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Understanding Biological Synchrony with Applied Mathematics: A Conversation with Daniel Abrams

“Synchrony is everywhere once you start to look for it.” 


The NSF-Simons National Institute for Theory and Mathematics in Biology is composed of expert mathematicians and biologists at the forefront of innovative research converging mathematics and biology to develop new math and inspire biological discovery. Each member of the NITMB brings a unique perspective that is vital for achieving the NITMB’s mission to integrate the disciplines of mathematics and biology. In order to highlight the diversity of expertise present, and the valuable contributions of NITMB members, the NITMB will be sharing insight into one of our members every month. 

Daniel Abrams, Professor of Engineering Science and Applied Mathematics at Northwestern University 

Daniel Abrams is a Professor of Engineering Sciences and Applied Mathematics at Northwestern University. He is also Co-Director of the Northwestern Institute on Complex Systems (NICO), as well as a courtesy member of the Department of Physics and Astronomy at Northwestern University. Abrams is also a member of the NITMB, where he is leading the NITMB internal research project, ‘Modeling and Analysis of Synchronous Behavior in Biological Systems.’ Abrams is the Principal Investigator on this project, and he is collaborating with his postdoctoral researcher, Guy Amichay.  


We reached out to Professor Daniel Abrams to learn more about his work, his inspirations, and his hopes for the NITMB. 

What are you currently working on? 

“My research that’s most relevant to the NITMB is a study of how fireflies can synchronize. About 5% of firefly species synchronize. They start flashing individually in the evening, and then they look around at each other, apparently respond to one another, and adjust their flashing until all of them are flashing on and off in sync like Christmas lights. The particular firefly species I’m interested in is native to Thailand and Southeast Asia in general. What makes this species a great subject of study is that it’s mostly immobile while it synchronizes. The fireflies in Tennessee that synchronize fly around while they’re flashing. The ones in Thailand tend to hold still, sitting on a tree branch and flashing. That means we can identify individuals and study in detail how they make this happen. I’m interested in biological synchrony in general, how species communicate, and how communication evolved.” 

Photo by Evan Leith on Unsplash 

Where do you find inspiration? 

“My research is inspired by curiosity. I think that’s one of the great things about studying applied mathematics. You don’t have to fit into any particular box. You can look for places where mathematical tools are applicable across fields. Another interest of mine that is relevant to NITMB is evolutionary theory, so how life evolved, and how it continues to evolve and adapt. That’s one area where a lot of mathematical tools have had some success in the past. I think there’s a lot more to be gained. But there’s also opportunity for mathematical modeling in engineering, in physics, in astronomy, and all over the place in science. I think that’s the great thing about applied math is that it lets us make those leaps between fields.” 

What inspired you to join the NITMB? 

“I thought it was a natural fit. It’s such a great opportunity to have an institute focused on combining math and biology here in Chicago. I’ve always thought we didn’t have sufficient collaboration with the University of Chicago and Northwestern, and I think we have a lot of people with complementary skills on the two campuses. This is the perfect opportunity to get together with them. We have great people on the biological side and great people on the mathematical side. It absolutely makes sense to pool our resources and do the best work we can together.” 

What are you working on now that relates to the goals of the NITMB? 

“I think there’s new math to be pursued in modeling the way these fireflies, and other organisms, accomplish their synchrony. One thing we’ve already seen some hints of is something called a chimera state. It’s a mathematical pattern that I’ve worked on for years, and it’s only been, in some ways, a theoretical construct of applied mathematics, of the study of coupled oscillators. It’s been created in the lab, but nobody has definitive evidence of it in nature. There have been some hints in the past, so we think we’re going to be the first to nail down that this is occurring in nature spontaneously. There’s new math there. We’re also going to touch on the theory of complex networks because of the way that the fireflies interact with one another. It’s not a perfect grid in two dimensions or three dimensions. It’s really a cloud of fireflies, some who can see one another and some who can’t. So, we’re going to try to incorporate network topology, but also real positions in three-dimensional space using stereo videography that lets us reconstruct positions of each firefly. We’re getting this amazing data that is going to feed into new theories and new mathematical models, and then hopefully that will feed back into new biological understanding of how they accomplish these amazing displays and why. This is exactly why we want something like the NITMB—to combine the strengths of both fields.” 

What career achievement are you most proud of? 

“The thing I’m most proud of is doing what I love by being able to work on a wide variety of problems. I have done work in a lot of different fields over the course of my career thus far, and the thread that ties it together is the mathematical modeling and mathematical approaches that I use. I’m proud I’ve been able to do science for the sake of science and follow my curiosity to different systems that are of interest.” 

What interests do you have outside of your research? 

“Just like my research has widespread areas of application, I have lots of other interests outside of science. A big one is foreign languages. I like learning what’s different and distinct in different languages and language families. I’ve studied Quechua, the language of the Incan empire that is still spoken by about 10 million people, mostly in Peru, Bolivia, and Ecuador. I’ve also studied Korean and Serbo-Croatian. I speak Spanish fairly fluently. In college I studied Mayan hieroglyphics. That may have been the first thing that really struck my interest. Deciphering Mayan hieroglyphics was really exciting to me, it’s kind of like code breaking.” 

What are you hoping to work on in the future? 

“Synchrony is everywhere once you start to look for it. The question is how universal can the model be?  We would like to see if the same synchrony model for fireflies works for fiddler crabs (which we’re also collecting new data for). And there are so many other examples of biological synchrony, like crickets and frogs synchronizing their calls. But there’s also synchrony at the organ level (e.g., in the heart) and cellular level. I also have a lot of interest in other evolutionary questions like, e.g., the origin of binary mating. Why are there two sexes? This question hasn’t been sufficiently answered, at least to my satisfaction, and there may be some more mathematical approaches to the question. Another thing I’d like to do related to this project comes from my postdoc Guy Amichay’s idea of trying to translate the mathematical models we’re using for biological synchrony to musical performers. These are some of many questions we want to explore, but we’re starting with fireflies because they are so charismatic and emblematic of the insect world. People have positive feelings about them as opposed to crickets or other insect species. A lot of insect species are threatened as insect habitats are threatened, so fireflies are an ambassador species that people can appreciate.” 


Daniel Abrams’ work with biological synchrony is a key example of the potential for new discoveries from the convergence of mathematics and biology. Applying mathematics in the study of biological synchrony will help to illuminate not just how fireflies flash in synchrony, but why such synchrony evolved in so many biological functions. Such findings will likely lead to further questions in biology, prompting new opportunities to apply mathematics in biology. This will contribute to the NITMB’s efforts to develop reinforced loops of discovery in the fields of mathematics and biology. We look forward not only to the findings of Abrams’ project, but also the new questions his work will inspire.  



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