Young woman with orange T-Shirt and chalk in the hand in front of a blackboart with mathematical formulas
Angelika Manhart combines molecular biology and mathematics. © Tom Harris

When a group of kindergarteners goes on an outing, all roles and responsibilities are usually clearly assigned: someone leads the group, others stay in the middle, and the person all the way in the back makes sure that nobody gets lost. Members of the group do different things – and this is exactly why the group can move ahead. What’s easy to see in this example can help us understand a complex phenomenon: cell migration.

Also cells sometimes travel in groups. They wander about, find paths through the terrain, respond to obstacles and signals, stick to or let go of each other. In the early developmental stages of an organism, cells have to get to the right place to form tissue and organs. When there is a wound to heal, they move to the place of injury to repair the tissue. And for somebody suffering from cancer, cell migration can be highly dangerous: in this case, tumor cells leave the place where they first developed and spread in the body. This process – metastasis – is one of the most difficult things to treat for oncologists.

But why do cancer cells cause greater damage when it’s not a single cell but a whole cluster that migrates to another part of the body? And how are roles assigned in such groups: leading the group, keeping it together, and staying in step?

This is what Angelika Manhart is interested in. The mathematician and molecular biologist at the University of Vienna combines her expertise in mathematics, computer science, and biology. In the ASTRA project, which is funded by the FWF, she investigates how heterogeneous cell groups, i.e., groups of cells with different properties, self-organize and migrate to other parts of the body.

Unraveling Cell Coordination

Using mathematics and computer simulations, FWF ASTRA Award winner Angelika Manhart is investigating how cells communicate with one another and coordinate their behavior. She aims to better understand why coordinated movement can give cancer cells a decisive advantage during metastasis.

Somewhere between a billiard ball and a human being

“For one thing, cells are way more complex than simple mechanical objects studied in physics, say billiard balls,” Manhart explains. “Then again, they are not as complex as human beings, who move and interact in different ways. Cells are somewhere in between, but you really shouldn’t underestimate their complexity.” It’s this ambiguous nature that makes cell migration so hard to describe. Physical factors play a role: forces, friction, adhesion, the topography of their surroundings. But cells are also living systems. They perceive signals, change their behavior, and communicate with other cells. In her work, Manhart tries to capture these processes in mathematical models.

“You really shouldn’t underestimate the complexity of cells.”

Why equations are the best answers to some questions

The scientist discovered this interdisciplinary field of research early in her career. The daughter of two mathematicians, Manhart took an interest in the natural sciences already as a young girl. When later she could not decide between mathematics and molecular biology, she simply chose both. At the University of Vienna, she completed studies in mathematics and molecular biology, after which she consistently found ways to connect these two worlds.

Manhart’s mathematical models don’t depict the full breadth of biological reality. They simplify. “Modelling means removing things,” she explains. The key is to delete enough to keep a model manageable – while keeping enough to adequately explain the phenomenon.

Biological assumptions turn into equations; hypotheses come to life in computer simulations. This way, Manhart can test how cell clusters behave when individual properties are changed: What happens when some cells are stickier than others? Or more agile? Which combinations keep a group together, even as the cluster migrates?

A simulation of the migration of cells (blue) through deformable surroundings (green)
A simulation of the migration of cells (blue) through deformable surroundings (green). © Angelika Manhart

How simulations complement experiments

Juliane Winkler of the Medical University of Vienna is a frequent collaborator of Manhart’s. Among other things, Winkler works on breast cancer cells, including those of patients. The models are not intended to replace experiments but to add further insights. They can point to plausible mechanisms and show where assumptions fall short.

Manhart finds situations that allow for different interpretations most intriguing. “When several hypotheses seem to make sense, I love to design not one but a whole set of models,” she says. Their comparison then shows which explanation fits the data – or does not.

Dangerous clusters

In her cancer research, Manhart’s project particularly focuses on the question why some cell clusters metastasize “more successfully” than others. Tumor cells can adopt various states. Some form very stable connections, while others are nimbler and easily detach from the tissue. A tumor can benefit from having different kinds of cells.

