Subcellular and supracellular mechanical stress prescribes cytoskeleton behavior in Arabidopsis cotyledon pavement cells

Arun Sampathkumar; Pawel Krupinski; Raymond Wightman; Pascale Milani; Alexandre Berquand; Arezki Boudaoud; Olivier Hamant; Henrik Jönsson; Elliot M Meyerowitz

doi:10.7554/eLife.01967

. 2014 Apr 16;3:e01967. doi: 10.7554/eLife.01967

Subcellular and supracellular mechanical stress prescribes cytoskeleton behavior in Arabidopsis cotyledon pavement cells

Arun Sampathkumar ^1,^2,^†, Pawel Krupinski ^3,^†, Raymond Wightman ², Pascale Milani ⁴, Alexandre Berquand ⁵, Arezki Boudaoud ⁴, Olivier Hamant ^4,^*, Henrik Jönsson ^2,^3,^*, Elliot M Meyerowitz ^2,^6,^*

Editor: Dominique Bergmann⁷

PMCID: PMC3985187 PMID: 24740969

Abstract

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

Research organism: Arabidopsis

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

Introduction

Epithelia have a crucial role during the development of most multicellular organisms. Consistently, several mechanisms ensure some level of coordination between epithelial cells. In addition to biochemical signals, such as morphogens that diffuse and provide regional coordination across several cell files (Wolpert, 1969; Jonsson et al., 2006; Jaeger et al., 2008; Wartlick et al., 2009), mechanical stress also contributes to growth coordination, for instance by synchronizing cell proliferation rate (Shraiman, 2005) and orientation (Thery et al., 2007), or by prescribing cell polarity (Asnacios and Hamant, 2012) and cell fate (Engler et al., 2006). In theory, these coordinating mechanisms could lead to relatively homogeneous cell shapes. While this is observed in some classic cases, such as the cells of Drosophila ommatidia or Arabidopsis petals, most epithelia exhibit variable cell sizes and shapes, demonstrating that each cell retains the ability to regulate its own growth and shape (Roeder et al., 2010, 2012). This heterogeneity has been studied in several systems. In Drosophila embryos, stochastic actomyosin-dependent constrictions of cells occur during gastrulation (Martin et al., 2009) and dorsal closure (Solon et al., 2009), and this stochasticity has been proposed to play a key role in invagination events (Pouille et al., 2009). In Arabidopsis sepals, stochastic events including cell division and entry into endoreduplication also play a critical role in the distribution of cells of different shapes (Roeder et al., 2010). Altogether this suggests that cell behavior results from both local and supracellular cues. The exact role of such heterogeneity remains poorly explored, and how cells can differentiate between local and global cues is completely unknown. In this study, we show that mechanical stress act as a common instructing signal for microtubule (MT) orientation at both subcellular and tissue scales.

Mechanical forces have been proposed to provide directional information in control of MT orientation in plant cells and changes in mechanical forces are known to affect microtubule alignment (Green, 1980; Williamson, 1990; Schopfer, 2006). MT arrays have been proposed to align along maximal mechanical stress directions in the shoot apical meristem, as prescribed by tissue shape, assuming tension in the epidermis (Hamant et al., 2008). Mechanical forces were recently found to modify MT organization in leaf epidermal cell layers (Jacques et al., 2013). In Arabidopsis and most angiosperms, the cotyledon and leaf epidermal cells, also called pavement cells, exhibit typical jigsaw puzzle shapes, with indented regions and lobe-like outgrowths. The intracellular effectors of these morphologies are being described in many reports. In particular, indenting regions are enriched in cortical MTs, which are thought to restrain growth expansion via the presumptive localized deposition of stiff cellulose microfibrils (CMF) (Fu et al., 2005; Yang, 2008). Although this model seems relatively parsimonious, these biophysical assumptions have not been tested. The MT severing enzyme katanin is required for local MT ordering in pavement cell indenting regions, downstream of the plant hormone auxin and Rho GTPases (Lin et al., 2013). How robust shapes could derive from such regulation is however a subject of debate.

The complex morphology of pavement cells is a system of choice to decipher the contribution of cell and tissue shape-derived mechanical stresses in MT behavior. In this study, we have combined computational models and experiments to determine the relation between physical forces, material elasticity, and the behavior of cortical MT. We first relate MT behavior to cell wall reinforcements. Second, we confirm (in a different tissue than investigated in the past and at a different scale) that MTs orient along the predicted maximal tensile stress direction—and in this case, that they can do so at a subcellular or a supracellular scale, depending on the stresses involved. Lastly, we take advantage of the large size of the pavement cells to show how the MT response to stress depends on MT severing-dependent self-organization events. Altogether, this provides a scenario, in which not only tissue shape, but also cell shape, depends on a mechanical feedback loop. Based on our results, we propose that cells sense mechanical stresses at the subcellular scale, and that they are hence able to integrate cell shape-derived stresses and tissue shape-derived stresses, with a single mechanism.

Results

Pavement cell shape correlates with microtubule organization and consistent mechanical reinforcements in cell walls

The presence of parallel bundles of MTs in pavement cells is spatially correlated with indenting neck regions of the cell (Figure 1A, Figure 1—figure supplement 1; Fu et al., 2005). However, this correlation is debated, as MT orientations can be very noisy and pavement cell growth has even been proposed to be rather isotropic (Zhang et al., 2011). To quantify MT behavior in pavement cells, we used a nematic tensor-based tool to measure MT anisotropy (Uyttewaal et al., 2012; Boudaoud et al., 2014). This showed that MT arrays in indenting regions were more anisotropic than the MT arrays in lobes (mean ± SE is 0.40 ± 0.02 for indenting region and 0.20 ± 0.02 for lobes, n = 18 cells; 3 seedlings; p<0.01, t test; Figure 1A,B, Figure 1—figure supplement 1). Time lapse imaging of pavement cells showed that the anisotropy of MTs was maintained in indenting regions after 3 hr (mean ± SE is 0.47 ± 0.01, n = 14 cells; 3 seedlings), consistent with previous studies (Zhang et al., 2011) (Figure 1A,B, Figure 1—figure supplement 1). Note that we focused our analysis on a stage where cells have already attained their jigsaw puzzle shape and are still growing; our conclusions do not necessarily apply to these cells at a younger, undifferentiated stage or at an older, fully grown stage. The correlation between pavement cell shape and the presence of stably aligned MTs in indenting regions suggests that pavement cell shape relies on the impact of MTs on the mechanical anisotropy of the cell wall in these regions. This however has never been demonstrated. To directly measure mechanical properties of the outer wall with sufficient resolution, we used atomic force microscopy (AFM) to probe different regions of pavement cells, using an established protocol (Milani et al., 2011). First, we probed guard cells, in which the presence of transverse MT and CMF is unequivocally established (Marcus et al., 2001). The stiffness map of the outer wall of guard cells revealed the presence of transverse wall reinforcements matching the CMF orientation (Figure 1C). Therefore, our AFM approach has sufficient spatial resolution to reveal mechanical heterogeneities in cell walls. The AFM-based stiffness map of pavement cells also revealed the presence of mechanical heterogeneities, with apparent elastic moduli spanning the range 2–8 MPa. In particular, we found fibrous patterns of higher elastic modulus congregating at sites of indenting regions (Figure 1D, Figure 1—figure supplement 2). These lines are independent of small-scale topography (Figure 1E). Note that with AFM, we are measuring the mechanical properties of the wall in the normal direction to the wall surface with an isotropic probe, and therefore, we are not assessing the very local mechanical anisotropy of the cell wall in-plane. Yet, our data reveal a spatial pattern of mechanical anisotropy at a larger scale, and thus can be used as a proxy for mechanical anisotropy in sub-regions of the cell’s outer wall. Staining for cellulose in mesophyll cells of wheat that exhibit alternating patterns of lobe like outgrowth and indenting regions has shown a strong presence of cellulose in the constricted regions of the cells (Jung and Wernicke, 1990). Altogether, this suggests that CMFs act as a brace around the indenting regions providing mechanical reinforcement of those regions.

Figure 1—figure supplement 1. — (A) Microtubule bundling persits in indenting regions of pavement cells over time. Scale bars 20 μm. (B) Microtubule anisotropy over time, lines represent average orientation of microtubule arrays at different time points within the region of interest (dashed box in A). Longer lines indicate higher degree of anisotropy. (C) Stiffness map of the outer walls in two guard cells obtained by atomic force microscopy revealing transverse wall reinforcements. Gray scale bar represents scale of the observed elastic modulus in MPa. (D) Siffness map of the outer walls in pavement cells obtained by atomic force microscopy (same scale bar). Indenting regions exhibit striations with increased values of elastic modulus, reflecting regions with strong mechanical anisotropy. (E) 3D rendering of pavement cell topography as obtained by atomic force microscopy.

**DOI:** http://dx.doi.org/10.7554/eLife.01967.003

Recent reports suggest that MT and cellulose synthase orientation could have different behaviors on the inner and outer face of hypocotyl epidermal cells (Chan et al., 2010; Crowell et al., 2011) and stems (Fujita et al., 2011). To test if this is the case in pavement cells, we visualized MT organization on the inner face of the pavement cells in confocal Z sections. The inner MT arrays appear to be identical to those observed on the outer face, thereby suggesting the cell walls of the indenting regions are reinforced on both faces of the cell (Figure 1—figure supplement 3A,B). These data thus consolidate a model in which pavement cell shape is maintained by localized MT-dependent wall reinforcements in indenting regions (Fu et al., 2005).

Microtubule organization correlates with cell geometry-derived mechanical stresses

Next, we investigated whether mechanical stress can act as an instructive signal in this MT organization. Physical models of the shoot apical meristem as a pressurized vessel have shown that the supracellular mechanical stress pattern can prescribe global MT organization and tissue morphology (Hamant et al., 2008). Scaling down, this model implicitly predicts that mechanical cues also contribute to single cell morphology. However, this question still remains to be explored.

To address this, we first computed the expected patterns of stress in pavement cells using a three-dimensional (3D) finite element model representing the outer face of the wall as a curved surface. Tensile stress experienced by the walls is caused by turgor pressure within the cells, therefore the main question was whether cell shape affects the anisotropy of stress in the wall. The 3D geometries of the cells were extracted from confocal microscope images of pavement cells processed with MorphographX and meshed with quadrilateral shell elements (Kierzkowski et al., 2012). The boundaries of the cells contain additional beam elements that account for increase in stiffness due to the presence of the anticlinal walls. For the material properties, we used a constitutive model of hyperelastic transversely isotropic material. To account for the mechanical anisotropy of the wall (Baskin et al., 1999), elasticity of the tissue was represented by the behavior of an isotropic matrix combined with the resistance of CMF oriented in a single-preferred direction per element. In the simulations, we have assumed that stress pattern arises due to turgor pressure in individual cells accompanied by tension in the epidermal layer (Dumais and Steele, 2000; Kutschera and Niklas, 2007; Hamant et al., 2008). The displacement of the anticlinal walls was restricted in z direction.

The outcome of the model with mechanically isotropic cell walls showed a strong anisotropic arrangement of stresses focused in indenting regions of the pavement cells (Figure 2A,C, Figure 2—figure supplement 1A). Despite the noisy behavior of MTs in pavement cells, visualization of MT organization with YFP:MBD (Wightman and Turner, 2007) showed a good correlation between the largest stress direction and MT arrangement, aggregating in indenting regions of the pavement cells (Figure 2B,D, Figure 2—figure supplement 1B). Furthermore, the clustering of MT arrays in the indenting regions also correlated with regions of predicted higher magnitude of stress (Figure 1E, Figure 2—figure supplement 1C). Stress directions were also computed in a model representing a 3D pavement cell shape along with the anticlinal and bottom walls. The model generated principal stress tensor direction pattern similar to the curved surface model (Figure 2—figure supplement 2A–C). Both cases showed a higher magnitude of tensile stresses in the indenting neck-like regions, matching the local MT pattern; compression forces at approximately 10% of the tension value were observed in some regions close to the cell boundary with no clear relation with MT behavior (Figure 2—figure supplement 2D–F). This suggests that tensile stress influences MT organization at a subcellular level in pavement cells, thereby indicating that the perception of stress must involve a mechanism that acts locally within each cell, rather than on a cell-wide or tissue-wide basis.

Figure 2. — (A) Mesh showing stress directions, with the corresponding microtubule organization shown in panel B. Highlighted cells in green are represented in panels C–E and Figure 2—figure supplement 1A–C. (C) Largest stress direction (red) and second principal stress direction (green) in mechanical models of the pavement cell. White arrowheads indicate regions of convergence of directional tensile stresses in necks of pavement cells. (D) Microtubule (YFP-MBD) orientations correlate with the maximal stress direction predicted in the mechanical model. (E) Heat map showing the magnitude of stress distribution in the mechanical model. Arrowheads indicate regions of highest stress magnitude in neck regions. Scale bars 20 μm. (F) Circumferential distribution of microtubules surrounding elevated guard cells represented as a depth color-coded Z-stack. (G) Mechanical model of stress patterns around a stomata reproduce the observed arrangements of microtubules surrounding guard cells. (H) Microtubule organization around a non-elevated stoma and a mechanical model of stress patterns of the same (I). Scale bars 25 μm.

**DOI:** http://dx.doi.org/10.7554/eLife.01967.007

Figure 2—figure supplement 1. — (A) Mesh showing stress directions, with the corresponding microtubule organization shown in panel B. Highlighted cells in green are represented in panels C–E and Figure 2—figure supplement 1A–C. (C) Largest stress direction (red) and second principal stress direction (green) in mechanical models of the pavement cell. White arrowheads indicate regions of convergence of directional tensile stresses in necks of pavement cells. (D) Microtubule (YFP-MBD) orientations correlate with the maximal stress direction predicted in the mechanical model. (E) Heat map showing the magnitude of stress distribution in the mechanical model. Arrowheads indicate regions of highest stress magnitude in neck regions. Scale bars 20 μm. (F) Circumferential distribution of microtubules surrounding elevated guard cells represented as a depth color-coded Z-stack. (G) Mechanical model of stress patterns around a stomata reproduce the observed arrangements of microtubules surrounding guard cells. (H) Microtubule organization around a non-elevated stoma and a mechanical model of stress patterns of the same (I). Scale bars 25 μm.

**DOI:** http://dx.doi.org/10.7554/eLife.01967.007

To check whether the mechanical anisotropy of the wall could alter stress direction in pavement cell models, we introduced a CMF direction with five times higher stiffness and subjected the cells to elastic expansion again. A feedback model between the stress perceived by a cell and orientation of the CMFs, which assumes an alignment of the CMF in the direction of maximal stress results in a very minor deviation of the stress pattern from the stress orientation obtained in the case of an isotropic material (Figure 2—figure supplement 3). The simulations thus suggest that for small elastic deformations the overall stress pattern is affected more strongly by the geometry of the cells than by the mechanical anisotropy of the existing cell wall material.

