Mathematical modelling of the HIF-1 mediated hypoxic response in tumours

Solid tumours frequently display areas of low oxygen concentration (hypoxia) due to their uncontrolled proliferation and the fact that the new blood vessels they develop are irregular and have poor blood flow. The capacity for a tumour to grow therefore crucially depends on its ability to adjust to hypoxic conditions. It is frequently observed that the hypoxia response pathways, such as angiogenesis (formation of new blood vessels) and glycolysis (use of glucose, rather than oxygen, metabolism) are adapted in tumour cells to allow for aggressive growth in hypoxic conditions. The response pathways are also often upregulated in normoxic conditions. The transcription factor Hypoxia-Inducible Factor 1 (HIF-1) has been found to control the expression of a battery of genes that are crucially involved in the hypoxic response, including key angiogenic growth factors and glycolytic enzymes. Intratumoural hypoxia and HIF-1 overexpression are both associated with poor patient prognosis. In this paper, we extend an ordinary differential equation (ODE) model by Kohn et al, Mol. Biol. of the Cell, 15:3042(2004)that measures HIF-1 mediated transcription activation as a function of oxygen concetration [1]. The model considers a core sub-system of elements from the HIF-1 regulatory network,and in so doing highlights the stabilisation pathway of the oxygen-regulated HIF-1alpha subunit. In normoxic conditions HIF-1alpha undergoes a post-translational modification known as hydroxylation which allows HIF-1alpha to be targeted for degradation. In hypoxic conditions, the hydroxylation reaction does not occur, leading to stabilisation of the HIF-1alpha protein, formation of the HIF-1 complex and activation of gene transcription. We extend the Kohn model by including mechanisms that may account for the rapid attenuation of the hypoxic response upon reoxygenation of cells, after a period of hypoxia. Our results show good qualitative agreement with experimentally obtained hypoxia dose-response curves by capturing all the important characteristics of the curve