Description du sujet de thèse

Many biological tissues build up, and maintain, internal mechanical stresses [2]. These residual stresses remain even when all external forces are removed. They can be clearly seen when cutting a tissue, immediately releasing elastic energy by opening up. Residual stresses likely contribute to the regulation of size in morphogenetic processes.

The origin of residual stresses remains elusive and remarkable, as growing tissues “voluntarily” set aside metabolic energy to create the incompatibility that underlies residual stress. Incompatibility represents the challenge of fitting together parts of a grown tissue without voids or overlaps, acting as the “geometric seed” of residual stress. The goal of the project is to better understand the mechanical origin of residual stress.

At the continuum level, differential geometry elegantly captures incompatibility, via Riemannian curvature ([3, 4]). However, how this tissue-scale incompatibility emerges through collective cell behaviour is unclear.

Cellular tissue behaviour has been successfully captured by “vertex models”, where cells are densely packed with shared edges and vertices. These models assign a reference area A0 and perimeter P0 to cells, and penalise deviations from these values energetically. However, the biological or micromechanical origin of A0, P0 are unknown.

Real cells do not share edges and vertices with their neighbours. Instead, the interaction between adhesion of the neighbouring cellular cortices is crucial for the cell's ability to move and change neighbours, which is critical for forming residual stress. The Apposed-Cortex Adhesion Model (ACAM) [8], developed between Grenoble (J. Etienne) and Cambridge (B. Sanson), bridges this gap, providing deeper understanding of A0, P0 through the cortex elasticity and binding/unbinding rates of adhesion molecules that connect cell cortices.

Experiments performed in S. Harmansa's group in Exeter, UK, will test our theory. We will measure the spatio-temporal evolution of incompatibility in the Drosophila wing disc. By laser cutting small tissue samples of the Drosophila wing disc and observing their opening patterns, we can infer incompatibility.

The project will blend continuum theory (morphoelasticity [6], differential geometry [1]), vertex model simulations [5] and model development (extending ACAM [8]) to investigate the concept of incompatibility across cell and tissue scales. Cutting experiments [7] will test our predictions.

[1] Sean M Carroll. Spacetime and geometry. Cambridge University Press, 2019. doi: 10.1017/9781108770385.
[2] Alexander Erlich, Jocelyn Étienne, Jonathan Fouchard, and Tom Wyatt. “How dynamic prestress governs the shape of living systems, from the subcellular to tissue scale”. In: Interface Focus 12.6 (2022), p. 20220038. doi: 10.1098/rsfs.2022.0038.
[3] Alexander Erlich and Giuseppe Zurlo. “Incompatibility-driven growth and size control during development”. In: Journal of the Mechanics and Physics of Solids (2024), p. 105660. doi: 10.1016/j.jmps.2024.105660.
[4] Alexander Erlich and Giuseppe Zurlo. “The geometric nature of homeostatic stress in biological growth”. In: Journal of the Mechanics and Physics of Solids (2025), p. 106155. doi: 10.1016/j.jmps.2025.106155.
[5] Reza Farhadifar, Jens-Christian Röper, Benoit Aigouy, Suzanne Eaton, and Frank Jülicher. “The influence of cell mechanics, cell-cell interactions, and proliferation on epithelial packing”. In: Current Biology 17.24 (2007), pp. 2095–2104. doi: 10.1016/j.cub.2007.11. 049.
[6] Alain Goriely. “The mathematics and mechanics of biological growth”. In: Springer Vol 45 (2017). doi: 10.1007/978-0-387-87710-5.
[7] Stefan Harmansa, Alexander Erlich, Christophe Eloy, Giuseppe Zurlo, and Thomas Lecuit. “Growth anisotropy of the extracellular matrix shapes a developing organ”. In: Nature Communications 14.1 (2023), p. 1220. doi: 10.1038/s41467-023-36739-y.
[8] Alexander Nestor-Bergmann, Guy B Blanchard, Nathan Hervieux, Alexander G Fletcher, Jocelyn Étienne, and Bénédicte Sanson. “Adhesion- regulated junction slippage controls cell intercalation dynamics in an Apposed-Cortex Adhesion Model”. In: PLoS computational biology 18.1 (2022), e1009812. doi: 10.1371/journal.pcbi.1009812.

Contexte de travail

Grenoble is the unique conjunction of a well-established university with world-class research groups, within a great mountain landscape.

The LIPhy is a mixed research unit CNRS - UGA. It is a highly interdisciplinary laboratory (solid/fluid mechanics, statistical physics, optics, applied mathematics, biology) mande up of nine groups.
You will be part of the group MC2 (Cell Mechanics in Complex Media) and you will be supervised by Alexander Erlich and Jocelyn Étienne as part of the ANR GROWSIZE programme, funded for three years.

This project will combine cutting-edge experiments led by S. Harmansa and sophisticated modelling/simulation under the guidance of A. Erlich and J. Étienne, with an aim to understand the fundamental mechanics governing residual stress in biological tissues. High-performance computing clusters are available.
The candidate should have a background in mechanical engineering, physics, or applied mathematics. The ideal candidate has experience in coding numerical solutions to partial differential equations via the finite element method / finite differences schemes and programming skills in Mathematica, Matlab, Python, or Julia. Additionally, modelling skills in a finite element framework such as Comsol Multiphysics are highly desirable.

If you would like more information, please contact us at alexander.erlich@univ-grenoble-alpes.fr.

Applicants must submit a single PDF file, entitled 'ANR GROWSIZE PhD applicant [NAME]' which contains the following:
- a CV
- a letter of motivation

Please note that applications must be submitted via the CNRS job portal.
No applications will be accepted by e-mail.

Applications will be accepted until the position is filled.

Le poste se situe dans un secteur relevant de la protection du potentiel scientifique et technique (PPST), et nécessite donc, conformément à la réglementation, que votre arrivée soit autorisée par l'autorité compétente du MESR.

Contraintes et risques

Short-term trips in France and abroad are to be expected, during collaborations and/or conferences.