Swimming through complex bodily fluids gets simpler

It’s an uncomfortable truth of life that our bodily fluids are chock full of microscopic swimming organisms — maybe even more uncomfortable to researchers that those little swimmers do laps faster than the theories describing their motion would allow.

“A lot of these organisms get studied because they have a hand in bad outcomes for human health — they are bacteria or parasites,” says Saverio Spagnolie, a UW–Madison math professor.

Spagnolie and collaborators from Brown University have developed a technique for measuring and predicting the mechanics of swimming microbes with applications for studying the spread of bacterial infections or the movement of sperm in infertility research.

“Even in a fluid as simple as water, movement for organisms this small is very counter-intuitive,” Spagnolie says.

To tiny bacteria, water feels more like molasses would to a swimming human.

“Your usual strategies for swimming in water wouldn’t work if you were their size,” Spagnolie says. “You’d kick to transfer your momentum and move yourself forward, but the fluid around you is so viscous — so thick — that as soon as you stop kicking, the fluid will stop moving. You’d go nowhere.”

Many organisms aren’t kicking. They use whip-like flagella to move through complex fluids like mucus — a liquid best described as viscoelastic, because of the various long protein molecules it contains.

“Viscoelastic fluids are a very common extra complication of the physics that you would see in a biological setting,” Spagnolie says. “Swimming through a fluid with all these long molecules stretches them out, and the forces that hold them together make them snap back. That’s why mucus can be bouncy.”

Our own stomach linings are coated in a fluid that is too thick and elastic for certain microbial invaders to penetrate — sparing us nasty infections.

Swimmers who have found success in complex, viscoelastic fluid have figured out how to take advantage of those forces. They spin flagella — often helical in shape — in ways that may actually pass energy to the springy fluid and then reclaim it to build speed.

For some time, math has been unable to describe how it is that some microorganisms (such as bacteria) can move faster through complex viscoelastic fluids than they can through simple non-elastic liquids — but others (such as the nematode C. elegans, a common organism in lab studies) slow down substantially.

In a study published Aug. 9 in the journal Physical Review Letters, Spagnolie and collaborators Bin Liu and Thomas Powers of Brown University plot a mathematical path connecting numerical theory to experimental results.

“Describing this swimming movement by solving partial differential equations in three dimensions with complicated fluid conditions is computationally very intensive,” says Spagnolile, whose work was funded by the National Science Foundation. “So what we’ve done is take advantage of the helical symmetry of successful swimmers’ flagella.”

Spagnolie’s technique takes a two-dimensional slice of fluid and flagellum to describe a steady state of fluid put in motion by an organism. To find conditions like fluid pressure or direction at any given point along the flagellum means simply rotating the two-dimensional mathematical picture of the bacterial propeller.

The results show that helical shapes wound at a sharper angle allow for faster swimming speeds — up to a point.

“Shallower angles don’t help with speed, which matches the experimental results people have found,” Spagnolie says. “Those results verify our approach, and that gives a leg up to anyone studying how these microorganisms move.”

That pool of researchers is deep and wide, according to Spagnolie, and any improvement can sharpen the way scientists understand and exploit microbes.

“It gives you an idea of where it’s even possible for an organism to swim or not, which is useful on all sorts of levels” Spagnolie says, possibly providing a way to confine the movement of bacteria. “One might think of strategies for changing the fluid environments so that certain unwelcome organisms can’t swim through them.”