A mathematical model quantifies proliferation and motility effects of TGF--$\beta$ on cancer cells

Transforming growth factor (TGF) $\beta$ is known to have properties of both a tumor suppressor and a tumor promoter. While it inhibits cell proliferation, it also increases cell motility and decreases cell–cell adhesion. Coupling mathematical modeling and experiments, we investigate the growth and motility of oncogene–expressing human mammary epithelial cells under exposure to TGF–$\beta$. We use a version of the well–known Fisher–Kolmogorov equation, and prescribe a procedure for its parametrization. We quantify the simultaneous effects of TGF–$\beta$ to increase the tendency of individual cells and cell clusters to move randomly and to decrease overall population growth. We demonstrate that in experiments with TGF–$\beta$ treated cells \textit{in vitro}, TGF–$\beta$ increases cell motility by a factor of 2 and decreases cell proliferation by a factor of 1/2 in comparison with untreated cells.