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Bull Math Biol. 2012 Nov;74(11):2752-77. doi: 10.1007/s11538-012-9776-3. Epub 2012 Oct 17.

Hypoxia inducible factors-mediated inhibition of cancer by GM-CSF: a mathematical model.

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Mathematical Biosciences Institute, The Ohio State University, Columbus, OH, USA.


Under hypoxia, tumor cells, and tumor-associated macrophages produce VEGF (vascular endothelial growth factor), a signaling molecule that induces angiogenesis. The same macrophages, when treated with GM-CSF (granulocyte/macrophage colony-stimulating factor), produce sVEGFR-1 (soluble VEGF receptor-1), a soluble protein that binds with VEGF and inactivates its function. The production of VEGF by macrophages is regulated by HIF-1α (hypoxia inducible factor-1α), and the production of sVEGFR-1 is mediated by HIF-2α. Recent experiments measured the effect of inhibiting tumor growth by GM-CSF treatment in mice with HIF-1α-deficient or HIF-2α-deficient macrophages. In the present paper, we represent these experiments by a mathematical model based on a system of partial differential equations. We show that the model simulations agree with the above experiments. The model can then be used to suggest strategies for inhibiting tumor growth. For example, the model qualitatively predicts the extent to which GM-CSF treatment in combination with a small molecule inhibitor that stabilizes HIF-2α will reduce tumor volume and angiogenesis.

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