Mathematical model of heterogeneous cancer growth with an autocrine signalling pathway
Article first published online: 11 JUL 2012
© 2012 Blackwell Publishing Ltd
Volume 45, Issue 5, pages 445–455, October 2012
How to Cite
Hu, G.-M., Lee, C.-Y., Chen, Y.-Y., Pang, N.-N. and Tzeng, W. J. (2012), Mathematical model of heterogeneous cancer growth with an autocrine signalling pathway. Cell Proliferation, 45: 445–455. doi: 10.1111/j.1365-2184.2012.00835.x
- Issue published online: 27 AUG 2012
- Article first published online: 11 JUL 2012
- Manuscript Accepted: 20 APR 2012
- Manuscript Received: 18 NOV 2011
- National Science Council of the Republic of China. Grant Numbers: NSC 100-2112-M-002-007, NSC 100-2112-M-032-002-MY3
- National Center for Theoretical Sciences
Cancer is a complex biological occurrence which is difficult to describe clearly and explain its growth development. As such, novel concepts, such as of heterogeneity and signalling pathways, grow exponentially and many mathematical models accommodating the latest knowledge have been proposed. Here, we present a simple mathematical model that exhibits many characteristics of experimental data, using prostate carcinoma cell spheroids under treatment.
Materials and methods
We have modelled cancer as a two-subpopulation system, with one subpopulation representing a cancer stem cell state, and the other a normal cancer cell state. As a first approximation, these follow a logistical growth model with self and competing capacities, but they can transform into each other by using an autocrine signalling pathway.
Results and conclusion
By analysing regulation behaviour of each of the system parameters, we show that the model exhibits many characteristics of actual cancer growth curves. Features reproduced in this model include delayed phase of evolving cancer under 17AAG treatment, and bi-stable behaviour under treatment by irradiation. In addition, our interpretation of the system parameters corresponds well with known facts involving 17AAG treatment. This model may thus provide insight into some of the mechanisms behind cancer.