How cells work together: the mathematics behind biological shapes
How do biological cells join forces to form a structure? In her PhD research, Daphne Nesenberend uses mathematics to show how forces and cooperation between cells create structure – and how simulations and experiments can reinforce each other.
Cells work together to build structures. Take the intestines: highly curved and folded, with an enormous surface area needed to absorb nutrients. But how do such shapes arise?
This process is called morphogenesis. ‘We know that cells communicate with each other through signalling molecules and forces,’ Nesenberend says. ‘But exactly how this leads to a particular shape is often unclear. Mathematics can help us understand that.’
Understanding how shapes form is important. It can also give researchers insight into what goes wrong in conditions such as growth disorders or cancer.
‘Exactly how this leads to a particular shape is often unclear. Mathematics can help us understand that.’
Simulating what cells do
In one of her projects, Nesenberend worked with chemists who had developed a synthetic gel that mimics the environment of cells in the body. Human cells were placed inside this gel.
One striking observation was that cells at the edge became elongated and oriented themselves towards the centre. Order emerged. Nesenberend helped explain this behaviour using simulations and mathematical analyses.
She used the Cellular Potts model. ‘In the model, each cell is represented as a small cluster of points on a grid,’ she explains. ‘Each cell follows simple rules, such as how large it can grow and how it can change shape.’ These rules were developed together with the chemists. ‘Through their observations, they often already have an idea of the mechanism. With models, we can test which processes are essential.’
The role of stiffness and collective behaviour
The simulations showed that a specific property of the gel was crucial: ‘strain stiffening’. The more the gel is stretched, the stiffer it becomes. Without this property, the cells remained round.
Another important factor was the number of cells present. Alignment only appeared once their number passed a certain threshold. ‘It shows that they need each other,’ she says. ‘It’s a form of collective behaviour.’
The model’s results were later confirmed in the laboratory. ‘It really works both ways. The model suggests ideas for new experiments, and experiments help you improve the model.’
Simulations alone are not enough
Nesenberend stresses that simulations alone are not sufficient. The mathematical analysis is just as important. ‘In a simulation you choose specific values for the variables. But analysis shows what will always happen, regardless of the exact values. That means you can prove that a certain structure will appear if certain conditions are met.’
‘The nice thing about analysis is that you know the result is solid. By combining simulation and mathematics, you can eventually say something meaningful about how a particular situation works. That’s what makes mathematics so enjoyable.’
‘A PhD is ultimately still an individual journey, but collaboration was the part I enjoyed most. I’d like to do more of that.’
Collaboration: the most enjoyable – and the most challenging – part
For Nesenberend, collaboration was the most rewarding part of her PhD. ‘My background is in both mathematics and life sciences, so I speak both “languages”. I’m not the kind of mathematician who wants to sit alone in a room all day. I want to understand what biologists and chemists actually need – and contribute to that with mathematics.’
At the same time, collaboration can be challenging. ‘Setting up a project like this takes a lot of time, networking, and persuasion. And every field has its own abbreviations and jargon.’
‘A PhD is ultimately still an individual journey,’ she concludes. ‘But collaboration was the part I enjoyed most. I’d like to do more of that.’
PhD defence
Daphne Nesenberend will defend her thesis, titled ‘Mathematical models for mechanically induced morphogenetic pattern formation’, on 11 March 2026 at the Academy Building. Her supervisors are Arjen Doelman, Roeland Merks and Frits Veerman.