The authors note that as institutions have restructured curricula over the past half-dozen years to create math courses for the ” ‘quantitative biologists’ of the future,” the prevailing models in use are calculus-based — that is, they are built on differential equations. The success of DE methods have led educators to focus less on algebraic models, which Robeva argues are equally important to incorporate into modern biology programs.
Particularly in systems biology, where complex interactions occur at the molecular level, these new biologists will need a toolkit of diverse mathematical and computational approaches to frame hypotheses, design experiments and analyze results, the authors wrote.
The difficulty with abstract algebra, Robeva said in a phone interview, is that it has been considered highly theoretical. Yet researchers like Laubenbacher successfully use algebraic modeling in their work and educators such as herself are developing modules to fit into biology and mathematics curricula.
“It works,” she said simply, reiterating that it can and should enrich these undergraduate programs.
In Science magazine, Robeva and Laubenbacher argue that algebraic models for systems biology are more intuitive and don’t require the high level of detail often needed to construct differential equation models. A prose description of the problem can be translated into logical statements, an especially appealing feature for those entering mathematical modeling, they wrote.
Furthermore, they note, such algebraic modeling requires only a modest mathematical background, some of which is covered in low-level college math courses.
“Because the mathematics involved is more easily accessible to faculty in the life sciences, relative to DE, this could lead to increased engagement on their part,” they wrote. “Algebraic models will introduce problems from modern biology into the traditional mathematics courses, bringing life to the primarily theoretical abstract algebra curricula.”
For all these reasons, the authors call for educators to find ways to teach undergraduates algebraic modeling. One stumbling block to date is the lack of teaching materials “linking biology with modern algebra,” they wrote.
As the principal investigator on a curriculum development project funded by a $150,000 National Science Foundation grant, Robeva is creating teaching modules that can be “dropped” into existing mathematics and biology courses. Laubenbacher, a researcher at the Virginia Bioinformatics Institute at Virginia Tech, is a consultant for the project. Robeva and her team at Sweet Briar and the University of Western Michigan are developing educational materials based in part on components of Laubenbacher’s cutting-edge work using algebraic methods to solve problems in mathematical biology.
Last February, Robeva spoke about the NSF project at the American Association for the Advancement of Science annual meeting. Following the presentation, an editor asked her to submit an article making her case to Science, a journal of the AAAS. The magazine has been one of the most widely read general science publications for nearly 130 years. She seized the opportunity.
“It’s important because we hope that this will have some impact on the trends in mathematical biology education,” Robeva said.
As she and her colleagues are trying to do with the NSF project, the goal is to push the algebraic alternative into the mainstream alongside calculus-based models. “We are saying that this should be taught and we should find mechanisms to do it,” she said.
By Jennifer McManamay