One of the hallmarks of a cancer cell is its immortality. The term immortal does not imply that individual cells live forever, but refers to the ability of a cancer cell colony to replenish itself indefinitely under suitable conditions. This is contrary to the behavior of normal cell populations which exhibit the phenomenon of replicative or cellular senescence, where cells lose the ability to divide after a certain number of cell divisions, typically between 50 and 70 in human cell lines (Hayflick, 1997). It is widely believed that cellular senescence evolved to reduce the probability that cancer is initiated and spread. Somatic cells that have divided many times will have accumulated DNA mutations and would therefore be in danger of becoming cancerous if cell division continued (Campisi, 2005).

This cellular memory effect has been shown to be encoded in the telomeres located at the ends of linear chromosomes which decrease in length with each cell division as a result of the loss of terminal sequences required for enzyme attachment (Morin, 1989). When the chromosome shortening reaches a critical length, further events prevent the cell from dividing. In immortal cancer cells and somatic stem cells, the enzyme telomerase is produced that adds new sequences onto the ends of chromosomes at each DNA replication, thus maintaining the chromosome length. In this way cancer cells divide indefinitely and, thus, achieve immortality (Blackburn, 1994).

In essence, telomere shortening is a mitotic clock independent of chronological time that allows cells to keep track of the number of times it has divided since generation zero of a particular cell lineage. Senescence therefore prevents harmful mutations from proliferating indefinitely in a particular cell line. Figuratively speaking, this growth arrest ‘wipes the slate clean' and allows new cell lineages to take over from damaged ones.

Other than our previous work (Cheong et. al, 2006), there has been no known numerical study on the effect of cellular senescence in cancer, even though it appears to be a key bottleneck in carcinogenesis. However, our study indicates that the dynamics of cancer progression is not sensitive to cellular immortality, contrary to clinical observations that immortality appears to be a key bottleneck in cancer progression. This may be due to the deficient manner in which senescence is represented in our past model, handicapped no doubt by the dependencies on other rate processes.

In the present study, we aim to independently study the effects of cellular senescence in greater detail by building hypothetical models of cell reproduction that is able to capture the generational dependencies down a particular cell lineage, using kinetic data from literature as far as possible. This will allow us to quantitatively determine the distribution of cells down a particular lineage, as well as the limiting effect of cellular senescence, if any, for a variety of birth and death rates representative of those described in literature. We will also investigate the effect when some cells acquire the ability to bypass cellular senescence. Specifically, we will like to determine if uncontrolled growth will result when the Hayflick limit is removed.

It is hoped that further studies may be conducted using this framework, such as probing the relationship between cancer and aging (Campisi, 2003). For example, we hope to shed light on the effect of conferring immortality (e.g., through the introduction of telomerase) on cancer. These studies may reveal insights on the compatibility of prolonging human lifespan versus the treatment/prevention of cancer.

Both kinetic models based on ordinary differential equations as well as population balance equations (e.g., see Henson, 2003, for a review of the various types of dynamic models for microbial cell populations) will be explored for the system, followed by sensitivity analysis (e.g., Caracotsios and Stewart, 1985) and robustness analysis (e.g., Nagy & Braatz, 2003) to quantify the effects of uncertainties in the model parameters (e.g., in the mutation rates for the various types of mutations that occur during the progression to cancer) on the model predictions.

References:

1. J. Campisi, Cancer and aging: Rival demons? Nature Reviews Cancer 3, 339-349, 2003.

2. J. Campisi, Suppressing Cancer: The importance of being senescent, Science, Vol. 309. no. 5736, pp. 886 – 887, 2005.

3. M. Caracotsios and W. E. Stewart. Sensitivity analysis of initial-value problems with mixed odes and algebraic equations. Comp. & Chem. Eng., 9, 359-365, 1985.

4. K.S. Cheong, S. Farooq, R.D. Braatz, A population balance model of cancer progression, in preparation for journal submission, 2006, main ideas presented at the 2005 AIChE Fall Annual Meeting.

5. L. Hayflick, Mortality and immortality at the cellular level: A review, Biochemistry 62, 1180–1190, 1997.

6. Michael A. Henson, Dynamic modeling of microbial cell populations, Current Opinion in Biotechnology, 14, 460-467, 2003.

7. Z. K. Nagy and R. D. Braatz, Worst-case and distributional robustness analysis of finite-time control trajectories for nonlinear distributed parameter systems, IEEE Trans. on Control Systems Technology, 11, 494-504, 2003, and references cited therein.