Email updates

Keep up to date with the latest news and content from BMC Bioinformatics and BioMed Central.

Open Access Research article

Amino acid "little Big Bang": Representing amino acid substitution matrices as dot products of Euclidian vectors

Karel Zimmermann12* and Jean-François Gibrat2

Author Affiliations

1 Université Pierre et Marie Curie (Paris VI), France

2 INRA, Mathématique, Informatique et Génome UR1077, F-78352 Jouy-en-Josas, France

For all author emails, please log on.

BMC Bioinformatics 2010, 11:4  doi:10.1186/1471-2105-11-4

Published: 4 January 2010



Sequence comparisons make use of a one-letter representation for amino acids, the necessary quantitative information being supplied by the substitution matrices. This paper deals with the problem of finding a representation that provides a comprehensive description of amino acid intrinsic properties consistent with the substitution matrices.


We present a Euclidian vector representation of the amino acids, obtained by the singular value decomposition of the substitution matrices. The substitution matrix entries correspond to the dot product of amino acid vectors. We apply this vector encoding to the study of the relative importance of various amino acid physicochemical properties upon the substitution matrices. We also characterize and compare the PAM and BLOSUM series substitution matrices.


This vector encoding introduces a Euclidian metric in the amino acid space, consistent with substitution matrices. Such a numerical description of the amino acid is useful when intrinsic properties of amino acids are necessary, for instance, building sequence profiles or finding consensus sequences, using machine learning algorithms such as Support Vector Machine and Neural Networks algorithms.