In this paper we review the trajectory of a model proposed by Stauffer and Weisbuch in 1992 to describe the evolution of the immune repertoire and present new results about its dynamical behavior. Ten years later this model, which is based on the ideas of the immune network as proposed by Jerne, has been able to describe a multi-connected network and could be used to reproduce immunization and aging experiments performed with mice. The immunization protocol is simulated by introducing small and large perturbations (damages), and in this work we discuss the role of both. Besides its biological implications, the physical aspects of the complex dynamics of this network is very interesting per se. In a very recent paper we studied the aging effects by using auto-correlation functions, and the results obtained apparently indicated that the small perturbations would be more important than the large ones, since their cumulative effects may change the attractor of the dynamics. However our new results indicate that both types of perturbations are important. It is the cooperative effects between both that lead to the complex behavior which allows to reproduce experimental results.
I IntroductionThe main task of the immune system is to protect the organism against dangerous elements: antigens (virus, bacteria, poison, cell residues, etc). Depending on the antigen the immune system may elicit different kinds of responses: the cell-mediated immune response or the humoral response. The models discussed in this paper are related to the humoral responses generated by B cells (one of the main classes of lymphocytes), which are the cells that produce the antibodies. The antibodies produced by a given population of B cells are replicas of its molecular receptor. Each molecular receptor exhibited by a given B cell population recognize different recognition sites (epitopes) of the antigen by lockkey interactions.The clonal selection theory [1] is the most accepted theory about the B cells and was proposed by Burnet in 1959. It states that the antigen chooses by pattern recognition the clones of B cells (population of B cell and antibodies) that will proliferate. In order to recognize any foreign (or dangerous) element the immune repertoire must be complete. According to estimates the human immune system is able to express at least the order of 10 11 different receptors [1]. Due to the completeness of the repertoire, the immune system would be able to recognize and be recognized (recognizing epitopes of its own antibodies), therefore the same mechanism of recognition should work for both antibodyantigen and antibody-antibody reactions. In 1974 Jerne [2], taking into account these different mechanisms, suggested that when the antigen is presented to the organism it will activate a set of clones of B cells, leading to the production of specific antibodies; those antibodies will in turn be recognized by a second set of clones activating them, and so on. Due to the interplay of the mechanisms of activation and suppression, this chain of...