Sperm's Superhuman Swimming: Breaking Physics Laws

Human sperm cells have been found to break Newton's third law of motion, which states that for every action, there is an equal and opposite reaction. This law describes how forces function, with interacting pairs of objects exerting equal and opposite forces on each other. However, human sperm cells and Chlamydomonas algae swim by deforming their bodies in a way that does not elicit a response from their surroundings, breaking Newton's third law. This discovery has led to further research and potential applications in robotics.

Sperm's flagella

Human sperm cells and some microorganisms, including Chlamydomonas algae, are able to move in a way that breaks Newton's third law of motion. This law states that "for every action, there is an equal and opposite reaction". However, these biological swimmers can deform their bodies in a way that does not elicit an equal and opposite reaction from their surroundings.

This movement is facilitated by hair-like appendages called flagella, which protrude from the cell and resemble a tail. The sperm flagellum is composed of a core of microtubules, whose sliding is powered by flagellar dynein. This array of microtubules and associated motor and linker proteins is known as an axoneme. The axoneme has a characteristic "9+2" structure, with two central singlet microtubules encircled by nine outer doublet microtubules. The outer and inner dynein arms slide along each outer doublet microtubule, causing the flagellum to bend and propel the sperm forward.

The midpiece of the sperm contains a prominent array of mitochondria, which are required to produce large amounts of ATP. The hydrolysis of ATP powers the conformational changes in flagellar dynein that mediate microtubule sliding. Prior to fertilization, sperm exhibit dramatic motility changes, such as the initiation and activation of motility and chemotaxis toward the egg. These changes are triggered by alterations in the extracellular ionic environment and substances released from the female reproductive tract or egg.

The elasticity of the flagellum allows it to change shape and drive the cell forward without expending a significant amount of energy. This is where the concept of "odd elasticity" comes into play. Odd elasticity allows the flagellum to wave without suffering significant energy loss, improving the cell's ability to advance in a manner that defies physics. The odd elastic modulus, or the internal mechanics of the flagellum, further contributes to its propulsion through the wave-like motion.

Non-reciprocal mechanical interactions

The non-reciprocal nature of sperm movement can be attributed to the odd elasticity of the flagellum. This odd elasticity allows the flagellum to wave without losing a significant amount of energy, which increases the cell's ability to advance. The concept of odd elasticity is further supported by the introduction of the term "odd elastic modulus," which describes the internal mechanics of flagella and helps explain their wave-like motion.

The understanding of odd elasticity and non-reciprocal interactions in sperm has potential applications in the development of small, self-assembling robots that can mimic living materials. Additionally, the modeling techniques used in this research provide insights into the underlying principles of collective behavior in complex systems.

Non-reciprocal interactions are not limited to sperm cells and can be found in other biological systems, such as flocking birds, swarming fish, and some microorganisms. These interactions occur when there is a disruption in the equilibrium, often caused by the self-generated energy of the system, which creates a loophole for equal and opposite forces.

Odd elasticity

Human sperm cells and some microorganisms, such as Chlamydomonas algae, exhibit a unique property called "odd elasticity". This property allows them to swim and move through fluids in a way that seemingly breaks Newton's third law of motion.

Newton's third law of motion states that "for every action, there is an equal and opposite reaction". This means that when an object exerts a force on another object, the second object will exert an equal and opposite force in response. However, human sperm cells and some microorganisms have been observed to move in a way that defies this law.

The concept of odd elasticity challenges the traditional understanding of elastic materials, which assumes that they will resist a change in shape and return to their original form after being distorted. In the case of odd elasticity, a non-reciprocal relationship is observed, where the flagella can bend and create wave-like shapes without the surrounding fluid "pushing back" and straightening them out. This non-reciprocal relationship allows the sperm and algae to move forward with minimal energy loss.

To quantify the degree of odd elasticity, researchers introduced the term "odd elastic modulus", which measures how much a flagellum can move without its movement being suppressed by the surrounding fluid. A higher odd elastic modulus score indicates greater freedom of movement and faster swimming capabilities. This concept may have broader applications in understanding the non-reciprocal motions of other cell types and species.

Asymmetrical interactions

The flagellar beat is highly symmetric in both planar and out-of-plane directions, beating equally on all sides in 3D. This symmetry is achieved through asymmetry, with a coordinated 360-degree rotation of asymmetric one-sided bends around the rolling axis. This results in an optical illusion of bilateral symmetry in 2D microscopy.

The flagellar movement in 3D is a combination of a planar and out-of-plane motion, captured by the b and z planes, respectively. The flagellum motion in each plane is a sum of two independent shape modes: a static mode whose shape does not change in time and a dynamic mode that oscillates in time. The waveform of each beating plane shares antagonistic properties: the static mode of the b plane is asymmetric along the flagellum, while the z plane is symmetric. Likewise, the dynamic mode of the b plane is a travelling wave, while the z plane pulsates as a standing wave. The 3D flagellar beating is thus anisotropic and given by the coaction of two transversal controls that regulate an asymmetric travelling wave and a pulsating wave along the flagellum.

The standing wave in the z plane critically modulates the three-dimensionality of the beat, thus vital for the spontaneous coordination of sperm rolling. No rolling motion of the spermatozoa may emerge without the out-of-plane component of the beat. Thus, if the waveform amplitude of the z plane is negligible, the spermatozoa would potentially only swim in circles, driven by the asymmetric one-sided stroke of the b plane.

The rapid movement of human sperm flagella was recorded with high spatiotemporal resolution in 3D. This allowed the description of the flagellar waveform relative to both the comoving and rolling frame of reference of the sperm flagellum. This unveiled the true nature of the waveform unbiased by the sperm swimming and rolling motions.

Energy conservation

Human sperm cells and some microorganisms are able to break Newton's third law of motion, which states that "for every action, there is an equal and opposite reaction". This law, also known as the "action-reaction law" or the "reciprocity principle", suggests that opposing forces act against one another. For example, if you push against a wall, the wall pushes back with an equal amount of force.

However, human sperm cells and some microorganisms, such as algae, are able to swim by thrashing their tails, or flagella, in a viscous fluid without eliciting an equal and opposite reaction from their surroundings. This movement should dissipate their energy, bringing them into equilibrium with their surroundings and bringing their motion to a halt. Yet, sperm are able to keep swimming.

Scientists at Kyoto University in Japan, including mathematical scientist Kenta Ishimoto, have discovered that sperm tails have an "odd elasticity", which allows them to whip around without losing much energy to the fluid. This "odd elasticity" is a non-reciprocal mechanical interaction that violates Newton's third law because it does not elicit an equal and opposite reaction from the fluid.

The ability of a flagellum to wave without suffering significant energy loss increases with a cell's odd elasticity score (or odd elastic modulus), which improves the cell's ability to advance in a manner that defies physics. This discovery could have implications for the design of small, self-assembling robots that mimic living materials and could help us better understand the underlying principles of collective behaviour.

Frequently asked questions