The model also predicts that the topography of the epidermis impact stress patterns and can have a dominant role on MT behavior as compared to cell shape. In particular, assuming that the epidermis is under tension, the largest stress direction should be circumferential around a local bump. Stomata being often in such an elevated position, we analyzed the MT arrays around guard cells and we found circumferential orientations, consistent with the predicted stress directions (Figure 2F,G). Conversely, no circumferential MT pattern could be observed near stomata that were not elevated (Figures 2H,I).

The results suggest that, analogously to what was observed in the shoot meristem, patterns of cellular and supracellular mechanical stress and MT orientation are correlated. Furthermore, we find that this correlation holds down to the sub-cellular level.

Mechanical compression of cotyledon pavement cells affects microtubule anisotropy

Recent observations of MT organization in epidermal cells of leaves shows a supracellular response of MTs after changes in physical forces (Jacques et al., 2013). Application of compressive forces resulted in hyper-alignment of MTs. We tested whether mechanical stress can act as an instructive signal to organize MTs in cotyledon pavement cells by performing mechanical perturbations. Our finite element model predicts that when subjected to compression from above, there is an increase in overall stress in physical models (Figure 3—figure supplement 1A,B). Note that this response would however largely depend on the ability of the epidermis epidermal wall to maintain a constant volume while under compression. We directly applied compressive forces to pavement cells by using a coverslip that was pressed on the surface of the cotyledons and kept in place using adhesive silicone applied on the margins (Figure 3—figure supplement 1C). Depth color-coded Z stacks of MT organization and transects of the confocal Z-stack showed flattening of cells due to compression (Figure 3—figure supplement 1C,D). Imaging of MTs in the cells immediately after and 7 hr after compression showed rearrangement of MTs into more aligned arrays by 7 hr (Figure 3—figure supplement 1C,D,F; Video 1; mean ± SE is 0.37 ± 0.06 for 0 hr, n = 95 cells, 5 seedlings and 0.57 ± 0.06 for 7 hr, n = 95 cells; 5 seedlings; p<0.0001; Mann–Whitney U test; Figure 3H). This increased MT anisotropy persisted for longer periods when the tissue was maintained in the compressed condition (Figure 3—figure supplement 2). This response was also reversible: 24 hr following removal of compression, nematic tensor values for MT anisotropy were reduced to a value close to that obtained during the time point immediately after compression (mean ± SE is 0.24 ± 0.02; Figure 3E,G,H). It should be noted that the nematic tensor values between the 0 hr time point and the recovery state are not identical which could be the result of changes in imaging conditions (‘Materials and methods’). However, despite this the reported nematic tensor values clearly show a trend in the increase and decrease of the MT anisotropy in the compression experiments. These results on cotyledon epidermal cells are thus consistent with the recently published report on contribution of mechanical stress in controlling MT behavior in leaf epidermal cells (Jacques et al., 2013).

Video 1. Depth color-coded time series images showing changes in microtubule organization following compression.

Download video file^{(5.4MB, mov)}

DOI: 10.7554/eLife.01967.011

Open in a new tab

Scale bar 20 µm.

DOI: http://dx.doi.org/10.7554/eLife.01967.011

Figure 3. — (A and B) Mechanical models showing changes in stress directions upon ablation. (C) Large scale ablation of cotyledons result in circumferential distribution of microtubule arrays around the site of physical perturbations, reproducing the results of the physical model. (D) Microtubule arrays in pavement cells of mutant *botero 1-7* shows random organization 7 hr after perturbation. Asterisk marks site of laceration. Scale bar 25 μm.

**DOI:** http://dx.doi.org/10.7554/eLife.01967.012

Figure 3—figure supplement 1. — (A and B) Mechanical models showing changes in stress directions upon ablation. (C) Large scale ablation of cotyledons result in circumferential distribution of microtubule arrays around the site of physical perturbations, reproducing the results of the physical model. (D) Microtubule arrays in pavement cells of mutant *botero 1-7* shows random organization 7 hr after perturbation. Asterisk marks site of laceration. Scale bar 25 μm.

**DOI:** http://dx.doi.org/10.7554/eLife.01967.012

Large scale changes in tissue-wide stresses can override cell shape-derived stresses

A limit of the compression test is that water movements may be induced, and while it is extremely difficult to monitor, water flow may alter turgor pressure in the long term and thus the predicted stress pattern. So to further investigate the link between MT behavior and stress in pavement cells, we next induced large cuts to change stress patterns in cotyledons and observed the resulting MT pattern. The observation of tissue deformations after large cuts has long been used to deduce the stress pattern (Dumais and Steele, 2000) and has recently been adapted to calculate solid stresses in animal tumors (Stylianopoulos et al., 2012). Macroscopically, large cuts in cotyledons resulted in an immediate outward displacement of the cut edges, consistent with release of tension (Figure 3—figure supplement 3A,B; Video 2). We also observed upward movement of mesophyll cells from the layer below (Figure 3—figure supplement 3C), consistent with the epidermis being under tension as observed in other plant tissues (Kutschera and Niklas, 2007). Simulation of such a large-scale nick in physical models was done with the assumption that laceration would lead to removal of turgor pressure from the cut cells followed by a reduction of wall elasticity, as previously published in more local (Hamant et al., 2008) and more global (Dumais and Steele, 2000; Kutschera and Niklas, 2007) tissue contexts. Our physical model suggests that maximal stress directions become circumferential to the laceration after treatment and independent of cell geometry (Figure 3A,B; Video 3). To test the model predictions, we performed similar lacerations on cotyledons of seedlings expressing fluorescent reporters of MTs. Time series imaging of MT rearrangements showed a progressive change in the organization of MT arrays around the site. After 3.5 hr, we observed hyper-aligned MT arrays in cells adjacent to the damaged region and at 7 hr the alignment advanced to cell layers farther away from the site of laceration, independently of cell shape (Figure 3C). Quantification of MT anisotropy showed a significant increase in MT anisotropy 7 hr after laceration (mean ± SE is 0.080 ± 0.007 for 0 hr, n = 61 cells and 0.37 ± 0.02 for 7 hr, n = 65 cells; 3 seedlings each; p<0.0001; Mann–Whitney U test), indicating that changes in tissue-wide stresses could override cellular level control of MT anisotropy.

Video 2. Laceration of cotyledon shows outward displacement of cut edges.

Download video file^{(44.2KB, mov)}

DOI: 10.7554/eLife.01967.017

Open in a new tab

Scale bar 500 µm.

DOI: http://dx.doi.org/10.7554/eLife.01967.017

Video 3. Video of computational simulation showing circumferential distribution of stress and increase in MT anisotropy after ablation.

Download video file^{(4.4MB, mov)}

DOI: 10.7554/eLife.01967.018

Open in a new tab

DOI: http://dx.doi.org/10.7554/eLife.01967.018

Microtubule response to mechanical perturbation is dependent on the magnitude of change in stress intensity

To decipher if the response of MTs to mechanical perturbation depended on the intensity of stress imposed on the tissue, we performed simulation in which single cells were removed and the resulting patterns of stress computed. Similar to the large scale laceration experiments, a circumferential rearrangement of stresses was observed. However, the rearrangement was less pronounced than after cotyledon dissection, and observed in cells only adjacent to the site of perturbation (Figure 4A,B). To test this experimentally, we ablated single cells using a pulsed dye-coupled laser to see if small-scale perturbations could decouple the cellular level control of microtubule organization. 7 hr after ablation, we observed that MT alignment had responded to treatment by tending toward a circumferential alignment around the ablated cell site. The MTs around the site of ablation were not completely circumferential, consistent with a scenario in which stress anisotropy is weaker in single cell ablation cases than in cases of large-scale dissection, therefore leading to a comparatively reduced alignment of MTs around the site of ablation (Figure 4C,D,E). The alignment observed after single-cell ablation was significantly different from that resulting from large-scale perturbation, in which a strong circumferential response was obtained.

Figure 4. — (A and B) Simulation showing less pronounced circumferential rearrangements of stresses after ablation of single cell. Images of microtubule reporter line before (C) and 7 hr after (D) ablation of single cell, showing aligned microtubule arrays not completely circumferential after ablation of single cell. Scale bars 50 μm. (E) Magnified images of cells in figure D (Images not to scale). Asterisk shows the location of the ablated cell.

**DOI:** http://dx.doi.org/10.7554/eLife.01967.019

Figure 4—figure supplement 1. — (A and B) Simulation showing less pronounced circumferential rearrangements of stresses after ablation of single cell. Images of microtubule reporter line before (C) and 7 hr after (D) ablation of single cell, showing aligned microtubule arrays not completely circumferential after ablation of single cell. Scale bars 50 μm. (E) Magnified images of cells in figure D (Images not to scale). Asterisk shows the location of the ablated cell.

**DOI:** http://dx.doi.org/10.7554/eLife.01967.019

To further test if a directional force field could alter transverse MT organization observed in guard cells, we monitored MT arrays in guard cells adjacent to the region of large scale laceration. Single optical sections show that MT arrays still remain transverse in majority of the guard cells (Figure 4—figure supplement 1) indicating that these cells retain a certain degree of control of their MTs while being under the influence of a directional force field.

The observed rearrangement of MTs around the site of laceration supports our hypothesis but several other possibilities could exist. The changes observed could be due to a modified pattern of mechanical stress but also to the biochemical consequences of wounding of the sample. To investigate this we used the cellulose synthase inhibitor isoxaben, as a pharmacological means of increasing mechanical stress in pavement cells. Isoxaben was shown previously to induce hyperbundling and hyperalignment of cortical microtubules along the predicted directions of maximal stress in shoot meristem cells (Heisler et al., 2010), consistent with increased stress levels in the cell walls compared to non-treated plants. Treatment of 3-day-old seedlings with 40 μM isoxaben for 16 hr led to a sizeable increase in the anisotropy of microtubules (mean ± SE is 0.27 ± 0.04 for 0 hr, n = 53 cells and 0.54 ± 0.08 for 16 hr, n = 53 cells; 3 seedlings; p<0.0001, Mann–Whitney U test; Figure 4—figure supplement 2A–C). These observations add further evidence that mechanical forces are responsible for MT rearrangement. However, it should be noted that a much more complex scenario, involving both mechanics and wound responses, could govern this aspect of MT rearrangements.

The microtubule response to subcellular and supracellular stresses depends on katanin-dependent severing activity

Homozygotes for the katanin loss-of-function allele ktn1-3 exhibit severe pavement cell shape defects, consistent with the role of MTs in neck formation (Lin et al., 2013). When quantifying MT anisotropy in the bot 1-7 katanin allele, we found a 60% reduction when compared to the wild type (Mean ± SE is 0.09 ± 0.01 for bot 1-7, n = 83 cells; 4 seedling and 0.23 ± 0.05 for WT, n = 53 cells; 3 seedlings), thus confirming the relation between MT ordering and pavement cell shape. It has been shown in the shoot meristem that the response of MTs to tissue stress relies on MT self-organization. In particular, MT rearrangement after changes in mechanical stress is promoted by katanin-dependent MT severing (Uyttewaal et al., 2012). To test whether, as in the shoot meristem, katanin activity is required for the MT response to stress in pavement cells, we performed lacerations and compressions in the katanin mutant background bot1-7. In both assays, MT arrays in pavement cells remained relatively isotropic after the micromechanical perturbations (Figure 3D, Figure 3—figure supplement 4A–C; Video 4). Measurement of MT anisotropy showed no significant difference before and 7 hr after ablation in bot 1-7 (mean ± SE is 0.09 ± 0.02 for 0 hr, n = 83 cells and 0.10 ± 0.02 for 7 hr, n = 74 cells; 3 seedlings; p>0.05, t test; Figure 3D). Only subtle alignments could be detected in the immediate vicinity of the ablated zone in large-scale lacerations, but no alignment over several cell files was observed (Figure 3D). These results are consistent with observations made in the shoot apical meristem (Uyttewaal et al., 2012) and suggest that the MT response to stress is not only conserved in different tissues and at different scales, but also relies on a similar mechanism.

Video 4. Depth color-coded time series images showing microtubule arrays in botero 1-7 does not induce hyper-alignment of microtubule arrays after compression.

Download video file^{(1.5MB, mov)}

DOI: 10.7554/eLife.01967.022

Open in a new tab

Scale bar 50 µm.

DOI: http://dx.doi.org/10.7554/eLife.01967.022

As quantification of severing events in meristems is impractical due to difficulties in accessing the cells for high-resolution imaging, we took advantage of the large size of pavement cells to further test this conclusion. To do so, we directly scored single MT-severing events in YFP-MBD cells adjacent to the lacerated region in pavement cells (Figure 4A). Using time-series imaging of MT arrays, we could observe severing of MTs occurring at sites of crossover points of MTs (Figure 5A; Wightman and Turner, 2007; Lindeboom et al., 2013; Wightman et al., 2013; Zhang et al., 2013). The severing rate in mock-treated control seedlings of 0.08 ± 0.02 × 10⁻³ events μm⁻² min⁻¹ (mean ± SD, N = 16 cells, 4 seedlings, total area of 2.99 × 10⁴ μm²) is in agreement with what has been previously published (Wightman and Turner, 2007; Wightman et al., 2013; Zhang et al., 2013). However, in seedlings subjected to changes in mechanical forces, cell files close to the site of ablation showed a significant increase in severing rate to 0.93 ± 0.45 × 10⁻³ events μm⁻² min⁻¹ (mean ± SD, N = 16 cells, 4 seedlings, total area of 1.5 × 10⁴μm², p<0.01, t test) 3 hr after ablation (Figure 5B; Video 5). Measurement of number of crossover points (i.e., two polymerizing MT crossing each other without experiencing severing or catastrophe) immediately after and 3 hr after mock treatment showed a 9% increase (mean ± SE is 11.0 ± 1.4 per 10 μm² for 0 hr, n = 6 cells and 12 ± 1.5 per 10 µm² for 3 hr) whereas the cells experiencing changes in mechanical stress showed a 65% decrease in the number of cross over points (mean ± SE is 15 ± 3 per 10 μm² for 0 hr, n = 6 cells and 5 ± 2 per 10 μm² for 3 hr). These measurements demonstrate an up-regulation in the severing of MTs at crossover sites after changes in mechanical stress. This mechanism could enrich the population of free MTs, while removing the MTs that do not align parallel to maximal tensile stress, thereby resulting in the generation of anisotropic MT arrays.

Video 5. Video showing severing of microtubule immediately after and 4 hr post ablation of cells. Red dots mark sites of microtubule severing.

Download video file^{(10.2MB, mov)}

DOI: 10.7554/eLife.01967.024

Open in a new tab

Scale bar 25 µm.

DOI: http://dx.doi.org/10.7554/eLife.01967.024

Figure 5. — 3D surface plot of YFP microtubule time series images representing a typical microtubule severing event (A), arrowheads indicate microtubule-severing at a crossover sites. Scale bar 5 μm. (B) Histogram representing microtubule severing rates of mock treated seedlings and in seedling of cells adjacent to site of ablation after 4 hours. Error bars represent standard deviation. Asterisk shows significance. (Student’s t test). N = 16 cells, 4 seedlings, total area of 2.99 × 10 μm for mock and N = 16 cells, 4 seedlings, total area of 1.5 × 10 μm for ablation.

