Cilia physics explains the successful swimming of sperm

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Sperm can’t claim all the credit for strong swimming. Hairy rugs lining the inside of the fallopian tubes give an extra boost that pushes them upward.

Now, theoretical physicist John UO Toner has an explanation for how these hairs, called cilia, move fluids and small molecules in the body.

He created a mathematical model that explains how cilia align to move particles in a fixed direction. The fluid flowing over the cilia helps the hair to curl in the same direction and push the particles along. He and his colleagues describe the equations in two new papers, published in December in physical review And Physical Review Letters.

Toner has been studying flow physics for years. He previously developed equations that explain how hundreds of birds swoop simultaneously across the sky, or how flocks of fish swim in unison. He received the 2020 Lars Onsager Award from the American Physical Society for his work.

But considering the issue of cilia requires a slightly different approach. “In biological systems, a lot of important action takes place at a surface where a solid meets a liquid,” Toner said. “What I’ve come to realize is that this is a completely different kind of flow than I was thinking.”

Cilia move not only sperm, but many other types of crucial movements within the body, including removing mucus from the lungs. They present an interesting challenge from a physical perspective, Toner said, because the hair is held in place on one end.

Alignment is easier when it comes to movement. For example, Toner envisions a large group of people standing in a foggy field. They can see people who are close to them, but not everyone in the crowd. If they were asked to all point in the same way, they wouldn’t. But ask the group to all go in the same direction, and they will succeed.

It turns out that the fluid moving over the cilia has an important effect. It provides movement that helps the cilia align in one direction, creating a feedback loop that in turn pushes the fluid in a consistent direction. That is, the system stabilizes and corrects itself.

“Individual hairs make little mistakes, but the overall fluid pulls it back in,” Toner said, like being drawn into a stream.

In the future, Toner wants to improve his model to more closely replicate what is seen in biological systems.

“We treated the fluid over the carpet of cilia as if it were infinitely deep,” he said. But fluids in the body usually move through small channels. Determining the fluid depth in the model will change the expected interactions between cilia. How this changes the overall behavior of the entire system remains an open question, Toner said.

Are the movements of tiny hair-like structures a key to our health?

more information:
Niladri Sarkar et al., Hydrodynamic theory of flow at a solid-liquid interface: long-range ordering and giant number fluctuations, physical review (2021). DOI: 10.1103/ PhysRevE.104.064611

Niladri Sarkar et al, Flowing Bottom Feeders: Flowing at Solid-Liquid Interfaces, Physical Review Letters (2021). DOI: 10.1103/ PhysRevLett.127.268004

Provided by University of Oregon

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