Why plants make puzzle cells, and how their shape emerges
During growth and morphogenesis , plant cells undergo dramatic changes in size and shape . Starting from small isodiametric cells in proliferative tissues , cells stop dividing and can expand to over 100 times their original size . This results in large elongated cells , such as those in roots and stems , or much more intricate forms , such as the jigsaw puzzle-shaped epidermal cells of Arabidopsis thaliana leaves and cotyledons ( Figure 1A ) , which we call puzzle cells . The processes underlying the formation of these cells are presently unclear , and it has been proposed that they emerge from either the localized outgrowth of lobes ( also called protrusions ) ( Fu , 2002; Mathur , 2006; Xu et al . , 2010; Zhang et al . , 2011 ) , localized restriction of indentations ( Fu et al . , 2009; Sampathkumar et al . , 2014; Lin et al . , 2013 ) , or a combination of both ( Fu et al . , 2005; Abley et al . , 2013; Armour et al . , 2015; Higaki et al . , 2016; Majda et al . , 2017 ) . Specific members of the Rho GTPase of plants ( ROP ) family of proteins play a key role in shaping these cells . ROP2 and ROP6 mutually inhibit each other's accumulation at the plasma membrane , creating a co-repression network that divides the plasma membrane into alternating expression domains , with ROP2 in lobes and ROP6 in indentations ( Fu et al . , 2009 ) . These proteins are thought to regulate pavement cell interdigitation through their interactions with RIC proteins , with ROP2 recruiting actin through RIC4 in the lobes , and ROP6 recruiting cortical microtubules through RIC1 and katanin to restrict growth in indentations . Disruptions in the ROP/RIC pathways lead to defects in puzzle cell formation ( Fu , 2002; Fu et al . , 2005; Fu et al . , 2009; Xu et al . , 2010; Lin et al . , 2013 ) . Since a lobe in one cell must be matched by an indentation in its neighbor , some manner of extracellular communication is required . The plant hormone auxin has been proposed to act as this signal ( Fu et al . , 2005; Xu et al . , 2010; Li et al . , 2011 ) , although recent data call for a re-evaluation of this hypothesis ( Gao et al . , 2015; Belteton et al . , 2018 ) . Although these studies have elucidated many of the molecular players involved in puzzle cell patterning , a mechanistic theory is lacking , in part because the function of the puzzle-shape in epidermal cells is unclear ( Bidhendi and Geitmann , 2018 ) . It has been hypothesized that the interdigitation of the lobes and indentations may strengthen the leaf surface ( Glover , 2000; Jacques et al . , 2014; Sotiriou et al . , 2018 ) , with material sciences studies supporting the plausibility of this idea ( Lee et al . , 2000 ) . Alternatively , puzzle-shaped cells may allow for the correct spacing of the other epidermal cell types , such as guard cells and stomata ( Glover , 2000 ) . However there is little experimental support for these hypotheses at present . Here we propose a different function for the puzzle shape , that it is an adaptation to a developmental constraint related to the mechanical forces that act on turgid plant cells that reside in the epidermis . Mechanically , plant cells are like small balloons inflated with considerable turgor pressure , up to 10 bar in Arabidopsis leaf cells ( Forouzesh et al . , 2013 ) , reaching values up to 50 bar in specialized cells such as stomata ( Franks et al . , 2001 ) . Turgor pressure induces mechanical stress in the cell wall , which is the ratio of the force acting on a cross-section of the material ( cell wall ) scaled by the area of the material resisting the force . If the wall is made of a homogeneous material , then for a given turgor pressure , cell size and shape provide a good predictor of mechanical stress ( Niklas , 1992; Geitmann and Ortega , 2009 ) , with larger cells subject to more stress than smaller ones ( Bassel et al . , 2014 ) . Although the composition of the cell wall is undoubtedly more complex ( reviewed by Cosgrove , 2005; Cosgrove , 2014 ) , this suggests that cell shape and mechanical stress are intimately connected . Most plant tissues emerge from undifferentiated cells that are initially small and isodiametrically shaped , and subsequently proliferate , differentiate and expand . For epidermal cells composing the outermost cell layer in each organ , minimizing mechanical stress on their walls is likely particularly important as the epidermis limits organ growth and is under tension from internal tissues ( Savaldi-Goldstein et al . , 2007; Kutschera and Niklas , 2007; Beauzamy et al . , 2015 ) . Here we explore the relationship between cell shape and mechanical stress , to understand if mechanical stress is a morphological constraint in shaping epidermal cells . We propose a plausible driver for the creation of the intricate , commonly observed puzzle cell forms by demonstrating that they reduce the forces the cell wall has to withstand . We present computer simulation models that show that actively minimizing force leads to the emergence of the puzzle cell shape , reducing stress and thus potentially lowering the amount of cellulose and other wall material required to maintain mechanical integrity of the cell wall .
Using the Finite Element Method ( FEM ) , we performed simulations on single cells with idealized shapes to explore the effect of cell shape on turgor-induced mechanical stresses ( the trace of the Cauchy stress tensor ) in the cell wall ( Bassel et al . , 2014 ) . To assess basic relations between cell shape and stress we used uniform , isotropic elastic properties for cell walls , which were assumed to have cell wall thickness of 1 µm , and pressurized the cells to 5 bar ( note that this neglects inhomogeneities in the cell wall , as for example observed by Majda et al . , 2017 ) . Starting with a small cube-shaped cell ( 10 × 10 × 10 µm ) we increased the initial cell size in different dimensions to observe the effect on stress following pressurization . We observed that an increase of cell length in one direction ( 50 × 10 × 10 µm ) does not significantly increase maximal stress in the cell wall ( Figure 1B ) . This suggests that anisotropic growth that results in long thin cells is a mechanically advantageous strategy to limit stress magnitude , limiting the wall thickness required to maintain the cell's integrity . Next , we simulated a cell expanded in two directions ( 50 × 50 × 10 µm ) and observed that the maximal stress was much higher . Enlarging the cell in two directions created a large open surface area , causing the cell wall to bulge out in response to turgor pressure , greatly increasing the stress . When the third dimension is enlarged to form a cube ( 50 × 50 × 50 µm ) , only a small increase in maximal stress is observed compared to the 50 × 50 × 10 µm case . Thus if a cell must increase its size , an effective way to do it without increasing stress is to elongate along a single axis , instead