**DOI:** http://dx.doi.org/10.7554/eLife.01967.023

Discussion

The role of mechanical stress in animals has mainly been investigated in single cells. Some pioneering studies in Drosophila have investigated the role of mechanical stress in tissues, and most notably in germ band extension (Lecuit and Lenne, 2007; Sherrard et al., 2010), dorsal closure (Martin et al., 2009; Solon et al., 2009), and gastrulation (Pouille et al., 2009) in relation to actomyosin reorganization. However the mechanical properties of these tissues have not been studied, notably because of the difficult physical access to these embedded tissues, and because the rapid growth dynamics of these tissues is not compatible with high resolution mechanical measurements, using for instance, atomic force microscopy. Because plant growth is much slower and because tissues are easily accessible, such measurements are possible in plants. Here, we could correlate the behavior of the microtubular cytoskeleton with the predicted stress pattern and with quantified mechanical properties. This validates a number of previous studies assuming that pavement cell shape depends on mechanical heterogeneities (Fu et al., 2005), albeit relying only on MT behavior, and further supports plant tissues as facile systems to investigate the relation between the biophysics of growth and development.

Current models on pavement cell morphology suggest an influence of a ROP-based signaling mechanism on the cytoskeletal network (Fu et al., 2005; Yang, 2008). The findings suggest that growth is restricted in pavement cell indenting regions due to localized accumulation of anticlinal MT arrays by regulating CMF deposition, whereas local outgrowths are associated with the presence of an actin cytoskeleton that promotes growth. More recently it has been proposed that an auxin-dependent self-organizing mechanism controls the ROP-based signaling network (Xu et al., 2010). This model of differential growth is challenged by time lapse-imaging studies of pavement cell development, which shows an initial phase of multiple lobe initiations, followed by a phase of isotropic expansion during which the cell shape is maintained (Zhang et al., 2011). These studies do not take into account the mechanical aspects of the cell. In our study we show how subcellular mechanical stresses control MT organization, which in turn affects the mechanical anisotropy of the cell wall thereby contributing to cell shape irrespective of the previously proposed mechanisms. We believe that such a signaling module could add robustness to shape changes at the cellular scale.

Our studies further shed light on two theories that are at the center of many debates in biology. The organismal theory of multicellular organisms states that comprehension of tissue properties is essential to understanding the development of the organism, as opposed the view of cell theory, that proposes that the function of individual cells is what dictates development of the entire organism (Kaplan, 1992; Baluska et al., 2004). Previous findings on the shoot meristem suggest that MT organization depends on tissue shape-derived stresses (Hamant et al., 2008). Here, we found that cells can also interpret mechanical signals that are generated by their own shape. As this response is lost in large-scale mechanical perturbations, we propose that MT behavior depends on stress intensity, which is cell autonomous as long as tissue stresses do not override it. Such a balance between cell autonomous and non-cell autonomous stresses could control subcellular events in animal systems too.

Mechanical forces are known to cause changes to single MT dynamics in vivo by regulating the activity of MT-associated proteins (Trushko et al., 2013). In several organisms tensile forces acting on the kinetochore complex-attached MT ends are known to influence MT elongation rates during mitosis (Nicklas, 1988; Skibbens et al., 1993; Gardner et al., 2005; Franck et al., 2007). It remains to be tested if changes in mechanical forces could alter single MT dynamics in whole organism based studies. Previous studies on the shoot apical meristem show that katanin-mediated MT severing is required for MT response to changes in mechanical stresses (Uyttewaal et al., 2012). Our data not only show that a similar mechanism is present in pavement cells, but also show that severing itself is promoted by mechanical stress. One possible mechanism for stress-dependent regulation of MT alignment, where each MT is stressed due to their coupling with CMFs potentially by means of the cellulose synthesizing complexes which ride along the MT synthesizing the CMFs parallel to the MTs (Paredez et al., 2006; Bringmann et al., 2012). In such a scenario, a MT under tension is strained producing a conformational change to the MT lattice, which then could bias the binding of katanin to the less strained MTs at crossover sites, leading to preferential severing of the MTs that are not aligned to the principal stress direction. Reports have shown that conformation changes to the MT lattice act as hotspots promoting katanin binding and activity (Davis et al., 2002; Díaz-Valencia et al., 2011). As a result, this strain in MTs would lead to a MT alignment parallel to the anisotropic stress, not to overall cellular strain. MT behavior would thus depend on two parameters of mechanical stress (Figure 6): stress direction from cell and tissue shape determine the dominant MT orientation, which dictates wall reinforcement, and thus in turn contributes to cell and tissue shape; and stress intensity modulates severing activity, which controls the response of MTs to stress. Based on these results, there is no need for several rules to explain MT behaviors at different scales or in different tissues in response to mechanical signals and perturbations, and this parsimony might be one of the defining features of mechanical signaling, when compared to molecular signaling. As shape rather relies on the actomyosin network in animals, the impact of mechanical forces on actin dynamics may in principle have a similar multiscale role in animals.

Figure 6. — **DOI:** http://dx.doi.org/10.7554/eLife.01967.025

Materials and methods

Plant material and growth conditions

Arabidopsis thaliana lines expressing microtubule (MT) reporters YFP:MBD (Landsberg erecta) was previously used by Wightman and Turner (2007) and MBD:GFP (Col-0) was used by Hamant et al. (2008). botero 1-7 (WS) was isolated previously by Bichet et al. (2001), YFP:MBD in a botero 1-7 background and YFP:MBD (Wassilewskija) (Wightman et al., 2013) was a kind gift from Simon Turner (University of Manchester). All seeds were surface sterilized, stratified for 2 days, and grown vertically on plates containing half strength Murashige and Skoog (MS) media in light (16-hr photoperiod) at 21°C for 5 days for confocal microscopy.

Specimen preparation and confocal imaging

5 days after germination plants were transferred to sterile plastic boxes containing MS media. The plants were fixed by adding lukewarm 1% agarose to the hypocotyls and roots submerging them, thereby exposing the cotyledons. Plants were imaged using a Zeiss LSM-780 or Zeiss LSM-700 as described in Heisler et al. (2010).

Mechanical perturbations

Laser-induced ablation was performed using an Andor Micropoint ablation laser fitted to a Zeiss LSM-780 scanning confocal microscope as described (Hamant et al., 2008) using a 63X or 40X water dipping objective. Compression was achieved by placing cotyledons tightly mounted between a cover glass and slide with silicon grease. Imaging of the compressed tissue was performed using an oil immersion lens. To image MT recovery after compression, seedlings were transferred to MS media containing Petri dishes after carefully removing the coverslip and treated as described above before imaging with a water-dipping lens. Laceration of the cotyledon was performed using a sharp forceps or a scalpel. Isoxaben treatment was preformed as described in Heisler et al. (2010).

Image processing

All images were processed and analyzed using the FIJI or ImageJ software. Background subtraction was performed using the ‘Subtract Background’ tool (rolling ball radius 30–40 pixels), and the ‘StackReg’ plugin was used to correct focal drift of the sample. Depth color-coding was performed using the ‘Temporal-color code’ tool. Cell boundaries in Figure 2B are pseudo projection of the lower most stack in a different color. Walking average function was performed on time series data sets used for analysis of severing events.

Quantification of MT alignments for anisotropy

Quantification of MT alignments for anisotropy was done using the ImageJ macro described in Uyttewaal et al. (2012) and Boudaoud et al. (2014) for Figure 1 and for the laceration experiments in which a score of 0 indicates completely isotropic pattern and 1, a case of completely aligned pattern. For all other experiments, the macro was modified in order to include in the output the visual and numerical measure of anisotropy of the nematic and texture tensors. The modified macro displays directions of both eigenvectors of the tensor of which relative length is an indication of the anisotropy of the signal. The score is calculated as a difference between the principal eigenvalues divided by the sum of diagonal elements of the tensor. The score gives 0 in case of completely isotropic pattern and 2 in case of completely aligned pattern. Analysis was carried out in each cell by drawing an outline of the region of interest, using the ‘Polygon selection’ tool in ImageJ. The outlines covered the entire area of the cell, without the anticlinal wall signal. These regions were then recorded using the ‘ROI manager’ tool in ImageJ and saved for automatic selection of the same cells in other time points.

Severing quantification

Severing quantification was preformed manually using ImageJ, where severing events are scored using the point picker tool in ImageJ based on the criteria described in Wightman et al. (2013). Quantification was carried out in cell files extending up to four layers from the site of ablation. A total of 15 events were observed in the mock treated samples in a total of 27.2 min and 66 events 3 hr after ablation in a total of 20.9 min.

Statistical analysis

Statistics is preformed in Excel or OriginPro. For data sets that do not have a normal distribution, we have preformed Mann–Whitney U test, a non-parametric test of the null hypothesis; for normally distributed data sets, we have used the t test to estimate statistical significance.

Atomic force microscopy

AFM indentation experiments were carried out with a Catalyst Bioscope (Bruker Nano Surface, Santa Barbara, CA), that was mounted on a optical macroscope (MacroFluo, Leica) using an objective (5x plano objective, Leica). To record surface topology and to create an elastic modulus map, PeakForce QNM AFM mode is used. A Nanoscope V controller and Nanoscope software versions 8.15 were utilized. All quantitative measurements were performed using standard pyramidal tips (ScanAsyst Air, Bruker, Inc.). The tip radius is given by the manufacturer to be between 2 nm and 10 nm. The spring constant of cantilevers was measured using the thermal tuning method (Hutter and Bechhoefer, 1993; Levy and Maaloum, 2002) and was ranged from 0.3–0.5 N/m. The deflection sensitivity of cantilevers was calibrated against a clean silicon wafer. All measurements were made under water at room temperature and the standard cantilever holder for operation in liquid was used. Cotyledons were detached from the stem with a fine blade and the abaxial (lower) side of the cotyledon was used for the measurement. The upper side of the sample was adhered to a Petri dish using a tissue section adhesive (Biobond, Ted Pella, Inc.). Then the Petri dish was positioned on an XY motorized stage and held by a magnetic clamp. Then, the AFM head was mounted on the stage and an approximated positioning with respect to the cantilever was done using the optical macroscope.

The foundation of material property mapping with PeakForce QNM is the ability of the system to acquire and analyze the individual force curves from each tap that occurs during the imaging process. In this mode, the probe is oscillated at a low frequency (0.5 kHz), capturing a force curve each time the AFM tip taps on the sample’s surface. The maximum force during imaging was 1 μN. For each sample, the topology and elastic modulus images were collected from different places of the sample over sizes of 70 × 70 to 150 × 150 µm² and at a digital resolution of 128 pixels × 128 pixels. The 0.3 Hz scanning rate was used. In this QNM mode technique, the elastic modulus is derived from the force–indentation curves by using 2 different models: (i) the Hertz–Sneddon model (Sneddon, 1965) or (ii) the Derjaguin-Muller-Toporov (DMT) model (Derjaguin et al., 1975). Both assumed a rigid cone indenting a flat surface. Unlike the Hertz–Sneddon model (Equation 1) that is applied on the approach curve, the DMT model is applied on the retract curve and accounts for adhesion (Equation 2).

F = \frac{2}{π} \frac{E}{(1 - ν^{2})} \tan (α) δ^{2}

(1)

F is the force from force curve, E is the Young’s modulus, ν is the Poisson’s ratio, α is the half-angle of the indenter and δ is the indentation.

F - F_{a d h} = \frac{4}{3} E * \sqrt{R {(d - d_{0})}^{3}}

(2)

F − F_adh is the force on the cantilever relative to the adhesion force, R is the tip end radius, and d − d₀ is the deformation of the sample. For this last model, the result of the fit is the reduced modulus E*. Moreover, if the Poisson’s ratio is known, the software can use that information to calculate the Young’s Modulus of the sample by the equation (Equation 3):

E * = \frac{E}{(1 - ν^{2})}

(3)

Here, we assumed our sample is perfectly incompressible so that the Poisson’s ratio used is 0.5. However, since neither the Poisson’s ratio nor the tip shape is accurately known, we report in this work only an ‘apparent modulus’ (Ea).

Computational models

For simulations of tissue mechanics, we have used a nonlinear Finite Element Method which provides an approximate solution of continuum elasticity problems on domains with complex geometry (Zienkiewicz et al., 2005). Simulations involving pavement cell geometries were performed with in-house written software, which is specialized and optimized for cellular geometries. The software is based on a procedure of minimization of nonlinear strain energy for a given constitutive model of the material (Bonet and Wood, 1997). We have used a hyperelastic transversely isotropic model of the material, which is particularly suited for description of fibrillar tissues (Weiss et al., 1996). For the matrix part of the material, we employed the Saint Venant–Kirchhoff model. The epidermal cell wall surface was modeled with shell elements, designed to handle thin curved surfaces. Additional beam elements accounting for the presence of the anticlinal cell walls were placed along the projections of the individual cell boundaries on the epidermal surface. These beam elements were assumed to have Young’s modulus of the matrix part of the material and thickness of 1/5 of the epidermal wall. For the model on feedback between wall anisotropy and mechanical stresses we have set the material anisotropy axis at each step of the Newton–Raphson iteration aligned with maximal principal stress measured in the previous step. The model parameter values were chosen from different experimental estimates of plant cell wall elasticity based on measurements of in vivo samples (Suslov et al., 2009; Hayot et al., 2012; Nezhad et al., 2013) and synthetic bio-composites (Chanliaud et al., 2002). We set Young’s modulus equal to 40 MPa for the matrix part of the material. The Young’s modulus of the CMF was assumed to be five times larger than the matrix. Turgor pressure was set to 0.2 MPa and thickness of the epidermal wall was assumed to be 1 μm. We have also tested different values of these parameters varying them in the range 0.5–2 times the presented values and found the results of the simulations to be qualitatively consistent within these limits. To account for tension in the epidermal layer the outer boundary of the templates was expanded by 1% in the x-y plane. The inner boundaries of individual cells were free in the x-y plane and restricted in the z direction. Pressure was applied on the surface of each cell. The choice of low turgor pressure was mainly dictated by convergence requirements of our model. Large turgor pressures caused instability of the model with respect to x-y movement of the cell boundaries, as a result of our approximate treatment of anticlinal walls. We have found, however, that the stress pattern does not show major qualitative changes for larger pressures. Thus, we have used the turgor within low range of experimentally reported values assuring good convergence with reasonable computational cost.

Most of the simulations involving the cell shapes extracted from experimental data were started from a flat geometry. The boundaries of the cells were obtained from the experimental data using MorphographX software (Kierzkowski et al., 2012) and the meshes constrained to those boundaries were constructed with the use of the CGAL algorithms (CGAL, 2014). For the stomata simulations (Figure 2), we have extracted information about the three-dimensional geometry of the cell surfaces using the three-dimensional confocal microscopy data and MorphographX software. In this case, the initial mesh was projected on the estimated real cell surface.

