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1.  Subcellular and supracellular mechanical stress prescribes cytoskeleton behavior in Arabidopsis cotyledon pavement cells 
eLife  2014;3:e01967.
Although it is a central question in biology, how cell shape controls intracellular dynamics largely remains an open question. Here, we show that the shape of Arabidopsis pavement cells creates a stress pattern that controls microtubule orientation, which then guides cell wall reinforcement. Live-imaging, combined with modeling of cell mechanics, shows that microtubules align along the maximal tensile stress direction within the cells, and atomic force microscopy demonstrates that this leads to reinforcement of the cell wall parallel to the microtubules. This feedback loop is regulated: cell-shape derived stresses could be overridden by imposed tissue level stresses, showing how competition between subcellular and supracellular cues control microtubule behavior. Furthermore, at the microtubule level, we identified an amplification mechanism in which mechanical stress promotes the microtubule response to stress by increasing severing activity. These multiscale feedbacks likely contribute to the robustness of microtubule behavior in plant epidermis.
DOI: http://dx.doi.org/10.7554/eLife.01967.001
eLife digest
The surfaces of plants are covered in epithelial cells that come in many different shapes, suggesting that individual cells must have some control over their own shape. An unusually shaped epithelial cell is the pavement cell, which looks like a jigsaw puzzle piece and is found in the leaves of many flowering plants. Relatively little was known about the exact contribution of mechanical properties of the wall to this shape. Furthermore, although it was known that parts of pavement cells are rich in microtubules—tubes of protein that act as a scaffold inside the cell— the possibility that shape impacts the behavior of microtubules was not fully addressed.
Now, using a combination of computer modelling and experiments, Sampathkumar et al. reveal that the shape of the pavement cells relies in part on the response of the microtubules to stress. In an individual cell, microtubules align along the direction of the largest stress, with a protein severing those microtubules that are not aligned in this direction. As the stress inside a cell is determined in part by the cell’s shape, this sets up a feedback loop: the stress resulting from the cell shape aligns the microtubules that reinforce the cell wall, thus maintaining the shape of the cell.
An external stress applied to the epithelium can override this internal stress. Because all of the plant cells are under turgor pressure from the inside, pressure from the outside, like squeezing a balloon, changes the stress pattern, causing the realignment of the microtubules so as to resist the new stress. This shows that the microtubules respond to local stresses within a cell, and are continually responsive to stress changes.
DOI: http://dx.doi.org/10.7554/eLife.01967.002
doi:10.7554/eLife.01967
PMCID: PMC3985187  PMID: 24740969
microtubule; biomechanics; computational modeling; cytoskeleton; cell wall; Arabidopsis
2.  Stress and Strain Provide Positional and Directional Cues in Development 
PLoS Computational Biology  2014;10(1):e1003410.
The morphogenesis of organs necessarily involves mechanical interactions and changes in mechanical properties of a tissue. A long standing question is how such changes are directed on a cellular scale while being coordinated at a tissular scale. Growing evidence suggests that mechanical cues are participating in the control of growth and morphogenesis during development. We introduce a mechanical model that represents the deposition of cellulose fibers in primary plant walls. In the model both the degree of material anisotropy and the anisotropy direction are regulated by stress anisotropy. We show that the finite element shell model and the simpler triangular biquadratic springs approach provide equally adequate descriptions of cell mechanics in tissue pressure simulations of the epidermis. In a growing organ, where circumferentially organized fibers act as a main controller of longitudinal growth, we show that the fiber direction can be correlated with both the maximal stress direction and the direction orthogonal to the maximal strain direction. However, when dynamic updates of the fiber direction are introduced, the mechanical stress provides a robust directional cue for the circumferential organization of the fibers, whereas the orthogonal to maximal strain model leads to an unstable situation where the fibers reorient longitudinally. Our investigation of the more complex shape and growth patterns in the shoot apical meristem where new organs are initiated shows that a stress based feedback on fiber directions is capable of reproducing the main features of in vivo cellulose fiber directions, deformations and material properties in different regions of the shoot. In particular, we show that this purely mechanical model can create radially distinct regions such that cells expand slowly and isotropically in the central zone while cells at the periphery expand more quickly and in the radial direction, which is a well established growth pattern in the meristem.
Author Summary
Development and morphogenesis of tissues are dependent on a coordination between cell differentiation, proliferation and growth. Plants, which lack cell migration, control directional growth of tissues by adjusting cellulose fiber directions so forming the organ shapes. It has recently been shown that mechanical cues can guide these fibers. We developed detailed mechanical models to investigate how fiber directions may be responding to mechanical cues and what consequences this may have for positional and directional growth patterns. We show that a model in which fibers align to maximal stress directions spontaneously generates a radial zonation in the shoot, recapitulating the slowly growing center and more rapidly growing peripheral region previously observed in the meristem. These radial patterns emerging from mechanics are in striking correspondence to the expression patterns of the genes important for stem cell maintenance, which attain similar radial domains. We also show that the stress model can robustly define anisotropically growing organs, which emphasizes the potential importance of stress in generating correct organ shapes in plants.
doi:10.1371/journal.pcbi.1003410
PMCID: PMC3886884  PMID: 24415926
3.  Simulating the Mammalian Blastocyst - Molecular and Mechanical Interactions Pattern the Embryo 
PLoS Computational Biology  2011;7(5):e1001128.
