High-dimensional simulation of the shape-space model for the immune system

For the reactions among the antibodies of the immune system, fighting against a foreign antigen, the recent model of de Boer, Segel and Perelson introduced a cellular automata approximation for the interaction of different types of B cells (bone marrow derived lymphocytes). In contrast to most physics models, here each lattice site interacts mainly with its mirror image (with respect to the lattice center) in the opposite part of the lattice. We simplify their model and then generalize it to include more than one or two shape-space parameters. Thus instead of simulating a chain or square lattice, we simulate a d-dimensional hypercubic lattice with dimension d up to 10. In particular, we check for the concentration of B cells and the stability against localized perturbations (“damage spreading”).