Simulations involving simpler geometries were performed with Abaqus (Simulia, Providence, RI) finite element modeling software (Figure 2—figure supplement 2, Figure 3—figure supplement 1), using the same material model as in other simulations and shell finite elements. These compression simulations were performed with a constant volume assumption and node to surface frictionless contact. Similar results were obtainable with a constant pressure assumption, but in that case the outcome of the simulation was dependent on material properties and the degree of deformation from pressing. To investigate the importance of the anticlinal walls on the stiffness of the epidermal wall model, we performed simulations with a simplified pavement cell shape including anticlinal walls in Abaqus (Dassault Systemes; Figure 2—figure supplement 2). The results were quantitatively consistent with our approximate model of the anticlinal walls. A detailed description of models is provided in supplemental information (Supplementary file 1).

Acknowledgements

We would like to thank An Yan, Division of Biology, California Institute of Technology for his comments on the manuscript and Nathan Hervieux, ENS Lyon, for help with quantification of nematic tensor values in large scale laceration experiments. This work is supported by the Gatsby Charitable Foundation to HJ and EMM, the Department of Energy Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences and Biosciences, of the US Department of Energy [DE-FG02-88ER13873] to EMM, the Howard Hughes Medical Institute and the Gordon and Betty Moore Foundation (through Grant GBMF3406) to EMM, Agence Nationale de la Recherche ANR-10-BLAN-1516 ‘Mechastem’ to OH, the European Research Council starting grant (PhyMorph, #307387) to AB and by the Swedish Research Council and the Crafoord Foundation to HJ.

Funding Statement

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

Funding Information

This paper was supported by the following grants:

Howard Hughes Medical Institute and the Gordon and Betty Moore Foundation GBMF3406 to Elliot M Meyerowitz.
Gatsby Charitable Foundation FundRef identification ID: http://dx.doi.org/10.13039/501100000324 to Henrik Jönsson, Elliot M Meyerowitz.
US Department of Energy DE-FG02-88ER13873 to Elliot M Meyerowitz.
Agence Nationale de la Recherche ANR-10-BLAN-1516 to Olivier Hamant.
European Research Council FundRef identification ID: http://dx.doi.org/10.13039/501100000781 307387 to Arezki Boudaoud.
Swedish Research Council to Henrik Jönsson.
Crafoord Foundation to Henrik Jönsson.

Additional information

Competing interests

The authors declare that no competing interests exist.

Author contributions

AS, Conception and design, Acquisition of data, Analysis and interpretation of data, Drafting or revising the article.

PK, Conception and design, Acquisition of data, Analysis and interpretation of data, Drafting or revising the article.

OH, Conception and design, Acquisition of data, Analysis and interpretation of data, Drafting or revising the article.

RW, Acquisition of data, Analysis and interpretation of data.

PM, Acquisition of data, Analysis and interpretation of data.

AB, Acquisition of data.

AB, Conception and design, Drafting or revising the article.

HJ, Conception and design, Analysis and interpretation of data, Drafting or revising the article.

EMM, Conception and design, Analysis and interpretation of data, Drafting or revising the article.

Additional files

Supplementary file 1.

Additional information about computational models.

DOI: http://dx.doi.org/10.7554/eLife.01967.026

elife01967s001.pdf^{(99.9KB, pdf)}

DOI: 10.7554/eLife.01967.026

References

Asnacios A, Hamant O. 2012. The mechanics behind cell polarity. Trends in Cell Biology 22:584–591. doi: 10.1016/j.tcb.2012.08.005 [DOI] [PubMed] [Google Scholar]
Baluska F, Volkmann D, Barlow PW. 2004. Eukaryotic cells and their cell bodies: cell theory revised. Annals of Botany 94:9–32. doi: 10.1093/aob/mch109 [DOI] [PMC free article] [PubMed] [Google Scholar]
Baskin TI, Meekes HTHM, Liang BM, Sharp RE. 1999. Regulation of growth anisotropy in well-watered and water-stressed maize roots. II. Role of cortical microtubules and cellulose microfibrils. Plant Physiology 119:681–692. doi: 10.1104/pp.119.2.681 [DOI] [PMC free article] [PubMed] [Google Scholar]
Bichet A, Desnos T, Turner S, Grandjean O, Hofte H. 2001. BOTERO1 is required for normal orientation of cortical microtubules and anisotropic cell expansion in Arabidopsis. The Plant Journal: for Cell and Molecular Biology 25:137–148. doi: 10.1046/j.1365-313x.2001.00946.x [DOI] [PubMed] [Google Scholar]
Bonet J, Wood RD. 1997. Nonlinear continuum mechanics for finite element analysis. Cambridge, NY: Cambridge University Press [Google Scholar]
Boudaoud A, Burian A, Borowska-Wykret D, Uyttewaal M, Wrzalik R, Kwiatkowska D, Hamant O. 2014. FibrilTool, an ImageJ plug-in to quantify fibrillar structures in raw microscopy images. Nature Protocols 9:457–463. doi: 10.1038/nprot.2014.024 [DOI] [PubMed] [Google Scholar]
Bringmann M, Li E, Sampathkumar A, Kocabek T, Hauser M-T, Persson S. 2012. POM-POM2/cellulose synthase interacting1 is essential for the functional association of cellulose synthase and microtubules in Arabidopsis. The Plant Cell 24:163–177. doi: 10.1105/tpc.111.093575 [DOI] [PMC free article] [PubMed] [Google Scholar]
CGAL Computational geometry algorithms library. 2014. [Online] Available: http://www.cgal.org [Google Scholar]
Chan J, Crowell E, Eder M, Calder G, Bunnewell S, Findlay K, Vernhettes S, Hofte H, Lloyd C. 2010. The rotation of cellulose synthase trajectories is microtubule dependent and influences the texture of epidermal cell walls in Arabidopsis hypocotyls. Journal of Cell Science 123:3490–3495. doi: 10.1242/jcs.074641 [DOI] [PubMed] [Google Scholar]
Chanliaud E, Burrows KM, Jeronimidis G, Gidley MJ. 2002. Mechanical properties of primary plant cell wall analogues. Planta 215:989–996. doi: 10.1007/s00425-002-0783-8 [DOI] [PubMed] [Google Scholar]
Crowell EF, Timpano H, Desprez T, Franssen-Verheijen T, Emons AM, Hofte H, Vernhettes S. 2011. Differential regulation of cellulose orientation at the inner and outer face of epidermal cells in the Arabidopsis hypocotyl. The Plant Cell 23:2592–2605. doi: 10.1105/tpc.111.087338 [DOI] [PMC free article] [PubMed] [Google Scholar]
Davis LJ, Odde DJ, Block SM, Gross SP. 2002. The importance of lattice defects in katanin-mediated microtubule severing in vitro. Biophysical Journal 82:2916–2927. doi: 10.1016/S0006-3495(02)75632-4 [DOI] [PMC free article] [PubMed] [Google Scholar]
Derjaguin BV, Muller VM, Toporov YP. 1975. Effect of contact deformations on the adhesion of particles. Journal of Colloid and Interface Science 53:314–326. doi: 10.1016/0021-9797(75)90018-1 [DOI] [Google Scholar]
Díaz-Valencia JD, Morelli MM, Bailey M, Zhang D, Sharp DJ, Ross JL. 2011. Drosophila Katanin-60 Depolymerizes and Severs at microtubule defects. Biophysical Journal 100:2440–2449. doi: 10.1016/j.bpj.2011.03.062 [DOI] [PMC free article] [PubMed] [Google Scholar]
Dumais J, Steele CR. 2000. New evidence for the role of mechanical forces in the shoot apical meristem. Journal of Plant Growth Regulation 19:7–18. doi: 10.1007/s003440000003 [DOI] [PubMed] [Google Scholar]
Engler AJ, Sen S, Sweeney HL, Discher DE. 2006. Matrix elasticity directs stem cell lineage specification. Cell 126:677–689. doi: 10.1016/j.cell.2006.06.044 [DOI] [PubMed] [Google Scholar]
Franck AD, Powers AF, Gestaut DR, Gonen T, Davis TN, Asbury CL. 2007. Tension applied through the Dam1 complex promotes microtubule elongation providing a direct mechanism for length control in mitosis. Nature Cell Biology 9:832–837. doi: 10.1038/ncb1609 [DOI] [PMC free article] [PubMed] [Google Scholar]
Fu Y, Gu Y, Zheng Z, Wasteneys G, Yang Z. 2005. Arabidopsis interdigitating cell growth requires two antagonistic pathways with opposing action on cell morphogenesis. Cell 120:687–700. doi: 10.1016/j.cell.2004.12.026 [DOI] [PubMed] [Google Scholar]
Fujita M, Himmelspach R, Hocart CH, Williamson RE, Mansfield SD, Wasteneys GO. 2011. Cortical microtubules optimize cell-wall crystallinity to drive unidirectional growth in Arabidopsis. The Plant Journal: for Cell and Molecular Biology 66:915–928. doi: 10.1111/j.1365-313X.2011.04552.x [DOI] [PubMed] [Google Scholar]
Gardner MK, Pearson CG, Sprague BL, Zarzar TR, Bloom K, Salmon ED, Odde DJ. 2005. Tension-dependent regulation of microtubule dynamics at kinetochores can explain metaphase congression in yeast. Molecular Biology of the Cell 16:3764–3775. doi: 10.1091/mbc.E05-04-0275 [DOI] [PMC free article] [PubMed] [Google Scholar]
Green PB. 1980. Organogenesis-a biophysical view. Annual Review of Plant Physiology 31:51–82. doi: 10.1146/annurev.pp.31.060180.000411 [DOI] [Google Scholar]
Hamant O, Heisler MG, Jonsson H, Krupinski P, Uyttewaal M, Bokov P, Corson F, Sahlin P, Boudaoud A, Meyerowitz EM, Couder Y, Traas J. 2008. Developmental patterning by mechanical signals in Arabidopsis. Science 322:1650–1655. doi: 10.1126/science.1165594 [DOI] [PubMed] [Google Scholar]
Hayot CM, Forouzesh E, Goel A, Avramova Z, Turner JA. 2012. Viscoelastic properties of cell walls of single living plant cells determined by dynamic nanoindentation. Journal of Experimental Botany 63:2525–2540. doi: 10.1093/jxb/err428 [DOI] [PMC free article] [PubMed] [Google Scholar]
Heisler MG, Hamant O, Krupinski P, Uyttewaal M, Ohno C, Jonsson H, Traas J, Meyerowitz EM. 2010. Alignment between PIN1 polarity and microtubule orientation in the shoot apical meristem reveals a tight coupling between morphogenesis and auxin transport. PLOS Biology 8:e1000516. doi: 10.1371/journal.pbio.1000516 [DOI] [PMC free article] [PubMed] [Google Scholar]
Hutter JL, Bechhoefer J. 1993. Calibration of atomic-force microscope tips. Review of Scientific Instruments 64:1868–1873. doi: 10.1063/1.1143970 [DOI] [Google Scholar]
Jacques E, Verbelen JP, Vissenberg K. 2013. Mechanical stress in Arabidopsis leaves orients microtubules in a ‘continuous’ supracellular pattern. BMC Plant Biology 13:163. doi: 10.1186/1471-2229-13-163 [DOI] [PMC free article] [PubMed] [Google Scholar]
Jaeger J, Irons D, Monk N. 2008. Regulative feedback in pattern formation: towards a general relativistic theory of positional information. Development 135:3175–3183. doi: 10.1242/dev.018697 [DOI] [PubMed] [Google Scholar]
Jonsson H, Heisler MG, Shapiro BE, Meyerowitz EM, Mjolsness E. 2006. An auxin-driven polarized transport model for phyllotaxis. Proceedings of the National Academy of Sciences of the United States of America 103:1633–1638. doi: 10.1073/pnas.0509839103 [DOI] [PMC free article] [PubMed] [Google Scholar]
Jung G, Wernicke W. 1990. Cell shaping and microtubules in developing mesophyll of wheat (Triticum aestivum L.). Protoplasma 153:141–148. doi: 10.1007/BF01353998 [DOI] [Google Scholar]
Kaplan DR. 1992. The relationship of cells to organisms in plants: problem and Implications of an organismal perspective. International Journal of Plant Sciences 153:S28–S37. doi: 10.1086/297061 [DOI] [Google Scholar]
Kierzkowski D, Nakayama N, Routier-Kierzkowska AL, Weber A, Bayer E, Schorderet M, Reinhardt D, Kuhlemeier C, Smith RS. 2012. Elastic domains regulate growth and organogenesis in the plant shoot apical meristem. Science 335:1096–1099. doi: 10.1126/science.1213100 [DOI] [PubMed] [Google Scholar]
Kutschera U, Niklas KJ. 2007. The epidermal-growth-control theory of stem elongation: an old and a new perspective. Journal of Plant Physiology 164:1395–1409. doi: 10.1016/j.jplph.2007.08.002 [DOI] [PubMed] [Google Scholar]
Lecuit T, Lenne PF. 2007. Cell surface mechanics and the control of cell shape, tissue patterns and morphogenesis. Nature Reviews Molecular Cell Biology 8:633–644. doi: 10.1038/nrm2222 [DOI] [PubMed] [Google Scholar]
Levy R, Maaloum M. 2002. Measuring the spring constant of atomic force microscope cantilevers: thermal fluctuations and other methods. Nanotechnology 13:33–37 [Google Scholar]
Lin D, Cao L, Zhou Z, Zhu L, Ehrhardt D, Yang Z, Fu Y. 2013. Rho GTPase signaling activates microtubule severing to promote microtubule ordering in arabidopsis. Current Biology: CB 23:290–297. doi: 10.1016/j.cub.2013.01.022 [DOI] [PubMed] [Google Scholar]
Lindeboom JJ, Nakamura M, Hibbel A, Shundyak K, Gutierrez R, Ketelaar T, Emons AMC, Mulder BM, Kirik V, Ehrhardt DW. 2013. A mechanism for reorientation of cortical microtubule arrays driven by microtubule severing. Science 342:1245533. doi: 10.1126/science.1245533 [DOI] [PubMed] [Google Scholar]
Marcus AI, Moore RC, Cyr RJ. 2001. The role of microtubules in guard cell function. Plant Physiology 125:387–395. doi: 10.1104/pp.125.1.387 [DOI] [PMC free article] [PubMed] [Google Scholar]
Martin AC, Kaschube M, Wieschaus EF. 2009. Pulsed contractions of an actin-myosin network drive apical constriction. Nature 457:495–499. doi: 10.1038/nature07522 [DOI] [PMC free article] [PubMed] [Google Scholar]
Milani P, Gholamirad M, Traas J, Arneodo A, Boudaoud A, Argoul F, Hamant O. 2011. In vivo analysis of local wall stiffness at the shoot apical meristem in Arabidopsis using atomic force microscopy. The Plant Journal: for Cell and Molecular Biology 67:1116–1123. doi: 10.1111/j.1365-313X.2011.04649.x [DOI] [PubMed] [Google Scholar]
Nezhad AS, Naghavi M, Packirisamy M, Bhat R, Geitmann A. 2013. Quantification of the Young’s modulus of the primary plant cell wall using Bending-Lab-On-Chip (BLOC). Lab on a Chip 13:2599–2608. doi: 10.1039/c3lc00012e [DOI] [PubMed] [Google Scholar]
Nicklas RB. 1988. The forces that move chromosomes in mitosis. Annual Review of Biophysics and Biophysical Chemistry 17:431–449. doi: 10.1146/annurev.bb.17.060188.002243 [DOI] [PubMed] [Google Scholar]
Paredez AR, Somerville CR, Ehrhardt DW. 2006. Visualization of cellulose synthase demonstrates functional association with microtubules. Science 312:1491–1495. doi: 10.1126/science.1126551 [DOI] [PubMed] [Google Scholar]
Pouille PA, Ahmadi P, Brunet AC, Farge E. 2009. Mechanical signals trigger Myosin II redistribution and mesoderm invagination in Drosophila embryos. Science Signaling 2:ra16. doi: 10.1126/scisignal.2000098 [DOI] [PubMed] [Google Scholar]
Roeder AH, Chickarmane V, Cunha A, Obara B, Manjunath BS, Meyerowitz EM. 2010. Variability in the control of cell division underlies sepal epidermal patterning in Arabidopsis thaliana. PLOS Biology 8:e1000367. doi: 10.1371/journal.pbio.1000367 [DOI] [PMC free article] [PubMed] [Google Scholar]
Roeder AH, Cunha A, Ohno CK, Meyerowitz EM. 2012. Cell cycle regulates cell type in the Arabidopsis sepal. Development 139:4416–4427. doi: 10.1242/dev.082925 [DOI] [PubMed] [Google Scholar]
Schopfer P. 2006. Biomechanics of plant growth. American Journal of Botany 93:1415–1425. doi: 10.3732/ajb.93.10.1415 [DOI] [PubMed] [Google Scholar]
Sherrard K, Robin F, Lemaire P, Munro E. 2010. Sequential activation of apical and basolateral contractility drives ascidian endoderm invagination. Current Biology: CB 20:1499–1510. doi: 10.1016/j.cub.2010.06.075 [DOI] [PMC free article] [PubMed] [Google Scholar]
Shraiman BI. 2005. Mechanical feedback as a possible regulator of tissue growth. Proceedings of the National Academy of Sciences of the United States of America 102:3318–3323. doi: 10.1073/pnas.0404782102 [DOI] [PMC free article] [PubMed] [Google Scholar]
Skibbens R, Skeen V, Salmon E. 1993. Directional instability of kinetochore motility during chromosome congression and segregation in mitotic newt lung cells: a push-pull mechanism. The Journal of Cell Biology 122:859–875. doi: 10.1083/jcb.122.4.859 [DOI] [PMC free article] [PubMed] [Google Scholar]
Sneddon IN. 1965. The relation between load and penetration in the axisymmetric boussinesq problem for a punch of arbitrary profile. International Journal of Engineering Science 3:47–57. doi: 10.1016/0020-7225(65)90019-4 [DOI] [Google Scholar]
Solon J, Kaya-Copur A, Colombelli J, Brunner D. 2009. Pulsed forces timed by a ratchet-like mechanism drive directed tissue movement during dorsal closure. Cell 137:1331–1342. doi: 10.1016/j.cell.2009.03.050 [DOI] [PubMed] [Google Scholar]
Stylianopoulos T, Martin JD, Chauhan VP, Jain SR, Diop-Frimpong B, Bardeesy N, Smith BL, Ferrone CR, Hornicek FJ, Boucher Y, Munn LL, Jain RK. 2012. Causes, consequences, and remedies for growth-induced solid stress in murine and human tumors. Proceedings of the National Academy of Sciences of the United States of America 109:15101–15108. doi: 10.1073/pnas.1213353109 [DOI] [PMC free article] [PubMed] [Google Scholar]
Suslov D, Verbelen JP, Vissenberg K. 2009. Onion epidermis as a new model to study the control of growth anisotropy in higher plants. Journal of Experimental Botany 60:4175–4187. doi: 10.1093/jxb/erp251 [DOI] [PubMed] [Google Scholar]
Thery M, Jimenez-Dalmaroni A, Racine V, Bornens M, Julicher F. 2007. Experimental and theoretical study of mitotic spindle orientation. Nature 447:493–496 [DOI] [PubMed] [Google Scholar]
Trushko A, Schaffer E, Howard J. 2013. The growth speed of microtubules with XMAP215-coated beads coupled to their ends is increased by tensile force. Proceedings of the National Academy of Sciences of the United States of America 110:14670–14675. doi: 10.1073/pnas.1218053110 [DOI] [PMC free article] [PubMed] [Google Scholar]
Uyttewaal M, Burian A, Alim K, Landrein B, Borowska-Wykret D, Dedieu A, Peaucelle A, Ludynia M, Traas J, Boudaoud A, Kwiatkowska D, Hamant O. 2012. Mechanical stress acts via katanin to amplify differences in growth rate between adjacent cells in Arabidopsis. Cell 149:439–451. doi: 10.1016/j.cell.2012.02.048 [DOI] [PubMed] [Google Scholar]
Wartlick O, Kicheva A, Gonzalez-Gaitan M. 2009. Morphogen gradient formation. Cold Spring Harbor Perspectives in Biology 1:a001255. doi: 10.1101/cshperspect.a001255 [DOI] [PMC free article] [PubMed] [Google Scholar]
Weiss JA, Maker BN, Govindjee S. 1996. Finite element implementation of incompressible, transversely isotropic hyperelasticity. Computer Methods in Applied Mechanics and Engineering 135:107–128. doi: 10.1016/0045-7825(96)01035-3 [DOI] [Google Scholar]
Wightman R, Chomicki G, Kumar M, Carr P, Turner SR. 2013. SPIRAL2 determines plant microtubule organization by modulating microtubule severing. Current Biology: CB 23:1902–1907. doi: 10.1016/j.cub.2013.07.061 [DOI] [PMC free article] [PubMed] [Google Scholar]
Wightman R, Turner SR. 2007. Severing at sites of microtubule crossover contributes to microtubule alignment in cortical arrays. The Plant Journal: for Cell and Molecular Biology 52:742–751. doi: 10.1111/j.1365-313X.2007.03271.x [DOI] [PubMed] [Google Scholar]
Williamson RE. 1990. Alignment of cortical microtubules by anisotropic wall stresses. Functional Plant Biology 17:601–613 [Google Scholar]
Wolpert L. 1969. Positional information and the spatial pattern of cellular differentiation. Journal of Theoretical Biology 25:1–47. doi: 10.1016/S0022-5193(69)80016-0 [DOI] [PubMed] [Google Scholar]
Xu T, Wen M, Nagawa S, Fu Y, Chen JG, Wu MJ, Perrot-Rechenmann C, Friml J, Jones AM, Yang Z. 2010. Cell surface- and rho GTPase-based auxin signaling controls cellular interdigitation in Arabidopsis. Cell 143:99–110. doi: 10.1016/j.cell.2010.09.003 [DOI] [PMC free article] [PubMed] [Google Scholar]
Yang Z. 2008. Cell polarity signaling in Arabidopsis. Annual Review of Cell and Developmental Biology 24:551–575. doi: 10.1146/annurev.cellbio.23.090506.123233 [DOI] [PMC free article] [PubMed] [Google Scholar]
Zhang C, Halsey LE, Szymanski DB. 2011. The development and geometry of shape change in Arabidopsis thaliana cotyledon pavement cells. BMC Plant Biology 11:27. doi: 10.1186/1471-2229-11-27 [DOI] [PMC free article] [PubMed] [Google Scholar]
Zhang Q, Fishel E, Bertroche T, Dixit R. 2013. Microtubule severing at crossover sites by katanin generates ordered cortical microtubule arrays in arabidopsis. Current Biology 23:2191–2195. doi: 10.1016/j.cub.2013.09.018 [DOI] [PubMed] [Google Scholar]
Zienkiewicz OC, Taylor RL, Zhu JZ. 2005. The finite element method: its basis and fundamentals. Oxford, UK: Elsevier Butterworth Heinemann [Google Scholar]

