05/04/2018

Mathematics can help to unravel the secrets of cancer.

What do foxes and white blood cells have in common? The question is posed and answered by Irina Kareva, a scientist who calls herself a translator. And the languages she masters are Biology and Mathematics.

“I write mathematical models that, in my case, are systems of differential equations, which describe biological mechanisms, such as cell growth. Basically, it works like this: first, I identify the main elements that I believe are influencing the behavior of a specific mechanism over time. Then, I formulate theories about how these elements interact with each other and with their environment. Next, I translate these theories into equations. Finally, I analyze my equations and translate the results back into the language of biology.”

This is how she explains, in a didactic way, the main focus of her research in her TED talk "Mathematics can help unlock the secrets of cancer," given last December.

Irina, a theoretical biologist with a PhD in Applied Mathematics for Life and Social Sciences, uses mathematical modeling to study cancer. She considers cancer an evolving ecosystem within the human body, where cancer cells compete for limited resources – in this case, oxygen and glucose – cooperate with each other to fight off predators – that is, the immune system – and migrate, giving rise to metastases. According to her, thinking about the disease from an ecological perspective has the power to change the approach to cancer treatment.

“A fundamental aspect of mathematical models is that we, who create them, don't think about what things are, but about what they do. We think about the relationships between individuals, whether they are cells, animals, or people, and how they interact with each other and with their environment.”

This is precisely where foxes and white blood cells come in. Both are predators. They hunt, respectively, rabbits and invaders, such as cancer cells. “From a mathematical point of view, a similar qualitative predator-prey system of equations would describe the interactions between foxes and rabbits, as well as between cancer and white blood cells. And what does conservation biology tell us about most ecosystems? That one of the best ways to extinguish a species is not to attack it directly, but to attack its environment.”

In her talk, which can be viewed on the TED website, Irina highlights that "the power and beauty of mathematical models lie in the fact that we can formalize, in a very methodical way, what we think we know."