An algorithm for neuronal wiring: unravelling the mystery

Changed on 26/04/2024
In a paper published in the journal Physical Review Letters, researchers Fabrizio de Vico Fallani (Inria) and Vito Dichio (ICM) outlined a breakthrough in our understanding of the development of the architecture of natural brains. Their research has shown that the connections between the nerve cells inside living organisms follow simple, algorithmic rules that can be modelled. This innovative concept in complex systems paves the way for exciting clinical applications that could help to deepen our understanding of the progression of neurodegenerative diseases or how people recover from strokes. Let’s explore the great mystery of neuronal wiring, from DNA to algorithms...
Image générée par l'IA représentant un réseau neuronal.

When it comes to the evolution of biological systems, there is a general theoretical consensus that this evolution is driven primarily by molecular and chemical mechanisms, in addition to complex DNA coding. In order to explain the development process for neuronal systems, it is first necessary to ask how neurons form the “wiring” of the brain (known as the connectome) and how they “decide” on the optimal connection to form. 

A new approach inspired by the theory of evolution could help solve the mystery of how connectomes are deployed - and put this into an equation. Not only would this help to create an entirely new methodological framework, but it would also open up new avenues for research in neuroscience, with the possibility of significant breakthroughs in clinical applications long-term.

Searching for the evolutionary algorithm

The aim of the thesis undertaken by Vito Dichio, a former PhD student with the joint project team NERV (Inria, Sorbonne University, CNRS, Inserm), which was supervised by Fabrizio de Vico Fallani[1], was to demonstrate that the deployment of a full map of the neuronal connections within the brain follows simple mathematical rules. 

On 1 March 2024, the results of Vito Dichio’s thesis were published in the prestigious journal Physical Review Letters under the heading: “Exploration-Exploitation Paradigm for Networked Biological Systems” (DOI: 10.1103/PhysRevLett.132.098402).  

Studying living systems can be extremely daunting, given that they are often subject to random events which make their behaviour difficult to predict. The large number of interactions, the multiple levels of organisation and the constant dynamic which characterises them all make understanding them an arduous endeavour.  In order to survive, these systems are forced to choose configurations which produce optimal functions, i.e. configurations which maximise their capacity to survive in their environment. They are also governed by functional constraints resulting from the laws of physics, time and energy, all of which dictate evolutionary compromises. As a result, analysing biological systems remains a significant challenge for those researchers seeking to model such systems.

If we are to deepen our understanding of the development of biological systems, it is imperative to grasp: 

  • How they explore the space of possible configurations (the “functional landscape”) in order to discover new things – the dynamic of “exploration”.
  • How they identify the optimal states for responding to specific functional requirements, which enable them to survive – the dynamic of “exploitation”. 

Vito Dichio and Fabrizio de Vico Fallani set out from the premise that biological processes are governed by simple organisational rules which seek out an optimal balance between chance and necessity in order to maintain a viable functional configuration. The researchers sought to describe this in mathematical terms, the goal being to simulate the development of the brain.

How is the mind “woven”?

In response to this problem, Vito Dichio turned to the only organism for which a complete map of its neuronal connections was available at the time he was writing his thesis in 2023: the nematode Caenorhabditis elegans. A worm that is not even a millimetre in length. 

Illustration du ver C. elegans.
It may be one of the smallest known nervous systems, but the worm C. elegans is capable of locomotion, mating, chemical sensation, etc., meaning it is able to carry out a wide range of functions.

The simplicity of its connectome, comprising only 302 neurons, has attracted the attention of neuroscientists.  The full brain map of the nematode C. elegans paved the way for multiple breakthroughs in our understanding of how the nervous system works, providing a solid basis for studying the mechanisms underlying cognition and behaviour.


Instantané du développement des réseaux cérébraux du ver C. elegans à différents stades de développement.
Snapshot of the development of the brain networks of the worm C. elegans at different stages of development: each stage is represented by a continuous or dotted line, while each snapshot is represented by a microscope.


The great mystery of brain wiring, from DNA to algorithms

Inspired by Charles Darwin's theory of evolution, Vito Dichio came up with a solution inspired by nature itself: setting out from the premise that evolutionary processes constitute a specific form of the “exploration-exploitation” dynamic (EE dynamic) in functional environments, they devised a new theoretical framework which harnesses this general dynamic for use with biological networks.

Image conceptualisée du développement du réseau cérébral du ver C. elegans.
This image conceptualises the development of the brain network of the worm C. elegans through the dynamic exploration of a functional landscape and the exploitation of the most effective states. The peaks in the landscape represent optimal configurations.

The exploration/exploitation dynamic can be compared to exploring a playing field, where although changes occur at random, they are guided by an overarching objective. Imagine you are exploring a huge map containing mountains and valleys, where the movements you make are somewhat random, but where you always seek to arrive at the best possible location. In our example, the “best locations” are determined by the peaks of the mountains, which correspond here to specific network characteristics of the adult worm.

