The Geometry of Adhesion

Simulating the encounter

A single cell caught up in the flow of blood, air, or water often depends on its ability to latch onto passing surfaces—in short, its ability to stick. That’s why researchers in Germany created a model that addresses what geometry makes some cells stickier than others. According to their model, reported in Physical Review Letters in September 2006, a cell that efficiently initiates adhesion is dotted with elevated receptor patches—knobby protrusions tipped with receptor molecules. The taller the patches, the better.


“Once you start thinking about it, it’s obvious.” says Christian Korn, a PhD candidate in theoretical physics at the Max Planck Institute of Colloids and Interfaces and one of the authors. “You need these protrusions.”


Cell adhesion requires two steps: encounter and docking. Korn and Ulrich Schwarz, PhD, a theoretical bio-physicist and assistant professor at the University of Heidelberg, modeled the encounter step—to identify the cells that are best at initiating adhesion.


The knobby surface of a white blood cell (top) facilitates sticking, and the smooth surface of a healthy red blood cell (bottom) discourages it. Scanning electron micrograph courtesy of CDC/Janice Carr.To create the model, the researchers simulated spheres sporting receptor patches and flowing above a flat surface with the corresponding ligands. The stickiness of cells was measured by how long it took for the first receptor-ligand encounter to occur. Korn and Schwarz then varied the number, size, and height of the receptor patches to discover the optimum receptor patch geometry. Plastering the cell with as many receptor patches as possible—akin to fully wrapping a bouncy ball in tape—is not the best strategy, they found. “The cell can have only 1% of the surface covered with receptors, and it works almost as efficiently as if it were 100% covered,” Korn says. In addition, increasing the lateral size of the patches—placing bigger bits of tape on the ball—doesn’t make much difference. Yet increasing the height of those receptor patches—using raised stickers instead of tape—helps the receptor patches find their target ligands sooner compared to lower receptor patches on a cell of the same size.


The researchers point to similar geometry repeated across vastly different systems in nature. Wrinkled white blood cells, which often need to dock close to an infection, place their receptor patches on the tips of finger-like microvilli. Red blood cells, in contrast, are surfboard smooth. But when a red blood cell becomes infected with malaria, it also grows knobs and new receptors on its surface to slow its progress toward destruction in the spleen. Even sticky pollen grains and wandering diatoms in the ocean, Korn says, display spiky geometry.


For experimentalists now probing such systems, says Cheng Zhu, PhD, a professor of biomedical engineering at Georgia Tech, the model is interesting, but only part of the equation. “Their model may explain cases where encounter is the limiting step,” he says. “Without the complete equation, it’s difficult to say how this might affect data interpretation in cases where docking is limiting.”


Korn is now extending the model to include binding as well as encounter. He is optimistic that his model will continue to uncover general characteristics of sticky cells. “The big strength of theoretical modeling,” he says, “is that you can get the big picture because you focus on a few essential aspects.”


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