Mathematics Explains Genetic Instability in Cancer

Natalia Komarova (photo courtesy: UC Irvine)

Natalia Komarova is an associate professor at the University of California, Irvine. One of her research interests lies in developing mathematical models to study initiation and development of cancer, viewed as somatic evolution in populations of cells. She has investigated the following crucial issues related to the understanding of cancer: the role of genetic instability in cancer progression, cellular origins of cancer, the role of stem cells in carcinogenesis, and even questions like 'how can we fight resistance to drug therapies'? Natalia formulated important questions of cancer biology in the language of mathematics, and used experimental data to validate her mathematical models.

In a recent publication in the Journal of the Royal Society Interface, Natalia and her colleagues Alexander Sadovsky and Frederic Wan of UC Irvine provided a good insight into how cancerous tumors thrive and formulated a potential foundation for future cancer treatments. Their research focused on the phenomenon of genetic instability, a common feature of cancer in which cells mutate at an abnormally fast rate. Such mutations can cause cancer cells to grow, or they can cause the cells to die.

The UC Irvine team tried to find an answer to a question: How can a tumor optimize its own growth? They formulated an optimal control problem for the mutation rate in cancer cells and then developed a method to find optimal time-dependent strategies. The results from a wide range of parameters showed that cancerous tumors grow best in an early 'unstable' stage of development when cancerous cells mutate to speed up malignant transformation. The growth stabilizes at later stages by turning off the mutation rate, a fact that agrees very well with the growing biological evidence for such phenomena. They also succeeded in identifying parameter regimes where it is advantageous to keep the state stable (or unstable) constantly throughout the growth.

Previous studies have observed such genetic pattern by using laboratory techniques, but the UC Irvine results could explain for the first time by using a mathematical model why this pattern leads to tumor growth.

Reference:
"Selective pressures for and against genetic instability in cancer: a time-dependent problem"
Natalia L. Komarova, Alexander V. Sadovsky, Frederic Y.M. Wan
The Journal of the Royal Society Interface Link to Abstract