A dynamical model for the immune repertoire

In this paper we use exact numeration techniques and multispin coding to study the dynamics of a bit-string model proposed to describe the time evolution of B-cell repertoire. Each clone of B-cells and antibodies is characterized by its molecular receptor, associated to a bit-string, and the model dynamics simulates the evolution of interacting populations. We take into account the effects of cell death, caused by different mechanisms, and cell production, both due to bone marrow action and to clone proliferation caused by interaction between complementary forms. We also simulate antigen presentations and our results indicate that after primary response specific populations may be sustained at high levels, keeping the memory about the exposition; and subsequent presentations of the same antigen arouse faster responses. Furthermore, the aroused populations form isolated clusters in shape (bit-string) space, and, provided that the number of memorized antigens is not too high, presentations of other uncorrelated antigens do not disturb the memory of previous antigen presentations. We have estimated the memory capacity of the system by periodically presenting randomly chosen antigens. We found that, in certain regions of the parameter space, the system is able to respond to all antigens, keeping information only about a constant number of recently presented antigens. The number of simultaneously memorized antigens is used to define the capacity of the network.