Newton’s third law can be summed up as “for every action, there is an equal and opposite reaction”. It signifies a particular symmetry in nature where opposing forces act against each other. In the simplest example, two equal-sized marbles colliding as they roll along the ground will transfer their force and rebound based on this law.<\/p>\n
However, nature is chaotic, and not all physical systems<\/a> are bound by these symmetries. So-called non-reciprocal interactions show up in unruly systems made up of flocking birds, particles in fluid<\/a> \u2013 and swimming sperm.<\/p>\n These motile agents move in ways that display asymmetric interactions with the animals behind them or the fluids that surround them, forming a loophole for equal and opposite forces to skirt Newton’s third law.<\/p>\n Because birds and cells generate their own energy<\/a>, which gets added to the system with each flap of their wings or movement of their tails, the system is thrust far from equilibrium, and the same rules don’t apply.<\/p>\n In their study published in October 2023, Ishimoto and colleagues analyzed experimental data on human sperm and also modeled the motion of green algae<\/a>, Chlamydomonas. Both swim using thin, bendy flagella<\/a> that protrude from the cell body and change shape<\/a>, or deform, to drive the cells forward.<\/p>\n Highly viscous fluids<\/a> would typically dissipate a flagellum’s energy, preventing a sperm or single-celled algae from moving much at all. And yet somehow, the elastic flagella can propel these cells along without provoking a response from their surroundings.<\/p>\n The researchers found that sperm tails and algal flagella have an ‘odd elasticity’<\/a>, which allows these flexible appendages to move about without losing much energy to the surrounding fluid.<\/p>\n But this property of odd elasticity didn’t fully explain the propulsion from the flagella’s wave-like motion. So from their modeling studies, the researchers also derived a new term, an odd elastic modulus, to describe the internal mechanics of flagella.<\/p>\n “From solvable simple models to biological flagellar waveforms for Chlamydomonas and sperm cells, we studied the odd-bending modulus to decipher the nonlocal, nonreciprocal inner interactions within the material,” the researchers concluded<\/a>.<\/p>\n The findings could help in the design of small, self-assembling robots<\/a> that mimic living materials, while the modeling methods could be used to better understand the underlying principles of collective behavior, the team said<\/a>.<\/p>\n![\"Scanning](\"https:\/\/www.europesays.com\/us\/wp-content\/uploads\/2025\/06\/ScanningElectronMicrographOfASpermCellR_U_642.jpg\")
Scanning electron micrograph of a sperm cell in a fallopian tube. (Science Photo Library\/Canva<\/a>)<\/p>\n![\"A](\"https:\/\/www.europesays.com\/us\/wp-content\/uploads\/2025\/06\/Untitled-design-1.jpg\")
Green algae (Chlamydomonas globosa) with two flagella just visible at bottom left. (Picturepest\/CC BY 2.0\/Wikimedia Commons<\/a>)<\/p>\n