of expanding in two or three dimensions . Plant organs such as roots , hypocotyls , sepals , many grass leaves and stems grow primarily in one direction and have elongated cells , which would maintain low stress during growth . But how do cells avoid excessive stress if they are part of a tissue that grows in two directions , such as the surface of broad leaves ? Here we propose that the puzzle cell shape , with lobes and indentations , provides a solution to this problem . To test this hypothesis , we began by analyzing the stress in a mechanical model of the cotyledon epidermis of Arabidopsis thaliana . A cellular surface mesh was extracted from confocal images using the image analysis software MorphoGraphX ( Barbier de Reuille et al . , 2015 ) . The mesh was then extruded to form a layer of 3D cells of uniform thickness representing the cotyledon epidermis ( Mosca et al . , 2017 ) . Next , the cells were pressurized , and the stresses visualized ( Figure 1C , F ) . In order to examine the effect of lobes on the stress , we created a second template with simplified cell shapes using only the junctions ( points shared by three different cells ) of the original cells ( Figure 1D ) . While the total and average cell area in the original and simplified tissue is the same , the overall stress is much lower in the original ( puzzle-shaped ) tissue , especially for large cells ( Figure 1C , D ) . Next , we asked how the presence of lobes affects mechanical stress in the cell wall . We computed mechanical stress in idealized circular cells , adding protrusions to simulate the lobes of a puzzle cell . While stress increases with diameter ( Figure 1E ) , adding lobes to the original cell does not significantly affect stress in the central part of the cell . Furthermore , increasing lobe length has no impact on stress , although the total volume of the cell increases . Similarly , changing lobe width or number does not affect stress in the cell center ( Figure 1E , inset ) . However , there are stress hot spots located between the protrusions , where values appear to be inversely correlated with the width of the protrusion ( the distance between the flanks of two consecutive lobes ) , and increase with the radius of the central part of the cell . This is similar to what we observed in pressurized puzzle cells ( Figure 1C , F ) . In both cases , high stress values appear in open areas and in the indentions between protrusions , consistent with previous observations ( Sampathkumar et al . , 2014 ) . In the absence of lobes , the load acting in the middle of the cell is transmitted approximately evenly to the cell contour , whereas in puzzle-shaped cells , the central load is transferred to the area between the lobes , creating stress hot spots in the indentations . The magnitude of stress in the indentations is therefore a direct reflection of the large open areas of the cell that they support , and is thus higher when cells bulge more . Despite the stress hot spots between protrusions , overall stress at both the cell and tissue level is much lower in puzzle shaped cells than in the simplified cell shape template ( Figure 1C , D ) . Following these observations , we propose that the size of the largest empty circle ( LEC ) that can fit into the cell contour ( Figure 1G , yellow ) can serve as a proxy for mechanical stress magnitude in both puzzle and non-puzzle shaped cells . For long thin cells , such as in roots or stems , the size of the empty circle is the cell diameter , which is known to predict stress for cylindrical cells ( Geitmann and Ortega , 2009 ) . We hypothesize that in a strongly anisotropically growing organ the plant would make long thin cells , whereas in more isotropic organs puzzle cells would be produced . Counter-intuitively , it is the requirement for isotropic expansion at the tissue scale that drives the irregular shape of puzzle cells . To test our hypothesis , a method to quantify the puzzle shape of cells was required . As the epidermis is a surface of relatively uniform thickness , most shape measures applied to puzzle cells consider only the 2D form of cells , and several methods have been developed for this purpose ( see Zhang et al . , 2011; Wu et al . , 2016 , and references therein ) . A common measure to estimate the complexity of a contour is circularity , indicating how closely a given object resembles a circle . Circularity is calculated using the ratio of the perimeter to the square root of area ( Zhang et al . , 2011; Majda et al . , 2017 ) . However , it is not suitable for our purposes as both simple , elongated cells and lobed puzzle cells have increased circularity values . Consequently , it cannot be used to reliably distinguish between these cell shapes . Another common approach is to calculate a skeleton based on the cell contour and count its branches ( Le et al . , 2006 ) . Unfortunately skeletonization methods can be very sensitive to small changes in shape ( such as the error produced by discretization ) making it difficult to robustly quantify the geometric features of cells . Here we use a method based on the convex hull ( Wu et al . , 2016 ) , the smallest convex shape containing the cell ( think of a rubber band surrounding the cell ) . We define cell lobeyness as the perimeter of the cell divided by the perimeter of its convex hull ( Figure 1G , white and red , respectively ) . The higher this value , the more lobed the cell is expected to be . The ratio of the cell's convex hull area to that of the cell is another possibility , however we found that for important special cases , such as worm or boomerang-shaped cells , using the area may produce high ratios even when cells do not have significant lobes . The ratio of perimeters ( perimeter of the cell/perimeter of its convex hull ) is less affected in these cases . Cortical microtubules are thought to direct the deposition of cellulose fibrils in the cell wall ( Green , 1962; Paredez et al . , 2006 ) . These fibrils stiffen the cell wall , causing growth to be favored in the direction perpendicular to the fibrils ( Suslov and Verbelen , 2006 ) . Cortical microtubules have also been shown to orient along the maximal direction of tensile stress ( Hejnowicz et al . , 2000; Hamant et al . , 2008 ) . The fact that growth anisotropy affects cell shape and cell shape affects stress , suggests a feedback mechanism linking cell shape and growth via the response of cortical microtubules to mechanical stress directions . This idea is supported by experimental and modeling work showing that predicted stress directions in puzzle cells align with cortical microtubule direction in Arabidopsis cotyledons ( Sampathkumar et al . , 2014 ) . Here we propose a dynamic simulation model of puzzle cell patterning based on the idea that cells can respond to mechanical signals generated by cell geometry . The model focuses on the developmental stage when cells stop dividing and begin to expand . The basic principle behind the