7.12. Alignment of Human Myoglobin and Lupine Leghemoglobin. The use of the Blosum-62 substitution matrix yields the alignment shown between human myoglobin and lupine leghemoglobin, illustrating identities (orange) and conservative substitutions (yellow). These sequences are 23% identical.

Which alignment has a higher score if the identity-based scoring system (Section 7.2) is used Which alignment has a higher score if the Blosum-62 substitution matrix (Figure 7.9) is used ... 

However, using the Blosum-62 substitution matrix, the scores would be +7 for the first sequence and -12 for the second. Here is the result of summing the pairvhse values for alignments (a) and (b) using Figure 7.9 ("with -12 for a gap) ... 

PAM matrix PAM (percent accepted mutation) and BLOSUM (blocks substitution matrix) are matrices that define scores for each of the 210 possible amino acid substitutions. The scores are based on empirical substitution frequencies observed in alignments of database sequences and in general reflect similar physicochemical properties (e.g., a substitiution of leucine for isoleucine, two amino acids of similar hydrophobicity and size, will score higher than a substitution of leucine for glutamate.)... 

Specification of the relative rates of substitution among particular residues usually takes the form of a square matrix the nmnber of rows/colmnns is fom in the case of bases, 20 in the case of amino acids (e.g., in PAM and BLOSUM matrices), and 61 in the case of codons (excluding stop codons). The off-diagonal elements of the matrix correspond to the relative costs of going from one base to another. The diagonal elements represent the cost of having the same base in different sequences. 

The most widely used models of amino acid substitution include distance-based methods, which are based on matrixes such as PAM and BLOSUM. Again, such matrices are described fiuther in other chapters in this book. Briefly, Dayhoff s PAM 001 matrix (Dayhoff, 1979) is an empirical model that scales probabilities of change from one amino acid to another in terms of an expected 1% change between two amino acid sequences. This matrix is used to make a transition probability matrix that allows prediction of the probability of changing from one amino acid to another and also predicts equilibriiun amino acid composition. Phylogenetic distances are calculated with the assumption that the probabilities in the matrix are correct. The... 

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