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1.  A Computational Framework for 3D Mechanical Modeling of Plant Morphogenesis with Cellular Resolution 
PLoS Computational Biology  2015;11(1):e1003950.
The link between genetic regulation and the definition of form and size during morphogenesis remains largely an open question in both plant and animal biology. This is partially due to the complexity of the process, involving extensive molecular networks, multiple feedbacks between different scales of organization and physical forces operating at multiple levels. Here we present a conceptual and modeling framework aimed at generating an integrated understanding of morphogenesis in plants. This framework is based on the biophysical properties of plant cells, which are under high internal turgor pressure, and are prevented from bursting because of the presence of a rigid cell wall. To control cell growth, the underlying molecular networks must interfere locally with the elastic and/or plastic extensibility of this cell wall. We present a model in the form of a three dimensional (3D) virtual tissue, where growth depends on the local modulation of wall mechanical properties and turgor pressure. The model shows how forces generated by turgor-pressure can act both cell autonomously and non-cell autonomously to drive growth in different directions. We use simulations to explore lateral organ formation at the shoot apical meristem. Although different scenarios lead to similar shape changes, they are not equivalent and lead to different, testable predictions regarding the mechanical and geometrical properties of the growing lateral organs. Using flower development as an example, we further show how a limited number of gene activities can explain the complex shape changes that accompany organ outgrowth.
Author Summary
In recent years, much research in molecular and developmental biology has been devoted to unravelling the mechanisms that govern the development of living systems. This includes the identification of key molecular networks that control shape formation and their response to hormonal regulation. However, a key challenge now is to understand how these signals, which arise at cellular scale, are physically translated into growth at organ scale, and how these shape changes feed back into molecular regulation systems. To address this question, we developed a computational framework to model the mechanics of 3D tissues during growth at cellular resolution. In our approach, gene regulation is related to tissue mechanical properties through a constitutive tensorial growth equation. Our computational system makes it possible to integrate this equation in both space and time over the growing multicellular structure in close to interactive time. We demonstrate the interest of such a framework to study morphogenesis by constructing a model of flower development, showing how regulation of regional identities can, by dynamically modulating the mechanical properties of cells, lead to realistic shape development.
doi:10.1371/journal.pcbi.1003950
PMCID: PMC4288716  PMID: 25569615
2.  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
3.  A correlative microscopy approach relates microtubule behaviour, local organ geometry, and cell growth at the Arabidopsis shoot apical meristem 
Journal of Experimental Botany  2013;64(18):5753-5767.
Cortical microtubules (CMTs) are often aligned in a particular direction in individual cells or even in groups of cells and play a central role in the definition of growth anisotropy. How the CMTs themselves are aligned is not well known, but two hypotheses have been proposed. According to the first hypothesis, CMTs align perpendicular to the maximal growth direction, and, according to the second, CMTs align parallel to the maximal stress direction. Since both hypotheses were formulated on the basis of mainly qualitative assessments, the link between CMT organization, organ geometry, and cell growth is revisited using a quantitative approach. For this purpose, CMT orientation, local curvature, and growth parameters for each cell were measured in the growing shoot apical meristem (SAM) of Arabidopsis thaliana. Using this approach, it has been shown that stable CMTs tend to be perpendicular to the direction of maximal growth in cells at the SAM periphery, but parallel in the cells at the boundary domain. When examining the local curvature of the SAM surface, no strict correlation between curvature and CMT arrangement was found, which implies that SAM geometry, and presumed geometry-derived stress distribution, is not sufficient to prescribe the CMT orientation. However, a better match between stress and CMTs was found when mechanical stress derived from differential growth was also considered.
doi:10.1093/jxb/ert352
PMCID: PMC3871827  PMID: 24153420
Arabidopsis thaliana; cortical microtubules; growth; mechanical stress; organ geometry; shoot apical meristem.
4.  Cracking the elusive alignment hypothesis: the microtubule–cellulose synthase nexus unraveled 
Trends in Plant Science  2012;17(11):666-674.
Directed plant cell growth is governed by deposition and alterations of cell wall components under turgor pressure. A key regulatory element of anisotropic growth, and hence cell shape, is the directional deposition of cellulose microfibrils. The microfibrils are synthesized by plasma membrane-located cellulose synthase complexes that co-align with and move along cortical microtubules. That the parallel relation between cortical microtubules and extracellular microfibrils is causal has been named the alignment hypothesis. Three recent studies revealed that the previously identified pom2 mutant codes for a large cellulose synthases interacting (CSI1) protein which also binds cortical microtubules. This review summarizes these findings, provides structure–function models and discusses the inferred mechanisms in the context of plant growth.
doi:10.1016/j.tplants.2012.06.003
PMCID: PMC3492759  PMID: 22784824
5.  Regulatory Role of Cell Division Rules on Tissue Growth Heterogeneity 
The coordination of cell division and cell expansion are critical to normal development of tissues. In plants, cell wall mechanics and the there from arising cell shapes and mechanical stresses can regulate cell division and cell expansion and thereby tissue growth and morphology. Limited by experimental accessibility it remains unknown how cell division and expansion cooperatively affect tissue growth dynamics. Employing a cell-based two dimensional tissue simulation we investigate the regulatory role of a range of cell division rules on tissue growth dynamics and in particular on the spatial heterogeneity of growth. We find that random cell divisions only add noise to the growth and therefore increase growth heterogeneity, while cell divisions following the shortest new wall or along the direction of maximal mechanical stress reduce growth heterogeneity by actively enhancing the regulation of growth by mechanical stresses. Thus, we find that, beyond tissue geometry and topology, cell divisions affect the dynamics of growth, and that their signature is embedded in the statistics of tissue growth.
doi:10.3389/fpls.2012.00174
PMCID: PMC3414725  PMID: 22908023
growth regulation; stochasticity; morphogenesis; mechanical forces; vertex model; cell division
6.  Quantitative imaging strategies pave the way for testable biological concepts 
BMC Biology  2011;9:10.
In developmental biology, the accumulation of qualitative phenotypic descriptions has fueled the need for testable parsimonious hypotheses, giving a fresh impetus to quantitative strategies. As an illustration, thanks to the precise quantification of cell growth and microtubule behavior in a study published in BMC Plant Biology, Zhang and collaborators have identified sequential phases of polarized and isotropic growth in puzzle-shaped leaf epidermal cells, thus providing new clues to explore how growth coordination occurs in this tissue.
doi:10.1186/1741-7007-9-10
PMCID: PMC3045392  PMID: 21352557
7.  Is cell polarity under mechanical control in plants? 
Plant Signaling & Behavior  2011;6(1):137-139.
Plant cells experience a tremendous amount of mechanical stress caused by turgor pressure. Because cells are glued to their neighbors by the middle lamella, supracellular patterns of physical forces are emerging during growth, usually leading to tension in the epidermis. Cortical microtubules have been shown to reorient in response to these mechanical stresses, and to resist them, indirectly via their impact on the anisotropic structure of the cell wall. In a recent study, we show that the polar localization of the auxin efflux carrier PIN1 can also be under the control of physical forces, thus linking cell growth rate and anisotropy by a common mechanical signal. Because of the known impact of auxin on the stiffness of the cell wall, this suggests that the mechanical properties of the extracellular matrix play a crucial signaling role in morphogenesis, notably controlling the polarity of the cell, as observed in animal systems.
doi:10.4161/psb.6.1.14269
PMCID: PMC3122027  PMID: 21258209
development; growth; auxin; microtubule; PIN1; stiffness; cell wall; biophysics; meristem
8.  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

Results 1-8 (8)