Deterministic and stochastic aspects of VEGF-A production and the cooperative behavior of tumoral cell colony

A model is proposed to study the process of hypoxia-induced angiogenesis in cancer cells. The model accounts for the role played by the vascular endothelial growth factor (VEGF)-A in regulating the oxygen intake. VEGF-A is dynamically controlled by the HIF- 1 α concentration. If not degraded, HIF- 1 α can bind to the subunit termed HIF- 1 β and so experience translocation to the nucleus, to exert its proper transcriptional activity. The delicate balance between these opposing tendencies translates into the emergence of distinct macroscopic behaviors in terms of the associated molecular concentrations that we here trace back to normoxia, hypoxia and death regimes. These aspects are firstly analyzed with reference to the ideal mean-field scenario. Stochastic fluctuations are also briefly discussed and shown to seed a cooperative interaction among cellular units, competing for the same oxygen reservoir.