Journal Article

Pro‐inflammatory–anti‐inflammatory cytokine dynamics mediated by cytokine‐receptor dynamics in monocytes

R. M. Seymour and B. Henderson

in Mathematical Medicine and Biology: A Journal of the IMA

Published on behalf of Institute of Mathematics and its Applications

Volume 18, issue 2, pages 159-192
Published in print June 2001 | ISSN: 1477-8599
Published online June 2001 | e-ISSN: 1477-8602 | DOI:
Pro‐inflammatory–anti‐inflammatory cytokine dynamics mediated by cytokine‐receptor dynamics in monocytes

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  • Applied Mathematics
  • Biomathematics and Statistics


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Many of the major human diseases, both infectious (septic shock syndromes) and idiopathic (for example, rheumatoid arthritis), are driven by the production of the pro‐inflammatory cytokines interleukin‐1 (IL‐1) and tumour necrosis factor‐α (TNF‐α) produced by monocytes and macrophages. These key pro‐inflammatory cytokines can, in turn, stimulate the production of additional cytokines which, in totality, generate tissue pathology. A major deactivator of activated, cytokine‐producing monocytes and macrophages is the anti‐inflammatory cytokine interleukin‐10 (IL‐10). It is known that the interactions between these three cytokines are pivotal in terms of health and patholgy, but almost nothing is known of the dynamics of these interactions. In this study we have modelled the autocrine interactions of TNF‐α, IL‐1 and IL‐10 with monocytes. The model constructed is a six‐dimensional, continuous‐time dynamical system, with free IL‐1 and IL‐10 concentrations in the cell's vicinity, and the proportions of bound and free IL‐1 and IL‐10 cell‐surface receptors, which transduce the cell's response to stimulation, as the state variables. The monocyte is assumed to be initially in a quiescent state, and it is stimulated to produce IL‐1 by an external stimulus (e.g. exposure to TNF‐α or lipopolysaccharide, LPS). This in turn invokes an autocrine IL‐1 response, and also induces the production of the anti‐inflammatory cytokine IL‐10, which acts to downregulate IL‐1 production. These responses are mediated by specific cell‐surface receptors, the concentrations of which may also be subject to stimulated upregulation. We analyse a reduced, four‐dimensional version of the model, and explore its asymptotic states. We find a variety of possible outcomes: runaway IL‐1 production, multiple stable equilibria, stable limit cycles, and, exceptionally, quasi‐periodic behaviour. These behaviours depend crucially on the form of the cell's response functions. The possible biological implications of these phenomena are discussed.

Keywords: cytokine; interleukin‐; 1; interleukin‐; 10; tumour necrosis factor; monocyte

Journal Article.  0 words. 

Subjects: Applied Mathematics ; Biomathematics and Statistics

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