A mathematical model quantifies proliferation and motility effects of TGF--$β$ on cancer cells
Transforming growth factor (TGF) $β$ 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--$β$. 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--$β$ 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--$β$ treated cells \textit{in vitro}, TGF--$β$ increases cell motility by a factor of 2 and decreases cell proliferation by a factor of 1/2 in comparison with untreated cells.