Randomly Evolving Idiotypic Networks: Analysis of Building Principles

We investigate a minimalistic model of the idiotypic network of B-lymphocytes where idiotypes are represented by bitstrings encoding the nodes of a network. A node is occupied if a lymphocyte clone of the corresponding idiotype exists at the given moment, otherwise it is empty. There is a continuous influx of B-lymphocytes of randomly (by mutation) generated idiotype from the bone marrow. B-lymphocytes are stimulated to proliferate if its receptors (antibodies) are cross-linked by complementary structures. Unstimulated lymphocytes die. Thus, the links of the network connect nodes encoded by complementary bitstrings allowing for a few mismatches. The random evolution leads to a network of highly organized architecture depending on only few parameters. The nodes can be classified into different groups with clearly distinct properties. We report on the building principles which allow to calculate analytically characteristics as the size and the number of links between the groups previously found by simulations.