Human sperm exhibit remarkable agility, swimming through highly viscous fluids while seemingly defying Sir Isaac Newton’s third law of motion. A research team led by Kenta Ishimoto, a mathematical scientist at Kyoto University, has investigated how sperm and other microscopic swimmers navigate these challenging environments, revealing insights that challenge long-held principles of physics.
Newton’s third law, established in 1686, posits that “for every action, there is an equal and opposite reaction.” This principle typically explains the interactions of larger physical objects but does not apply uniformly to microscopic entities like sperm and green algae. In their study, published in October 2023 in the journal PRX Life, Ishimoto and colleagues explored the unique dynamics of motile agents that engage in asymmetric interactions with the fluids around them.
Understanding Non-Reciprocal Interactions
The researchers found that sperm and similar organisms exhibit what are known as non-reciprocal interactions. These interactions occur in complex systems where the movement of one entity does not directly correspond to the reactions of another. For example, when birds fly or cells swim, they generate their own energy, pushing the system away from equilibrium. This energy generation allows them to skirt the constraints imposed by Newton’s laws.
By analyzing experimental data on human sperm and modeling the motion of Chlamydomonas, a type of green algae, the team discovered that both organisms swim using flexible flagella. These structures extend from their cell bodies and can change shape to propel themselves forward. Under typical conditions, the highly viscous fluids would absorb much of the energy produced by the flagella, limiting the movement of both sperm and algae. Surprisingly, these organisms continue to swim effectively, suggesting a unique property of their flagella.
Revealing Odd Elasticity
The team identified a phenomenon they termed “odd elasticity.” This property allows sperm tails and algal flagella to move through viscous environments without losing significant energy to the surrounding fluid. Yet, odd elasticity alone did not account for the propulsion generated by the wave-like motion of the flagella. To address this gap, they introduced a new term: odd elastic modulus, which describes the internal mechanics at play within the flagella.
The researchers concluded, “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.” This finding could have implications beyond biology, aiding in the design of small, self-assembling robots that mimic living materials.
The insights gained from this research could enhance our understanding of collective behavior in biological systems and inspire innovative applications in technology. By bridging the gap between physics and biology, Ishimoto’s team is contributing to a broader understanding of how life operates on a microscopic level.
