Tolerance vs Intolerance: How Affinity Defines Topology in an Idiotypic Network

Idiotypic network models of the immune system have long attracted interest in immunology as they offer a potential explanation for the maintenance of immunological memory. They also give a possible justification for the appearance of tolerance for a certain category of cells while maintaining immunization for the others. In this paper, we provide new evidence that the manner in which affinity is defined in an idiotypic network model imposes a definite topology on the connectivity of the potential idiotypic network that can emerge. The resulting topology is responsible for very different qualitative behaviour of the network. We show that using a 2D shape-space model with affinity based on complementary regions, a cluster-free topology results that clearly divides the space into tolerant and non-tolerant zones in which antigen are maintained or rejected respectively. On the other hand, using a 2D shape-space with an affinity function based on cell similarity, a highly clustered topology emerges in which there is no separation of the space into isolated tolerant and non-tolerant zones. Using a binary shape-space, both similar and complementary affinity measures also result in highly clustered networks. In the networks whose topologies exhibit high clustering, the tolerant and intolerant zones are so intertwined that the networks either reject all antigen or tolerate all antigen.