A sperm’s tail creates a characteristic rhythm that pushes the sperm forward, but also pulls the head backwards and sideways in a coordinated way, report researchers.

They developed a mathematical formula based on these movements, which could make it easier to understand and predict how sperm make the difficult journey towards fertilizing an egg.

The team aims to use these new findings to understand how larger groups of sperm behave and interact, a task that would be impossible using modern observational techniques. The work could provide new insights into treating male infertility.

“In order to observe, at the microscale, how a sperm achieves forward propulsion through fluid, sophisticated microscopic high precision techniques are currently employed,” says Hermes Gadêlha of the University of York’s mathematics department.

“Measurements of the beat of the sperm’s tail are fed into a computer model, which then helps to understand the fluid flow patterns that result from this 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. 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. This would help us understand why some sperm succeed and others fail.”

##### Could sperm-blocking hydrogel replace vasectomy?

By analyzing the head and tail movements of the sperm, researchers have now shown that the sperm moves the fluid in a coordinated rhythmic way, which can be captured to form a relatively simple mathematical formula. This means complex and expensive computer simulations are no longer necessary to understand how the fluid moves as the sperm swim.

The research demonstrates that the sperm has to make multiple contradictory movements, such as moving backwards, in order to propel itself forward towards the egg.

The whip-like tail of the sperm has a particular rhythm that pulls the head backwards and sideways to create a jerky fluid flow, countering some of the intense friction that their small size creates.

“It is true when scientists say how miraculous it is that a sperm ever reaches an egg, but the human body has a very sophisticated system of making sure the right cells come together,” says Gadêlha.

“You would assume that the jerky movements of the sperm would have a very random impact on the fluid flow around it, making it even more difficult for competing sperm cells to navigate through it, but in fact you see well defined patterns forming in the fluid around the sperm.

“This suggests that the 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. 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.”

Now that the team has a mathematical formula that can predict the fluid movement of one sperm, the next step is to use the model for predictions on larger numbers of cells.

The research appears in the journal *Physical Review Letters*. Coauthors are from the Universities of York, Birmingham, and Oxford, and Kyoto University.

*Source: University of York*