Mathematical formula describes how sperm swim

The movement of sperm can be explained by a relatively simple mathematical formula, according to new research.

The research team – from the Universities of York, Birmingham, Oxford and Kyoto University, Japan – believe that this formula will remove the need for complex, expensive computer simulations currently required to understand how sperm moves through fluid. It could help them to understand how larger groups of sperm move and interact, and provide new insights into treating male infertility by explaining why some men's sperm don't swim strongly enough to fertilise an egg.

'Around 55 million spermatozoa are found in a given sample, so it is understandably very difficult to model how they move simultaneously,' said mathematician Dr Hermes Gadêlha of University of York, one of the co-authors of the study. '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.'

The researchers filmed a sample from a sperm donor under a microscope and analysed the beat of individual sperm tails. They found that the sperm's tail creates a characteristic, jerky rhythm that propels the sperm forward but simultaneously pulls the head backwards and sideways. The backwards and sideways movements counter some of the intense friction created as the tiny sperm cell moves through fluid. This combination of movements help sperm move towards the egg.

'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,' said Dr Gadêlha, '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.'

The research team then recreated the movements of a single sperm in a mathematical formula. They plan to use the formula to predict the movements of large numbers of sperm – a task that would have been impossible using modern observational techniques alone.

However, Professor Allan Pacey, a sperm expert from the University of Sheffield, told the BBC: 'This might help infertility treatment in some small way but there are lots of other factors to consider too.'

While successful fertilisation relies on sperm's movements through fluid, it can also be affected by many other factors such as the number of sperm available, the DNA present in the head of the sperm, and whether the sperm is in the right place at the right time.

The research was published in Physical Review Letters.