eLife. 2014 Apr 16;3:e01967. doi: 10.7554/eLife.01967.027

Decision letter

Editor: Dominique Bergmann¹

eLife posts the editorial decision letter and author response on a selection of the published articles (subject to the approval of the authors). An edited version of the letter sent to the authors after peer review is shown, indicating the substantive concerns or comments; minor concerns are not usually shown. Reviewers have the opportunity to discuss the decision before the letter is sent (see review process). Similarly, the author response typically shows only responses to the major concerns raised by the reviewers.

Thank you for sending your work entitled “Subcellular and supracellular mechanical stress prescribes cytoskeleton behavior in Arabidopsis cotyledon pavement cells” for consideration at eLife. Your article has been favorably evaluated by a Senior editor, Detlef Weigel, and 2 reviewers, one of whom is a member of our Board of Reviewing Editors.

The Reviewing editor and the other reviewer discussed their comments before we reached this decision, and the Reviewing editor has assembled the following comments to help you prepare a revised submission.

Mechanical influences on developmental and cellular properties are an important topic of broad impact in plants and animals. After having been out of fashion for a few decades, this topic (aided by new tools) is experiencing a renaissance. This manuscript complements recent work on tissue-level dynamics in the plant shoot meristem by examining the relationships between growth, stress patterns and microtubules (MTs) in crenulated pavement cells of the leaf epidermis. New data here provide more convincing experimental support that MTs respond to stress, and novel work with an AFM system shows that MT patterns and cellulose MF patterns match. Exploiting the large size of pavement cells and using mechanical manipulations (ablations), the authors show a correlation between the frequency of katanin-mediated MT severing events and reactions to mechanical stress. Their observation that tissue level stress can override cell level stress was also documented in a recent paper from Jacques et al. (2013). Altogether these experiments and models have the potential to have a broad impact on our thinking about mechanical influences on development.

There are a number of improvements that should be made to the models, and the manuscript could benefit from some clearer writing and some further analysis of data already collected. Specific major issues to be addressed in a revised manuscript are enumerated below.

1) Re-evaluation of models used to represent cells.

Reviewers were concerned about the models used to represent cells in this manuscript, specifically what appears to be a balloon-type model representing only the surface cell wall, whose stresses reported may not be representative of real pavement cells. When looking at the finer details of stress patterns of individual cells, the patterns do not look like what would be expected from a proper 3D model of a cell – the necks should be under compression and the lobes under tension (see for example Dumais and Steele 2000 paper, which the authors cite). In the presented model all stresses are tensional, even after ablation, which may not be realistic. Moreover, the text is misleading in making this appear to be a 3D model when it may be a 2D surface of cells, tethered to a substrate by springs at the anticlinal walls. If it is too difficult or inappropriate to apply the 3D model based on their previous shoot apex work (where cells have a very different shape), please explain. Similarly, the model used (and assumptions) should be much more clearly explained in the main text, as the difference between a 2D model with springs and a full 3D model is potentially very important. It is a bit hard to justify making a fine-grained analysis of stresses in a situation where the geometry of the model itself has not been shown to be representative of the system. For example, in 3D one would expect the neck of a pressurized, isolated pavement cell to be under compression.

Minimal additions to the models include:

Begin by representing the compressional stresses in the model in a different color. If the neck regions are indeed under compression (at least after ablation of neighbor), this would be a satisfactory test of the utility of the model. A hand-drawn model with a few pavement cells in Abaqus would be OK. The cells do not have to be perfect, just qualitatively similar in shape (with lobes and necks). Then apply similar loading conditions as in previous simulations and compare it with the simulation where one cell is removed. Please show both tangential stresses, with a color scheme that also indicates compression.

Correct (or explain) why in Figure panels 4A and B (the model ablation) the cell outlines exactly overlap. Shouldn't the borders move a bit in B next to the cells that are ablated? What exactly does ablation change in the model, if not the boundary next to the ablated cells?

2) Dissect the cell vs. tissue response to stress

A major conceptual advance would come from a deeper analysis of the continuum of cell and tissue responsiveness to stress. The authors propose that “MT behavior depends on stress intensity, which is cell autonomous as long as tissue stresses do not override it”. It would be extremely valuable to calculate or model under what conditions a tissue-level stress would override a cellular stress.

Along these lines, the authors might test whether pavement cell lobes that differ in their orientation relative to the overall growth direction of the leaf and/or relative to the cut sites, have different sensitivities or degrees of MT anisotropies. The answer to this will give a parameter to address the cell autonomy vs. tissue response. Another simple test would be to look at whether guard cell MTs respond to cuts. Given the evidence that GCs created their own local zones of stress and oriented MTs, my guess would be no, but there might be an interesting correlation with “elevated” vs. planar and open vs. closed stomata with respect to responsiveness. This could provide another example of differential “set points” in the cell vs. tissue continuum.

Also, if cutting experiments release tension globally, then wouldn't the MTs be expected to become less oriented?

3) Formulate a compelling argument for how plant cells sense stress and how this generates shape.

The Abstract states “Force patterns in plant tissues control cell shapes...”. In support, the authors point to their (very nice) previous work that suggests that MT orientation is controlled by stresses in the tissue, which can be deduced from organ shape (Introduction, paragraph 2). However, this is difficult to reconcile even in the shoot apex. If cells start out with a random orientation creating isotropic growth, why doesn't the plant just create a globular structure? How can MTs be responsible for both tissue shape and cell shape if their orientation is primarily controlled by stress? Another interpretation would be that MT orientation is specified by a mechanism other than stress. Genetically defined organizing centers could control tissue and cell polarity, controlling the orientation of MTs. The shape change induced by the MT orientation would then direct the cellulose orientation, and thus cell wall anisotropy, and create non-trivial shapes. The resulting shape would then have a stress pattern that correlates with the MT orientation, which the authors observe. What is the mechanism for sensing stress? It is relatively easy to sense strains, but how can you sense stress, without invoking strain at some point?

4) Reword section on cell-wall anisotropy to reflect indirect measure of this property.

The claim that pavement cell shape relies on oriented MTs affecting cell wall anisotropy has not actually been clearly demonstrated. The AFM results that show the technique can see the CMF bundles in walls. The results are very nice and convincing, and it is believable that you are indeed making a map of the CMF network with the AFM. However this are not measuring cell wall anisotropy in-plane with these experiments as the text seems to claim. However I see nothing wrong with using this data as a proxy for cell wall anisotropy. One should also note that this still does not show a causal relationship between MT and CMF orientation in this system, but it is convincing correlative data given what is already know about the interaction there.

5) Separate the effects of material properties from those that arise from cellular geometry.

The authors propose that lack of movement of the necks after ablation proves that they are stiffer in this region (second paragraph of the Results section entitled “Pavement cell wall shape correlates with microtubule organization…”). However, intuitively, effects of geometry would dominate stiffness here. I would be surprised if the ablation of a neighbor cell in a model with uniform material properties would show an equal displacement in necks and lobes, and this should be tested.

6) Revisit cell-pressing experiments with better images and proper citations of previous literature.

It is difficult to see the differences in the experiments were cells are pressed by slides (Figure 3). In the text the differences are reported to be 0.37 vs 0.57 by their anisotropy measure. They report the same amount of difference (0.2) for necks vs lobes where the orientation is obvious. Why is it so much harder to see here? Also it is claimed that the effect is reversible, and that the value goes to 0.24 a day after the slide is removed. But this is quite a bit less than the starting point of 0.37, unless 0.13 of the difference appears instantly. If this is the case, the “before” condition needs to be quantified and presented for comparison. Jacques et al. (2013) have done similar experiments pressing on leaf epidermal cells; these previous results need to be mentioned and evaluated more extensively in this manuscript.

