Scientists Caught Sperm Ignoring A Major Law of Physics
In the tiniest corners of biology, even familiar rules can bend. Researchers have observed human sperm navigating through surprisingly thick, gel-like fluids with a level of ease that seems at odds with conventional physics.
A study team based at Kyoto University examined the motion of these microscopic swimmers alongside single-celled algae that use tail-like appendages to move. Both kinds of organisms rely on flexible, whip-like structures to push themselves forward, yet they operate in environments where viscosity should sap energy and slow motion to a crawl.
Newton’s third law—every action has an equal and opposite reaction—serves as a foundational guideline for macroscopic objects. But in systems driven far from equilibrium—where organisms continuously consume energy to move—the familiar symmetry can break down. Active swimmers generate propulsion by actively deforming their own bodies, creating interactions with the surrounding fluid that aren’t simply reciprocal. In such settings, the classic action-reaction balance loosens, opening a way for unusual propulsion mechanisms to emerge.
By analyzing experimental data on human sperm and comparing it with the motion of Chlamydomonas cells (a green alga also propelled by flagellar waves), the researchers uncovered a surprising feature: the flagella appear to exhibit what scientists call “odd elasticity.” This property helps flexible tails bend and beat in ways that keep propulsion efficient even when the surrounding fluid would normally dampen those motions. In other words, the internal mechanics of these appendages are tuned to exploit nonreciprocal interactions with their environment rather than fighting against them.
To capture this behavior, the team introduced a concept known as an odd elastic modulus, a mathematical descriptor of how internal forces within the flagellum respond during deformation in a non-symmetric, out-of-equilibrium setting. Their modeling extended to a specific term used in simulations—an odd-bending modulus—that characterizes how the flagellum’s shape and the fluid influence one another beyond conventional elasticity. Together, these ideas describe how the micro-scale motor can convert shape changes into forward thrust while minimizing energy loss to the surrounding liquid.
From simple, solvable models to more detailed representations of actual flagellar waveforms, the investigation traced how nonlocal and nonreciprocal interactions drive propulsion. The upshot is a theoretical framework in which flexible filaments push off their own deformations and the fluid in asymmetric ways, enabling sustained movement in environments that would otherwise hinder locomotion.
The implications extend beyond understanding a single species. The insights could inform the design of tiny, self-assembling machines that mimic living materials and adapt to complex environments. The modeling approach also offers a lens into how groups of microswimmers coordinate and exhibit collective behavior when their surroundings impose strong resistance.
In the end, what seems like a straightforward law—action and reaction—reveals a richer picture at small scales. The ability of flexible flagella to exploit odd elasticity shows how life can harness nontraditional mechanics to achieve propulsion, opening avenues for technologies inspired by nature’s own strategies for moving through viscous media.
