Mathematical Characterization of Private and Public Immune Repertoire Sequences

Abstract

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 use a general probabilistic model for T/B cell receptor clone abundances to define "publicness" or "privateness" and information-theoretic measures for comparing the frequency of sampled sequences observed across different individuals. We derive mathematical formulae to quantify the mean and the variances of clone richness and overlap. Our results can be used to evaluate the effect of different sampling protocols on abundances of clones within an individual as well as the commonality of clones across individuals. Using synthetic and empirical TCR amino acid sequence data, we perform simulations to study expected clonal commonalities across multiple individuals. Based on our formulae, we compare these simulated results with the analytically predicted mean and variances of the repertoire overlap. Complementing the results on simulated repertoires, we derive explicit expressions for the richness and its uncertainty for specific, single-parameter truncated power-law probability distributions. Finally, the information loss associated with grouping together certain receptor sequences, as is done in spectratyping, is also evaluated. Our approach can be, in principle, applied under more general and mechanistically realistic clone generation models.

arXiv comment35 pages, 8 figures, 1 table

References in corpus (11)

• Statistical inference of the generation probability of T-cell receptors from sequence repertoires
• Inferring processes underlying B-cell repertoire diversity
• Quantifying selection in immune receptor repertoires
• Replicate immunosequencing as a robust probe of B cell repertoire diversity
• Predicting the spectrum of TCR repertoire sharing with a data-driven model of recombination
• A Characterization of Entropy in Terms of Information Loss
• Bias Analysis in Entropy Estimation
• Early life imprints the hierarchy of T cell clone sizes
• Diversity in Biology: definitions, quantification, and models
• Exact steady-state distributions of multispecies birth-death-immigration processes: effects of mutations and carrying capacity on diversity
• Estimation of Distribution Overlap of Urn Models