Involvement of tumor macrophage HIFs in chemotherapy effectiveness: mathematical modeling of oxygen, pH, and glutathione.

The four variables, hypoxia, acidity, high glutathione (GSH) concentration and fast reducing rate (redox) are distinct and varied characteristics of solid tumors compared to normal tissue. These parameters are among the most significant factors underlying the metabolism and physiology of solid tumors, regardless of their type or origin. Low oxygen tension contributes to both inhibition of cancer cell proliferation and therapeutic resistance of tumors; low extracellular pH, the reverse of normal cells, mainly enhances tumor invasion; and dysregulated GSH and redox potential within cancer cells favor their proliferation. In fact, cancer cells under these microenvironmental conditions appreciably alter tumor response to cytotoxic anti-cancer treatments. Recent experiments measured the in vivo longitudinal data of these four parameters with tumor development and the corresponding presence and absence of tumor macrophage HIF-1α or HIF-2α in a mouse model of breast cancer. In the current paper, we present a mathematical model-based system of (ordinary and partial) differential equations to monitor tumor growth and susceptibility to standard chemotherapy with oxygen level, pH, and intracellular GSH concentration. We first show that our model simulations agree with the corresponding experiments, and then we use our model to suggest treatments of tumors by altering these four parameters in tumor microenvironment. For example, the model qualitatively predicts that GSH depletion can raise the level of reactive oxygen species (ROS) above a toxic threshold and result in inhibition of tumor growth.