This thesis addresses various sources of diversity in the vertebrate immune system. In particular, we study the differences between thediversity of lymphocytes and major istocompatibility (MHC) molecules.While any individual expresses a huge\ud diversity of B and T ymphocytes, the diversity of MHC molecules is mainly expressed at the population level. We use various\ud mathematical models and computer simulations to study which evolutionary selection pressures mayunderlie the diversity of\ud lymphocytes and MHC molecules. Central is the hypothesis that the adaptive immune system stores immunological decisions\ud in lymphocytes. Instructed lymphocytes recall their appropriate mode of response whenever they recognise their specific\ud epitope. The vertebrate immune system thereby combines the evolutionary wisdom of the innate immune system with somatic\ud learning by the adaptive immune system. \ud \ud It has been proposed that het need for self-nonself discrimination is the driving force for the diversity of the adaptive immune\ud system. Using mathematical models it has been shown that the diversity of lymphocytes giving optimal protection against\ud infections reflects the number of self antigens that need to be tolerized. We show, however, that avoidance of inappropriate\ud immune responses, such as autoimmune responses against self antigens that fail to induce tolerance, calls for an even higher\ud specificity and diversity than was concluded from these previous models. According to our calculations, lymphocytes should\ud be as specific as possible within the constraints imposed by the size of the immune repertoire. \ud \ud We show that the need to avoid inappropriate immune responses can also explain the limited diversity of MHC molecules\ud within an individual. The fact that individuals express only a limited number of different MHC molecules out of the huge\ud MHC population diversity, is usually attributed to the need to avoid repertoire depletion during self-tolerance induction. We\ud dispute this explanation by showing that expression of extra MHC molecules tends to increase the functional T cell\ud repertoire and that repertoire depletion only occurs at an unrealistically high individual MHC diversity. Expression of a\ud large individual MHC diversity, however, increases the chance of inducing inappropriate immune responses. Foreign\ud peptides presented by MHC molecules may form complexes that -- from the T cell point of view -- look similar to comlexes of\ud MHC molecules presenting ignored self molecules. Excessive MHC diversity therefore increases the chance that lymphocytes\ud that have been triggered by foreign peptides cause autoimmune responses against so-far ignored self antigens. \ud \ud Despite the limited diversity of MHC molecules within any individual, we show that there is selection for a large diversity of\ud MHC molecules at the population level. A large population diversity of MHC molecules allows an individual to respond to\ud different epitopes of an antigen than the other individuals in the population, thereby giving protection against coevolving\ud pathogens. We show that the MHC polymorphism arising under host-pathogen coevolution is significantly larger than the\ud polymorphism arising under selection for heterozygosity only. \ud \ud Finally, using a combined theoretical-experimental approach, we have found evidence for competition between T\ud lymphocytes for antigen-presenting sites on antigen-presenting cells. We conjecture that the immune system may employ the\ud MHC diversity that is left at the individual level to allow the presentation of multiple epitopes per antigen. It may thereby\ud allow the distributed storage of immunological decisions in lymphocytes, despite the presence of T cell competition
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