Sometimes, the more agile cells assume certain positions in a group while the more sticky cells serve as glue. Just as in a group hike, not every member has to do the same job. It is possible that heterogeneous cells help the group move through tissue more efficiently.

Mathematics can reveal which setups work best: Does it make more sense for all cells to be very nimble? Or for some to have more pronounced adhesive properties? Which combinations make cell clusters most adaptable?

Microscopic image of heterogeneous cancer tissue. The colors show the different states of the cells: vimentin, which is typical for mesenchymal cells (M), is shown in red; E-cadherin, which is typical for epithelial cells, in yellow, and cell nuclei in blue.
Microscopic image of heterogeneous cancer tissue. The colors show the different states of the cells: vimentin, which is typical for mesenchymal cells (M), is shown in red; E-cadherin, which is typical for epithelial cells, in yellow, and cell nuclei in blue. © Juliane Winkler

Basic research with a medical horizon

Manhart does basic research. It is her goal to better understand how cells with various properties work together and how they benefit from such cooperation. This “basic” knowledge might prove highly valuable in the future. A better understanding of why some groups of cells are more prone to metastasize can help us develop new hypotheses for the diagnosis, therapy, and treatment of breast and other types of cancer. We might one day even be able to assess which tumors are especially likely to metastasize. “It would be terrific to understand why one tumor metastasizes while another doesn’t. It’s possible that we could use this information in some way to reduce or prevent metastasis,” Manhart explains.

The robustness of life

Cell migration not only matters in cancer treatment. Similar principles come to play in embryonic development and tissue repair. In the course of their development, cells must adopt their identity, assume different tasks, and get to the right places. To heal a wound, immune system cells, blood platelets, and other types of cells migrate to the place of injury. Also this movement must be coordinated.

Manhart is particularly fascinated by the many feedback loops and control mechanisms she has witnessed in the processes of these live systems. Cells regulate their own activity, react to disturbances, activate safety procedures. When something goes wrong, there are often safety nets in place that come to the fore. “It is truly astonishing how robust these regulation mechanisms are.”

“It is truly astonishing how robust these regulation mechanisms are.”

Research outside the ivory tower

Manhart is not only passionate about research but also about science communication. “I really think it’s important for researchers to make an effort to explain to the next generation and the public at large what they are working on and what’s so fascinating about it,” Manhart says. She explains complex topics not only to her students and colleagues but also to audiences outside the university. She even taught her four-year-old son about cells and how they are so tiny that they are invisible to the naked eye.

“Research is still the best system of knowledge production we know.”

Manhart also engages in visual science communication: among other things, she uses illustrations and watercolor paintings to make scientific knowledge more accessible. For Manhart, this is part of her responsibilities as a researcher. She is convinced that research needs to leave the ivory tower. It’s often questions asked by people outside of a researcher’s discipline that help them remember what’s most important.

At a time when trust in science can no longer be taken for granted, Manhart considers it crucial to show people that scientific methods are extremely meticulous, critical, and can always be tested. “After all, it is still the best system of knowledge production we know,” she says.

This makes sense for a researcher who works across the boundaries of various disciplines. In her models, she translates biology into mathematics. In her communication work, she turns research into images, analogies, and explanations. Both require simplification – but in a way that allows us to see what’s essential.

About the researcher

Angelika Manhart is a mathematician at the University of Vienna focusing on mathematical biology. She studied mathematics and molecular biology at the University of Vienna. As a researcher, she connects mathematical modelling, computer simulations, and biology in her work. In her ASTRA Project, which is funded by the FWF, she explores how heterogeneous cell groups organize themselves and travel through their surroundings. She is particularly interested in collective cell migration and its role in cancer and metastasis.

In a collaboration with Juliane Winkler from the Medical University of Vienna, she investigates, among other things, breast cancer cells to gain insights about why cell groups metastasize more successfully than individual cells. Her findings are highly valuable for processes taking place in embryonic development, tissue repair, and the self-organization of living systems.