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We can observe the composition of the immune system through high-throughput immune repertoire sequencing data, which give access to a subsample of the repertoire in a given instant, i.e., a list of lymphocyte receptors with their abundance. This is, however, an infinitesimal fraction of the whole repertoire at a given time point, also subject to experimental errors, making the extraction of quantitative information a hard task. I will show three examples where we tackle this challenge, focusing on different properties of the immune dynamics. The first is about the coevolution with HIV in infected patients, where we look for temporal correlations between the two evolutionary processes (of the virus and the immune repertoire), and we interpret the signal with population genetics models. The second uses an inference scheme that takes into account the experimental noise for finding receptors that are likely responding to vaccinations. The third uses a similar scheme to investigate the repertoire stability in healthy conditions, looking for the typical time scales that govern the immunological memory.