model is that as cells grow , stresses gradually increase , and when they reach a threshold level the cell wall is reinforced to resist these stresses . Using simulations on idealized cell templates , we test whether this basic principle is sufficient to generate different cell shapes , depending on the anisotropy of tissue growth . The emerging cell shapes primarily arise from the growth direction imposed at the tissue level that is locally modulated by stress-based growth restriction . We present the essential aspects of the model here ( Figure 2 ) , but refer the reader to the Appendix for further details . Cells are represented as polygons ( Figure 2A ) , with wall segments between nodes acting like linear springs ( Prusinkiewicz and Lindenmayer , 1990 ) , and nodes having resistance to bending between adjoining segments ( Matthews , 2002 , Figure 2—figure supplement 1 ) . Thereby the model accounts for cell wall thickness and penalizes sharp features , which are usually not observed in nature . A simulation step consists of 3 phases ( Figure 2B , C ) . During the first phase , springs are inserted across cells in addition to those defining the cell polygon . These additional springs account for the presence of oriented cell wall stiffening components , such as cellulose microfibrils whose deposition is guided by cortical microtubules ( Paredez et al . , 2006 ) that are thought to respond to stress ( Hejnowicz et al . , 2000; Hamant et al . , 2008 ) . The springs also only exert force when they exceed a given target length , related to the LEC , which provides a proxy for stress ( Figure 1 ) . These connections across the cells introduce growth restrictions into the model , and are placed according to two criteria . First , these springs connect each node to the closest node across the cell falling within a given angle from the normals of the two nodes . Second , connections are inhibited if the the cell wall is convex ( see Appendix , Microtubule placement ) . This facilitates lobe formation , gives a pattern that both follows the patterns of stress previously reported by Sampathkumar et al . ( 2014 ) and is consistent with the proposed action of ROP2 in excluding ROP6 from lobes . In the second phase , growth is simulated by displacing the wall segments , based on the specified tissue growth ( e . g . isotropically or anisotropically ) , and relaxing stretched cell-wall springs so that the rest lengths match their actual length . The connections across the cells do not grow . Once placed , their reference length is unaffected by growth and is fixed until the connection is removed . In the third and final phase , a new resting state is found by updating cell shapes to achieve mechanical equilibrium . The next simulation step commences by reassigning microtubule/cellulose connections based on the new cell shape and updating the rest-length of cell wall segments . This highly dynamic arrangement of microtubules is consistent with a similar assumption underlying mechanistic explanations of cell division patterns ( Lloyd , 1991; Besson and Dumais , 2011 ) . If tissue growth is isotropic , cells quickly approach their target LEC , and connections representing the cellulose and microtubules begin to stretch . Lobes emerge as the indentations ( concave regions ) attract more connections and protrusions ( convex regions ) lose connections ( Figure 2C , Video 1 ) . The increased number of connections at indentations is an emergent geometric effect . As the indentation deepens , and its tip becomes more exposed , it becomes the closest node to a larger number of nodes on the opposing cell wall , thus attracting more connections . This is consistent with the findings of Sampathkumar et al . ( 2014 ) , who detected oriented patterns of mechanical anisotropy with atomic force microscopy , consistent with the proposed directed accumulation of cellulose microfibrils in the indentations of puzzle cells . These connections act as a proxy for the additional stress in the indentations ( Figure 1 ) . Interestingly , the accumulation of connections in the indentations is consistent with the observed auto-catalytic effect of microtubule bundling in indentations in real pavement cells , via induced ROP6/RIC1/katanin-dependent microtubule severing activity ( Lin et al . , 2013; Sampathkumar et al . , 2014 ) . Conversely , protrusions gradually lose connections as neighboring nodes become closer to opposing portions of the cell wall . This is enhanced by the model assumption that connections cannot be made across the cell to opposite walls from regions that are too convex ( i . e . in the lobes , Figure 3A , D ) . If the simulation is performed with anisotropic growth , the cellulose-microtubule connections are never stretched significantly beyond the LEC , and cells simply elongate , and lobes do not emerge ( Figure 3B , E ) . In other words , stress-based activation of connections induces indentations , coinciding with locations of ROP6 activity , which necessarily generate incipient lobes in adjacent portions of the cell-wall where ROP2 is localized , accentuating their outgrowth . Thus , although phrased in geometric terms , our model is consistent with both the antagonistic local molecular interactions of ROP2-ROP6 and the stress-based feedbacks proposed by Sampathkumar et al . ( 2014 ) . The main parameters of the model are the stiffness of the cell walls and the cellulose-microtubule connection springs , the target LEC , the angle within which connections can be made , and the convexity criteria for attachment to the opposing wall ( see Appendix Table 1 for parameter values ) . To examine the contribution of growth distribution to cell shape we varied growth anisotropy while all other model parameters remained constant ( Figure 3A–C ) . In this case , the emergence of puzzle vs . elongated cells depends only on the anisotropy of growth at the tissue scale , with puzzle cells appearing for isotropic growth , and elongated cells for anisotropic growth ( Video 1 , Video 2 ) . If the growth specified has a gradient of anisotropy at the tissue scale , a gradient of cell shapes from elongated to lobed is produced ( Video 3 ) . Similar gradients in cell shape are seen in A . thaliana leaves , where elongated cells cover the anisotropically growing midrib , whereas lobed cells adorn the adjacent isotropically growing leaf blade ( Figure 3C ) . To explore the effect of model parameters on cell morphology we performed a parameter space exploration using the simulation with isotropic growth as a reference ( Figure 3A ) . We varied isotropy within a range of 40–100% of the reference value and all other parameters within a range of at least 25–200% ( Figure 3—figure supplement 1 , Videos 5–10 ) . This exploration showed that when growth is anisotropic , there is no strict 'threshold' for the onset of lobing , but rather it is a continuous characteristic . This feature is preserved when the initial template and additional