Mathematical models in the study of the amino acid sequence of HLA class I molecules in reference to their ability to present peptides

Abstract

T cell recognition of antigen requires that peptides derived from foreign or self-altered antigen be displayed within the cleft of a MHC molecule on the membrane of a cell. Considerable effort has focused on characterizing the specificity of MHC molecules in order to predict peptide binding. The similarity of HLA alleles in reference to their ability to present peptides to T cells is evaluated by calculating the correlation matrix between the binding affinity tables for the sets of peptides presented by each allele. This correlation matrix is an empirical similarity matrix between HLA alleles, and it is modeled in terms of possible structures defined in the metric space of HLA class I amino acid sequences. The following clusters of HLA class I molecules are identified in reference to their ability to present peptides: (Cluster I) HLA-A3/HLA-A11/HLA-A31/HLA-A33/HLA-A68; (Cluster II) HLA-B35/HLA-B51/HLA-B53/HLA-B54/HLA-B7/; and (Cluster III) HLA-A29/HLA-B61/HLA-B44. In modeling these natural clusters, the geometric structures with more predictive power confirm the importance of those positions in the peptide-binding groove, particularly those in the B pocket. Other positions (46, 79, 113, 144, and 177) not noticed before are also revealed to bear relevance in determining peptide-binding specificity. In addition, all known HLA class I alleles are classified into different clusters at four different levels. The binding specificity of peptides to MHC molecules is studied by representing amino acid sequences as vectors in a metric feature-space whose transformations make conceptual models of MHC peptide binding in terms of the amino acid sequence of the respective MHC alleles. Such models allow the prediction of peptide binding not only for those HLA class I alleles with sufficient data, but also for those alleles for which peptide binding data is not yet available. The use of this novel metric space approach with the application of geometric and algebraic concepts to study amino acid sequences and peptide-binding lead to the successful development of computational algorithms for MHC peptide-binding predictions which have important implications for the design of new peptide vaccines for clinical interventions.