Architecture Of Randomly Evolving Idiotypic Networks

Ulrich Behn, Institut für Theoretische Physik, Leipzig University, Germany

B-Lymphocytes express on their surface receptors (antibodies) of a given specifity (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 minimalistic model we represent idiotypes by bitstrings and reduce the population dynamics of the idiotype clones to a zero-one scheme. An idiotype survives only if it meets enough but not too much complementary structures. We describe 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, and by the local population dynamics. The vertices can be classified into different groups which are clearly distinguished, e.g., by the mean life time of the occupied vertices. We have found the microscopic building principles of the network patterns which allow to calculate size and interconnectivity of the groups. These groups include densely connected core groups and peripheral groups of isolated vertices, resembling central and peripheral part of the biological network.

Slides