Thermodynamics reveals coordinated motors in sperm tails

Physics 16, 126

By monitoring fluctuations in the tail beat of macroscopic sperm, the researchers retrieve information about the behavior of the nanoscale motors that drive the tail beat.

Christoph Burgstedt/

At human body temperature, a healthy sperm thumps its tail approximately once every 0.05 seconds. Now the researchers show that fluctuations in that beat tempo can provide insight into the molecular motors behind that motion.

It takes hundreds of thousands of molecular motors working around the clock for a sperm to beat its tail, which is known as a flagellum. These motors are only a few nanometers in size, making them too small to be visualized in live, active sperm. Now Andrea Puglisi of the Sapienza University of Rome and his colleagues have demonstrated a way to deduce how these motors behave by observing the precise rhythm at which a sperm’s flagellum beats [1]. Their findings, which could provide the basis for a sperm health test, indicate that the motors that drive the tail interact strongly and directly with each other, a finding that goes against previous understanding of how these motors behave. “It’s amazing to me that we can figure out anything about what’s happening at the molecular scale by monitoring what’s happening at the microscale,” says Puglisi. “I didn’t expect that.”

In the body, the flagellum of healthy sperm beats about 20 times a second. On average this means a tail flick every 0.05 seconds. But for any given sperm there will be some variation in that cadence. “Overall, the beating is periodic. But there are many errors in the average behavior, even for a normal sperm,” says Puglisi. “Healthy sperm can still have very erratic behavior.”

Thermodynamics provides limits to such errors, linking the accuracy of an object’s motion – in this case how much the velocity of each blow deviates from its average value – to the energy expended by the object. Specifically, the accuracy cannot be greater than the power consumption, normalized so that the two quantities, which have different units, can be compared. Inequality provides useful information, Puglisi says. “Put simply, this inequality tells us that if we want to make a sperm’s motor more precise, so that its tail beats closer to its mean value, we need to pump out more energy.”

Previous measurements on single molecular motors have shown that they perform very close to the thermodynamic limit, meaning their accuracies are close to their maxima relative to the energy they consume. Thus, Puglisi and his colleagues realized that if they could determine the accuracy of the beat of a collection of sperm cells and compare it to energy consumption, they could learn something about the thousands of molecular motors behind that movement.

In their experiments, the researchers trapped the sperm heads in micro-fabricated ‘cages’, which held the sperm in place while allowing the flagella to beat normally. They filmed the beating for a few hours and analyzed the variation of the beats during that time. “Spermatozoa are very stupid; they swim into these traps and then continue swimming straight ahead,” Puglisi says. “They continue to wag their tails exactly as they would if they were free.”

By analyzing how precisely the flagella beat, the team found a value that was significantly lower than what they expected to find from the known energy consumption of sperm. This value instead corresponded to the energy consumption of a single molecular engine. So what was going on? The team performed calculations that indicated an extremely strong interaction between the molecular motors. This interaction causes the thousands of motors within a sperm cell to act as one, rather than as independent motors. “For independent engines, the error – the variance, for example – should decrease with increasing number of [motors]”, says Puglisi. “The big mistake we see suggests that the engines are not independent.”

Claudio Maggi, who worked with Puglisi on this study, notes that this finding goes against the prevailing opinion about how these motors behave. “Of course, the motors would have to have a coordinated behavior so they could generate the beating of flagella needed for sperm to swim,” he says. “Our results show that it’s more than that: they interact very closely with each other, with the engines all working together.” Further experiments performed by the team confirm this conclusion.

“THE [researchers] shed light on the tightly coupled dynamics of molecular motors in a sperm flagellum,” says Maria Tătulea-Codrean, a biological physicist at the University of Cambridge who has studied the behavior of bacterial flagella. The evidence for coordination between the motors is very exciting, she says, as this behavior could not be probed at the molecular level with current state-of-the-art techniques.

Kirsty Wan, a biological physicist who studies flagella at the University of Exeter in the UK, says the team puts “an interesting twist” on the noise in flagella oscillations. He would like to see the team perform similar experiments with flagella of different lengths. This, he says, would allow them to “really confirm” the relationship between flagella fluctuations and the interactions of the molecular motors that drive flagella movement.

In addition to improving understanding of how these reproductive cells behave, Puglisi and Maggi think their findings could help boost positive outcomes in fertility treatments. Healthy and “diseased” sperm consume different amounts of energy, which relates to the accuracy of the beat. “From the fluctuations, clinics could learn something about the health of a cell and make choices accordingly,” Puglisi says. “We have shown that it is quite easy to measure this precision in the laboratory.” She notes that more investigations are needed to determine the exact correlations between sperm health and beat accuracy. But he thinks this method could provide the basis for a diagnostic tool. “It’s another way to help decide which cell is the most ‘suitable’ for seeding. This is important,” says Puglisi.

Catherine Wright

Katherine Wright is the Assistant Director of Physics magazine.


  1. C.Maggi et al.Thermodynamic limits of sperm swimming accuracy, PRX life 1013003 (2023).

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