An algorithm for neuronal wiring: unravelling the mystery

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.

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.

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. 

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.

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.

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.

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.

• 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.