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

By Karmela Padavic-Callaghan
20 October 2023

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.”

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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.

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Odd Elastohydrodynamics: Non-Reciprocal Living Material in a Viscous Fluid
Kenta Ishimoto, Clément Moreau, and Kento Yasuda

PRX Life 1, 023002 – Published 11 October 2023

ABSTRACT
Motility is a fundamental feature of living matter, encompassing single cells and collective behavior. Such living systems are characterized by nonconservativity of energy and a large diversity of spatiotemporal patterns. Thus, fundamental physical principles to formulate their behavior are not yet fully understood. This study explores a violation of Newton's third law in motile active agents, by considering non-reciprocal mechanical interactions known as odd elasticity. By extending the description of odd elasticity to a nonlinear regime, we present a general framework for the swimming dynamics of active elastic materials in low-Reynolds-number fluids, such as wavelike patterns observed in eukaryotic cilia and flagella. We investigate the nonlocal interactions within a swimmer using generalized material elasticity and apply these concepts to biological flagellar motion. Through simple solvable models and the analysis of Chlamydomonas flagella waveforms and experimental data for human sperm, we demonstrate the wide applicability of a nonlocal and non-reciprocal description of internal interactions within living materials in viscous fluids, offering a unified framework for active and living matter physics.

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