Stability of symmetric idiotypic networks—A critique of Hoffmann's analysis

✍ Scribed by Rob J. De Boer; Pauline Hogeweg

• Publisher: Springer
• Year: 1989
• Tongue: English
• Weight: 384 KB
• Volume: 51
• Category: Article
• ISSN: 1522-9602
• DOI: 10.1016/s0092-8240(89)80069-2

✦ Synopsis

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.