A mathematical study suggests that when neighboring cells adjust their pulling forces in response to one another, they create an attraction that could help explain why cells gather on soft surfaces.
Imagine two people standing on a stretchy sheet. When one pulls, the other feels the fabric move and responds with a pull of their own. Each adjustment changes what the other feels.
Something similar happens between living cells. They tug on the material around them, sense the stretching caused by their neighbors, and adjust their own forces. Now, a new theoretical study suggests that this back-and-forth can create an attraction that helps draw cells together.
The research, by Dr. Assaf Zemel of the Hebrew University of Jerusalem , published in Proceedings of the National Academy of Sciences (PNAS) offers a physical explanation for a puzzling observation: cells grown on soft surfaces often gather into groups or networks, while those on harder surfaces can remain more dispersed.
Cells live within a supporting material called the extracellular matrix—a network of fibers surrounding them that provides structure and transmits forces. By pulling on this material, a cell changes the mechanical environment its neighbors experience.
Scientists have long known that cells communicate this way. The challenge is understanding what happens when both sides keep responding.
Zemel’s study develops a mathematical framework that accounts for this mutual adjustment. Rather than treating each cell’s pull as fixed, the theory allows it to change in response to the stretching produced by surrounding cells.
The calculations reveal an additional, short-range interaction. For cells that strengthen their pulling forces when stretched, this interaction is attractive: their responses generate stresses in the surrounding material that tend to pull them together.
In other words, the cells’ ability to react to one another becomes part of what draws them closer.
The mechanism is physically analogous to the universally attractive van der Waals interactions between molecules, which drive molecular cohesion and the condensation of matter.
Here, however, the interaction is carried by the deformation of the cells’ surroundings. Living cells actively adjust their internal force-generating machinery, and those adjustments change the forces experienced by their neighbors.
“What drew me to this problem is that a question about living cells leads to a familiar idea from molecular physics: how stereotyped cellular responses to external perturbations can give rise to a universal attraction between cells,” said Dr. Assaf Zemel. “Cells are far more complex than molecules—they actively sense and respond to their surroundings. Bringing a fundamental physical principle into biology helps us understand how those responses could turn a neighbor’s pull into a force that brings cells together.”
One of the study’s most striking predictions concerns softness.
The conventional elastic interaction considered in earlier models is strongest at an intermediate surface stiffness and weakens as the surface becomes very soft. The additional attraction identified in this study behaves differently: it strengthens as the supporting material softens.
Distance also matters. The theory predicts that cells whose overall mechanical interaction is repulsive when they are farther apart can become attractive at closer separations, as the effect of their mutual adjustments grows stronger.
Together, these findings offer a possible explanation for why soft environments can encourage cells to accumulate.
The study is based on mathematical analysis rather than new experiments with living cells. It uses simplified representations of cells to uncover a physical principle, and more detailed models will be needed to describe their behavior accurately at very close distances.
Its predictions nevertheless suggest clear experimental questions. Researchers could position cells at controlled distances on surfaces of different stiffnesses, then measure how their pulling forces and internal structures change in response to one another.
Understanding these interactions could help explain how cells organize into tissues and networks. Mechanical communication is also relevant to processes such as fibrosis and cancer, although the study does not test treatments or establish clinical applications.
The work points to a simple possibility with broad implications: part of what brings cells together may lie in how they respond to each other’s pull.
Proceedings of the National Academy of Sciences
Observational study
Not applicable
Elastic interactions of mechanically polarizable cells
13-Nov-2026