The Rectangular BLOSUM matrices give scores to compare amino acid groups from different alphabets. In some indexing applications, memory constraints require some grouping of amino acids. The ReBLOSUM matrices can be used when only one alphabet is compressed : for example, a 4×20 matrix is far more precise than a square 4×4 matrix.
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BMC Bioinformatics. 2008 Dec 16;9:534. doi: 10.1186/1471-2105-9-534.
Optimal neighborhood indexing for protein similarity search.
Peterlongo P, Noé L, Lavenier D, Nguyen VH, Kucherov G, Giraud M.