In many applications in biology, engineering and economics, identifying similarities and differences between distributions of data from complex processes requires comparing finite categorical samples of discrete counts. Statistical divergences quantify the difference between two distributions. However, their estimation is very difficult and empirical methods often fail, especially when the samples are small. We develop a Bayesian estimator of the Kullback-Leibler divergence between two probability distributions that makes use of a mixture of Dirichlet priors on the distributions being compared. We study the properties of the estimator on two examples: probabilities drawn from Dirichlet distributions, and random strings of letters drawn from Markov chains. We extend the approach to the squared Hellinger divergence. Both estimators outperform other estimation techniques, with better results for data with a large number of categories and for higher values of divergences.

The development of the human immune system lasts for several years after birth. The impact of this maturation phase on the quality of adaptive immunity and the acquisition of immunological memory after infection at a young age remains incompletely defined. Here, using an antigen-reactive T cell (ARTE) assay and multidimensional flow cytometry, we profiled circulating severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2)-reactive CD3(+)CD4(+)CD154(+) T cells in children and adults before infection, during infection, and 11 months after infection, stratifying children into separate age groups and adults according to disease severity. During SARS-CoV-2 infection, children younger than 5 years old displayed a lower antiviral CD4(+) T cell response, whereas children older than 5 years and adults with mild disease had, quantitatively and phenotypically, comparable virus-reactive CD4(+) T cell responses. Adults with severe disease mounted a response characterized by higher frequencies of virus-reactive proinflammatory and cytotoxic T cells. After SARS-CoV-2 infection, preschool-age children not only maintained neutralizing SARS-CoV-2-reactive antibodies postinfection comparable to adults but also had phenotypically distinct memory T cells displaying high inflammatory features and properties associated with migration toward inflamed sites. Moreover, preschool-age children had markedly fewer circulating virus-reactive memory B cells compared with the other cohorts. Collectively, our results reveal unique facets of antiviral immunity in humans at a young age and indicate that the maturation of adaptive responses against SARS-CoV-2 toward an adult-like profile occurs in a progressive manner.

One of the feats of adaptive immunity is its ability to recognize foreign pathogens while sparing the self. During maturation in the thymus, T cells are selected through the binding properties of their antigen-specific T-cell receptor (TCR), through the elimination of both weakly (positive selection) and strongly (negative selection) self-reactive receptors. However, the impact of thymic selection on the TCR repertoire is poorly understood. Here, we use transgenic Nur77-mice expressing a T-cell activation reporter to study the repertoires of thymic T cells at various stages of their development, including cells that do not pass selection. We combine high-throughput repertoire sequencing with statistical inference techniques to characterize the selection of the TCR in these distinct subsets. We find small but significant differences in the TCR repertoire parameters between the maturation stages, which recapitulate known differentiation pathways leading to the CD4 + and CD8 + subtypes. These differences can be simulated by simple models of selection acting linearly on the sequence features. We find no evidence of specific sequences or sequence motifs or features that are suppressed by negative selection. These results favour a collective or statistical model for T-cell self non-self discrimination, where negative selection biases the repertoire away from self recognition, rather than ensuring lack of self-reactivity at the single-cell level.

One of the feats of adaptive immunity is its ability to recognize foreign pathogens while sparing the self.During maturation in the thymus, T cells are selected through the binding properties of their antigen-specific T-cell receptor (TCR), through the elimination of both weakly (positive selection) and strongly (negative selection) self-reactive receptors. However, the impact of thymic selection on the TCR repertoire is poorly understood. Here, we use transgenic Nur77-mice expressing a T-cell activation reporter to study the repertoires of thymic T cells at various stages of their development, including cells that do not pass selection. We combine high-throughput repertoire sequencing with statistical inference techniques to charactarize the selection of the TCR in these distinct subsets. We find small but significant differences in the TCR repertoire parameters between the maturation stages, which recapitulate known differentiation pathways leading to the CD4+ and CD8+ subtypes. These differences can be simulated by simple models of selection acting linearly on the sequence features. We find no evidence of specific sequences or sequence motifs or features that are suppressed by negative selection. These results are consistent with a collective or statistical model for T-cell specificity, where negative selection biases the repertoire away from self recognition, rather than ensuring lack of self-reactivity at the single-cell level.