ABSTRACT
This chapter examines the immunological control networks using topological and graph theoretical methods similar to those previously used for chemical reaction networks. It aims to extend the approach of Eisenfeld and DeLisi by considering the flow topologies rather than the stabilities of immunological control networks and treats the Herzenberg models rather than the models of Kaufman, Urbain, and Thomas. Topological models of immunological control networks provide guidance for much more complicated continuous analyses using specific systems of differential equations. An immunological control network, thus, can be represented by a bipartite graph. Conversion of an immunological control network into the corresponding influence diagram can require several stages if removal of a weak vertex and its associated edges converts a strong vertex into a weak vertex. The Herzenberg models for immunological control networks are well suited for the flow topological methods and lead to the locking in stable "help" and/or "suppression" configurations observed experimentally.
