Stability of symmetric idiotypic networks--a critique of Hoffmann's analysis.
Hoffmann (1982) analysed a very simple model of suppressive idiotypic immune networks and showed that idiotypic interactions are stabilizing. He concluded that immune networks provide a counterexample to the general analysis of large dynamic systems (Gardner and Ashby, 1970; May, 1972). The latter is often verbalized as: an increase in size and/or connectivity decreases the system stability. We here analyse this apparent contradiction by extending the Hoffmann model (with a decay term), and comparing it to an ecological model that was used as a paradigm in the general analysis. Our analysis confirms that the neighbourhood stability of such idiotypic networks increases with connectivity and/or size. However, the contradiction is one of interpretation, and is not due to exceptional properties of immune networks. The contradiction is caused by the awkward normalization used in the general analysis.
De Boer
R J
RJ
Hogeweg
P
P
D000818:Animals; D007108:Immune Tolerance; D007130:Immunoglobulin Idiotypes; D008954:Models, Biological; D008962:Models, Theoretical
D007130:Immunoglobulin Idiotypes