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The motion of snakes has long fascinated humans: they undulate, they sidewind, they crawl, they even fly.

Together with herpetologists, researchers in the Harvard John A. Paulson School of Engineering and Applied Sciences (SEAS) have discovered and quantified a new type of locomotion in juvenile anacondas.

As adults, these large snakes are better known for their slow, lumbering gait, but the researchers discovered that young anacondas are much more spry—capable of a quick, one-off, skating movement the researchers dubbed the "S-start" due to the shape the snake makes with its body.

A team led by SEAS professor L. Mahadevan, the Lola England de Valpine Professor of Applied Mathematics, ÌÇÐÄÊÓƵics and Organismic and Evolutionary Biology in SEAS and the Faculty of Arts and Sciences, is the first to describe this peculiar movement using a mathematical model that quantifies exactly how the snake executes it. The research is in Nature ÌÇÐÄÊÓƵics.

"This movement is the serpentine analog of the moonwalk—a fast, graceful glide that seems to defy common sense," Mahadevan said. "We used observations to create a mathematical framework, in order to understand under what conditions movements like this are possible, and why they are lost as the snake gets older, heavier, and relatively less strong."

Study co-author and Missouri herpetologist Bruce Young first noticed several years ago that young anacondas, when gently prodded, displayed what he could only describe as a startle reflex.

"This behavior involved not only forming the body into a very characteristic shape, and moving using a gait previously undescribed in snakes, but also moving remarkably fast," Young said, noting that anacondas are known for their mass and strength, but not for their speed. "It was clear to me that this was something new, involving different biophysics, than what had been described in snakes."

Young had at this point never met Mahadevan but was a "big fan" of his work—stating, "He has such a mastery of describing and modeling shape and movement"—that Young pitched to Mahadevan a collaborative analysis. The result was the Nature ÌÇÐÄÊÓƵics study, co-authored by former Harvard graduate student Nicholas Young and Indian Institute of Technology Bombay researcher Raghu Chelakkot, who developed the computational model to quantify the movement, along with Mattia Gazzola from the University of Illinois.

In their computational analysis, backed up by experiment and observation, the Harvard researchers found that the S-start is present in the "Goldilocks" zone of an anaconda's weight and relative strength. An adult snake is too heavy to execute the movement, while a newborn snake is too strong and tends to either flail upward or unravel. A youthful anaconda has just the right physical attributes to perform the S-start, in which it neither flies off the ground, nor is it overwhelmed by ground friction.

In describing the S-start, Mahadevan's team helped correct misconceptions about the better-known sidewinding—the continuous, sideways motion snakes use to slide down sandy hills. In their analysis they found that the S-starts are "non-planar," meaning that some segments of the snake are off the ground, almost as if the snake were walking.

"We realized that the sidewinding motion is very similar to this S-motion, in that it consists of S-starts that are repeated again and again," Mahadevan said.

"Perhaps, from an evolutionary point of view, this transient movement was taken up and then repeated, and this became the origin of sidewinding," Mahadevan said.

Overall, the findings seed new insights into how the S-start reflex works in snakes and could serve to inspire new robotic systems or other innovations.