Section: New Results

Mechanics of tissue morphogenesis

Participants : Olivier Ali, Arezki Boudaoud [External Collaborator] , Guillaume Cerutti, Ibrahim Cheddadi [External Collaborator] , Christophe Godin, Bruno Leggio, Jonathan Legrand, Hadrien Oliveri, Jan Traas [External Collaborator] .

• Research Axes: RA2 (Data-driven models) & RA3 (Plasticity & robustness of forms)

• Key Modeling Challenges: KMC2 (Efficient computational mechanical models of growing tissues) & KMC3 (Realistic integrated digital models)

As deformations supporting morphogenesis require the production of mechanical work within tissues, the ability to simulate accurately the mechanical behavior of growing living tissues is a critical issue of the MOSAIC project. From a macroscopic perspective, tissues mechanics can be formalized through the framework of continuum mechanics. However, the fact that they are composed, at the microscopic level, by active building blocks out of equilibrium (namely cells) offers genuine modeling challenges and opportunities. This section describes the team's efforts on integrating cellular behaviors such as mechano-sensitivity, intercellular fluxes of materials and cell division into a macroscopic mechanical picture of morphogenesis.

Mechanical influence of inner tissues. Mechanical stress patterns within plant tissues emerge from the balance between inner-pressure-induced forces and the elastic response of the cell wall (A thick protective exoskeleton surrounding plant cells) over the entire tissue. Being able to derive, from a specific cellular architecture, the corresponding pattern of stresses within a tissue is crucial for the study of morphogenesis. It requires a precise description of the tissue as a network of connected cells and the ability to run numerical simulations of force balance on such heterogeneous structures.

To that end, we developed numerical methods to generate finite element meshes from: i) 3D microscopic images with sub-cellular resolution (referred to as bio-inspired structures) and ii) 3D cellularized geometrical volumes (referred to as artificial structures). Combined with a FEM-based simulation framework previously developed within the team [20], we generated quantitative maps of stress distributions in multilayered reconstructed tissues. The combined analysis of stress patterns on bio-inspired and artificial structures showed how mechanical stresses experienced by cells convey geometrical information to cells about the global shape of the tissue as well as the local shape of cells.

This work was part of the Morphogenetics IPL and Jan Traas ERC grant Morphodynamics.

This work is currently under review in the Bulletin of Mathematical Biology and has been presented at the 19th International Conference of System Biology held in Lyon at fall.

Shape regulation. Reproducible and robust morphogenesis requires growth coordination of thousands of cells. How such coordination can be “implemented” in living organism is a core question for RA3. One identified mechanism in plant to coordinate growth rely on cells mechano-sensitivity (the ability to probe mechanical stress around them and to modify accordingly their growth behavior). Combined with the geometrical dependency of mechanical stress (c.f. previous subsection), this suggests the existence of a feedback mechanism that regulates tissue shape changes. We have been investigating closely the consequences of such a mechanism.

To that end, we first modeled the bio-molecular pathway relating mechanical stress experienced by cells to actual modification of their mechanical properties (e.g. cell wall stiffness). This work enabled us to describe plant tissues as an active material featuring large-scale properties, such as stress stiffening (the ability of the tissue to re-enforce itself in the directions of high mechanical solicitations), emerging from sub-cellular dynamics. This work has been published in Journal of Mathematical Biology [5].

In parallel, we modeled the influence of cell wall elasticity (value, orientation) on the growth dynamics of tissues. This was done in the context of plant organogenesis, in close collaboration with biologists investigating the effect of cell-wall-related mutations on plant organ initiation. Our modeling approach was based on our previously developed strain-based growth model [20]. This joint study has been published in Development earlier this year [1].

We then studied how initial spherical symmetry (e.g. dome-shaped primordia) can be potentially broken during development in such active tissues and lead to elongated or flat shapes. For this, we integrated the stress feedback model with the strain-based growth model to investigate how their interplay could influence the morphogenesis of 3D cellularized structures. In particular, we showed that a stress-based feedback mechanism can maintain the typical plant growth modes (i.e. axial elongation or 2D flat expansion) and amplify asymmetries. This computational approach to symmetry breaking in growing tissues has been developed in parallel to experimental investigations addressing the shape evolution of sepals (leaf-like organs surrounding and protecting flowers).

This work was part of the Mophogenetics IPL and Jan Traas ERC grant Morphodynamics.

The whole story has been presented at the 9th International Plant Biomechanics Conference in Montreal this summer. A journal article combining both our modeling approach and experimental work in the context of symmetry breaking during plant organogenesis is currently being written.

Influence of water fluxes on plant morphogenesis. Since pressure appears as the “engine” behind growth-related deformation in plants, its regulation by cells is a major control mechanism of morphogenesis. We developed 2D computational models to investigate the morphological consequences of the interplay between cell expansion, water fluxes between cells and tissue mechanics. This interdisciplinary work, combining experiments and modeling, addresses the influence of turgor pressure heterogeneities on relative growth rate between cells. We showed that the coupling between fluxes and mechanics allows us to predict observed morphological heterogeneities without any ad hoc assumption. It also reveals the existence of a putative inhibitory action of organ growth on growth in immediatemy neighboring regions, due to the hydraulic coupling between cells during growth.

This work was part of the Agropolis fundation project MecaFruit3D and Arezki Boudaoud's ERC PhyMorph.

Two papers report the results of this work (one currently under review in Nature Physics [21] and a second one that is about to be submitted. These results have also been presented last summer at the 9th International Plant Biomechanics Conference in Montreal.

Influence of dividing cells on tissue mechanics during morphogenesis in ascidians. The control of cell division orientation is of prime importance for patterning and shape emergence, especially in animal embryos where the first developmental stages happen at constant volume. In recent years, the Hetwig's rule appeared as a physical model accounting for orientation of cell division. Within animal tissues it has been shown that the coupling of externally induced strain and Hertwig's rule leads to the orientation of cell divisions with the main stress direction.

We investigated through modeling the consequences, in a multicellular context, of such stress-based regulation of cell division orientation. To that end, we developed a theoretical standpoint on the many-body energetic thermodynamics of cell divisions in the presence of external anisotropic stress. We showed that Hertwig's rule emerges as a limiting-case behavior and how anisotropic mechanical stresses can provide important cues to guide cell divisions. Our model accounts for the division pattern observed in the epidermis of the embryo of ascidian Phallusia mammillata, including those reproducible observed deviations from Hertwig's rule which have so far eluded explanation.

This work was part of the Digem project.

This work has been presented in two national conferences: the IBC Scientific Days and the Cell Cycle Days both held in Montpellier. A paper is currently being written.

Automatic quantification of adhesion defects in microscopy images. Direct measurements of mechanical stresses experienced by living tissues are not yet feasible. To circumvent this limitation, we developed an indirect method based on measurements of cracks in tissues: Our biologist colleagues developed cell-adhesion mutants in which strong connections between epithelial cells are impaired. As a consequence, mechanical stresses within the tissue produce cracks. Distribution and orientation of these cracks can be related to the main directions of the mechanical forces at play. We developed a 2D image analysis pipeline to detect and quantify these cracks in microscopy projections of epithelia, and deduce the magnitude and orientation of tensions in organs and tissues. This tool has been used to evidence new mechanical signaling mechanisms in Arabidopsis.

This analysis pipeline has been published in [6] and used by collaborators in the analysis performed in [26].