Bayesian multivariate Poisson abundance models for T-cell receptor data

Abstract

A major feature of an adaptive immune system is its ability to generate B- and T-cell clones capable of recognizing and neutralizing specific antigens. These clones recognize antigens with the help of the surface molecules, called antigen receptors, acquired individually during the clonal development process. In order to ensure a response to a broad range of antigens, the number of different receptor molecules is extremely large, resulting in a huge clonal diversity of both B- and T-cell receptor populations and making their experimental comparisons statistically challenging. To facilitate such comparisons, we propose a flexible parametric model of multivariate count data and illustrate its use in a simultaneous analysis of multiple antigen receptor populations derived from mammalian T-cells. The model relies on a representation of the observed receptor counts as a multivariate Poisson abundance mixture (m PAM). A Bayesian parameter fitting procedure is proposed, based on the complete posterior likelihood, rather than the conditional one used typically in similar settings. The new procedure is shown to be considerably more efficient than its conditional counterpart (as measured by the Fisher information) in the regions of m PAM parameter space relevant to model T-cell data.

A Public Database of Memory and Naive B-Cell Receptor Sequences

“…Finally, the many-replicate experimental design employed in this study, in which each of the 188 PCR wells corresponds to a replicate sample, constitutes a sample abundance probe robust to the inherent stochasticity of PCR amplification. Moreover, this approach represents a crucial quantitative advance over previous sequencing studies of antigen receptor repertoire diversity, which have been limited by either poor quantitation or by the lower throughput of single-cell methods[ 27 , 62 , 63 ]. We expect that these data will be used by other experts in the field of immunology to address additional fundamental questions about BCR development and in vivo antigen binding in humans.…”

Estimating T-cell repertoire diversity: limitations of classical estimators and a new approach

“…Because the size of a sample is dwarfed by the size of the total population (and therefore sampling does not drastically alter clonotype relative abundances), these authors approximated the multivariate hypergeometric distribution using a Poisson distribution. Incorporation of a varying sampling rate for clonotypes of varying frequencies leads to the class of PAMs [ 41 , 82 ]. They applied their method to previously published data on mice with different phenotypes, and evaluated the consistency of their method by excluding clonotypes above successively higher cut-off frequencies.…”

“…Rempala et al [ 41 ] focused on one such model, the bivariate Poisson-lognormal distribution, and concluded that under-sampling in their repertoire datasets is more severe (and thus the population is more diverse) than would be estimated using the Good-Turing estimator [ 77 ]. Other extensions of the class of PAMs have been developed [ 41 , 82 ] that estimate the similarity between populations in the presence of unseen clonotypes.…”

Quantification of Inter-Sample Differences in T-Cell Receptor Repertoires Using Sequence-Based Information

“…This approach can overcome the substantial sampling fluctuations derived from the huge diversity in TCR repertoires and provides a stable result related to the inter-sample distances on the basis of statistical interpretations. Variations of PA models have also been proposed ( 8 – 10 ), and methods to combine both approaches were also developed recently. For example, Rempala et al ( 11 ) used a bivariate Poisson log-normal (BPLN) distribution to model joint abundance distributions for classifying eight different samples of the following sample conditions: donor sites, types of T cells, and the genetic backgrounds of different mouse lines.…”