How do cells behave collectively? A conversation with Andreas Buttenschoen

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 our understanding of collective cell behavior is Andreas Buttenschoen.

Andreas Buttenschoen, assistant professor, Department of Mathematics and Statistics, University of Massachusetts Amherst

Andreas Buttenschoen is an assistant professor in the Department of Mathematics and Statistics at the University of Massachusetts Amherst. The Buttenschoen Lab uses mathematical modeling and computational approaches to understand how cells organize into functional tissues.

We spoke with Andreas Buttenschoen to learn more about his work applying mathematical tools and models to collective behavior at the subcellular, cellular, and tissue levels. 

What is a big question you’ve been asking throughout your research?

“The central motivation that connects the various things I do is that I really want to understand the underlying communication mechanisms, signaling pathways, and chemical and mechanical interactions that allow cells to behave collectively. In particular, I’m interested in spatial collective problem solving, like how do they migrate from one place to another? How do they find and identify pathogens in immune cells? How do they aggregate around them, or how do they close a wound? We observe a behavior, and then my job is to develop mathematical tools and models, computational or analytical, to identify the universal principles or essential mechanisms that generate those behaviors.”

What disciplines does your research integrate?

“I am very comfortable calling myself an applied mathematician. What that means for me is that I do scientific computing and analytical work, but I also like to interact with experimental folks to find interesting problems and see whether my approaches provide them any insight or contributions for their pursuits. More specifically, I develop models that live at multiple scales: at the subcellular, cellular, and tissue level. Each requires different techniques. At the cellular and subcellular levels, I really like agent-based models that almost look like little computer games. At the tissue level, I like to work on nonlocal partial differential equation models because they capture the mean behavior of these agent-based models. But contrary to agent-based models are analyzable by well-developed mathematical techniques.”

Where do you find inspiration?

“Biology is a great place to find interesting mathematical problems. Often my inspiration comes from an unexpected phenomenon in cell biology, which inspires interesting model constructions that frequently lead to interesting mathematics. And occasionally you get to contribute back to biology with insights that would have remained elusive without mathematical modeling”. 

What aspects of your research could be interesting to mathematicians or applied to biology?

“On the mathematical side, this connection of detailed agent-based models to nonlocal mean-field equations is something that folks are interested in. The mean-field models describe what we can observe, and then the microscopic detail models describe the underlying microscopic mechanism. Connecting these two things formally is something that mathematicians, physicists, and others have worked on for a very long time. Mathematicians will appreciate that fundamental connection. For biologists, the ones that I’ve interacted with ask questions on problems that are very data sparse. In my opinion, mechanistic modeling is crucial in data- sparse situations. In those cases, I want my models to be able to test biological hypotheses and, as a next step, suggest new experimental setups that could distinguish between competing hypotheses.

What about the NITMB do you find exciting?

“There are two things that I really like about the NITMB. One is that the mission clearly is to integrate experimentalists and mathematicians, which is a difficult task. On the experimentalist side, the folks that I have the easiest time talking with had some exposure to mathematical modelling somewhere before. But these folks are still rare. Having a national institute focused on cultivating the integration of mathematics and biology will make it easier to convince folks on both sides that this is a fruitful endeavor. The other thing that I like is the emphasis on mentorship and education for young folks working at this interface. It’s one thing to have the institute, but then, you need to cultivate the talent for these pursuits. The training aspect aligns very well with how I like to train, and what I want to achieve with my own students and mentees. 

What career achievement are you most proud of?

“My most recent one is that I had my first independent student. Together we put out our first truly independent lab preprint. That was a nice milestone. The other thing that I am proud of is that my PhD thesis on nonlocal models was published as a small book. 

Outside of your research, what other interests do you have?

“I really like to ski. I did my postdoc in British Columbia, and before that I did my PhD in Alberta, so the mountains were right there, and I spent a lot of time in them. Having moved to the east coast, I’ve switched to various types of cycling. Road, gravel, and I even have a mountain bike now to explore the hills of Western Massachusetts.”

What are you hoping to work on in the future?

“I’m at a stage where I’ve become good at a number of computational and mathematical tools, and I want to challenge them and myself by applying them to more challenging biological problems. My plan is to work on digital twins for certain experimental systems. I have built some 3D cell-based models, which can handle complex environments and cell-matrix and cell-cell interactions, and they could form a great starting point for a digital twin of an experimental system in which those features are crucial. Naturally, I expect to encounter challenges along the way, but I view those as a source of novel interesting mathematical problems for the years to come.

More information on Andreas Buttenschoen and his lab’s work is available on his website and Google Scholar.