Immune network behavior—II. From oscillations to chaos and stationary states View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

1993-07

AUTHORS

Rob J. De Boer, Alan S. Perelson, Ioannis G. Kevrekidis

ABSTRACT

Two types of behavior have been previously reported in models of immune networks. The typical behavior of simple models, which involve B cells only, is stationary behavior involving several steady states. Finite amplitude perturbations may cause the model to switch between different equilibria. The typical behavior of more realistic models, which involve both B cells and antibody, consists of autonomous oscillations and/or chaos. While stationary behavior leads to easy interpretations in terms of idiotypic memory, oscillatory behavior seems to be in better agreement with experimental data obtained in unimmunized animals. Here we study a series of models of the idiotypic interaction between two B cell clones. The models differ with respect to the incorporation of antibodies, B cell maturation and compartmentalization. The most complicated model in the series has two realistic parameter regimes in which the behavior is respectively stationary and chaotic. The stability of the equilibrium states and the structure and interactions of the stable and unstable manifolds of the saddle-type equilibria turn out to be factors influencing the model's behavior. Whether or not the model is able to attain any form of sustained oscillatory behavior, i.e. limit cycles or chaos, seems to be determined by (global) bifurcations involving the stable and unstable manifolds of the equilibrium states. We attempt to determine whether such behavior should be expected to be attained from reasonable initial conditions by incorporating an immune response to an antigen in the model. A comparison of the behavior of the model with experimental data from the literature provides suggestions for the parameter regime in which the immune system is operating. More... »

PAGES

781-816

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/bf02460673

DOI

http://dx.doi.org/10.1007/bf02460673

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1040077929

PUBMED

https://www.ncbi.nlm.nih.gov/pubmed/8318930


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