Open any biology textbook and it becomes instantly clear that this area of study is incredibly complex. From the atomic-level structure of DNA to the relationships between prey and predator populations, biology encompasses an incredibly broad spectrum of molecules, organisms, and systems, all of which scientists are trying to understand in detail.

Yoichiro Moris career is focused on developing mathematical solutions to help address unanswered questions in biology and, in turn, to invigorate mathematics by introducing new questions inspired by biological problems. His research demonstrates how a fundamental mathematical understanding can provide new insights into complex systems and lead to new theoretical developments. Now, as the Calabi-Simons Visiting Professorof Mathematics and Biology, he aims to foster connections between researchers at Penn.

Moris latest research, published in the Proceedings of the National Academy of Sciences, stems from his interest in cell movement. Biologists have studied how cells rearrange their cytoskeleton, internal filaments that give cells structure, and use mechanical forces to move themselves forward. But theres a second force always acting on cells whose role in movement is less understood: osmosis. Osmotic and ionic regulation is a key component of cell biology, but biologists have yet to figure out if it could also play a role in how cells move.

Through a combination of experiments, conducted by collaborators at Johns Hopkins University, and mathematical models, the researchers found that its more advantageous for cells to use their osmosis-powered engines to move when they are in environments with high mechanical resistance, or where the space is crowded by cells or particles. They also found that having a cell membrane thats permeable to water also helped cells move more easily.

This paper is also one of the few studies that could directly compare osmotic engines with cell movement powered by the cytoskeleton, thanks in part to Moris previous work on how cells control their size. Mori was able to apply the thermodynamic framework to this problem, a technique that could be extended to other areas of biology in the future.

Despite his success in using math to help solve biological problems, Mori tries to stay humble. There are a lot of interesting biological questions, but many questions are not inherently mathematical, he says. Part of the challenge is that many systems in biology are quite complicated, especially compared to other natural sciences, like physics, where systems can be modeled more easily. Biology data are also more variable, and there is more uncertainty about how systems actually work.

Science has different phases, Mori explains. At the beginning you have to name things; the first thing is to list everything, and its only then that you can start to understand relationships. Most of biology up to the end of the 20th century was spent on naming things, but with molecular biology we can now start talking about relationships. Now, mathematics can start to play an important role.

Moris own unique academic path has also helped him see firsthand the role of math in biology. While attending medical school at the University of Tokyo, he realized that his passion for math and physics was stronger than for clinical medicine or benchtop research. After finishing his board exams, he made the seemingly unorthodox decision to join a Ph.D. program in mathematics at New York University. I have a lot of respect for experimentalists, in particular because I failed so miserably, says Mori. I found that scribbling equations on paper is the only thing I can actually do, and what I do is comparatively quite easy.

As the Calabi-Simons Visiting Professor, and co-director of the Center for Mathematical Biology, Mori aims to promote this area of research at Penn by bringing together faculty, graduate students, and researchers working at the interface of fundamental mathematics and other fields in the natural sciences like biology and medicine.

Theres so much exciting science going on in every corner of Penn, and I think there can be some really interesting collaborations and synergies, says Mori, adding that Penns strong history in soft condensed matter physics and the research portfolio of the medical school will also be instrumental in his own work on mathematical physiology and biophysics.

Mori also emphasizes Penns collaborative spirit as essential for future progress in this field. What I found through the years is that if you want to do really interesting things, you dont just sit in your office and think, you have to go talk to people. Getting ideas from other people, sharing your ideas with other people, and working with people are essential.

This research was supported by National Science Foundation Grant DMS-1620316.

Yoichiro Mori is the Calabi-Simons Visiting Professor ofMathematics and Biology with appointments in the Department of Mathematics and the Department of Biology in the School of Arts and Sciences at the University of Pennsylvania.

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Where math meets biology - Penn: Office of University Communications