Mechanics and growth of walled cells
The role of mechanics in morphogenesis has been known for more than a century, but the investigation of its interaction with biochemical signals and growth is much more recent.
In 1917 already, D’Arcy Thompson recognized the importance of mechanics by showing that many shapes observed in biological systems are similar to the shapes generated by surface tension in a fluid possessing some geometrical constraints. Turing himself, in his famous work on chemical patterning, recognized the importance of ‘the interdependence of the chemical and mechanical data’. Nevertheless, he chose to focus on systems where the mechanical aspects could be ignored.
The middle of the 20th century, with the rapid development of biochemistry and the subsequent knowledge of the molecular actors of development in great details, led to the a view of morphogenesis driven mostly by biochemical processes. And although the shape of an organism does rely on complex biochemical interactions, they are not sufficient to understand the translation of the genetic information into shape. The different part of an organism interact mechanically and the control of their growth and shape changes necessarily involves mechanical constraints.
Walled cells, such as plants and yeasts, are particularly well suited to study the mechanics of morphogenesis, since their stiffness and huge internal pressure generate forces, which are larger than the forces involved in animal tissues by several orders of magnitude. In these cells, growth corresponds to the yielding of the cell wall under the tension generated by the internal pressure. Pressure being isotropic, the mechanical properties of the cell wall needs to be spatially regulated in order to break the symmetry and generate anisotropic shapes. More precisely, the formation of shapes in these organisms relies on mechanical heterogeneities and anisotropies. As Franklin M. Harold wrote in 1990, ‘the forms of many walled cells can be understood as localized compliance with global force’ .
Since then, it has become clear the role of mechanics is not just to passively orient growth via the properties of the material. Mechanical stress is sensed and transduced into innumerable responses that modify the cellular and tissular behavior. In plants, one of the most striking example for such a fundamental role of mechanical stress is provided by its complex interaction with the microtubule cytoskeleton. At the Arabidopsis shoot apex, mechanical stress reorients the microtubules. They in turn direct the deposition of cellulose, a stiff, fibrous material, which can orient growth thanks to its anisotropic mechanical properties. This feedback is for instance responsible for the directionnal growth of plants stem, and is just one example of how mechanics and growth play together to shape walled cells.
In plants, the phytohormone auxin and its active directional transport are essential for the formation of robust patterns of organs, such as flowers or leaves, which are known as phyllotactic patterns. The transport of auxin was recently shown to be affected by mechanical effects, and conversely, auxin accumulation in incipient organs affects the mechanical properties of the cells. The precise interaction between mechanical fields and auxin transport, however, is not understood. In particular, it is unknown whether transport is sensitive to the strain or to the stress exerted on a given cell. We investigate the nature of this coupling with the help of theoretical models.
We introduce the effects of either mechanical stress or mechanical strain in a model of auxin transport, and compare the patterns predicted with known experimental results, where the tissue is perturbed by ablations, chemical treatments, or genetic manipulations. We also study the robustness of the patterning mechanism to noise and investigate the effect of a shock that changes abruptly its parameters. Although the model predictions with the two different feedbacks are often indistinguishable, the strain-feedback leads to a better agreement in some experimental conditions.
- Strain- or Stress-sensing in mechanochemical patterning by the phytohormone auxin
Jean-Daniel Julien, Alain Pumir, Arezki Boudaoud
Cell geometry has long been proposed to play a key role in the orientation of symmetric cell division planes. In particular, the recently proposed Besson–Dumais rule generalizes Errera’s rule and predicts that cells divide along one of the local minima of plane area. However, this rule has been tested only on tissues with rather local spherical shape and homogeneous growth. Here, we tested the application of the Besson–Dumais rule to the divisions occurring in the Arabidopsis shoot apex, which contains domains with anisotropic curvature and differential growth.
