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Computational and Mathematical Methods in Medicine
Volume 10, Issue 1, Pages 71-83
Original Article

A Mathematical Model Quantifies Proliferation and Motility Effects of TGF-β on Cancer Cells

1Department of Cancer Biology, Vanderbilt University, Nashville, TN, USA
2Institute for Mathematics and Its Applications, University of Minnesota, Minneapolis, MN, USA
3Department of Mathematics, Vanderbilt University, Nashville, TN, USA

Received 3 March 2008; Accepted 29 April 2008

Copyright © 2009 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Transforming growth factor (TGF)-β is known to have properties of both a tumour suppressor and a tumour promoter. While it inhibits cell proliferation, it also increases cell motility and decreases cell–cell adhesion. Coupling mathematical modelling 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 parametrisation. 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 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.