7) A devil's advocate position would be that the stress sensing mechanism the authors observe is just a secondary role for MTs in case of damage, etc. and that their orientation is primarily determined by other factors (i.e., geometry, genes, gradients, etc.). The authors should point to data to rule out this hypothesis, or an explicit statement that this position cannot be ruled out should be made.

[Editors' note: further clarifications were requested prior to acceptance, as described below.]

Thank you for resubmitting your work entitled “Subcellular and supracellular mechanical stress prescribes cytoskeleton behavior in Arabidopsis cotyledon pavement cells” for further consideration at eLife.

Your revised article has been favorably evaluated by a Senior editor, Detlef Weigel, and two reviewers, one of whom is a member of the Board of Reviewing Editors. We appreciate the careful consideration of review comments and the new models included in the rebuttal letter. Some of the data provided only in the rebuttal letter we felt would be useful to the readers of the manuscript and so we ask you to make a few minor revisions before acceptance, as outlined below:

1) There is one point regarding the modeling that should be addressed more directly in the paper, and not just the rebuttal, and that is the choice of low turgor pressure (2 bar) in the models. This was used to explain why there wasn't more movement in the model after ablation, and why this level was necessitated by their model (if it is higher they get larger deformations and the models do not converge).

A more realistic model seems simply not to be possible with the technology available and our expert reviewer agrees that that a more realistic model would probably behave in a qualitatively similar way, and thus would not change their results. However, it is important for the reader to be aware why the low turgor choice was made, the difficulties in model convergence in such a system, and the issue with anticlinal walls. This information should be in the paper in either the main text or as supplemental material, not just in the rebuttal letter.

2) The experiments in which single cells were ablated (Author response image 6 and in revised text) and in which guard cell MTs were monitored after ablation (Author response image 7) were quite informative and the latter should also be included in the manuscript in either the main text or as supplemental material.

eLife. 2014 Apr 16;3:e01967. doi: 10.7554/eLife.01967.028

Author response

1) Re-evaluation of models used to represent cells.

Reviewers were concerned about the models used to represent cells in this manuscript, specifically what appears to be a balloon-type model representing only the surface cell wall, whose stresses reported may not be representative of real pavement cells. When looking at the finer details of stress patterns of individual cells, the patterns do not look like what would be expected from a proper 3D model of a cell – the necks should be under compression and the lobes under tension (see for example Dumais and Steele 2000 paper, which the authors cite). In the presented model all stresses are tensional, even after ablation, which may not be realistic. Moreover, the text is misleading in making this appear to be a 3D model when it may be a 2D surface of cells, tethered to a substrate by springs at the anticlinal walls. If it is too difficult or inappropriate to apply the 3D model based on their previous shoot apex work (where cells have a very different shape), please explain. Similarly, the model used (and assumptions) should be much more clearly explained in the main text, as the difference between a 2D model with springs and a full 3D model is potentially very important. It is a bit hard to justify making a fine-grained analysis of stresses in a situation where the geometry of the model itself has not been shown to be representative of the system. For example, in 3D one would expect the neck of a pressurized, isolated pavement cell to be under compression.

In general, for structures of complex shapes under complex loading and boundary conditions, it is difficult to predict a pattern of stresses. In simpler cases (like a pressurized, rotationally symmetric Mexican hat shape as in Dumais and Steele, 2000) one can infer stresses from curvature of the surface, and in our simulation of a hat shape we also observe compression in some regions of this structure (similar to Dumais and Steele 2000). While Dumais and Steele report circumferential compression in more simple dome-shaped structures, we tend not to see this in our simulations (Hamant et al. (2008), Bozorg et al. (2014)). We can get a decrease in circumferential stresses. However, we mainly ascribe this to boundary effects, since if we smoothly continue the surface into a cylindrical shape we have tensional circumferential stresses throughout the tissue. In more complex structures, this is dependent on the precise geometry, boundary and loading conditions, especially for doubly curved surfaces (Author response image 1, Bozorg et al (2014)).

Author response image 1. — The color map shows the value of the second principal stress. Blue-low, red-high, black-values below zero. The region in the valley close to the boundary is under compression, which transforms to tension at the top as the curvature changes. This demonstrates the complex stress pattern depending on the geometry, loading and boundary conditions.

Furthermore the shapes described in Dumais and Steele are not comparable to those of pavement cells. Their model of a sunflower capitulum is a continuum surface, whereas in our cellular model of pavement cells we encounter discontinuities at the boundaries of the cells.

We have clarified the description of the model assumptions in the text. The model concerns a curved epidermal wall surface in 3D, which is where we experimentally observe microtubules and from where we obtain the geometry. The sub-epidermal walls are not considered explicitly, but their effect is taken into account by the boundary conditions at the cell borders. The turgor is applied to individual cells.

For simulations we developed FEM software that allowed us to obtain the geometry of cells directly from experimental pictures. We used shell elements, which are specifically designed for thin curved structures. These elements use surface description of geometry, but take into account the thickness as well. Previously (Hamant et al. 2008) we used volumetric (hexahedral) elements in our model of meristem. These elements are of general applicability, but to maintain acceptable dimension ratios large numbers of them must be used for a description of thin wall structures. For pavement cells this restriction led to extensive computational cost and we argue that shell elements are the much better choice here. At present, however, representation of T-junction shells in our software is not accurate and this is another reason why we did not model geometry of anticlinal walls explicitly.

To address the reviewers comment we performed simulations in Abaqus (Dassault Systemes) comparing behavior of models with and without anticlinal walls present. Despite some quantitative differences, the pattern of principal stress, which is the measure in which we are most interested in our model, is qualitatively similar in all cases. The first principal stress is tensional everywhere (Author response image 2 D to F). In particular in the neck regions the dominant stress is directed towards boundary. The second principal (tensional) direction is parallel to the boundary. The second principal stress becomes slightly compressive (∼10 % of tension value) in some regions close to the cell boundary in the lobes (Author response image 2 A to C). We did not find any clear correlation between compressive forces and microtubule orientation. The models are consistent with our postulated relation between the direction of maximal tension and MT orientation.

Author response image 2. — A and D. 3D cell with epidermal, bottom and anticlinal wall. B and E. The cell model with bottom wall removed and replaced with boundary conditions at the bottom of anticlinal walls. C and F surface model of epidermal wall only with anticlinal walls replaced by boundary condition. A to C. The color map shows the value of the second principal stresses. Blue to red mark positive values (tension). The black represents negative values (compression). D to F. The color map shows (blue to red) shows the value of the first principal stresses. No compression is observed.

In summary, we acknowledge the approximate character of our model of pavement cell epidermal walls, but we do not think that the types of potential discrepancies that might be seen with more detailed models affect our conclusions.

Minimal additions to the models include:

Our assumptions of the ablation simulation were tension in the epidermal layer and loss of turgor pressure together with deterioration of the epidermal wall in the ablated cells. We were mostly interested in the stress pattern in outer walls and did not explicitly represent anticlinal walls. Now we have also performed the simulation for a few cells including their anticlinal walls in Abaqus (Author response image 3). In either case we do not observe compressive stresses in the epidermal wall. Small compressions (an order of magnitude smaller than tension) are found in anticlinal walls in a few places close to the ablated region. The first principal stress direction is tensional and circumferential around the ablated region in the model with only the epidermal wall also in the simulation including anticlinal walls (Author response image 3, cf. Figure 3 and Figure 3–figure supplement 4).

Author response image 3. — Simulation of ablation with 3D anticlinal walls included. The color map shows the value of first (A, C) and second (B, D) principal stresses (blue-low, red-high) before (A, B) and after (C, D) ablation. Red and yellow arrows (red: first principal stress, yellow: second principal stress). We observe circumferential rearrangement of main principal (tensile) stress around the ablation in the epidermal wall with some compressive (black in color scale) second principal stress in anticlinal walls.

The cell outlines in our ablation simulations do change. The observed shift in the stress pattern is a result of this change. The movement of the cell outlines is not very large, though, and not visible on the large scale of tissue. It can be observed in the close-up picture (Author response image 4).

Author response image 4. — Scale bar 1 micrometer.

Since we are mostly interested in the stresses in the epidermal wall and our model treats anticlinal walls in a simplified manner we do not account for bulging of anticlinal walls in the ablation simulation.

More importantly, the ablation simulation in our model turned out to be quite unstable for large forces and displacements thus we remained in the small displacement limit, i.e., in a window where results could be analyzed. Regardless of the magnitude of the displacements, the simulations show the general principle by which the tension in the epidermal wall leads to circumferential pattern of stresses around the ablation, even in the presence of complex stress pattern due to the turgor pressure of individual cells.

2) Dissect the cell vs. tissue response to stress

We agree that quantitative study of conditions at which tissue-level stress overrides cellular stress would be very valuable. This would require however the precise experimental measurements of the parameters used as an input to the simulations.

These include material properties, turgor pressure, stretch of the epidermal wall, and geometry of initial shape. At this point we have only approximate and general knowledge of these parameters estimated in the setups similar to our experiments.

That is why our conclusions are based on qualitative observations from simulations, for example the change in stress patterns resulting from changes in tissue surface geometry (Figure 2F-I). We did find that these are not extensively dependent on the choice of parameters, suggesting that the gap between cell and tissue responsiveness to stress is large and thus that a dose-dependent response can be detected experimentally.

To test this hypothesis, we first generated a computational simulation of a single cell ablation. In such case circumferential re-arrangement of stresses is less pronounced and more limited in scope than in the large-scale ablation simulation, but still visible (Author response image 5).

Author response image 5. — Simulation showing less pronounced circumferential rearrangements of stresses (white lines indicate maximal tensile stress directions) after ablation of a single cell (grey cell). **(A) Before ablation (B) After ablation.**

We observe a weak circumferential orientation of microtubules around single-cell ablation sites experimentally (see below and Author response image 6). Although these data are qualitative, they clearly show that the response to ablation is dose-dependent: when the magnitude of stress is predicted to increase, microtubules become less sensitive to cell shapes and mainly align according to the supracellular stress pattern.

We agree with the reviewer that this is an interesting point. To test this we ablated single cells using a dye-coupled laser to see if small-scale perturbations could affect the cellular level control of microtubule organization. Seven hours after ablation we observed that microtubule alignment became independent of cellular geometry. However, the microtubules around the site of ablation were not completely circumferential, consistent with a scenario in which stress anisotropy is weaker in single cell ablation cases, therefore leading to weaker alignment of microtubules around the site of ablation (Author response image 6). This observation is significantly different from the large-scale perturbation in which a strong circumferential response was obtained. Quantification in nematic tensor values of microtubule anisotropy near the site of a single cell ablation shows a mean value of 0.20 ± 0.06 (SE) as opposed to the 0.37 ± 0.02 (SE) in cells near large-scale ablations. Altogether, this supports our conclusion that microtubule response is dependent on stress intensity.

As suggested by the reviewer we also observed microtubule arrays in guard cells close to site of large-scale ablations. Single optical sections show that microtubule arrays still remain transverse in majority of the guard cells (Author response image 7) indicating that these cells retain a certain degree of control of their microtubules while being under the influence of a directional force field.

Also, if cutting experiments release tension globally, then wouldn't the MTs be expected to become less oriented?

Cutting experiments change the pattern of stress by releasing it in mainly one direction, with much lower affect in other directions (for the tensional stress in the epidermis, they release it in one direction, but not in the orthogonal one) – so they change an isotropic pattern to one that is anisotropic, thereby causing microtubule alignment.

3) Formulate a compelling argument for how plant cells sense stress and how this generates shape.

To start, we say nothing in this paper about how the shape of the pavement cells is generated. This is an interesting topic, but the experiments we have done to date are with pavement cells after they already are in their characteristic jigsaw puzzle piece shape. The initial generation of this shape would require elements that we have not yet studied. In the meristem, we could propose that tissue-derived stresses contribute to tissue shape emergence, because we analyzed the formation of young primordia and we had quantitative data on growth, from which we could argue that an initial differential growth would be sufficient to generate anisotropic stress, and thus a microtubule pattern, which in turn would promote organ outgrowth and organ separation from the meristem (Hamant et al. 2008, cf Bozorg et al. 2014) where different models are compared to explicitly show that a stress feedback promotes anisotropic organ growth). In pavement cells, as we did not analyze growth at a subcellular level, it is more cautious to focus our conclusion on cell shape maintenance.

Second, it is clear that other signals than stress can control microtubule orientation (e.g., light, see Lindeboom 2013). Yet, our data are consistent with mechanical stress playing a primary role in microtubule orientation. Could it be strain instead? Stress sensing mechanism will certainly involve an initial and very local measurement of strain (as that is the only way stress can be measured). There is however no convincing evidence that cell strain would act as a cue for microtubule orientation: the alignment of the microtubules is parallel to the principal direction of maximal stress both globally (Hamant et al. 2008) and locally (this paper) but the alignment of the microtubules is not always correlated with the direction of maximal cell strain. In particular, microtubules tend to be perpendicular to the maximal strain direction in cells (e.g., in the peripheral zone of the meristem), whereas they are parallel to maximal strain in the boundary regions between shoot apical meristem and floral meristems, a region which is also under highly anisotropic tensile stress parallel to the microtubules (Burian et al. 2013, Bozorg et al. 2014). Thus a response to stress provides a more parsimonious explanation than a response to cell strain.

What sort of mechanism could account for this? To begin with, one of the primary findings of this paper are that the stress sensing mechanism is subcellular, and not at the whole cell level, as the microtubules in pavement cells are aligned to stress where it is anisotropic (at the necks) but not where it is isotropic, and in different directions within one cell, directions that correspond to the predicted principal direction of maximal stress in each different cell region where the stress is anisotropic.

One possible mechanism, then, one that we are proposing in the current version of the manuscript is that each microtubule is stressed (perhaps through its attachment to the cell wall cellulose fibrils – this indirect attachment could for instance be mediated by cellulose synthase complexes that ride the microtubules and project cellulose fibrils into the wall parallel to the microtubules Paredez et al. 2006; Bringmann et al. 2012). If a microtubule under tension is strained so as to make the severing enzyme katanin bind more poorly than to an unstrained microtubule, then severing will prefer MTs that are not aligned to the stress direction, and will eliminate them. This fits with the finding in the paper and in our previous work (Uyttewaal et al. 2012) that severing is necessary to achieve alignment upon mechanical perturbation. There is also evidence from the literature that katanin activity can discriminate between microtubule domains with different properties (Davis et al. 2002; Diaz-Valencia et al. 2011). In this way a strain in microtubules results in alignment parallel to anisotropic stress, not to overall cellular strain. There are certainly other possibilities (e.g., a role of tension-induced microtubule polymerization (see Trushko et al. 2013)), and this mechanism is not proven in any way, but this is an example where an initial strain imposed by a specific mechanism and specific subcellular complex could lead to alignment to stress.

