Optimal response to pathogen evolution in immune repertoires

In order to target threatening pathogens, the adaptive immune system performs a continuous reorganization of its repertoire of cells. Following an immune challenge, the B cell repertoire can evolve cells of increased specificity for the encountered strain. This process of affinity maturation generates a memory pool whose diversity and size remain difficult to predict. Here we assume that the immune system follows a strategy that maximizes the long term immune coverage and minimizes the short term metabolic costs associated with affinity maturation. This strategy is defined as an optimal decision process on a d-dimensional phenotypic space, where a pre-existing population of naive cells is sequentially challenged with a neutrally evolving strain. We unveil a trade-off between immune protection against future strains and the necessary reorganization of the repertoire. This plasticity of the repertoire drives the emergence of distinct regimes for the size and diversity of the memory pool, depending on the density of naive cells and on the mutation rate of the strain.