Sperm caught breaking Newton’s third law of motion

Some biological cells swim freely in a way that apparently breaks one of Newton’s laws of motion – but only if they have strange elastic properties.

Human sperm cells are law-breakers

Human sperm cells and some microorganisms swim by deforming their bodies in a way that breaks Newton’s third law of motion – and we’re closer to understanding how they do it. The findings could eventually inspire researchers to develop tiny robots that also violate this law as they swim.

Famously, Newton’s third law can be summed up in the phrase “for every action, there is an equal and opposite reaction”. This means that as you push against a wall, the wall pushes back on you. “But recently, physicists started to explore mechanics without Newton’s third law,” says Kenta Ishimoto at Kyoto University in Japan. “Here, if you push a wall, it does not necessarily push back – it may escape away from you.”

Ishimoto and his colleagues wanted to study this property in tiny biological swimmers.

They focused on human sperm cells and Chlamydomonasalgae. Both swim using flagella – slender, hair-like filaments that stick out from the cell’s main body. Flagella are elastic, and can change shape to interact with the fluid surrounding the cell. This helps propel the cell forward in a so-called “non-reciprocal” way, meaning that they violate Newton’s third law.

But the details of this process are still unclear. At the microscopic scale, researchers would usually expect the fluid to dissipate most of the cell’s energy. This should prevent it from travelling very far – or even at all – no matter how much it wiggles its elastic flagellum.

To work out how the cells manage to move despite this apparent obstacle, the researchers analysed the motion of sperm and algal cells’ flagella as they swam. They found that these flagella have an unusual property, dubbed “odd” elasticity, which allows them to wave without losing much energy to the surrounding fluid.

The researchers quantified the cells’ odd elasticity and arrived at a number called the “odd elastic modulus”. The higher this number, the more a flagellum can wave without the surrounding liquid suppressing its motion. This allows the cell to move forward non-reciprocally.

Clément Moreau at Kyoto University, who also worked on the study, says calculating the odd elastic modulus for many different micro-swimmers could help scientists classify them and work out whether there are additional features that help them disobey Newton’s third law.

At present, we don’t know of all the microscopic process that help tiny swimmers defy this law of motion, says Piotr Surówka at the Wrocław University of Science and Technology in Poland. He says being able to calculate the odd elastic modulus and similar numbers could help create a “dictionary” of organisms that are capable of non-reciprocal movement.

Ishimoto says that the team’s approach could also inform the design of artificial swimmers, helping researchers build small soft elastic robots that can violate Newton’s third law.

Journal reference

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