A dynamical model of apoptosis and its role in tumor progression

Apoptosis is a biological process crucial for the development and maintenance of healthy living organism. A deregulated apoptosis underlies many diseases, including cancer. Under hypoxic conditions, p53 starts to accumulate and competes with HIF-1 for their common binding target p300. This can lead to the repression of HIF-1, and trigger the apoptotic derive. In addition apoptosis is accompanied by an enhancement of potassium (K+) fluxes, which in turn create a low-potassium intracellular micro-environment, which cooperates to the activation of caspases, the final actors of the apoptotic cascade. Based on this scenario, we elaborate a dynamical model aimed at resolving the complex dynamical interplay between the aforementioned processes. In the ideal continuum limit, the model reduces to a system of coupled differential equations, whose dynamics is analytically inspected.