Many sequence alignment programs use the BLOSUM62 score matrix to score pairs of aligned residues. Where did BLOSUM62 come from?
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References
Henikoff, J.G. Amino acid substitution matrices from protein blocks. Proc. Natl. Acad. Sci. USA 89, 10915–10919 (1992).
Karlin, S. & Altschul, S.F. Methods for assessing the statistical significance of molecular sequence features by using general scoring schemes. Proc. Natl. Acad. Sci. USA 87, 2264–2268 (1990).
Altschul, S.F. Amino acid substitution matrices from an information theoretic perspective. J. Mol. Biol. 219, 555–565 (1991).
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Supplementary Notes
A program for taking a (possibly arbitrary) alignment score matrix and back-calculating the implied target frequencies pab. (DOC 81 kb)
Doing this requires solving for a nonzero lambda in: \sum_ab f_a f_b e{\lambda s_ab} = 1 and this is a good excuse to demo two methods of root-finding: bisection search and the Newton/Raphson method.
The program is ANSI C, and should compile on any machine with a C compiler: % cc -o lambda lambda.c -lm Any questions about this program should be addressed directly to the author.
Further study
Further study
You can download an ANSI C program for calculating the implicit target frequencies pab of a score matrix (see Supplementary Notes). The BLOSUM62 score matrix and its background frequencies are included as an example. The code also contains two basic methods of solving for roots of equations like the one for λ: the bisection method, and the Newton/Raphson method.
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Eddy, S. Where did the BLOSUM62 alignment score matrix come from?. Nat Biotechnol 22, 1035–1036 (2004). https://doi.org/10.1038/nbt0804-1035
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DOI: https://doi.org/10.1038/nbt0804-1035
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