We have therefore made the following additions in the discussion of our revised manuscript:

“One possible mechanism for tension-dependent regulation of MT alignment, where each MT is stressed due to their coupling with CMFs potentially by means of the cellulose synthesizing complexes which ride along the MT synthesizing the CMFs parallel to the MTs (Paredez et al. 2006; Bringmann et al. 2012). In such a scenario a MT under tension is strained producing a conformational change to the MT lattice, which then could bias the binding of katanin to the less strained MTs at crossover sites leading to preferentially severing only the MTs not aligned to the principal stress direction. Reports have shown that conformation changes to the MT lattice act as hotspots promoting katanin binding and activity properties (Davis et al. 2002; Diaz-Valencia et al. 2011). As a result, this strain in MTs results in a MT alignment parallel to the anisotropic stress, not to overall cellular strain.”

4) Reword section on cell-wall anisotropy to reflect indirect measure of this property.

We agree with the reviewers that by indenting in the normal direction to the wall with an isotropic probe, in principle, we could not deduce mechanical anisotropy in the wall in the orthogonal/periclinal direction. Yet, as we observe lines on the resulting stiffness map, this reveals the anisotropic nature of the cell wall at a large scale. In other words, each indentation point is not providing any information on the mechanical anisotropy of the wall, but the spatial pattern does provide this information. We also agree that the data remain correlative. We have clarified these two points in the revision.

5) Separate the effects of material properties from those that arise from cellular geometry.

The referees are right that geometry can have an effect on the stiffness of the structure and thus the displacements. We performed a simulation in which a single isotropic pavement cell was pressurized, with part of its anticlinal walls fixed. This is similar to ablation of the surrounding cells on one side of the cell (right in our case). The results show that the displacement in such a situation is indeed not completely uniform (Author response image 8). If we consider the deformation of epidermal wall only it is largest in the neck regions (Author response image 8A). If we include deformation of anticlinal walls we observe swelling of the lobed regions (Author response image 8B). We are thus thankful to the reviewer and in light of these new result that show that geometry can have a major impact on the cell deformation after ablation, we decided to remove this part from our manuscript: while the observed experimental result remains true and consistent with neck stiffening, it can depend on both cell geometry and neck stiffening, and therefore is too weak to support neck stiffening exclusively.

Author response image 8. — The left edges of the cell were fixed, simulating attachment to unaltered tissue. The right side of the cell is next to ablated region. The tips of the lobes in ablation neighborhood show low values of displacements (blue). The displacement of the necks is larger . The black outline shows initial position of the edges. A) Deformation of the epidermal wall alone. B) Deformation including anticlinal walls.

6) Revisit cell-pressing experiments with better images and proper citations of previous literature.

It is difficult to see the differences in the experiments were cells are pressed by slides (Figure 3). In the text the differences are reported to be 0.37 vs 0.57 by their anisotropy measure. They report the same amount of difference (0.2) for necks vs lobes where the orientation is obvious. Why is it so much harder to see here? Also it is claimed that the effect is reversible, and that the value goes to 0.24 a day after the slide is removed. But this is quite a bit less than the starting point of 0.37, unless 0.13 of the difference appears instantly. If this is the case, the “before” condition needs to be quantified and presented for comparison. Jacques et al. (2013) have done similar experiments pressing on leaf epidermal cells; these previous results need to be mentioned and evaluated more extensively in this manuscript.

We do agree with the reviewers that ideally, we should observe exactly the same values before compression and after recovery. Nevertheless, and despite these differences, the reported nematic tensor values clearly show a trend in the increase and decrease of the microtubule anisotropy in the compression experiments. The reason for the lower value and less clear images in the recovery phase is due to the change in the magnification factor and the different objectives used. The compressed state is imaged with a cover glass and higher NA objectives, whereas the uncompressed recovery state is imaged with a water-dipping lens having lower NA. This has already been explained in the Materials and Methods section in the previous version. This experimental setup could not be avoided because of the need to demonstrate the removal of cover slip to allow the surface geometry to recover to its curved state.

During the preparation of the manuscript, similar results were reported by Jacques et al. 2013. For this reason we have moved this entire figure section to the supplementary data and more emphasis on Jacques et al. 2013 is given in that section.

We do agree that the observed changes could be a result of other factors as suggested by the reviewer. However our claims are based on already published work on the shoot apical meristem in which similar perturbation was performed (Hamant et al. 2008; Heisler et al. 2010; Uyttewaal et al. 2012). Evidence of microtubule rearrangements are also shown under conditions where wounding (ablation) or a change in cell geometry (compression) are not induced: isoxaben was used as a pharmachological agent to mechanically reduce the strength of the cell wall thereby increasing tension (Heisler et al. 2010). Treatment of pavement cells with isoxaben resulted in a hyperaligned microtubule array, supporting our claim.

However as suggested by the reviewer we cannot rule out the possibility of other factors. We have modified the text and included this in our text.

[Editors' note: further clarifications were requested prior to acceptance, as described below.]

We appreciate the careful consideration of review comments and the new models included in the rebuttal letter. Some of the data provided only in the rebuttal letter we felt would be useful to the readers of the manuscript and so we ask you to make a few minor revisions before acceptance, as outlined below:

We agree with the reviewers’ comments and we have included this section in the section describing the computation models in the Methods part of the main text (“Computational models” section).

We have now included the results of single cells ablation as part of the main figures (Figure 4) and include the observation of microtubules in guard cells in the main text along with a supplemental figure (Results section entitled “Microtubule response to mechanical perturbation is dependent on the magnitude of change in stress intensity”, Figure 4–figure supplement 1).

Associated Data

This section collects any data citations, data availability statements, or supplementary materials included in this article.

Supplementary Materials

Supplementary file 1.

Additional information about computational models.

DOI: http://dx.doi.org/10.7554/eLife.01967.026

elife01967s001.pdf^{(99.9KB, pdf)}

DOI: 10.7554/eLife.01967.026

[bib1] Asnacios A, Hamant O. 2012. The mechanics behind cell polarity. Trends in Cell Biology 22:584–591. doi: 10.1016/j.tcb.2012.08.005 [DOI] [PubMed] [Google Scholar]

[bib2] Baluska F, Volkmann D, Barlow PW. 2004. Eukaryotic cells and their cell bodies: cell theory revised. Annals of Botany 94:9–32. doi: 10.1093/aob/mch109 [DOI] [PMC free article] [PubMed] [Google Scholar]

[bib3] Baskin TI, Meekes HTHM, Liang BM, Sharp RE. 1999. Regulation of growth anisotropy in well-watered and water-stressed maize roots. II. Role of cortical microtubules and cellulose microfibrils. Plant Physiology 119:681–692. doi: 10.1104/pp.119.2.681 [DOI] [PMC free article] [PubMed] [Google Scholar]

[bib4] Bichet A, Desnos T, Turner S, Grandjean O, Hofte H. 2001. BOTERO1 is required for normal orientation of cortical microtubules and anisotropic cell expansion in Arabidopsis. The Plant Journal: for Cell and Molecular Biology 25:137–148. doi: 10.1046/j.1365-313x.2001.00946.x [DOI] [PubMed] [Google Scholar]

[bib5] Bonet J, Wood RD. 1997. Nonlinear continuum mechanics for finite element analysis. Cambridge, NY: Cambridge University Press [Google Scholar]

[bib6] Boudaoud A, Burian A, Borowska-Wykret D, Uyttewaal M, Wrzalik R, Kwiatkowska D, Hamant O. 2014. FibrilTool, an ImageJ plug-in to quantify fibrillar structures in raw microscopy images. Nature Protocols 9:457–463. doi: 10.1038/nprot.2014.024 [DOI] [PubMed] [Google Scholar]

[bib7] Bringmann M, Li E, Sampathkumar A, Kocabek T, Hauser M-T, Persson S. 2012. POM-POM2/cellulose synthase interacting1 is essential for the functional association of cellulose synthase and microtubules in Arabidopsis. The Plant Cell 24:163–177. doi: 10.1105/tpc.111.093575 [DOI] [PMC free article] [PubMed] [Google Scholar]

[bib8] CGAL Computational geometry algorithms library. 2014. [Online] Available: http://www.cgal.org [Google Scholar]

[bib9] Chan J, Crowell E, Eder M, Calder G, Bunnewell S, Findlay K, Vernhettes S, Hofte H, Lloyd C. 2010. The rotation of cellulose synthase trajectories is microtubule dependent and influences the texture of epidermal cell walls in Arabidopsis hypocotyls. Journal of Cell Science 123:3490–3495. doi: 10.1242/jcs.074641 [DOI] [PubMed] [Google Scholar]

[bib10] Chanliaud E, Burrows KM, Jeronimidis G, Gidley MJ. 2002. Mechanical properties of primary plant cell wall analogues. Planta 215:989–996. doi: 10.1007/s00425-002-0783-8 [DOI] [PubMed] [Google Scholar]

[bib11] Crowell EF, Timpano H, Desprez T, Franssen-Verheijen T, Emons AM, Hofte H, Vernhettes S. 2011. Differential regulation of cellulose orientation at the inner and outer face of epidermal cells in the Arabidopsis hypocotyl. The Plant Cell 23:2592–2605. doi: 10.1105/tpc.111.087338 [DOI] [PMC free article] [PubMed] [Google Scholar]

[bib12] Davis LJ, Odde DJ, Block SM, Gross SP. 2002. The importance of lattice defects in katanin-mediated microtubule severing in vitro. Biophysical Journal 82:2916–2927. doi: 10.1016/S0006-3495(02)75632-4 [DOI] [PMC free article] [PubMed] [Google Scholar]

[bib13] Derjaguin BV, Muller VM, Toporov YP. 1975. Effect of contact deformations on the adhesion of particles. Journal of Colloid and Interface Science 53:314–326. doi: 10.1016/0021-9797(75)90018-1 [DOI] [Google Scholar]

[bib14] Díaz-Valencia JD, Morelli MM, Bailey M, Zhang D, Sharp DJ, Ross JL. 2011. Drosophila Katanin-60 Depolymerizes and Severs at microtubule defects. Biophysical Journal 100:2440–2449. doi: 10.1016/j.bpj.2011.03.062 [DOI] [PMC free article] [PubMed] [Google Scholar]

[bib15] Dumais J, Steele CR. 2000. New evidence for the role of mechanical forces in the shoot apical meristem. Journal of Plant Growth Regulation 19:7–18. doi: 10.1007/s003440000003 [DOI] [PubMed] [Google Scholar]

[bib16] Engler AJ, Sen S, Sweeney HL, Discher DE. 2006. Matrix elasticity directs stem cell lineage specification. Cell 126:677–689. doi: 10.1016/j.cell.2006.06.044 [DOI] [PubMed] [Google Scholar]

[bib17] Franck AD, Powers AF, Gestaut DR, Gonen T, Davis TN, Asbury CL. 2007. Tension applied through the Dam1 complex promotes microtubule elongation providing a direct mechanism for length control in mitosis. Nature Cell Biology 9:832–837. doi: 10.1038/ncb1609 [DOI] [PMC free article] [PubMed] [Google Scholar]

[bib18] Fu Y, Gu Y, Zheng Z, Wasteneys G, Yang Z. 2005. Arabidopsis interdigitating cell growth requires two antagonistic pathways with opposing action on cell morphogenesis. Cell 120:687–700. doi: 10.1016/j.cell.2004.12.026 [DOI] [PubMed] [Google Scholar]

[bib19] Fujita M, Himmelspach R, Hocart CH, Williamson RE, Mansfield SD, Wasteneys GO. 2011. Cortical microtubules optimize cell-wall crystallinity to drive unidirectional growth in Arabidopsis. The Plant Journal: for Cell and Molecular Biology 66:915–928. doi: 10.1111/j.1365-313X.2011.04552.x [DOI] [PubMed] [Google Scholar]

[bib20] Gardner MK, Pearson CG, Sprague BL, Zarzar TR, Bloom K, Salmon ED, Odde DJ. 2005. Tension-dependent regulation of microtubule dynamics at kinetochores can explain metaphase congression in yeast. Molecular Biology of the Cell 16:3764–3775. doi: 10.1091/mbc.E05-04-0275 [DOI] [PMC free article] [PubMed] [Google Scholar]

[bib21] Green PB. 1980. Organogenesis-a biophysical view. Annual Review of Plant Physiology 31:51–82. doi: 10.1146/annurev.pp.31.060180.000411 [DOI] [Google Scholar]

[bib22] Hamant O, Heisler MG, Jonsson H, Krupinski P, Uyttewaal M, Bokov P, Corson F, Sahlin P, Boudaoud A, Meyerowitz EM, Couder Y, Traas J. 2008. Developmental patterning by mechanical signals in Arabidopsis. Science 322:1650–1655. doi: 10.1126/science.1165594 [DOI] [PubMed] [Google Scholar]

[bib23] Hayot CM, Forouzesh E, Goel A, Avramova Z, Turner JA. 2012. Viscoelastic properties of cell walls of single living plant cells determined by dynamic nanoindentation. Journal of Experimental Botany 63:2525–2540. doi: 10.1093/jxb/err428 [DOI] [PMC free article] [PubMed] [Google Scholar]

[bib24] Heisler MG, Hamant O, Krupinski P, Uyttewaal M, Ohno C, Jonsson H, Traas J, Meyerowitz EM. 2010. Alignment between PIN1 polarity and microtubule orientation in the shoot apical meristem reveals a tight coupling between morphogenesis and auxin transport. PLOS Biology 8:e1000516. doi: 10.1371/journal.pbio.1000516 [DOI] [PMC free article] [PubMed] [Google Scholar]

[bib25] Hutter JL, Bechhoefer J. 1993. Calibration of atomic-force microscope tips. Review of Scientific Instruments 64:1868–1873. doi: 10.1063/1.1143970 [DOI] [Google Scholar]

[bib26] Jacques E, Verbelen JP, Vissenberg K. 2013. Mechanical stress in Arabidopsis leaves orients microtubules in a ‘continuous’ supracellular pattern. BMC Plant Biology 13:163. doi: 10.1186/1471-2229-13-163 [DOI] [PMC free article] [PubMed] [Google Scholar]

[bib27] Jaeger J, Irons D, Monk N. 2008. Regulative feedback in pattern formation: towards a general relativistic theory of positional information. Development 135:3175–3183. doi: 10.1242/dev.018697 [DOI] [PubMed] [Google Scholar]

[bib28] Jonsson H, Heisler MG, Shapiro BE, Meyerowitz EM, Mjolsness E. 2006. An auxin-driven polarized transport model for phyllotaxis. Proceedings of the National Academy of Sciences of the United States of America 103:1633–1638. doi: 10.1073/pnas.0509839103 [DOI] [PMC free article] [PubMed] [Google Scholar]

[bib29] Jung G, Wernicke W. 1990. Cell shaping and microtubules in developing mesophyll of wheat (Triticum aestivum L.). Protoplasma 153:141–148. doi: 10.1007/BF01353998 [DOI] [Google Scholar]

[bib30] Kaplan DR. 1992. The relationship of cells to organisms in plants: problem and Implications of an organismal perspective. International Journal of Plant Sciences 153:S28–S37. doi: 10.1086/297061 [DOI] [Google Scholar]

