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Mathematics sheds new light on the chaotic interplay between neurons

18 April 2023
How does your brain know which way you are facing? Specific neurons switch on and ‘fire’ in a disordered fashion, out of sync with other similarly active neurons. Mathematicians at VU Amsterdam and University of Exeter have shed new light on this interplay between neurons, and have discovered a link between the neuronal chaos and chaotic turbulence in a pipe.

Imagine you are sitting on a sofa, watching TV with your cat, with your head facing forward. In this configuration, a group of neurons responsible for encoding the front-facing direction fires repetitively. Now your cat jumps to the table and your head turns left. The previously active "front-facing" neurons become quiet, and a group of neurons encoding the ‘left-facing’ direction become active. In this way, the brain is able to distinguish your head direction.

Chaotic firing of neurons
Regardless of which way you face, the group of neurons associated to that direction becomes active. Even though the whole group is active, individual neurons within the group fire chaotically and out of step with each other. Understanding how this chaotic firing gives rise to robust representation of head direction in the brain is an open and important challenge. An example of this behaviour can be seen on the cover of the latest issue of the Society for Industrial and Applied Mathematics' flagship journal, SIAM Review, where the work was published jointly by Daniele Avitabile, Joshua Davis, and Kyle Wedgwood.

Mapping out the waves
Reflecting on the discovery, Daniele Avitabile (VU Amsterdam), explains: “Chaotic brain activity is hard to study. The key ingredient in this discovery is that chaotic behaviour can be decomposed into waves, which are more tractable. Chaotic brain activity, much like that in a turbulent pipe, makes frequent hops between waves, spending some time near each one it visits. We charted out a map of the wave states, thus providing a blueprint for understanding the chaotic brain activity.

Fluid-dynamics analogy
“Mathematical neuroscience has provided a great deal of insight into the general head-direction problem, but it has proved difficult to describe it in terms of single-neuron behaviour. We were struck by the fact that we could understand these states by thinking in terms of simple waves”, said Avitabile.

Co-author Kyle Wedgwood (University of Exeter) adds: “We are excited to have drawn a mathematical link with the well-studied problem of turbulence. We look forward to using the fluid-dynamics analogy to accelerate understanding in neuroscience. For instance, we aim to test our theory by revisiting the head-direction problem, incorporating more sophisticated descriptions of single neuron behaviour.”