The connectome of a functional adult brain is characterised by the presence of so-called “triad” patterns, which enable groups of neurons to pass on information at a local level (in red in the figure below). These patterns are associated with what are known in graph theory as clusters. Each cluster can be thought of as a group of computers capable of working independently from the rest of the network. Another typical pattern concerns hubs, which are neurons (in blue in the figure below) with multiple connections which are used to circulate information quickly around the brain.


Illustration des triades et hubs du connectome.
Triads and hubs: triads are trios of connected nodes (see example in red) which are used to process information locally. Hubs are nodes with multiple connections (see example in blue) which are used to circulate information quickly around a network. The presence of triads and nodes increases as the brain network of the worm C. elegans develops.

Using brain connectivity data from the nematode C. elegans as a starting point, Vito Dichio and Fabrizio de Vico Fallani were able to develop their exploration-exploitation model in order to retrace the history of this organism's brain development. They worked out the optimal neuronal characteristics for an adult worm and identified the dynamic that would lead to this desired end state.

The researchers discovered that worms often follow a predictable development model, although details do vary between individuals. The results indicated that knowledge of the brain at birth and in adulthood is enough for the exploration-exploitation dynamic to be able to accurately describe the full development trajectory of the neuronal network.

No two nematodes ever had identical brain development trajectories. But statistically speaking, the formation of the neuronal network reproduced the same intermediate steps. (…) We see this as further proof that the wiring of the brain follows rules which are very simple from a mathematical perspective, but which are responsible for the remarkable complexity of the nervous system.

Vito Dichio, former PhD student with the team and first author of the paper published in PRL.

Not only is this breakthrough expected to help deepen our understanding of natural brain development, but it also has serious implications for future research, as there will be no reason to focus only on the nematode C. elegans when seeking to study the development of the connectome. The basic principles governing it are not dependent on the specific system in which they are used. 

Creating new avenues for research by exploring the brain

The exploration-exploitation model could be used as a basis for comparing other models through different natural nervous systems in other organisms which have also been studied in laboratory settings, including fruit flies, zebrafish and mice.

Connectomes vary between species, which have different amounts of neurons, as well as between individuals. They can also change shape over the course of an individual’s life to compensate for certain deficits: this is what’s known as brain plasticity.

Fabrizio de Vico Fallani, head of the joint project team NERV.

For example, we could explore how the human brain reorganises itself after traumatic events such as strokes. Modelling individual recovery and reorganisation dynamics will enable us to develop a better understanding of the connectivity mechanisms at play in brain plasticity. 

The exploration-exploitation model could also be used to study the formation and propagation of social networks, both on digital platforms and in real life. Using the EE paradigm could enable scientists to improve their models of how individuals explore and exploit possibilities for connection.

Finally, modelling the way in which organisms such as Physarum polycephalum (popularly known as “the blob”) react to attractive or repulsive stimuli could help to deepen our understanding of the mechanisms underlying the capacity for spatial navigation in complex environments.

This deep dive into the fascinating intricacies of complex biological systems and the mysteries of brain connectivity highlights the potential of the exploration-exploitation dynamic and paves the way for further research into the mechanisms which shape other phenomena in a range of scientific fields.

[1] Fabrizio de Vico Fallani is head of NERV, a joint project team (Inria, CNRS, Sorbonne University, Inserm) that is based at Institut du cerveau – ICM (Paris Brain Institute).

Find out more:

  • Paper: Dichio, V., De Vico Fallani, F. “Exploration-exploitation paradigm for networked biological systems”. Physical Review Letters, March 2024. DOI: 10.1103/PhysRevLett.132.098402.
  • Vito Dichio’PhD: The exploration-exploitation paradigm: a biophysical approach. Neurons and Cognition [q-bio.NC]. Sorbonne University, 2023. 
  • Paris Brain Institute Press Release.

Fabrizio de Vico Fallani - brief bio

Photo de Fabrizio.

Having first joined the ICM as a postdoc in 2013, in 2014 I got a Starting Research Position with the joint project team ARAMIS at the Inria Paris Centre. While continuing my involvement with the ICM, I became a tenured researcher at Inria in 2017, focusing my research on a theoretical component linked to modelling the brain as a network, and a more experimental component aimed at improving brain-computer interfaces (BCI). Launching NERV was the next logical step after the previous 10 years.


Vito Dichio - brief bio

Portrait de Vito Dichio.

On summer nights in the small town in southern Italy where I grew up, the skies were clear. It was therefore a natural choice to study physics at university, and then theoretical physics, graduating from the University of Trieste in 2020. Tired of wave functions and particles, I looked for a new and fresh kind of physics, which I found in the complex, living world of biology. I finished my PhD in theoretical neuroscience with Fabrizio at the Sorbonne (ICM) at the end of 2023. My field of research - and there is no doubt left - is the physics of biological systems.