parameters are varied ( Figure 3—figure supplement 2 ) . Parameter variation also demonstrates that the model can generate a diverse range of plausible cell shapes , similar to those observed in nature ( e . g . Figure 3—figure supplement 2B 60% isotropy; which are reminiscent of epidermal cells in maize leaves ) . To validate the model , we confirmed in a FEM analysis that limiting the size of the LEC by creating lobes during growth reduces the cellular stress ( Figure 3F–G ) . This causes the maximum stress in simulated tissues to plateau , greatly reducing it compared to isodiametric cells of the same size ( Figure 3H ) . The model thus illustrates how a mechanism actively limiting the mechanical stress of cells by restricting large open areas ( LECs ) can lead to the formation of puzzle-shape cells in the context of isotropic growth . The model relies on cell-autonomous mechanical restriction of indentations through controlled cellulose deposition and does not require cell-cell signaling molecules to synchronize the indentations in one cell with the protrusions of its neighbor . Nonetheless , synergies exist between the mechanical and biochemical control of cell morphogenesis . In particular , the ROP6 in the indentation of one cell must coincide with ROP2 in the corresponding lobe of the neighboring cell . Although mobile biochemical signals cannot be ruled out ( Xu et al . , 2010 ) , our model predicts that this signal could be passed through the geometry of the cells via its effect on stress patterns or geometry , with indentations attracting microtubule-cellulose deposition and ROP6 , and lobes suppressing microtubules via the cell-autonomous co-repression of ROP2 and ROP6 . Our model predicts that puzzle cells should appear when cells stop dividing and tissue growth is not primarily in one direction . To test this prediction experimentally , we performed time-lapse confocal imaging on cotyledons ( n = 3 time-lapse series ) , which have a blade of roughly isodiametric shape , growing from 2 to 4 days after germination ( DAG ) . Epidermal cells of Arabidopis thaliana cotyledons begin to acquire a puzzle-shaped morphology roughly 2 DAG , whereas the organ achieves its characteristic round shape at approximately 3 DAG , long before reaching its final size ( Zhang et al . , 2011 ) . We used MorphoGraphX ( Barbier de Reuille et al . , 2015 ) to extract growth rates and directions , and these results confirm that the overall growth of cotyledons is isotropic as suggested by its round shape . To examine the correlation between growth anisotropy and lobeyness we pooled the data from the final time-point of our time-lapse series . We then extracted the largest 100 cells from this set ( i . e . those most likely to be affected by the stress-minimizing mechanism ) and found a significant correlation between growth anisotropy and lobeyness ( Pearson correlation coefficient r = −0 . 46 , p=0 . 6 × 10−6 ) . This supports our hypothesis that growth anisotropy and lobeyness are inversely related in the isotropically growing cotyledons of Arabidopsis ( see also Figure 4A , Figure 4—figure supplement 1C ) . In contrast to cotyledons , the Arabidopsis sepal is an elongated organ with epidermal cells that are either small and relatively isodiametric in shape , or large and elongated . Sepals initiate from a band of cells in the floral meristem , undergoing strongly anisotropic growth ( Hervieux et al . , 2016 ) which produces giant cells that are far less lobed than those of the cotyledon ( compare Figure 4—figure supplement 1A and C ) . Thus growth isotropy and final organ shape correlate with lobeyness in these two organs . Next we examined cases where genetic modifications changed growth anisotropy and overall organ shape . Sepals of the ftsh4 mutant show increased variability of organ shape ( Hong et al . , 2016 ) . In some samples , the growth is more isotropic than wild type , and cells of more isodiametrically shaped organs exhibit decreased growth anisotropy and increased lobeyness , and start to become puzzle shaped ( compare Figure 4—figure supplement 1A and B ) . The shift from anisotropic to isotropic growth in the sepal is thus correlated with a shift from elongated giant cells to puzzle-shaped cells . The opposite change in growth anisotropy and organ shape can be seen in plants overexpressing the LONGIFOLIA1 ( TRM2 , LNG1 ) gene . This causes an elongated cell and organ phenotype in A . thaliana cotyledons and leaves ( Lee et al . , 2006; Drevensek et al . , 2012 ) , consistent with effects of a related protein in rice grains ( Wang et al . , 2015 ) . We created transgenic plants where LNG1 is overexpressed under the CaMV 35S promoter ( p35S::LNG1 ) . Our T1 lines had phenotypes ranging from highly elongated cotyledons and leaves to wild type ( Figure 4C–E ) . Plants with the elongated phenotype grew more anisotropically than wild type and had epidermal cells with reduced lobeyness ( n = 3 time-lapse series for each genotype , Figure 4A–B and F–I ) . Thus the change in growth and organ shape from isodiametric to elongated correlated with a decrease in cell lobeyness . To further test the generality of the correlation between organ and cell shape , we examined fruit epidermal cells in a sample of 21 species from the Brassicaceae family ( full dataset shown in Hofhuis and Hay , 2017 ) . These fruit pods were either elongated siliques or short , rounded silicles and we only observed puzzle-shaped cells in silicles , not in siliques ( Figure 4J , K ) . This strict correspondence between fruit shape and puzzle-shaped epidermal cells fits the prediction of our model that puzzle shapes are required to allow cells to enlarge in isotropically growing tissues , but are not required in elongated organs . Our model predicts that plant cells regulate their shape to prevent their LEC , a proxy for stress , from becoming too large . To test this hypothesis , we imaged cells of young cotyledons at different stages of growth and tracked changes in cell and LEC area . We reasoned that if the cell area increases faster than LEC area , cells must have a mechanism to maintain a low LEC radius . We imaged 1 , 2 , 4 and 6 DAG seedlings , as within this time window we could qualitatively observe the most dramatic increase in cellular lobeyness . In the epidermal cells of 2 DAG seedlings , lobes were small or absent in most cells , while 6 days after germination most cells were puzzle-shaped ( Figure 5C ) . For each time point we imaged up to 10 plants and segmented several hundred cells from each plant using MorphoGraphX . We then pooled all cells from each timepoint and calculated average cell area and LEC area for the largest 20% of cells ( Figure 5A , Figure 5—source data 1 ) . We compared these values to the case where cells are perfectly isodiametric ( i . e . circles ) so that the cell area and LEC area are equal ( Figure 5A , red line ) . Our results show that as the cotyledon grows , the ratio of average LEC area to