Towards a Mathematical Foundation of Immunology and Amino Acid Chains

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.