A computable probability landscape for T cell receptor repertoire sampling and comparison

Finite sampling complicates interpretation and comparison of T cell receptor (TCR) repertoires. We introduce BEAM, a probability model for TCR{beta} complementarity-determining region 3 amino-acid sequences that combines local sequence dependence with exact normalisation. Its tractable local structure permits deterministic evaluation of sequence-pattern probabilities and sampling expectations without enumerating or Monte Carlo sampling the sequence domain. A reference built from 38,538 human repertoires links sampling depth to expected sequence recovery, recurrence, overlap and publicness, the number of cohort repertoires containing a sequence. Models built from individual repertoires define distances attributable to sequence lengths and local patterns. BEAM improves held-out sequence prediction over controls matched for length and individual-position frequencies, ranks sequence publicness in an external cohort and matches CD4 and CD8 repertoires across independent studies. BEAM therefore provides a tractable observational probability landscape for depth-aware sampling calculations and interpretable repertoire comparison.