Scientists Observe Sperm Defying a Fundamental Law of Physics

According to a recent study, human sperm use their slender tails to navigate through thick fluids, appearing to defy Newton’s third law of motion. This research also examines the movement patterns of these sex cells alongside single-celled algae.

Exploring Non-Reciprocal Interactions in Microscopic Swimmers

Kenta Ishimoto, a mathematical scientist at Kyoto University, and his team explored the unique, non-reciprocal interactions of sperm and other microscopic swimmers to understand how they move through substances that, theoretically, should resist their motion.

When Newton formulated his famous laws of motion in 1686, he aimed to clarify the relationship between physical objects and forces with straightforward principles—principles that don’t necessarily apply to tiny cells moving through thick fluids. Newton’s third law, often stated as “for every action, there is an equal and opposite reaction,” suggests a natural symmetry where opposing forces counterbalance each other. A simple illustration is two equal-sized marbles colliding and rebounding as they roll on the ground in accordance with this law.

Nature is complex, and not all physical systems adhere strictly to these symmetries. Non-reciprocal interactions emerge in unpredictable systems like flocks of birds, particles in fluid, and swimming sperm.

Asymmetric Motion and the Loophole in Newton’s Third Law

These motile agents move in ways that create asymmetric interactions with animals around them or the surrounding fluids, forming a kind of loophole in Newton’s third law. Since birds and cells generate their own energy—with each wing flap or tail movement adding energy to the system—this pushes the system far from equilibrium, making standard physical rules inapplicable.

Moreover, in their October 2023 study, Ishimoto and his team analyzed experimental data on human sperm and modeled the motion of green algae, Chlamydomonas. Both swim using slender, flexible flagella extending from the cell body, which change shape to propel them forward.

How Elastic Flagella Propel Cells in Viscous Fluids

However, highly viscous fluids would absorb much of a flagellum’s energy, making it difficult for sperm or single-celled algae to move effectively. Yet, elastic flagella somehow propel these cells without significant energy loss to the surrounding fluid.

The researchers discovered that sperm tails and algal flagella possess an “odd elasticity,” which enables these flexible structures to move with minimal energy dissipation. However, this odd elasticity alone didn’t fully explain how the flagella’s wave-like motion creates propulsion. Through their modeling, the researchers identified a new concept: an “odd elastic modulus,” to capture the internal mechanics of flagella more accurately.

“By studying solvable models and biological flagellar waveforms for Chlamydomonas and sperm cells, we explored the odd-bending modulus to understand the nonlocal, nonreciprocal interactions within the material,” the researchers concluded.

To conclude, the team noted that these findings could aid in designing small, self-assembling robots that imitate living materials. Additionally, the modeling methods might provide deeper insights into the fundamental principles behind collective behavior.

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