Abstract for

"Random Evolution of Idiotypic Networks: Dynamics and Architecture"

The talk deals with modelling a subsystem of the immune system, the so-called idiotypic network. Idiotypic networks, a concept conceived by N.K. Jerne in 1974, are functional networks of interacting antibodies and B-cells. In principle, Jernes' framework provides solutions to many issues in immunology, such as immunological memory, mechanisms for antigen recognition and the question of self/non-self discrimination. Explaining the interconnection between the elementary components' local dynamics, network formation and architecture, and possible modes of global system function appears to be an ideal playground of statistical mechanics. We present a simple cellular automaton model based on a graph representation of the system. From a simplified description of idiotypic interactions rules for the random evolution of networks of occupied and empty sites on these graphs are derived. In certain biologically relevant parameter regimes the resultant dynamics lead to stationary states. A stationary state is found to correspond to a typical pattern of network organization. It turns out that even these very simple rules give rise to a multitude of different kinds of patterns. In the talk methods are presented to characterize such stationary state networks. Based on this description, `static' and `dynamic' network-patterns are distinguished. The observed types of stationary state networks are related to possible operational modes of real idiotypic networks. A type of `dynamic' network is found that displays many features of real idiotypic networks and could explain transitions in the network structure if changes in essential parameters occur, e.g., the influx of new idiotypes from bone-marrow.