Scaredy Snakes: The Mathematics Behind a Peculiar Motion in Young Anacondas

Key Takeaways

• Applied physicists have described a particular movement observed mostly in young, teenaged anacondas, called an S-start, using a mathematical model
• The model shows that young anacondas, as opposed to babies and adults, exist in a “goldilocks zone” of relative weight and strength to allow them to execute the movement
• The researchers think sidewinding evolved from the S-start

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, Physics 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 published in Nature Physics.

“This movement is the serpentine analog of the moonwalk – a fast, graceful glide that seems to defy common sense,” Mahadevan said. “We created a mathematical framework 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.”

The Mathematics of Startled Snakes

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 from 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 – “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 Physics 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 a “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, about 2 years old, 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 both the S-start and sidewinding are “non-planar,” as in, some segments of the snake are off the ground, almost as if the snake were walking. “We realized that the sidewinding motion is the same as this S-motion, but 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 how it could even potentially lead to engineering robotic systems that mimic such movements.

The research was supported by National Science Foundation grants: BioMatter Division of Material Research 1922321, Materials Research Science and Engineering Centers Division of Materials Research 2011754, and Emerging Frontiers of Multidisciplinary Activities 1830901.