Mathematical Approach Helps Understand Complex Neural Systems

In an article published in the scientific journal PNAS Nexus, researchers from the Neuromorphic Engineering Laboratory at the University of Liège reveal a fascinating brain mechanism: the ability of neurons to maintain reliable functions despite significant variability in their physiological components.

Neuroscience has long known that each brain is unique, not only in its connections but also in the molecular composition of its neurons. These include ion channels, membrane proteins responsible for the passage of ions into neurons. However, these channels vary considerably from one individual to another, and even from one neuron to another. Yet this variability does not prevent the brain from functioning reliably. This paradox, known as "neuronal degeneration", has intrigued scientists for decades. This concept is different from degeneration in the pathological sense (as in neurodegenerative diseases) and focuses here on an adaptive and robust property of the nervous system.

ULiège researchers Arthur Fyon, Alessio Franci, Pierre Sacré and Guillaume Drion have adopted an original approach by applying mathematical tools to gain a better understanding of this property. Their dimensional reduction method made it possible to simplify the analysis of a complex system, revealing two distinct mechanisms behind the degeneration. 

Our study shows that these two mechanisms act simultaneously, each having a specific physiological origin and function," explains Arthur Fyon, researcher in the lab and first author of the article. Together, they ensure reliable modulation of neuronal signals, despite variations in ion channels. This discovery also lifts the veil a little further on the principles of neuromodulation, the process by which the brain adjusts its activity in response to internal or external signals. In practice, this deeper understanding makes it possible to define a universal rule for adjusting neuronal modulation, opening up promising prospects for anticipating the effect of neuroactive drugs and for improving computational models in neuroscience.

Implications Beyond the Human Brain

The results do not stop at understanding the biological brain. The team has developed a neuromodulation algorithm based on these discoveries, applicable to neuromorphic systems such as robots or artificial intelligence devices. These advances could revolutionize robotics by creating systems capable of dynamically adapting to their environment, just like the human brain.

Computational neuroscience is a rapidly expanding field that seeks to build bridges between experimental neuroscience and mathematical models. This study is part of this drive by answering a key question: how can we simplify the study of complex systems without losing critical details?

Our work shows how various parameters, such as ionic conductances, can be organized in a simplified space, making it easier to use neuronal models."

Guillaume Drion, Director, Neuromotor Engineering Laboratory, University of Liège

In addition to their fundamental interest, this work has important practical applications. In robotics, these algorithms could enable machines to adapt better to the unexpected, for example by adjusting their behavior according to changes in their environment. Similarly, in the medical field, they could help to design personalized treatments, precisely targeting the neuromodulation mechanisms affected by a disease or a drug.