Optimal random walks of swimming bacteria
Random walks are a cornerstone of statistical physics. While Brownian motion has long been under scrutiny, there is a growing interest in a different type of motion:
persistent random walks. Examples abound in active matter and biological world, from self-propelled particles and crawling cells to foraging animals and a plethora of swimming micro-organisms. The statistical properties of such random motions are often unknown yet they play a key role in many vital functions of the organisms and ultimately in their survival.
One striking instance of persistent random motion is the
run-and-tumble of bacteria. Bouts of persistent motion ("run") are interspersed with sudden changes of direction ("tumble"). Recent research reveals that bacteria display a fascinating repertoire of swimming patterns, which differ in their run and tumble characteristics. Why? Which benefits come with each swimming strategy? Why were they selected by billions of years of evolution? In spite of some recent progresses [1], answers remain at the nascent stage.
The goal of the internship is to understand theoretically the statistical properties of encounter of run-and-tumble. To address this question, you will use a combination of
numerical simulations and analytical approaches based on the Fokker-Planck equation.
There are many facets of swimming strategies that can be explored in a PhD thesis, from individual properties to collective effects. These include the ability to follow chemical gradients, self-assembly into bands [2] and active clustering. In each of these situations, we will ask whether swimming strategies of bacteria are, in some sense, optimal.
This topic lies at the confluence of
statistical physics and
active matter (no expertise in biology required). Strong background in one of these fields and a taste for theoretical and numerical approaches would be ideal.
Opening toward a PhD: yes (funding with «bourse ministère»).
Contact:
Francois Detcheverry,
francois.detcheverry@univ-lyon1.fr Team
Liquides et Interfaces, Institut Lumière Matière, Lyon
References:
[1] Universal law for the dispersal of motile microorganisms in porous media,
Pietrangeli, Foffi, Stocker, Ybert, Cottin-Bizonne, Detcheverry.
Physical Review Letters (2025)
[2] Exact model of aerotactic band: From Fokker-Planck equation to band structure and fluid flow,
Detcheverry.
arXiv (2025).
See full offer
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