Mathematics + Biology = ?
You may wonder what mathematics and biology could possibly have in common. Well, as luck would have it, the Oberlin Center for Computation and Modeling had just this question in mind when it brought Dr. Avner Friedman to give two talks on mathematical modeling on the biological sciences.
Friedman, distinguished professor of mathematics at Ohio State University, explained that although mathematicians enjoy working with equations of all sorts, they do not tend to ponder the physical applications of the theorems they solve. But, having worked in the industry of mathematics, he now sees the need for expertise in complex math in applied biology.
When asked how he became involved with the combination of these two fields, Friedman’s reply suggested that other professions do not seem to be picking up on what he feels is of utmost importance: “Someone should do it, and if no one is going to, I might as well.”
The significance of integrating math and biology was highlighted in Friedman’s first talk in which he gave examples of a specific problem his group is currently working on: using mathematical models to find a cure for cancer. Of course, nothing is as simple as just plugging in the numbers and seeing what comes out. Currently there is an effort to use a virus that attacks just the tumor while leaving the healthy cells alone.
The cancer that would be most affected by research such as this is the particular type of brain tumor known as glioma, which, when detected, tends to predict a life expectancy of nine to 12 months. So, the problem for researchers is to find a virus that reproduces fast enough and is able to avoid enough of the immune system to effectively reduce the tumor. Although Friedman’s group found some parameters that would cause the tumor to be reduced, it is now up to the biologists to create a virus that matches such parameters.
Friedman noted that “all models are wrong, but some are better than others.” This means that a mathematical model must take many assumptions into account that may make no sense when applied back to the actual biological process, showing that people are only beginning to understand the matter with which they are working.
The second talk addressed more biological processes that would benefit from mathematical modeling as well as a closer look at Ohio State’s Mathematical Biosciences Institute, where Friedman currently works. The Institute itself has come from the explosion of biological data created by the advancements in the technology used to study biological systems. Such a wealth of data has inspired the need to develop many mathematical models, statistical methods and computational algorithms.
A few of the biological processes that contain complex problems from which modeling could benefit encompass the neurological as well as the cellular. In neurological processes, Parkinson’s disease is a particularly complicated problem that is barely understood. There are around 1012 neurons in the human brain, and in order to properly understand their relationships with all of the other neurons, differential equations prove to be of great use.
In cellular processes, models can help people to understand the role of extracellular signaling in the processes that become muddled in cancerous cells. So, when scientists are able to understand this process more comprehensively in a healthy person or cell, it will ultimately be easier to attack cancerous cells.
Friedman said that he is not an advocate for a more general and comprehensive science education; however, he did emphasize that an education should stress the importance of learning through solving specific problems, one after the other, as that is extremely beneficial to students who wish to go into research after school. This method not only teaches main concepts in the particular field, but also teaches students the valuable tools they need to solve the problem. Science has become so expansive that it is impossible for students to learn everything they will need to know in their future research. Therefore, it then becomes vital at least to learn the tools they will need to use in lieu of what they have not had time to learn formally.
On mathematics classes for the biological sciences, Friedman did not suggest that students go out of their way to learn how formally to prove theorems in mathematics when statistical mathematics and specific differential equations are more fundamental to the problems they will have to solve. Instead, mathematics classes for the biological sciences can show the specific applications and techniques that will be most beneficial to the students’ futures.
Currently, the MBI offers positions for 15 post-doctorates as well as a
three-week summer program for both graduate and undergraduate students in the
sciences. There is also an opportunity for research during Winter Term for those
who are ambitious enough.