Systematics of the models of immune response and autoimmune disease

A dynamical model of normal immune response has been formulated in terms of cellular automata by Kaufmanet al. We generalize this model incorporating the antigens as a dynamical variable. This generalized model not only describes the kinetics of primary and secondary responses of humoral immunity, together with the appropriate memory cells, but also describes the vaccinated state as well as the states of low-dose and high-dose paralysis. Recently models of autoimmune response have also been developed in terms of discrete automata. But the models are underdetermined by the experimental facts, i.e., several models can account for the same set of observed biological facts. With an aim to find out how large this underdeterminacy is and how it can be reduced systematically, we have carried out an exhaustive computer-aided search of all those discrete three-cell and five-cell models of autoimmune response which at present cannot be ruled out by the existing biological informations. Out of the 3²⁵ possible five-cell models, only one fulfilled our criteria. We also carried out simulations of the dynamics of some of these models on a discrete lattice. We discuss the relevance of random interactions in the context of autoimmune disease.