  In order to target threatening pathogens, the adaptive immune system performs
a continuous reorganization of its lymphocyte repertoire. 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. 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 finite
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.
The model predicts power-law distributions of clonotype sizes observed in data,
and rationalizes antigenic imprinting as a strategy to minimize metabolic costs
while keeping good immune protection against future strains.