[bib31] Kierzkowski D, Nakayama N, Routier-Kierzkowska AL, Weber A, Bayer E, Schorderet M, Reinhardt D, Kuhlemeier C, Smith RS. 2012. Elastic domains regulate growth and organogenesis in the plant shoot apical meristem. Science 335:1096–1099. doi: 10.1126/science.1213100 [DOI] [PubMed] [Google Scholar]

[bib32] Kutschera U, Niklas KJ. 2007. The epidermal-growth-control theory of stem elongation: an old and a new perspective. Journal of Plant Physiology 164:1395–1409. doi: 10.1016/j.jplph.2007.08.002 [DOI] [PubMed] [Google Scholar]

[bib33] Lecuit T, Lenne PF. 2007. Cell surface mechanics and the control of cell shape, tissue patterns and morphogenesis. Nature Reviews Molecular Cell Biology 8:633–644. doi: 10.1038/nrm2222 [DOI] [PubMed] [Google Scholar]

[bib34] Levy R, Maaloum M. 2002. Measuring the spring constant of atomic force microscope cantilevers: thermal fluctuations and other methods. Nanotechnology 13:33–37 [Google Scholar]

[bib35] Lin D, Cao L, Zhou Z, Zhu L, Ehrhardt D, Yang Z, Fu Y. 2013. Rho GTPase signaling activates microtubule severing to promote microtubule ordering in arabidopsis. Current Biology: CB 23:290–297. doi: 10.1016/j.cub.2013.01.022 [DOI] [PubMed] [Google Scholar]

[bib36] Lindeboom JJ, Nakamura M, Hibbel A, Shundyak K, Gutierrez R, Ketelaar T, Emons AMC, Mulder BM, Kirik V, Ehrhardt DW. 2013. A mechanism for reorientation of cortical microtubule arrays driven by microtubule severing. Science 342:1245533. doi: 10.1126/science.1245533 [DOI] [PubMed] [Google Scholar]

[bib37] Marcus AI, Moore RC, Cyr RJ. 2001. The role of microtubules in guard cell function. Plant Physiology 125:387–395. doi: 10.1104/pp.125.1.387 [DOI] [PMC free article] [PubMed] [Google Scholar]

[bib38] Martin AC, Kaschube M, Wieschaus EF. 2009. Pulsed contractions of an actin-myosin network drive apical constriction. Nature 457:495–499. doi: 10.1038/nature07522 [DOI] [PMC free article] [PubMed] [Google Scholar]

[bib39] Milani P, Gholamirad M, Traas J, Arneodo A, Boudaoud A, Argoul F, Hamant O. 2011. In vivo analysis of local wall stiffness at the shoot apical meristem in Arabidopsis using atomic force microscopy. The Plant Journal: for Cell and Molecular Biology 67:1116–1123. doi: 10.1111/j.1365-313X.2011.04649.x [DOI] [PubMed] [Google Scholar]

[bib40] Nezhad AS, Naghavi M, Packirisamy M, Bhat R, Geitmann A. 2013. Quantification of the Young’s modulus of the primary plant cell wall using Bending-Lab-On-Chip (BLOC). Lab on a Chip 13:2599–2608. doi: 10.1039/c3lc00012e [DOI] [PubMed] [Google Scholar]

[bib41] Nicklas RB. 1988. The forces that move chromosomes in mitosis. Annual Review of Biophysics and Biophysical Chemistry 17:431–449. doi: 10.1146/annurev.bb.17.060188.002243 [DOI] [PubMed] [Google Scholar]

[bib42] Paredez AR, Somerville CR, Ehrhardt DW. 2006. Visualization of cellulose synthase demonstrates functional association with microtubules. Science 312:1491–1495. doi: 10.1126/science.1126551 [DOI] [PubMed] [Google Scholar]

[bib43] Pouille PA, Ahmadi P, Brunet AC, Farge E. 2009. Mechanical signals trigger Myosin II redistribution and mesoderm invagination in Drosophila embryos. Science Signaling 2:ra16. doi: 10.1126/scisignal.2000098 [DOI] [PubMed] [Google Scholar]

[bib44] Roeder AH, Chickarmane V, Cunha A, Obara B, Manjunath BS, Meyerowitz EM. 2010. Variability in the control of cell division underlies sepal epidermal patterning in Arabidopsis thaliana. PLOS Biology 8:e1000367. doi: 10.1371/journal.pbio.1000367 [DOI] [PMC free article] [PubMed] [Google Scholar]

[bib45] Roeder AH, Cunha A, Ohno CK, Meyerowitz EM. 2012. Cell cycle regulates cell type in the Arabidopsis sepal. Development 139:4416–4427. doi: 10.1242/dev.082925 [DOI] [PubMed] [Google Scholar]

[bib46] Schopfer P. 2006. Biomechanics of plant growth. American Journal of Botany 93:1415–1425. doi: 10.3732/ajb.93.10.1415 [DOI] [PubMed] [Google Scholar]

[bib47] Sherrard K, Robin F, Lemaire P, Munro E. 2010. Sequential activation of apical and basolateral contractility drives ascidian endoderm invagination. Current Biology: CB 20:1499–1510. doi: 10.1016/j.cub.2010.06.075 [DOI] [PMC free article] [PubMed] [Google Scholar]

[bib48] Shraiman BI. 2005. Mechanical feedback as a possible regulator of tissue growth. Proceedings of the National Academy of Sciences of the United States of America 102:3318–3323. doi: 10.1073/pnas.0404782102 [DOI] [PMC free article] [PubMed] [Google Scholar]

[bib49] Skibbens R, Skeen V, Salmon E. 1993. Directional instability of kinetochore motility during chromosome congression and segregation in mitotic newt lung cells: a push-pull mechanism. The Journal of Cell Biology 122:859–875. doi: 10.1083/jcb.122.4.859 [DOI] [PMC free article] [PubMed] [Google Scholar]

[bib50] Sneddon IN. 1965. The relation between load and penetration in the axisymmetric boussinesq problem for a punch of arbitrary profile. International Journal of Engineering Science 3:47–57. doi: 10.1016/0020-7225(65)90019-4 [DOI] [Google Scholar]

[bib51] Solon J, Kaya-Copur A, Colombelli J, Brunner D. 2009. Pulsed forces timed by a ratchet-like mechanism drive directed tissue movement during dorsal closure. Cell 137:1331–1342. doi: 10.1016/j.cell.2009.03.050 [DOI] [PubMed] [Google Scholar]

[bib52] Stylianopoulos T, Martin JD, Chauhan VP, Jain SR, Diop-Frimpong B, Bardeesy N, Smith BL, Ferrone CR, Hornicek FJ, Boucher Y, Munn LL, Jain RK. 2012. Causes, consequences, and remedies for growth-induced solid stress in murine and human tumors. Proceedings of the National Academy of Sciences of the United States of America 109:15101–15108. doi: 10.1073/pnas.1213353109 [DOI] [PMC free article] [PubMed] [Google Scholar]

[bib53] Suslov D, Verbelen JP, Vissenberg K. 2009. Onion epidermis as a new model to study the control of growth anisotropy in higher plants. Journal of Experimental Botany 60:4175–4187. doi: 10.1093/jxb/erp251 [DOI] [PubMed] [Google Scholar]

[bib54] Thery M, Jimenez-Dalmaroni A, Racine V, Bornens M, Julicher F. 2007. Experimental and theoretical study of mitotic spindle orientation. Nature 447:493–496 [DOI] [PubMed] [Google Scholar]

[bib55] Trushko A, Schaffer E, Howard J. 2013. The growth speed of microtubules with XMAP215-coated beads coupled to their ends is increased by tensile force. Proceedings of the National Academy of Sciences of the United States of America 110:14670–14675. doi: 10.1073/pnas.1218053110 [DOI] [PMC free article] [PubMed] [Google Scholar]

[bib56] Uyttewaal M, Burian A, Alim K, Landrein B, Borowska-Wykret D, Dedieu A, Peaucelle A, Ludynia M, Traas J, Boudaoud A, Kwiatkowska D, Hamant O. 2012. Mechanical stress acts via katanin to amplify differences in growth rate between adjacent cells in Arabidopsis. Cell 149:439–451. doi: 10.1016/j.cell.2012.02.048 [DOI] [PubMed] [Google Scholar]

[bib57] Wartlick O, Kicheva A, Gonzalez-Gaitan M. 2009. Morphogen gradient formation. Cold Spring Harbor Perspectives in Biology 1:a001255. doi: 10.1101/cshperspect.a001255 [DOI] [PMC free article] [PubMed] [Google Scholar]

[bib58] Weiss JA, Maker BN, Govindjee S. 1996. Finite element implementation of incompressible, transversely isotropic hyperelasticity. Computer Methods in Applied Mechanics and Engineering 135:107–128. doi: 10.1016/0045-7825(96)01035-3 [DOI] [Google Scholar]

[bib59] Wightman R, Chomicki G, Kumar M, Carr P, Turner SR. 2013. SPIRAL2 determines plant microtubule organization by modulating microtubule severing. Current Biology: CB 23:1902–1907. doi: 10.1016/j.cub.2013.07.061 [DOI] [PMC free article] [PubMed] [Google Scholar]

[bib60] Wightman R, Turner SR. 2007. Severing at sites of microtubule crossover contributes to microtubule alignment in cortical arrays. The Plant Journal: for Cell and Molecular Biology 52:742–751. doi: 10.1111/j.1365-313X.2007.03271.x [DOI] [PubMed] [Google Scholar]

[bib61] Williamson RE. 1990. Alignment of cortical microtubules by anisotropic wall stresses. Functional Plant Biology 17:601–613 [Google Scholar]

[bib62] Wolpert L. 1969. Positional information and the spatial pattern of cellular differentiation. Journal of Theoretical Biology 25:1–47. doi: 10.1016/S0022-5193(69)80016-0 [DOI] [PubMed] [Google Scholar]

[bib63] Xu T, Wen M, Nagawa S, Fu Y, Chen JG, Wu MJ, Perrot-Rechenmann C, Friml J, Jones AM, Yang Z. 2010. Cell surface- and rho GTPase-based auxin signaling controls cellular interdigitation in Arabidopsis. Cell 143:99–110. doi: 10.1016/j.cell.2010.09.003 [DOI] [PMC free article] [PubMed] [Google Scholar]

[bib64] Yang Z. 2008. Cell polarity signaling in Arabidopsis. Annual Review of Cell and Developmental Biology 24:551–575. doi: 10.1146/annurev.cellbio.23.090506.123233 [DOI] [PMC free article] [PubMed] [Google Scholar]

[bib65] Zhang C, Halsey LE, Szymanski DB. 2011. The development and geometry of shape change in Arabidopsis thaliana cotyledon pavement cells. BMC Plant Biology 11:27. doi: 10.1186/1471-2229-11-27 [DOI] [PMC free article] [PubMed] [Google Scholar]

[bib66] Zhang Q, Fishel E, Bertroche T, Dixit R. 2013. Microtubule severing at crossover sites by katanin generates ordered cortical microtubule arrays in arabidopsis. Current Biology 23:2191–2195. doi: 10.1016/j.cub.2013.09.018 [DOI] [PubMed] [Google Scholar]

[bib67] Zienkiewicz OC, Taylor RL, Zhu JZ. 2005. The finite element method: its basis and fundamentals. Oxford, UK: Elsevier Butterworth Heinemann [Google Scholar]

PERMALINK

Subcellular and supracellular mechanical stress prescribes cytoskeleton behavior in Arabidopsis cotyledon pavement cells

Arun Sampathkumar

Pawel Krupinski

Raymond Wightman

Pascale Milani

Alexandre Berquand

Arezki Boudaoud

Olivier Hamant

Henrik Jönsson

Elliot M Meyerowitz

Roles

Abstract

eLife digest

Introduction

Results

Pavement cell shape correlates with microtubule organization and consistent mechanical reinforcements in cell walls

Figure 1. Mechanical heterogeneity of pavement cells correlates with microtubule patterns.

Figure 1—figure supplement 1. Microtubule organization and mechanical heterogeneity.

Figure 1—figure supplement 2. Microtubule organization and mechanical heterogeneity.

Figure 1—figure supplement 3. Microtubule organization and mechanical heterogeneity.

Microtubule organization correlates with cell geometry-derived mechanical stresses

Figure 2. Microtubule patterns correlate with physical stress patterns.

Figure 2—figure supplement 1. Microtubule organization and correlation with stress patterns.

Figure 2—figure supplement 2. Simulation of single pressurized pavement cell shape A and D.

Figure 2—figure supplement 3. Microtubule organization and correlation with stress patterns.

Mechanical compression of cotyledon pavement cells affects microtubule anisotropy

Video 1. Depth color-coded time series images showing changes in microtubule organization following compression.

Figure 3. Extrinsic perturbation of mechanical forces induce directional changes in microtubule arrays.

Figure 3—figure supplement 1. Mechanical compression leads to increased microtubule anisotropy in pavement cells.

Figure 3—figure supplement 2. Compression of pavement cells results in stabilization of microtubule array orientation.

Figure 3—figure supplement 3. Cotyledon epidermis is under tension.

Figure 3—figure supplement 4. Microtubule response to changes in physical forces in katanin mutant.

Large scale changes in tissue-wide stresses can override cell shape-derived stresses

Video 2. Laceration of cotyledon shows outward displacement of cut edges.

Video 3. Video of computational simulation showing circumferential distribution of stress and increase in MT anisotropy after ablation.

Microtubule response to mechanical perturbation is dependent on the magnitude of change in stress intensity

Figure 4. Stress intensity regulates microtubule alignment.

Figure 4—figure supplement 1. Microtubule array organization in guard cells remains unaffected by changes in directional force field.

Figure 4—figure supplement 2. Microtubule response to isoxaben treatment.

The microtubule response to subcellular and supracellular stresses depends on katanin-dependent severing activity

Video 4. Depth color-coded time series images showing microtubule arrays in botero 1-7 does not induce hyper-alignment of microtubule arrays after compression.

Video 5. Video showing severing of microtubule immediately after and 4 hr post ablation of cells. Red dots mark sites of microtubule severing.

Figure 5. Mechanical perturbations increase bundling by promoting severing.

Discussion

Figure 6. Mechanical forces regulate pavement cell shape by controlling microtubule organization and cellulose deposition.

Materials and methods

Plant material and growth conditions

Specimen preparation and confocal imaging

Mechanical perturbations

Image processing

Quantification of MT alignments for anisotropy

Severing quantification

Statistical analysis

Atomic force microscopy

Computational models

Acknowledgements

Funding Statement

Funding Information

Additional information

Competing interests

Author contributions

Additional files

References

Decision letter

Roles

Author response image 6.

Author response image 7. Close up image of microtubule arrays in guard cell before and after large-scale ablation.

Author response

Author response image 1. Simulation of pressurized doubly curved, saddle-like shape.

Author response image 2. Simulation of single pressurized pavement cell shape.

Author response image 3.

Author response image 4. Close up of a merged image of cell boundary movement before (white) and after (red) ablation.

Author response image 5.

Author response image 8. Color map shows total displacement (including z coordinate) in a single pressurized 3D pavement cell model.

Associated Data

Supplementary Materials

ACTIONS

PERMALINK

RESOURCES