A Shannon entropy analysis of immunoglobulin and T cell receptor

In 1970, before any antigen-bound immunoglobulin structure had been solved, Elvin Kabat proposed that regions of high amino acid diversity would be the antigen binding sites of immunoglobulin (Kabat, 1970). Conversely, sites of low variability were proposed to be structural, framework regions. This variability was defined by Wu and Kabat as the number of different amino acids found at a site divided by the relative frequency of the most common amino acid at that site (Wu and Kabat, 1970). Several groups have subsequently devised improvements of Kabat-Wu variability analysis (Litwin and Jores, 1992). While these methods are somewhat better than Kabat Wu, they still suffer from Kabat-Wu's basic limitation: they account for only the most common one or two amino acids in estimating diversity. This leads to underestimates of low diversities and exaggerations of high diversities. Shannon information analysis eliminates serious bias and is more stable than Kabat-Wu and second generation measures of diversity (Jores et al. 1990; Wu and Kabat 1970). Statistical reliability can be measured using Shannon analysis, and Shannon measurements can be provided with error estimates. Here we use Shannon's method to analyze the amino acid diversity at each site of T cell receptor V α and V β to identify complementarity determining regions and framework sites. Our results reveal that the T cell receptor is significantly more diverse than immunoglobulin-suggesting T cell receptor has more than the previously-discovered four complementarity determining regions. These new complementarity determining regions may represent a larger antigen combining site, additional combining sites, or an evolutionary strategy to avoid inappropriate interaction with other molecules