Network Topology in Immune System Shape Space John Burns and Heather J. Ruskin School of Computing, Dublin City University, Dublin 9, Ireland {jburns,hruskin}@computing.dcu.ie http://www.dcu.ie/computing/msc/index.html Abstract. We consider the emergent network topology of an immune system shape space at the end of primary response. We extend the for- malism of shape space in order to model the relationship between acti- vated immune lymphocytes and stimulant antigen presentation cells by way of a graph consisting of a pair G =(V,E) of sets. The vertex set V is the set of activated genotypes, while the edge set E connects such activated immune lymphocytes and stimulant antigen presentation cell in shape space. This paper shows how shape space graph edge weight- ing can be viewed, from the biological perspective, as the vigour with which an activated cytotoxic immune cell suppresses the infected anti- gen presentation cell which stimulated it. In this research, we also iden- tify critical vertices (called α-vertices). These α-vertices act as bridging vertices in that they join subgraphs of unrelated immune response. As a consequence of this, such α-vertices ideally model immune cytotoxic lym- phocyte memory cells. By representing memory cells as highly connected vertices, we show how such cells play a significant role in the elimination of pathogenic agents. 1 Introduction In this paper we present results from recent work carried out to model the emer- gence of shape diversity within the immune system. Previously [1], we introduced a new process by which two formalisms, usually separately addressed, may be integrated. These formalisms are known as shape space and physical space. We highlighted a means by which localised dynamics effect global (or shape space) condition, and how global condition in turn may feed information down to local physical space. This approach is now further refined by treating shape space as a self-organising, dynamic network in 2-dimensional space. The system is consid- ered to be exposed to a set of genetically varied pathogens in order to simulate normal human immune experience over a fixed period of time. We then study the cytotoxic lymphocyte activation patterns which emerge naturally in shape space. The results presented here show that, at the end of primary response, a network of activated cytotoxic lymphocytes and pathogen challengers emerges in shape space. M. Bubak et al. (Eds.): ICCS 2004, LNCS 3038, pp. 1094–1101, 2004. c  Springer-Verlag Berlin Heidelberg 2004