A stochastic multiscale model for acid mediated cancer invasion

Cancer research is not only a fast growing field involving many branches of science, but also an intricate and diversified field rife with anomalies. One such anomaly is the consistent reliance of cancer cells on glucose metabolism for energy production even in a normoxic environment. Glycolysis is an inefficient pathway for energy production and normally is used during hypoxic conditions. Since cancer cells have a high demand for energy (e.g. for proliferation) it is somehow paradoxical for them to rely on such a mechanism. An emerging conjecture aiming to explain this behavior is that cancer cells preserve this aerobic glycolytic phenotype for its use in invasion and metastasis (see, e.g., Gatenby and Gillies (2004)  [1], Racker (1976)  [2]). We follow this hypothesis and propose a new model for cancer invasion, depending on the dynamics of extra- and intracellular protons, by building upon the existing ones. We incorporate random perturbations in the intracellular proton dynamics to account for uncertainties affecting the cellular machinery. Finally, we address the well-posedness of our setting and use numerical simulations to illustrate the model predictions.