Hypoxic response in cancer progression: modeling HIF activation

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The reprogramming of energy metabolism represents an important hallmark of cancer. The main cause of this alteration is represented by the presence of hypoxic areas. The decreased availability of oxygen activates the Hypoxia Inducible Factor (HIF) pathway which regulates the switch from an aerobic to an anaerobic metabolism, as well as an increased uptake of glucose. This thesis has two main objectives. In the first part we study and we nu- merically simulate a mathematical model consisting of four ordinary differential equations (ODEs): one for cancer cells with inactivated HIF signaling, one for cancer cells with activated HIF signaling and two for the metabolites cancer cells can consume in order to produce ATP. We model the dynamics of the transi- tion between the two different metabolic behaviors, of cancer growth under normoxic and hypoxic conditions and of cancer progression in a hostile environ- ment; furthermore we compare the behaviour of cancer cells in highlanders and lowlanders. In the second part we introduce a simple mathematical model to analyse the link between angiogenesis and the Warburg effect in cancer cells. We show that the increased expression of glucose receptors is an important factor in the transition from initiation to cancer progression. We also show that the genetic polymorphism considered in highlanders does not provide useful in- formation on cancer growth in the long term behaviour. The second model, despite only being introduced, will let us formulate new questions concerning the role of angiogenesis in cancer progression and links among different aspect of cancer metabolism.