Mathematical Characterization of Private and Public Immune Repertoire Sequences

Diverse T and B cell repertoires play an important role in mounting effective immune responses against a wide range of pathogens and malignant cells. The number of unique T and B cell clones is characterized by T and B cell receptors (TCRs and BCRs), respectively. Although receptor sequences are generated probabilistically by recombination processes, clinical studies found a high degree of sharing of TCRs and BCRs among different individuals. In this work, we formulate a mathematical and statistical framework to quantify receptor distributions. We define information-theoretic metrics for comparing the frequency of sampled sequences observed across different individuals. Using synthetic and empirical TCR amino acid sequence data, we perform simulations to compare theoretical predictions of this clonal commonality across individuals with corresponding observations. Thus, we quantify the concept of “publicness” or “privateness” of T cell and B cell clones. Our methods can also be used to study the effect of different sampling protocols on the expected commonality of clones and on the confidence levels of this overlap. We also quantify the information loss associated with grouping together certain receptor sequences, as is done in spectratyping.