average cell area increases slower than when the cell is circular . Consequently , as organ development progresses , cell area increases faster than LEC area , consistent with the idea that increased lobeyness allows surface area to increase faster than the magnitude of stress ( Figure 5A , blue signs ) . Our model and experiments show that a mechanism , likely cortical-microtubule dependent , generates puzzle shapes to limit stress in large cells when tissue growth is isotropic . It is commonly observed that the periclinal cell walls slightly bulge out in healthy , turgid cells . However , if stress is indeed a developmental constraint , then when cells grow isotropically without this mechanism , they should bulge excessively , reach their rupture point and burst . The shoot apex of Arabidopsis grows isotropically in areas without lateral organs ( Kwiatkowska and Dumais , 2003; Kierzkowski et al . , 2012 ) , with the cells presumably managing their mechanical stress by employing cell division to remain small . In plants grown with auxin transport inhibitor 1-N-naphtylphtalamic acid ( NPA ) , the shoot apex is unable to produce lateral organs , and is uniformly covered in small rapidly dividing cells of isodiametric shape ( Reinhardt et al . , 2000 ) . Treating these meristems with oryzalin , a chemical compound that depolymerizes cortical microtubules , blocks cell division and anisotropic growth restriction , preventing the formation of puzzle shapes . It has been shown in Arabidopsis hypocotyls that oryzalin treatment changes the trajectory of cellulose microfibril-producing molecules ( CESA ) , as there is no organized cortical microtubule array to follow , but does not appear to change the rate of cellulose production ( Chan et al . , 2010 ) . As such , although oryzalin makes cell walls mechanically isotropic by preventing the directionally organized deposition of cellulose , it does not necessarily reduce the overall deposition of cellulose , although this cannot be precluded . Cells of shoot apices in these conditions do not divide , but continue to grow developing large , isodiametric shapes that tend to balloon out ( Hamant et al . , 2008; Corson et al . , 2009; Grandjean , 2004 ) . After treating naked meristems of NPA-grown seedlings with oryzalin ( five biological replicates ) , 20 displayed full microtubule depolymerization following oryzalin treatment ( as assessed by the absence of cell division ) . In those 20 samples , we could see cell bursting in the latest time points of 13 samples , out of which 10 displayed bursting cells located in the flank of the meristem , where cells were substantially larger ( Figure 4L ) . Although it cannot be completely excluded that these lateral cells , under these experimental conditions , have different wall properties , the most parsimonious explanation is that their cell walls could not withstand the increasing mechanical stress induced by the isotropic expansion . This provides direct experimental support for the proposition that large isodiametrically shaped cells are not viable due to the high stresses on their walls . Previous reports have shown that lobe formation in pavement cells is compromised in spike1 ( spk1 ) mutants ( Qiu et al . , 2002 ) . The SPIKE1 protein is a guanine nucleotide exchange factor ( GEF ) and is required for the production of the active , GTP-bound form of ROP proteins molecular switches that deliver signals to downstream components . SPIKE1 regulates actin polymerization via WAVE and ARP2/3 complexes ( Basu et al . , 2008 ) . Furthermore , it activates ROP2 , ROP4 and ROP6 , thereby promoting isotropic cell expansion ( Ren et al . , 2016 ) . Mutant plants have a number of severe phenotypes including reduced trichome branching , altered organ shape and increased sensitivity to low humidity environments . Epidermal cells of spk1 plants have altered shape , with lobes either small or absent , and compared to wild type , their overall cell shape is much less complicated . Furthermore , the epidermis suffers from defects in cell-cell adhesion , which have been reported to result in gaps between cells that are clearly visible in the cotyledon epidermis from approximately 5 DAG on ( Qiu et al . , 2002; Ren et al . , 2016 ) . It has been reported that spk1 cotyledons are narrower , but not longer than wild type cotyledons ( Qiu et al . , 2002 ) and spk1 petals display an increase in growth anisotropy at late stages of development , after the general shape of the organ has been established ( Ren et al . , 2016 ) . In spk1 , epidermal cells of the cotyledons do not have puzzle-shaped forms ( Figure 5B , D , E , Figure 5—figure supplement 1B ) , even though the tissue growth isotropy is similar to wild type plants ( n = 3 time-lapse series , Figure 4B , Figure 5—figure supplement 1A – cellular growth anisotropy shows a small statistical difference in that spk1 grows more anisotropically than wild type ) . Given our hypothesis that lobes function to reduce mechanical stress ( LEC size ) during isotropic growth , we tested if LEC was higher in the simple-shaped cells of spk1 mutant than in the puzzle-shaped cells of wild type . In our time-lapse experiment , even though lobeyness is greatly reduced in spk1 , LEC radius in the final time point is comparable to wild type ( Figure 5B , Figure 5—figure supplement 1C ) . Our FEM simulations revealed that cellular stresses in wild type and spk1 cells are similar and scale with LEC ( compare Figure 1C and Figure 5—figure supplement 2 ) . We also performed the same analysis as for wild type , imaging spk1 cotyledons 1 , 2 , 4 and 6 DAG and measuring cell area and LEC area ( Figure 5C , D ) . This revealed a similar trend to that observed in the wild type , with cell area increasing faster than LEC area ( Figure 5A ) during the course of organ development . At the same time , mean average cell area in spk1 remained similar or lower than in wild type until 6 DAG ( Figure 5—figure supplement 3 ) . Cells of the spk1 mutant keep LEC low and overall organ growth remains isotropic . Similar LEC size in mutant and wild type suggests that LEC acts as a threshold for stress based cell shape modification . However , instead of forming lobes , the spk1 cells themselves seem to interdigitate generating worm-like shapes . It is possible that this strategy is insufficient , as holes appear between cells in the growing epidermis of cotyledons ( Figure 5E ) , which may be due to increased mechanical stress . However , since holes are already present in cotyledons at 1 DAG it is more likely that they result from direct disruption of the molecular process regulating cellular adhesion , such as actin-driven pectin delivery to cell walls , causing defects prior to the stress-based shape patterning where the final cell shape is established . The spk1 mutant is unable to make lobes because it fails to activate ROPs which interact with effector proteins to mediate cytoskeletal rearrangements and cell shape ( Basu et al . , 2008 ) . In our model framework , ROP2 activity would preclude connections where walls have high curvature , thus preventing connections from penetrating lobes . Apart from removing this assumption from the model , we increased the stiffness of connections and the cell-wall , and decreased the frequency at which connections were reset , to account for defects in ROP-mediated cytoskeletal rearrangement . These three changes to the initial simulation allowed us to reproduce the spk1 phenotype ( Figure 5F , Video 4 ) . This suggests that creating interdigitated worm-shaped cells provides an alternate strategy to cover an isotropically growing tissue , although possibly not as efficient in reducing stress as lobe formation . Our data indicates that the stress control mechanism we propose is conserved between various organs in A . thaliana , and within the fruit of Brassicaceae ( Figure 4J , K ) . This raises the question as to how broadly this mechanism is conserved , with large cell size and isotropic growth correlating with puzzle-shaped cells . Under this assumption , two geometric strategies are possible for cell expansion in isotropically growing organs without requiring excessively thick walls: ( 1 ) keeping cell size small by frequent divisions or ( 2 ) creating larger , puzzle-shaped cells . We measured cell area , LEC area and lobeyness in the adaxial epidermis of 19 unrelated plant species including trees , shrubs and herbs . A statistical analysis revealed that there was a positive correlation between cell size and lobeyness for each species ( Figure 6A–C ) . Species with the largest average lobeyness also tended to have the largest cells ( and vice-versa , Figure 6A–B ) . For average values of lobeyness and cell area of each species ( including sample size ) , see Figure 6—source data 1 . Pearson correlation coefficients ranged from 0 . 23 for Catharantus roseus to 0 . 94 for Solanum nigrum ( Figure 6D ) . When pooling cells of all species together , the Pearson correlation coefficient was 0 . 64 . Lobe formation is therefore more likely to be observed in big cells rather than small cells , which is intuitive if one considers cell division ( where cell size remains low ) as an alternative strategy to limit LEC size and cell wall stress . This suggests our hypothesis , that plants create puzzle-shaped cells in order to reduce stress in large isotropically growing cells , may be conserved among many plant species .
We propose that the puzzle shaped cells seen in the epidermis of many plant species emerge from a mechanism that evolved to limit mechanical stress in tissues that grow isotropically , such as the epidermis of leaves and cotyledons . FEM analysis of 3D pressurized cells shows that cell shape influences the direction and magnitude of mechanical stress exerted on the cell wall . When an epidermal cell becomes large in two directions ( i . e . has a large open area ) , stress is greatly increased . In stems , roots and siliques , growth is strongly anisotropic , and cells can simply elongate . This is , however , not possible for isodiametric organs such as broad leaves , cotyledons and silicle fruit pods . We propose that puzzle-shaped cells in the epidermis of more isodiametric plant organs provide a means to avoid large open areas in the cell and the high stresses that they induce . Since turgor pressure inside cells is high , minimizing mechanical stress by shape regulation may be a way of reducing the resources required to reinforce the cell wall and at the same time maintaining its structural integrity during growth . Although it is possible that the interlocking puzzle-shaped cells have a role in strengthening the epidermal cell layer ( Glover , 2000; Jacques et al . , 2014 ) , our experimental data shows that growth anisotropy correlates with cell shape , a prediction that does not appear to readily follow from this alternative hypothesis . Organs displaying isotropic planar growth have puzzle shaped cells while anisotropically growing organs have more elongated cells with fewer lobes . Genetic perturbations that modify growth anisotropy in either direction result in the predicted changes in cell shape . In the Arabidopsis thaliana cotyledon , a p35S::LNG1 overexpression line changes growth from isotropic to anisotropic , and cell shapes become more elongated with fewer lobes . Conversely , in sepals of the ftsh4 mutant , growth is switched from anisotropic to more isotropic , and the elongated giant cells become more puzzle shaped . Our hypothesis is also consistent with the mild lobing of pavement cells in grass leaves , which often have strongly anisotropic growth ( Sylvester et al . , 2001 ) Although studies often focus on anisotropic growth at the cellular level when analyzing puzzle cell development ( Armour et al . , 2015 ) , our hypothesis suggests that isotropic growth at the tissue level is a primary driver of cell shape . As a tissue grows the stress increases , and microtubules align to direct cellulose deposition to resist the stress . This causes small indentations in the cell , which transfers more stress to them , further recruiting microtubules and more cellulose deposition . The process generates a local activation feedback of cell shape on growth via the mechanical stresses that are induced by that shape . A geometric-mechanical simulation model of these processes confirms that the hypothesis is plausible , and the model is able to produce puzzle-shaped cells from a few simple assumptions . Since we use a geometric proxy for stress ( LEC ) , the possibility that the cells sense their geometry through chemical means is also compatible with the model . Our model explains the gradual emergence of lobed cells from polygons resembling meristematic cells , providing an explanation for the till now enigmatic morphogenesis of these distinctive cells . The model suggests that the main driver of the complex puzzle shape comes from the restriction of growth in the indentations , rather than the promotion of growth in the protrusions . It also predicts that the puzzle cell shape is triggered by isotropic growth , and that puzzle cell morphogenesis may not require any signaling molecules to coordinate a protrusion in one cell with the corresponding indentation of its neighbor . Nonetheless , the model does not preclude a role for inter-cellular signaling , which could reinforce patterns produced by geometry sensing or facilitate the initial steps of lobing ( Majda et al . , 2017 ) . The mechanism also predicts that spatial differences in cell wall material properties , corresponding to lobes and indentations , should appear in periclinal cell walls as organized cellulose distributions appear , consistent with observations that cellulose-bundles accumulate in high-stress indentations ( Sampathkumar et al . , 2014 ) . Spatial differences in stiffness corresponding to incipient lobes and indentations have recently been measured in cross-sections of anticlinal