Comparing mathematical models of cell adhesion in tumors

Cancer progression accompanies changes in cell adhesion characteristics, which is crucial for cancer cell invasion and metastasis. Drugs altering cell adhesion have been suggested as a possible therapeutic treatment for cancer. Tumor cell adhesion is thus an important topic of current investigation. Recently individual cell (agent)-based in silico tumor models have incorporated mathematical models of cell adhesion. However, cell adhesion has been modeled in various ways in different studies. The first, Lennard-Jones potential model, is extrapolated from attractive/repulsive interactions between inert molecules. The second, JKR model, is derived from van-der Waals contact forces between non-spontaneously adhering solid elastic bodies. The third, cellular Potts model, is an adaptation of the Ising model of ferromagnetism to a spontaneously adhering population of cells. We compare these three mathematical models of cell adhesion and show how they give different perspectives to tumor growth, morphology and effectiveness of therapy. We also discuss how these models predict multi-nodular tumor morphology which is hitherto unaddressed in the literature.