Frontier model of tumor growth

Stained p53-mutant cells (dark brown) in mouse epidermis, from Zhang et al 2001.

We created a computer model for simulating the growth of a pre-cancerous lesion (or a tumor) on a surface, such as skin. We used data from Zhang et al 2001 to test the model. In that study, mice were exposed to moderate doses of ultraviolet radiation (UVB) to mimic sun exposure. It is believed that UVB has the following effects on the skin: UVB causes characteristic p53 mutations that inactivate the protein. UVB causes cells to undergo cell death (apoptosis). p53-mutant cells are resistant to UVB-induced cell death. UVB can create p53-mutant cells while killing surrounding normal cells, which gives the mutants room to replicate. Therefore, clones of p53 mutants tend to grow over time under prolonged exposure to UVB. p53 mutants in skin can be detected by staining, as shown in the figure to the left.

In our computer model of tumor growth, cells are arranged in a hexagonal grid. Cells are killed at a low rate, which leaves their positions on the grid empty. When a cell is killed, the six neighboring cells replicate to fill the empty space. The first cell to replicate "wins" and copies itself into that space, while the other cells do nothing. A single mutant cell is placed on the grid at the beginning of a simulation. This mutant may be resistant to being killed or it may replicate faster in response to the death of a neighboring cell. Both traits allow the mutant to grow by slowly colonizing adjacent space. We call this model the frontier model of tumor growth because a lesion can grow only along its edges, as illustrated in the figure to the right. Growth of mutants in this model was consistent with that observed in mouse skin lesions.

A lesion (blue) can grow only by colonizing an adjacent space.

What are the features of our computer model?

• Our model simulates the growth of pre-cancerous lesions on a 2-dimensional surface, like skin. Most previous models assume that they grow exponentially fast or in 3d, like colon polyps. Lesions can not grow as quickly across a 2d surface because there is less room to expand.
• In our model, the tumor grows when the normal cells around it die. The faster these normal cells are killed, the faster the tumor expands. In fact, a mutant that does not replicate any faster than normal cells may still expand if it is resistant to apoptosis. The implication is that if a person is not exposed to ultraviolet radiation, the tumors would find it difficult to grow. Most mathematical models of tumor growth do not include these effects.
• Cells in our model are on a 2d lattice, so the shapes of simulated lesions can be observed and characterized.

What are potential applications of this work?

• We can used the model to determine how fast pre-cancerous lesions grow. In Chao et al 2008, we estimated the growth rates of the p53 mutants observed in Zhang et al 2001. The probability that a pre-cancerous lesion will become malignant increases as the lesion becomes larger, so prediction of lesion growth can help estimate cancer risk.
• We can change the model parameters to simulate different conditions. For example, we could predict how reducing UVB exposure would slow the expansion of pre-cancerous p53 mutants.

Download

We have made the source code for the simulations used in Chao et al 2008 available. To run this, you need to be able to compile Java source code. We used Sun's JDK 6, and we provide a simple Unix makefile. Click here to download the zip file containing the source code.

References

• D. L. Chao, J. T. Eck, D. E. Brash, C. C. Maley, and E. G. Luebeck. Pre-neoplastic lesion growth driven by the death of adjacent normal stem cells. Proceedings of the National Academy of Sciences, 105(39):15034-9. 2008.
  Faculty of 1000 Medicine evaluation
• W. Zhang, E. Remenyik, D. Zelterman, D. E. Brash, and N. M. Wikonkal. Escaping the stem cell compartment: sustained UVB exposure allows p53-mutant keratinocytes to colonize adjacent epidermal proliferating units without incurring additional mutations, Proceedings of the National Academy of Sciences, 98(24):13948-53. 2001.
• W. Zhang, A. N. Hanks, K. Boucher, S. R. Florell, S. M. Allen, A. Alexander, D. E. Brash, and D. Grossman. UVB-induced apoptosis drives clonal expansion during skin tumor development. Carcinogenesis, 26(1):249-57, 2005.