We found that the Besson–Dumais rule works well in the central part of the apex, but fails to account for cell division planes in the saddle-shaped boundary region. Because curvature anisotropy and differential growth prescribe directional tensile stress in that region, we tested the putative contribution of anisotropic stress fields to cell division plane orientation at the shoot apex. To do so, we compared two division rules: geometrical (new plane along the shortest path) and mechanical (new plane along maximal tension). The mechanical division rule reproduced the enrichment of long planes observed in the boundary region. Experimental perturbation of mechanical stress pattern further supported a contribution of anisotropic tensile stress in division plane orientation. Importantly, simulations of tissues growing in an isotropic stress field, and dividing along maximal tension, provided division plane distributions comparable to those obtained with the geometrical rule. We thus propose that division plane orientation by tensile stress offers a general rule for symmetric cell division in plants.
- Cell division plane orientation based on tensile stress in Arabidopsis thaliana
Marion Louveaux, Jean-Daniel Julien, Vincent Mirabet, Arezki Boudaoud, Olivier Hamant
The development of an organism involves a coordination between the differentiation of cells in well-defined spatial patterns and the growth of tissues towards their target shapes. While extensive research has addressed each of these key processes, their coordination has received less attention. In particular, when a pattern has formed and the tissue continues growing, is the pattern passively dilated like a drawing on an inflated balloon, or does the pattern remodel during tissue expansion?
We address this question in the context of leaf vasculature and examine the role of mechanics in leaf growth. We model the growing vascular network and identify quantities that compare network growth to background tissue growth. We apply this quantification to mature leaves that are stretched mechanically. We find that vasculature does not dilate passively and that veins reorient in the direction of external forces.
- Mechanical Stress Induces Remodeling of Vascular Networks in Growing Leaves
Yohai Bar-Sinai, Jean-Daniel Julien, Eran Sharon, Shahaf Armon, Naomi Nakayama, Mokhtar Adda-Bedia, Arezki Boudaoud
PLoS Computational Biology, 2016
The fission yeast, because of its rod-like shape, has been a perfect system for the study of morphogenesis. However, most studies focused on its vegetative growth phase, during which the yeast grows by tip elongation and divides in its middle. Here, we are interested in the germination of the spores, an intriguing process during which polarity is de novo established and stabilized. The spherical cells then regain their typical cylindrical shapes during a phase called outgrowth.
Using quantitative experiments and modeling, we reveal the mechanisms underlying outgrowth in fission yeast. We find that, following an isotropic growth phase during which a single polarity cap wanders around the surface, outgrowth occurs when spores have doubled their volume, concomitantly with the stabilization of the cap and a singular rupture in the outer spore wall. This rupture happens when the outer spore wall mechanical stress exceeds a threshold. The constraints of the outer spore wall on growth is then released, and polarity is stabilized by a positive feedback from growth.
- Symmetry Breaking in Spore Germination Relies on an Interplay between Polar Cap Stability and Spore Wall Mechanics
Daria Bonazzi, Jean-Daniel Julien, Maryse Romao, Rima Seddiki, Matthieu Piel, Arezki Boudaoud, Nicolas Minc
Developmental Cell, 2014
References and Further Reading
On Growth And Form
D’Arcy Wentworth Thompson
Cambridge University Press, 1917
The Chemical Basis of Morphogenesis
A. M. Turing
Philosophical Transactions of the Royal Society of London, 1952
Mechanism for Plant Cellular Morphogenesis
Paul B. Green
An analysis of irreversible plant cell elongation
J. A. Lockhart
Journal of Theoretical Biology, 1965
To shape a cell: an inquiry into the causes of morphogenesis of microorganisms
F. M. Harold
Microbiological Reviews, 1990
Mechanical feedback as a possible regulator of tissue growth
Boris I. Shraiman PNAS, 2005
How mechanical stress controls microtubule behavior and morphogenesis in plants: history, experiments and revisited theories
Benoit Landrein, Olivier Hamant New Phytologist, 2010
Turing’s next steps: the mechanochemical basis of morphogenesis
Jonathon Howard, Stephan W. Grill, Justin S. Bois
Nature Reviews Molecular Cell Biology, 2011
Beyond Turing: mechanochemical pattern formation in biological tissues
Moritz Mercker, Felix Brinkmann, Anna Marciniak-Czochra, Thomas Richter
Biology Direct, 2016