M/F Post-doc project: Curvature as a possible regulator of stress and size in morphogenesis

Job Description

Missions

Many biological tissues build up, and maintain, internal mechanical stresses [2]. These residual stresses remain even when all external forces are removed. 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. A proxy for incompatibility is the Ricci scalar curvature of a metric tensor associated with the growth field: The further Ricci is away from zero, the more incompatibility. The goal of this project is to better understand the mechanical origin of residual stress in terms of its source, the Ricci curvature.

[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.

Activity

Theoretical and computational aspects: In [3, 4], we introduced a morphogenetic action that combines the energetic cost of mass accretion with a quadratic penalisation of deviations from a target curvature. This action functional provides a unifying variational principle for growth, where incompatibility is measured by the Ricci curvature of the growth metric [1]. A central part of the post-doctoral work will be to explore this formulation in depth: to determine how incompatibility is correctly integrated into the action, to derive a consistent thermodynamical pendant of the variational growth law, and to analyse the dynamics it generates. This involves studying relaxation towards equilibrium as a coupled mechanical feedback and curvature flow, investigating stability and uniqueness of minimisers, and implementing numerical schemes to simulate the resulting non-linear PDE dynamics. In this way, the project aims to clarify how curvature-penalised growth can robustly encode homeostatic states of stress and size.

Drosophila wing disc experiment-driven modelling: Experiments performed in S. Harmansa's group in Exeter (https://morphomech.wordpress.com/), UK, will test our theory. We will measure the spatio-temporal evolution of incompatibility in the Drosophila wing disc [6]. By laser cutting small tissue samples of the Drosophila wing disc and observing their opening patterns, we can infer incompatibility. This will allows us to integrate insights from cell-level and tissue-level work into a 3D continuum model that captures residual stress build-up in the wing disc. The project will use a finite element framework for forward simulations of prescribed incompatibility fields, as well as inverse reconstruction from experimental data. Ultimately, the integration of incompatibility-based theory with continuum modelling of the wing disc will provide a mechanistic understanding of how residual stresses are implanted and maintained in developing tissues.

[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] 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.
[6] Stefan Harmansa and Thomas Lecuit. “Mechanical regulation of cuboidal-to-squamous epithelial transition in the Drosophila developing wing”. In: bioRxiv (2024), pp. 2024–09.

Your Profil

Skills

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.

Your Work Environment

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 two years.

Constraints and risks

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

Compensation and benefits

Compensation

Between €3,041 and €4,756 gross salary per month, depending on experience and the current CNRS pay scale

Annual leave and RTT

44 jours

Remote Working practice and compensation

Pratique et indemnisation du TT

Transport

Prise en charge à 75% du coût et forfait mobilité durable jusqu’à 300€

About the offer

About the CNRS

The CNRS is a major player in fundamental research on a global scale. The CNRS is the only French organization active in all scientific fields. Its unique position as a multi-specialist allows it to bring together different disciplines to address the most important challenges of the contemporary world, in connection with the actors of change.

CNRS

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