Evolution of Speci5city in an Immune Network

A dynamic antigen response of the immune network is discussed, based on shape-space modelling. The present model extends the shape-space modelling by introducing the evolution of speci"city of idiotypes. When the amount of external antigen increases, a measure of stability of the immune network is lost and thus the network can respond to the antigen. It is shown that speci"c and non-speci"c responses emerge as a function of antigen amounts. A speci"c response is observed with a "xed-point attractor, and a non-speci"c response is observed with a chaotic attractor for the lymphocyte population dynamics. The network topology also changes between "xed-point and chaotic attractors. For some antigen amounts, chaotic attractors will vanish or become long-lived super-transient states. A dynamic bellshaped response function will thus emerge. The relevance of long-lived chaotic transient states embedded in "xed-point attractors is discussed with respect to immune functions. ( 2000 Academic Press