Model for comparative analysis of antigen receptor repertoires

Abstract

In modern molecular biology one of the standard ways of analyzing a vertebrate immune system is to sequence and compare the counts of specific antigen receptor clones (either immunoglobulins or T-cell receptors) derived from various tissues under different experimental or clinical conditions. The resulting statistical challenges are difficult and do not fit readily into the standard statistical framework of contingency tables primarily due to the serious under-sampling of the receptor populations. This under-sampling is caused, on one hand, by the extreme diversity of antigen receptor repertoires maintained by the immune system and, on the other, by the high cost and labor intensity of the receptor data collection process. In most of the recent immunological literature the differences across antigen receptor populations are examined via non-parametric statistical measures of the species overlap and diversity borrowed from ecological studies. While this approach is robust in a wide range of situations, it seems to provide little insight into the underlying clonal size distribution and the overall mechanism differentiating the receptor populations. As a possible alternative, the current paper presents a parametric method that adjusts for the data under-sampling as well as provides a unifying approach to a simultaneous comparison of multiple receptor groups by means of the modern statistical tools of unsupervised learning. The parametric model is based on a flexible multivariate Poisson-lognormal distribution and is seen to be a natural generalization of the univariate Poisson-lognormal models used in the ecological studies of biodiversity patterns. The procedure for evaluating a model's fit is described along with the public domain software developed to perform the necessary diagnostics. The model-driven analysis is seen to compare favorably vis a vis traditional methods when applied to the data from T-cell receptors in transgenic mice populations.

Methods for diversity and overlap analysis in T-cell receptor populations

“…Each dataset consists of the counts of different TCRs in thymic T-cells derived from the transgenic ‘TCRmini’ mice (for a detailed description of the ‘TCRmini’ animal model, see Pacholczyk et al 2007; Rempala et al 2011) and represents a different stage in T-cells evolution. One dataset consists of the so-called ‘regulatory’ T-cells, expressing the FoxP3 protein (via the green fluorescent protein or GFP), whereas another one consists of the so-called ‘naive’ T-cells, which do not express the FoxP3 marker.…”

Non-random distribution of methyl-CpG sites and non-CpG methylation in the human rDNA promoter identified by next generation bisulfite sequencing

“…The threshold value Thres=0.5 was used, as suggested by the 10-fold cross-validation procedure. Overall, the similarity pattern analysis based on mcc followed the previously reported approach (Rempala et al 2011). The permutation test was used to determine similarity of the clusters between donor groups.…”

Bayesian multivariate Poisson abundance models for T-cell receptor data

“…the number of distinct clonotypes) by M and regard it as a parameter in the subsequent analysis of the m TCR repertoires of interest (in our specific data example below, m =4). Since PAM assumes (see, e.g., Chao, 2006; Rempala et al, 2011) that the recorded counts are arriving from a mixture of Poisson processes in some time interval, we consider therefore the observed counts of the ith clonotype ( i = 1, …, M ) as arriving according to an m -variate Poisson process with the marginal rates ( λ 1 , λ 2 , …, λ m ). If the detectability of individuals are assumed to be equal across all clonotypes (which is typically the case in TCR repertoire sequencing), then the rates may be interpreted as clonal species abundances (Nayak, 1991).…”

“…Rempala et al, 2011), they have suffered from a potentially very inefficient method of parameter estimation based on the truncated conditional (or partial) likelihood. Consequently, although they were able to deal with (iii) and to some extent with (ii) above, it was much harder for the conditionally fitted m PAMs to properly address the clonal diversity (i).…”