  We attempt to set a mathematical foundation of immunology and amino acid
chains. To measure the similarities of these chains, a kernel on strings is
defined using only the sequence of the chains and a good amino acid
substitution matrix (e.g. BLOSUM62). The kernel is used in learning machines to
predict binding affinities of peptides to human leukocyte antigens DR (HLA-DR)
molecules. On both fixed allele (Nielsen and Lund 2009) and pan-allele (Nielsen
et.al. 2010) benchmark databases, our algorithm achieves the state-of-the-art
performance. The kernel is also used to define a distance on an HLA-DR allele
set based on which a clustering analysis precisely recovers the serotype
classifications assigned by WHO (Nielsen and Lund 2009, and Marsh et.al. 2010).
These results suggest that our kernel relates well the chain structure of both
peptides and HLA-DR molecules to their biological functions, and that it offers
a simple, powerful and promising methodology to immunology and amino acid chain
studies.
