Architecture of randomly evolving idiotypic networks

Abstract

B lymphocytes express on their surface receptors (antibodies) of a given specificity (idiotype). Crosslinking these receptors by complementary structures, antigens or antibodies, stimulates the lymphocyte. Thus a large functional network of interacting lymphocytes, the idiotypic network, emerges. Idiotypic networks, conceived by Niels Jerne 30 years ago, experience a renewed interest, e.g., in the context of autoimmune diseases. In a previously proposed minimalistic model idiotypes are represented by bit strings. The population dynamics of the idiotype clones is reduced to a zero-one scheme. An idiotype survives only if it meets enough but not too many complementary structures. We investigate the random evolution of the network towards a highly organized functional architecture which is driven by the influx of new idiotypes, randomly generated in the bone marrow. The vertices can be classified into different groups, which are clearly distinguished, e.g., by the mean life time of the occupied vertices. They include densely connected core groups and peripheral groups of isolated vertices, resembling the central and peripheral parts of the biological network. We determine the building principles of the observed patterns and propose a description of their architecture, which is easily transferable to other patterns and applicable to different system sizes.