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The complexity of entire T cell receptor (TCR) repertoires makes their comparison a difficult but important task. Current methods of TCR repertoire comparison can incur a high loss of distributional information by considering overly simplistic sequence- or repertoire-level characteristics. Optimal transport methods form a suitable approach for such comparison given some distance or metric between values in the sample space, with appealing theoretical and computational properties. In this paper we introduce a nonparametric approach to comparing empirical TCR repertoires that applies the Sinkhorn distance, a fast, contemporary optimal transport method, and a recently-created distance between TCRs called TCRdist. We show that our methods identify meaningful differences between samples from distinct TCR distributions for several case studies, and compete with more complicated methods despite minimal modeling assumptions and a simpler pipeline. Author summary T cells are critical for a successful adaptive immune response, largely due to the expression of highly diverse receptor proteins on their surfaces. These T cell receptors (TCRs) recognize peptides that may be foreign invaders such as viruses or bacteria. Because of this, immunologists are often interested in comparing different sets (or repertoires) of these TCRs in hopes of identifying groups of particular interest, such as TCRs that are responding to a particular vaccination using pre- and post-vaccination samples. Current methods of comparing TCR repertoires either rely on statistical models which may not adequately describe the data, use summary statistics that may lose information, or are difficult to interpret. We present a complementary method of comparing TCR repertoires that detects significantly different TCRs between two given repertoires using a distance rather than a model, summary statistics, or dimension reduction. We demonstrate that our method can identify biologically meaningful repertoire differences using several case studies.