Mathematical model reveals how a viper is able to find its dinner in the middle of the night

In the animal kingdom, there are many remarkable examples of species that make sense of their world by expertly deciphering even faint signals from their environment.

An eagle soaring above the ground spots a river fish below, about to swallow an insect; a hungry black bear smells a morsel of food three kilometers away, in a dense thicket; A duck-billed platypus, swimming in a freshwater creek, closes its eyes and detects electrical impulses from a tasty tadpole nearby.

Then there are the vipers.

Found in a wide variety of habitats, from jungles to deserts, these snakes use powerful infrared sensors near their nostrils to hunt prey in the dark by detecting the slightest change in temperature. They achieve this through heat-sensitive ion channels that are only on par with the sensory apparatus of humans.

How do vipers do this? Two Yale physicists may have discovered the answer in a new mathematical model, described in a new study in the journal Proceedings of the National Academy of Sciences.

“To locate their prey, vipers must detect temperature changes of a thousandth Kelvin with their sensory organ, which requires the entire organ to be 1,000 times more sensitive than their underlying molecular sensors,” said Isabella Graf, postdoctoral researcher in physics at Yale University. Faculty of Arts and Sciences (FAS).

The Kelvin is the internationally accepted base unit for measuring temperature.

“In addition, these snakes sometimes live in deserts where the ambient temperature changes dramatically between day and night,” adds Graf. “How is it possible that temperature changes on the order of a few millikelvins can be robustly detected by much less sensitive sensors in a wide variety of environments?”

Graf and Benjamin Machta, assistant professor of physics at FAS and member of the Yale Quantitative Biology Institute, say the explanation could be a biological mechanism that allows vipers to amplify small signals and transmit them to their brains with high fidelity .

For the study, the researchers created a mathematical model that uses concepts from statistical physics and information theory to understand how the incoming temperature signal from a viper’s individual ion channels collectively affects the neuronal response. In the mathematical model, there is a “bifurcation”: a point where the neuronal response changes qualitatively and the individual, less sensitive temperature sensors exhibit a high degree of cooperation.

“Near this bifurcation point, we show that the snake’s brain can obtain almost as much information about temperature as if it could read the measurements from each individual sensor and then perfectly average them to obtain a measure of temperature. optimal precision,” said Machta.

This is how a viper finds its dinner in the middle of the night.

The new study also takes into account how vipers maintain their thermal sensitivity despite drastic changes in temperature between day and night. The researchers said their mathematical model includes a “feedback” function that automatically protects the overall sensitivity of the system during temperature variations.

Graf and Machta said their new model could have applications beyond the viper’s nocturnal wanderings.

“Similar feedback and design principles could be found in other sensory systems that also need to detect tiny signals in a variable environment,” Graf said.