cell walls ( Majda et al . , 2017 ) . Although the direction of the measurements ( z-direction ) is not explicitly represented in our model , it is nevertheless consistent with the idea that material properties in adjacent cell walls would be expected to be different in the lobe side vs the indentation side . The modeling results of Majda et al . , 2017 suggest these mechanical differences drive the formation of small lobes and indentations when the anticlinal walls are placed under tension by turgor pressure . Although this cannot explain deep lobes and indentations or lobes on lobes that emerge in maturing puzzle cells , the idea that both anticlinal cell walls and periclinal cell walls play a coordinated role in puzzle shape morphogenesis ( Belteton et al . , 2018 ) is appealing , and warrants further study using FEM models of pavement cell morphogenesis that represent the entire 3D geometry of cells ( c . f . Bidhendi and Geitmann , 2018 ) . Our model is also consistent with the functions attributed to the main molecular players that have been reported to influence puzzle cell formation , the ROP family of GTP-ases . The elaboration of puzzle shape is influenced by two antagonistic molecular pathways . On the convex side ( protrusion ) , ROP2 and ROP4 inactivate the microtubule-associated protein RIC1 , thereby suppressing the formation of microtubule arrays , and activate RIC4 which enhances the assembly of actin microfibrils . This was proposed to result in growth promotion ( Fu et al . , 2005 ) . On the concave side ( indentation ) , ROP6 activates RIC1 and katanin , promoting the formation of bundled microtubule arrays that restrict growth ( Fu et al . , 2009; Lin et al . , 2013 ) . The theory of coordinated outgrowth and restriction has struggled to provide an explanation as to how protrusions and indentations are coordinated between cells . As ROP2 and ROP6 were believed to be activated by auxin ( Xu et al . , 2010 ) , it was suggested that auxin could act as the mobile signal underlying in this coordination ( reviewed in Chen et al . , 2015 ) via ABP1 , however this scenario seems unlikely given recent genetic evidence that ABP1 alone does not have quantifiable effects on auxin response ( Gao et al . , 2015 ) . Nonetheless , our model is also consistent with the idea that ROP6 is a part of the stress sensing mechanism , and that stress ( or strain ) is the trigger for localized ROP6 accumulation . Currently , the molecular mechanism for how stress ( or strain ) could be sensed and its relationship to the ROPs is unknown , although microtubules have been proposed to respond to stress in planta ( Hejnowicz et al . , 2000; Hamant et al . , 2008 ) . Since stress is closely related to shape in pressurized plant cells , a curvature sensing mechanism could be involved ( Higaki et al . , 2016 ) , similar to that proposed for villi patterning during gut morphogenesis ( Shyer et al . , 2015 ) . Simulations have shown that a ROP2-ROP6 co-repression network can indeed partition a cell in discrete domains of ROP2 and ROP6 expression ( Abley et al . , 2013 ) . Our data suggest that this intracellular partitioning network works in concert with a mechanical or geometric signal , transmitted by the shape of the cell itself .
Plantlets were grown on 1/2 MS medium in long day conditions as previously described in Vlad et al . ( 2014 ) . Young cotyledons ( 2–6 days after germination , DAG ) were imaged using the Leica SP8 microscope with 20x ( HCX APO , numerical aperture 0 . 8 ) and 40x ( HCX APO , n . a . 0 . 5 ) long working distance , water immersion objectives . Col-0 and p35S::LNG1 plants contained a plasma membrane-localized fluorescent marker pUBQ10::myrYFP previously described in Hervieux et al . , 2016 and fluorescent signal was collected from 519 to 550 nm emission spectrum using 514 nm laser for excitation . Sepals were imaged as previously described in Hong et al . , 2016 and Hervieux et al . , 2016 . For spk1 plants and corresponding Col-0 controls , cell walls were stained with propidium iodide and fluorescent signal was collected from 605 to 644 nm emission spectrum using 488 nm laser for excitation . spk1 homozygous mutant cotyledons were chosen for time-lapse imaging 2 DAG based on their shape , which was more elongated compared to wild type cotyledons of comparable age . The LNG1 gene full-length CDS was PCR amplified and cloned into the pENTR/D-TOPO vector ( Invitrogen ) as described in the manual , using primer pair 5’-CACCATGTCGGCGAAGCTTTTGT ATAACT-3’ and 5’-GAACATAAGAAAGGGGTTCAGAGA-3’ . The resultant vector was LR recombined into the gateway vector pK7WG2 ( Karimi et al . , 2002 ) to generate the final construct p35S::LNG1 . The intermediate and final constructs were verified by sequencing . The p35S::LNG1 construct was individually transformed into Col-0 plants by Agrobacterium-mediated floral dipping . T1 seeds were sown on Kanamycin-containing medium and transferred into soil approximately 2 weeks after germination . Fruit shape was classified as an elongated silique or a silicle ( if the length was less than three times the width of the fruit ) for 21 species in the Brassicaceae family . Exocarp cells were stained with propidium iodide , imaged by CLSM ( as described in section 'Live imaging of cotyledons' ) and cell outlines extracted using MorphoGraphX . Arabidopsis seeds were sown on a 1/2 MS medium . 1 , 2 , 4 and 6 days after germination ( DAG ) 5–10 seedlings were taken out of the medium and imaged . Confocal stacks were processed in MorphoGraphX ( Barbier de Reuille et al . , 2015 ) . Cell area and LEC radius were calculated for each cell in each sample . For average values displayed in Figure 5A ( scatter plot ) , only the largest 20% of cells in each sample were considered , to eliminate stomata and small cells in the stomatal lineage . The p35S::LTI6b-GFP Arabidopsis lines have been described previously ( Cutler et al . , 2000 ) and were grown in tall petri dishes on a solid custom-made Duchefa ‘Arabidopsis’ medium ( DU0742 . 0025 , Duchefa Biochemie ) supplemented with 10 μM of NPA ( N- ( 1-naphthyl ) phthalamic acid ) as described in Hamant et al . ( 2008 ) . As soon as naked inflorescences had formed , the plants were transferred to a medium without inhibitor . First images ( T = 0 hr ) were taken 1 day after the plants were taken off the drug . The samples were then immersed for 3 hr in 20 μg/ml oryzalin at T0h , T24h and T48h , as described in Hamant et al . ( 2008 ) . Images were acquired using a Leica SP8 confocal microscope . GFP excitation was performed using a 488 nm solid-state laser and fluorescence was detected at 495–535 nm . We employed the Kolmogorov-Smirnov ( K-S ) test to statistically test if the distributions of growth anisotropy , lobeyness and LEC radius between WT and spk1 were the same . We used heat maps created in MorphoGraphX on data displayed in Figure 5B ( final time point ) to extract the values for each segmented cell . In the K-S test , the cumulative distribution of the corresponding quantity is first constructed as in Figure 5—figure supplement 1 . The test statistic in the K-S test is the maximum ( vertical ) distance between the two cumulative distributions from WT and spk1 . A large vertical distance signifies that the null hypothesis , i . e . , the distributions of WT and spk1 are the same , is more likely to be rejected . The significance level of 0 . 