Mammalian embryogenesis is a dynamic process involving gene expression and mechanical forces between proliferating cells. The exact nature of these interactions, which determine the lineage patterning of the trophectoderm and endoderm tissues occurring in a highly regulated manner at precise periods during the embryonic development, is an area of debate. We have developed a computational modeling framework for studying this process, by which the combined effects of mechanical and genetic interactions are analyzed within the context of proliferating cells. At a purely mechanical level, we demonstrate that the perpendicular alignment of the animal-vegetal (a-v) and embryonic-abembryonic (eb-ab) axes is a result of minimizing the total elastic conformational energy of the entire collection of cells, which are constrained by the zona pellucida. The coupling of gene expression with the mechanics of cell movement is important for formation of both the trophectoderm and the endoderm. In studying the formation of the trophectoderm, we contrast and compare quantitatively two hypotheses: (1) The position determines gene expression, and (2) the gene expression determines the position. Our model, which couples gene expression with mechanics, suggests that differential adhesion between different cell types is a critical determinant in the robust endoderm formation. In addition to differential adhesion, two different testable hypotheses emerge when considering endoderm formation: (1) A directional force acts on certain cells and moves them into forming the endoderm layer, which separates the blastocoel and the cells of the inner cell mass (ICM). In this case the blastocoel simply acts as a static boundary. (2) The blastocoel dynamically applies pressure upon the cells in contact with it, such that cell segregation in the presence of differential adhesion leads to the endoderm formation. To our knowledge, this is the first attempt to combine cell-based spatial mechanical simulations with genetic networks to explain mammalian embryogenesis. Such a framework provides the means to test hypotheses in a controlled in silico environment.
Author Summary
We elucidate by computational means the processes by which the development of the mammalian embryo during its first four to five days occurs, as it is transformed from a single stem cell into hundreds of cells of different tissue types. We are interested in understanding the fundamental processes of how gene expression dynamics within each cell is coupled to the mechanical forces between cells, such that cells move to take up their positions as part of different tissues depending on the genes they express. Recent experiments which track single cell movement and division in conjunction with their gene expression dynamics suggest various hypotheses as to how this coupling functions to pattern the embryo. We have developed a computational model which can test these hypotheses. The model consists of dividing cells, interacting with each other through mechanical forces, within a confinement of embryo boundary. Each cell contains a genetic network of specific genes which influence cell adhesion properties and cell division plane directions. We explicitly simulate the formation of the trophectoderm and endoderm layers of cells which illuminates the principles by which the embryo is robustly patterned.
doi:10.1371/journal.pcbi.1001128
PMCID: PMC3088645  PMID: 21573197
4.  Alignment between PIN1 Polarity and Microtubule Orientation in the Shoot Apical Meristem Reveals a Tight Coupling between Morphogenesis and Auxin Transport 
PLoS Biology  2010;8(10):e1000516.
Imaging and computational modeling of the Arabidopsis shoot meristem epidermis suggests that biomechanical signals coordinately regulate auxin efflux carrier distribution and microtubule patterning to orchestrate the extent and directionality of growth.
Morphogenesis during multicellular development is regulated by intercellular signaling molecules as well as by the mechanical properties of individual cells. In particular, normal patterns of organogenesis in plants require coordination between growth direction and growth magnitude. How this is achieved remains unclear. Here we show that in Arabidopsis thaliana, auxin patterning and cellular growth are linked through a correlated pattern of auxin efflux carrier localization and cortical microtubule orientation. Our experiments reveal that both PIN1 localization and microtubule array orientation are likely to respond to a shared upstream regulator that appears to be biomechanical in nature. Lastly, through mathematical modeling we show that such a biophysical coupling could mediate the feedback loop between auxin and its transport that underlies plant phyllotaxis.
Author Summary
The proper development of plant organs such as leaves or flowers depends both on localized growth, which can be controlled by the plant hormone auxin, and directional growth, which is dependent on each cell's microtubule cytoskeleton. In this paper we show that at the shoot apex where organs initiate the orientation of the microtubule cytoskeleton is correlated with the orientation of the auxin transporter PIN1, suggesting coordination between growth patterning at the tissue level and directional growth at the cellular level. Recent work has indicated that mechanical signals play a role in orienting the plant microtubule network, and here we show that such signals can also orient PIN1. In addition, we demonstrate through mathematical modeling that an auxin transport system that is coordinated by mechanical signals akin to those we observed in vivo is sufficient to give rise to the patterns of organ outgrowth found in the plant Arabidopsis thaliana.
doi:10.1371/journal.pbio.1000516
PMCID: PMC2957402  PMID: 20976043
5.  Modeling Auxin-regulated Development 
The phytohormone auxin plays an essential role in many aspects of plant growth and development. Its patterning, intercellular transport, and means of signaling have been extensively studied both in experiments and computational models. Here, we present a review of models of auxin-regulated development in different plant tissues. This includes models of organ initiation in the shoot apical meristem, development of vascular strands in leafs and stems, and auxin-related functioning in roots. The examples show how mathematical modeling can help to examine expected and unexpected behavior of the system, challenge our knowledge and hypotheses, obtain quantitative results, or suggest new experiments and ways to approach a problem.
Computer simulations of plant responses to auxin explain previously perplexing aspects of the transport, regulation, and metabolism of this phytohormone.
doi:10.1101/cshperspect.a001560
PMCID: PMC2828283  PMID: 20182620

Results 1-5 (5)