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 a...

Introduction In just a few years, molecular diversity techniques have revolutionized pharmaceutical design and experimental methods for studying receptor binding, consensus sequences, genetic regu- latory mechanisms, and many other issues in biochemistry and chemistry [30, 69 71, 78, 79]. Because of the enormous libraries of ligands that can be used and the rapidity of the techniques, methods of applied molecular evolution such as SELEX and phage display have become particularly popular [30, 78, 86,126,127, 142,151]. These methods have been enormously successful, yet the theoretical work developed for them so far is quite limited. The success of these methods is not trivial: the huge number of sequences being searched through, the low concentrations of individual species, and the noise and biases inherent in the techniques would seem to make these experiments very difficult. Understanding why they work so well, and showing how they can perform better and for more complex molecular se

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