05 is used in our analysis and we statistically conclude that the two distributions are different if the p-value<0 . 05 . The seeds of a heterozygous spk1 T-DNA insertion line ( SALK 125206 ) were purchased from Nottingham Arabidopsis Stock Centre . Segregating individuals were genotyped according to instructions provided by the SALK institute ( http://signal . salk . edu/ ) using primers 5’- GATTTCAGTCTCTCACCGCAG-3’ and 5’-ATGGTCGACTCCACATTTCTG-3’ for detecting individuals with no T-DNA insertion and primers 5’-ATTTTGCCGATTTCGGAAC-3’ ( recommended by SALK ) and 5’-ATGGTCGACTCCACATTTCTG-3’ for detecting individuals containing the T-DNA insertion ( mutant plants ) . Leaf surface impressions were taken from the adaxial side using transparent nail enamel ( Revlon ) . The impressions were viewed under the differential interference contrast ( DIC ) mode of an Olympus BX52a upright microscope ( Olympus , Japan ) and imaged using a CapturePro CCD camera ( Jenoptik , Germany ) . Images were loaded into MorphoGraphX and cell outlines were projected on a flat ( 2D ) mesh . The mesh was segmented , cell area , lobeyness and LEC radius were calculated for all segmented cells . The Lobeyness and Largest Empty Circle ( LEC ) measures are calculated using custom plugins developed for MorphoGraphX ( Barbier de Reuille et al . , 2015 ) . These measures are applied to 2D cell contours , obtained by projecting each 3D cell-contour extracted using MorphoGraphX on a local plane . For this purpose , the plane minimizing the loss of variance following projection is used . This plane is obtained from Principal Component Analysis ( PCA ) of the contour points , and is defined as the plane orthogonal to the third principal component ( i . e . the direction of minimal variance ) passing through the mean of the contour . Lobeyness captures the deviation of 2D cell contours from the convex polygonal forms typical of young undifferentiated cells . The measure is computed by taking the ratio of the cell’s perimeter to that of its convex hull ( the smallest convex shape containing the cell ) , and is the inverse of the convexity measure used in Wu et al . , 2016 . Lobeyness takes a value of 1 for convex shapes and increases with contour complexity . This provides a translation , scale and rotation invariant measure of contour complexity and overall pavement cell lobation . The LEC for each cell is computed using the Delaunay triangulation of the contour positions . The cell contour defines a bounded region of the plane , and the largest empty circle within this region must be either the circumscribed circle of a triangle in the Delaunay triangulation , or a point on the boundary ( Toussaint , 1983 ) . Thus , the LEC for each cell is calculated by: As the cell-contours extracted from MorphoGraphX are densely sampled compared to the size of cells , the possibility that the largest empty space corresponds to a point on the boundary is ignored .
The shape and function of plant cells are often highly interdependent . The puzzle-shaped cells that appear in the epidermis of many plants are a striking example of a complex cell shape , however their functional benefit has remained elusive . We propose that these intricate forms provide an effective strategy to reduce mechanical stress in the cell wall of the epidermis . When tissue-level growth is isotropic , we hypothesize that lobes emerge at the cellular level to prevent formation of large isodiametric cells that would bulge under the stress produced by turgor pressure . Data from various plant organs and species support the relationship between lobes and growth isotropy , which we test with mutants where growth direction is perturbed . Using simulation models we show that a mechanism actively regulating cellular stress plausibly reproduces the development of epidermal cell shape . Together , our results suggest that mechanical stress is a key driver of cell-shape morphogenesis .
Cells with complex interlocking shapes , similar to pieces of a jigsaw puzzle , cover the surface of many leaves . Why do these curious shapes form , and what benefit do they provide to the plant ? Plant cells are like small balloons surrounded by a strong cell wall . Their internal pressure can be higher than the pressure in a car tire . It is this pressure that gives non-woody plant tissue its shape . Take away the pressure , and the plant wilts . The pressure inside a cell creates a lot of mechanical stress on the epidermal cell walls – those that make up the surface of the plant . The extent of the stress depends on the shape and size of the cells; for example , large cells bulge out and experience more stress than small cells . This could mean that the shape of puzzle cells is an adaptation used by plants to reduce the stress on their surface . To investigate this possibility , Sapala , Runions et al . developed a computer simulation that models how a plant grows and re-creates a variety of realistic puzzle cell shapes . The simulations show that ‘paving’ the leaf surface with puzzle shaped cells instead of more regularly shaped cells reduces the stress in the epidermal cell walls . Counterintuitively , the simulations also show that complex puzzle shapes develop in parts of the plant that grow isotropically ( uniformly in all directions ) , such as leaves . If a plant organ grows mostly in one direction , like in a root or stem , long thin cells are sufficient to reduce the stress on the epidermal cell wall . Sapala , Runions et al . tested this idea by analyzing the shape of organs and cells in many plant species and by genetically modifying growth directions in Arabidopsis thaliana plants . This confirmed that puzzle cell shape is related to both organ shape and how isotropically the plant grows . It had previously been proposed that mobile chemical signals passed between cells coordinate the process by which a lobe in one puzzle cell matches an indentation in its neighbor . However , the model developed by Sapala , Runions et al . does not require such chemical signaling . Instead , mechanical forces and the shape the puzzle cells themselves may transmit this information . Mechanical forces are known to have important effects on the shape and behavior of cells from other species too . For example , animal cells can develop into different cell types depending on the stiffness of the surface they are placed on . Now that Sapala , Runions et al . have highlighted that plant cell shapes also adapt to mechanical forces , further research is needed to uncover how these forces are sensed .