The immune system uses many strategies to generate its enormous repertoire of diverse antibodies, but their relative importance is not understood. Here we address the contribution of antibody gene libraries to the antibody repertoire. We introduce a general framework, in which we can study many antibody-pathogen matching rules, including the widely-used shape-space model (Perelson and Oster, 1979). We use the genetic algorithm as a model of evolution to investigate the type of antibody repertoires that might evolve in relation to a given pathogenic environment. For the antibody/pathogen matching rules that we studied, the scaling relation between fitness and the size of the evolved antibody library is only a shifted variant of the scaling relation that we obtain with random libraries of the same size. We discuss how our results compare to the antibodies that are expressed in newborns, and we discuss the implications of our results for recent experiments with phage antibody libraries.
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