# Simple math uncovers the mystery of how sperm swim

Scientists have created a numerical formula to model the rhythmic motion of a sperm's head and tail, which considerably cuts down on the calculations needed to understand a sperm’s journey to fertilizing an egg, according to a new report.

Published in the journal Physical Review Letters, the study revealed the sperm's tail produces a distinctive rhythm that catapults the sperm forward but also draws the head laterally and backward in a synchronized manner.

Effective fertility depends on a sperm effectively traveling through a fluid, but understanding the specifics of this motion is a complex issue.

"In order to observe, at the microscale, how a sperm achieves forward propulsion through fluid, sophisticated microscopic high precision techniques are currently employed,” Hermes Gadêlha, a mathematician from the University of York in the United Kingdom, said in a news release.

### Utilizing Computer Models

To reach their conclusion, the study team incorporated measurements of the sperm tail’s rhythmic beating into a computer model. The result was a better understanding of the fluid flow patterns that result from the tail’s movement.

"Numerical simulations are used to identify the flow around the sperm, but as the structures of the fluid are so complex, the data is particularly challenging to understand and use,” Gadêlha said. “Around 55 million spermatozoa are found in a given sample, so it is understandably very difficult to model how they move simultaneously.

"We wanted to create a mathematical formula that would simplify how we address this problem and make it easier to predict how large numbers of sperm swim,” he added. “This would help us understand why some sperm succeed and others fail."

By examining the motions of the head and tail, study scientists showed a sperm moves in a synchronized rhythmic way. This motion was recorded and analyzed to create a fairly simple mathematical formula that eliminates the need for intricate and expensive computer models to study this motion.

"This suggests that sperm stirs the fluid around in a very coordinated way to achieve locomotion, not too dissimilar to the way in which magnetic fields are formed around magnets,” Gadêlha said. “So although the fluid drag makes it very difficult for the sperm to make forward motion, it does coordinate with its rhythmic movements to ensure that only a few selected ones achieve forward propulsion."

The new simple mathematical formula to predict the fluid motions of one sperm can now be used to create predictions on larger quantities of cells. The study team said they hope their work will have ramifications for new infertility breakthroughs.

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Image credit: University of New York