Mathematical modeling for cell behavior, complex social systems, and more: A conversation with Alexandria Volkening
- Apr 25
- 4 min read
The NSF-Simons National Institute for Theory and Mathematics in Biology is composed of investigators at the forefront of innovative research at the interface of mathematics and biology. NSF-Simons NITMB Affiliate Members each bring unique perspectives vital for developing new mathematics and inspiring biological discovery. One such NITMB Affiliate Member expanding understanding of biological systems through mathematical modeling is Alexandria Volkening.
Alexandria Volkening is an assistant professor in the Department of Mathematics and (by courtesy) the Weldon School of Biomedical Engineering at Purdue University. Volkening is also an NITMB Affiliate Member.
We spoke with Alexandria Volkening to learn more about how her work integrates biology and mathematical modeling, as well as how participating in NITMB programs empowers her research group.
What is a big question you’ve been asking throughout your research?
“I work in mathematical modeling for several biological systems. For example, for a long time, I’ve been modeling pigment cell behavior in zebrafish and other fish with prominent skin patterns. We are also building models of cell behavior in developing ferns to identify the molecular signals involved in tissue shape. In both cases, the central biological question is puzzling out the rules that cells follow to specify pattern and tissue during development. At its core, this is a question about genotype-to-phenotype relationships and cell fate decisions. I’m particularly interested in understanding variability and robustness to noise in this process. From a mathematical perspective, the models that I build are usually complex, stochastic, and not analytically tractable, so the central question becomes determining how we can build methods to understand the broader behavior of the models and evaluate choices in the modeling process.”
What disciplines does your research integrate?
“My academic background is applied mathematics, especially dynamical systems. Most of my research has been at the interface of math and developmental biology. I’ve also recently started collaborating with experimentalists in agriculture (e.g., how do diseases spread in crops?). Another side of my research, a side which is more undergraduate-focused now, is in complex social systems––there we’re using compartmental models to forecast U.S. elections. All of these topics fall broadly into complex systems, settings where individuals (cells, plants, voters…) come together to create collective group dynamics.”
Where do you find inspiration?
“I like to focus intently on each new biological system that my group takes on––I think getting to know the biology carefully over time can give rise to new mathematical questions and suggest projects that bring together multiple methods. Because my research is in pattern formation, walking around nature can provide inspiration for new applications. So can conversations with experimentalists. I also find new projects from critically evaluating my modeling choices and recognizing when I don’t know the answer to a question.”
What aspects of your research could be interesting to mathematicians or applied to biology?
“One thing that I’ve gotten very interested in over the last several years is developing methods to increase the predictive power of traditionally computational models. I’m especially interested in agent-based dynamics, which I loosely mean to include any type of model that considers individual agents, whether the agents are point masses, lattice sites, polygons in a vertex model, or something else. In my field, these models are often highly complex, and their large number of parameters can make it difficult to evaluate alternative assumptions. I think this sets up a challenge that is interesting both mathematically and biologically. From a mathematical perspective, I think we need new methods that can meet complex models where they are and more broadly characterize model behavior. From a biological perspective, developing such methods could open the door to matching altered parameters in models to mutant or diseased conditions and identifying alternative models consistent with biological data.”
What about the NITMB do you find exciting?
“I appreciate the NITMB’s dual emphasis on using mathematics and theory to generate new insight into biological questions and using biological challenges to drive new mathematical questions and perspectives. Differences in vocabulary and disciplinary cultures can make it challenging to draw new perspectives into questions at the math–theory–biology interface, and I think the NITMB is helping to start conversations. I’m fortunate to be an Affiliate Member and located a few hours from the NITMB, so I’m excited to participate in programs, and several of my group members have already attended NITMB workshops or plan to attend future events.”
What career achievement are you most proud of?
“One thing I’ve really enjoyed is the opportunity to think about how we teach mathematical biology and modeling and then put those reflections into creating my first courses and tutorials on these topics. My academic background did not include classes in modeling or math bio, so it’s been a process for me to think about these things over the last 5+ years. It’s a privilege to share what I’m most passionate about with students. I’m also very happy to be mentoring a group of students and postdoctoral researchers working on different applications and mathematical methods.”
Outside of your research, what other interests do you have?
“This year I’ve gotten into running, and I walk regularly, usually listening to a podcast or book. If I wasn’t a mathematician or scientist, I’d be a florist—I enjoy putting together flower arrangements.”
What are you hoping to work on in the future?
“I’m excited about a new collaboration with experimentalist Yun Zhou on cell behavior in ferns during one stage of the plant life cycle. This is a very tractable system with rich data, and we’re combining modeling, data-driven methods, and experiments to uncover the signals behind cell behavior there. More generally, I got into modeling with an interest in locust movement and traffic flow, and I still show videos of these dynamics to motivate what `complex systems’ are in my talks and classes. So long term, it would be fun to someday work on problems in those areas. In general, I appreciate that applied mathematics provides a lot of flexibility––I’m looking forward to my group’s research continuing to evolve into new areas based on the interests of my students and conversations with other scientists.”
More information about Volkening and her group’s work is available on her website and Google Scholar. She’s also happy to connect more over email.
