Modeling the effect of tumor cell growth when in the presence of natural killer cells

Cancer is the second leading cause of death in the United States. It is believed that many humans develop cancers in their lifetime, but the immune system kills these cells without the need for outside treatments. In cancer progression, however, tumor cells may evade the immune system. The mechanism is not fully understood. Natural killer cells (NK) are one of many immune cells capable of tumor cell lysis. Specifically, the natural cytotoxicity receptors NKp46, NKp44 and NKp30, and the c-type lectin receptor NKG2D on NK cells, are crucial in lysing tumor cells. MHC Class-1 related chain A (MICA), one of several possible activating ligands for NKG2D, is broadly expressed on human tumor cells of epithelial origin. MICA, in combination with various matrix metalloproteinases (MMPs), appears to be involved in both tumor elimination and tumor growth. Tumor growth tends to increase in the presence of soluble MICA but decreases when high levels of MICA bind to a tumor cell. MMPs have been implicated in the shedding of MICA from the tumor surface. A mathematical model was developed to simulate the interactions between NK cells and tumor cells in the presence of MMPs. A set of twelve continuous partial differential equations were created based on data from published literature and solved. These simultaneous equations describe the relationship between twelve state variables and various parameters which will be determined through experimentation. Results of model simulations with three different initial concentration values of MMPs show how this biochemical affects the ability of NK cells to attack tumor cells.