The immune system is composed of a large number of heterogenous interacting components that collectively recognize and clear pathogens. To cover the high-dimensional molecular space of all possible threats, including those that have never been seen before, the adaptive immune system is endowed with a wide variety of receptor proteins, which are created by random cutting-and-pasting of the DNA in each cell. I will show how the rules of that process can be statistically learned from high-throughput sequencing data, and can be used to calculate its entropy and to predict accurately receptor overlap between individuals. I will then present a theoretical framework for thinking about optimal designs for enacting and encoding immune memory through the self-organisation of the repertoire.
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