Mathematical Models of TGF-B on Cancer Cell Activities
Authors:Alissa Klinzmann, Alice Kwan
- Frederic Wan, Professor of Mathematics, University of California Irvine
- Cynthia Sanchez Tapia, Graduate Student of Mathematics, University of California Irvine
Transforming growth factor-B, or TGF-B, is a protein that activates many cellular responses, such as proliferation, differentiation, apoptosis, and homeostasis. One of its most studied activities is its role as a tumor inhibitor. Unlike traditional research methods that seek to suppress tumor growth, our research is conducted in finding the shortest time possible for cancer to reach its critical population size while under the inhibitory effects of TGF-B. First, we model cancerous growth due to genetic instability in the presence of TGF-B with a system of three ordinary diﬀerential equations. Second, it is theoretically known that the fastest time to tumor growth is achieved by maximum mutation rate at the start and low to no mutation as the tumor progresses. After computing the terminal time for relevant parametric values, our results found that when we allow the maximum mutation rate to be u_m=1 and the minimum mutation rate to be u_min=0, cancer growth is likely to be fastest at the time 2.376. Ultimately, this research is based on an optimal control model and assesses the effects of TGF-B as a tumor inhibitor on the time available for intervention prior to unacceptable cancerous growth.