Immune network behavior—I. From stationary states to limit cycle oscilations View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

1993-07

AUTHORS

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

ABSTRACT

We develop a model for the idiotypic interaction between two B cell clones. This model takes into account B cell proliferation, B cell maturation, antibody production, the formation and subsequent elimination of antibody-antibody complexes and recirculation of antibodies between the spleen and the blood. Here we investigate, by means of stability and bifurcation analysis, how each of the processes influences the model's behavior. After appropriate nondimensinalization, the model consists of eight ordinary differential equations and a number of parameters. We estimate the parameters from experimental sources. Using a coordinate system that exploits the pairwise symmetry of the interactions between two clones, we analyse two simplified forms of the model and obtain bifurcation diagrams showing how their five equilibrium states are related. We show that the so-called immune states lose stability if B cell and antibody concentrations change on different time scales. Additionally, we derive the structure of stable and unstable manifolds of saddle-tye equilibria, pinpoint their (global) bifurcations and show that these bifurcations play a crucial role in determining the parameter regimes in which the model exhibits oscillatory behavior. More... »

PAGES

745-780

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/bf02460672

DOI

http://dx.doi.org/10.1007/bf02460672

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1034931480

PUBMED

https://www.ncbi.nlm.nih.gov/pubmed/8318929


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