Feeling Stressed or Strained? A Biophysical Model for Cell Wall Mechanosensing in Plants

Mechanical signals have recently emerged as a major cue in plant morphogenesis, notably influencing cytoskeleton organization, gene expression, protein polarity, or cell division. Although many putative mechanosensing proteins have been identified, it is unclear what mechanical cue they might sense and how this would occur. Here we briefly explain the notions of mechanical stress and strain. We present the challenges to understand their sensing by plants, focusing on the cell wall and the plasma membrane, and we review putative mechanosensing structures. We propose minimal biophysical models of mechanosensing, revealing the modes of mechanosensing according to mechanosensor lifetime, threshold force for mechanosensor dissociation, and type of association between the mechanosensor and the cell wall, as the sensor may be associated to a major load-bearing structure such as cellulose or to a minor load-bearing structure such as pectins or the plasma membrane. Permanent strain, permanent expansion, and relatively slow variations thereof are sensed in all cases; variations of stress are sensed in all cases; permanent stress is sensed only in the following specific cases: sensors associated to minor load-bearing structures slowly relaxing in a growing wall, long-lived sensors with high dissociation force and associated to major-load-bearing structures, and sensors with low dissociation force associated to major-load-baring structures behaving elastically. We also find that all sensors respond to variations in the composition or the mechanical properties of the cell wall. The level of sensing is modulated by the properties of all of mechanosensor, cell wall components, and plasma membrane. Although our models are minimal and not fully realistic, our results yield a framework to start investigating the possible functions of putative mechanosensors.

Emergence of robust patterns from local rules during plant development

The formation of spatial and temporal patterns is an essential component of organismal development. Patterns can be observed on every level from subcellular to organismal and may emerge from local rules that correspond to the interactions between molecules, cells, or tissues. The emergence of robust patterns may seem in contradiction with the prominent heterogeneity at subcellular and cellular scales, however it has become increasingly clear that heterogeneity can be instrumental for pattern formation. Here we review recent examples in plant development, involving genetic regulation, cell arrangement, growth and signal gradient. We discuss how patterns emerge from local rules, whether heterogeneity is stochastic or can be patterned, and whether stochastic noise is amplified or requires filtering for robust patterns to be achieved. We also stress the importance of modelling in investigating such questions.

Evidence for the Regulation of Gynoecium Morphogenesis by ETTIN via Cell Wall Dynamics

ETTIN (ETT) is an atypical member of the AUXIN RESPONSE FACTOR family of transcription factors that plays a crucial role in tissue patterning in the Arabidopsis (Arabidopsis thaliana) gynoecium. Though recent insights have provided valuable information on ETT's interactions with other components of auxin signaling, the biophysical mechanisms linking ETT to its ultimate effects on gynoecium morphology were until now unknown. Here, using techniques to assess cell-wall dynamics during gynoecium growth and development, we provide a coherent body of evidence to support a model in which ETT controls the elongation of the valve tissues of the gynoecium through the positive regulation of pectin methylesterase (PME) activity in the cell wall. This increase in PME activity results in an increase in the level of demethylesterified pectins and a consequent reduction in cell wall stiffness, leading to elongation of the valves. Though similar biophysical mechanisms have been shown to act in the stem apical meristem, leading to the expansion of organ primordia, our findings demonstrate that regulation of cell wall stiffness through the covalent modification of pectin also contributes to tissue patterning within a developing plant organ.

Heterogeneity and Robustness in Plant Morphogenesis: From Cells to Organs

Development is remarkably reproducible, producing organs with the same size, shape, and function repeatedly from individual to individual. For example, every flower on the Antirrhinum stalk has the same snapping dragon mouth. This reproducibility has allowed taxonomists to classify plants and animals according to their morphology. Yet these reproducible organs are composed of highly variable cells. For example, neighboring cells grow at different rates in Arabidopsis leaves, sepals, and shoot apical meristems. This cellular variability occurs in normal, wild-type organisms, indicating that cellular heterogeneity (or diversity in a characteristic such as growth rate) is either actively maintained or, at a minimum, not entirely suppressed. In fact, cellular heterogeneity can contribute to producing invariant organs. Here, we focus on how plant organs are reproducibly created during development from these highly variable cells.

A tension-adhesion feedback loop in plant epidermis

Mechanical forces have emerged as coordinating signals for most cell functions. Yet, because forces are invisible, mapping tensile stress patterns in tissues remains a major challenge in all kingdoms. Here we take advantage of the adhesion defects in the Arabidopsis mutant quasimodo1 (qua1) to deduce stress patterns in tissues. By reducing the water potential and epidermal tension in planta, we rescued the adhesion defects in qua1, formally associating gaping and tensile stress patterns in the mutant. Using suboptimal water potential conditions, we revealed the relative contributions of shape- and growth-derived stress in prescribing maximal tension directions in aerial tissues. Consistently, the tension patterns deduced from the gaping patterns in qua1 matched the pattern of cortical microtubules, which are thought to align with maximal tension, in wild-type organs. Conversely, loss of epidermis continuity in the qua1 mutant hampered supracellular microtubule alignments, revealing that coordination through tensile stress requires cell-cell adhesion.

The parts of a plant that protrude from the ground are constantly shaken by the wind, applying forces to the plant that it must be able to resist. Indeed, mechanical forces are crucial for the development, growth and life of all organisms and can trigger certain behaviours or the production of particular molecules: for example, forces that bend a plant trigger gene activity that ultimately makes the stem more rigid.

Mechanical forces can also originate from inside the organism. For example, the epidermal cells that cover the surface of a plant are placed under tension by the cells in the underlying layers of the plant as they grow and expand. The exact pattern of forces in the plant epidermis was not known because they cannot be directly seen, although scientists have tried to map them using theoretical and computational modeling.

A mutant form of the Arabidopsis plant is unable to produce some of the molecules that allow epidermal cells to adhere to each other. Verger et al. placed the mutants in different growth conditions that lowered the pressure inside the plant, and consequently reduced the tension on the epidermal cells. This partly restored the ability of epidermal cells to adhere to each other, although gaps remained between cells in regions of the plant that have been predicted to be under high levels of tension. Verger et al. could therefore use the patterns of the gaps to map the forces across the epidermis, opening the path for the study of the role of these forces in plant development.

Further experiments showed that cell adhesion defects prevent the epidermal cells from coordinating how they respond to mechanical forces. There is therefore a feedback loop in the plant epidermis: cell-cell connections transmit tension across the epidermis, and, in turn, tension is perceived by the cells to alter the strength of those connections.

The results presented by Verger et al. suggest that plants use tension to monitor the adhesion in the cell layer that forms an interface with the environment. Other organisms may use similar processes; this theory is supported by the fact that sheets of animal cells use proteins that are involved in both cell-cell adhesion and the detection of tension. The next challenge is to analyse how tension in the epidermis affects developmental processes and how a plant responds to its environment.

Elongation and shape changes in organisms with cell walls: A dialogue between experiments and models

The generation of anisotropic shapes occurs during morphogenesis of almost all organisms. With the recent renewal of the interest in mechanical aspects of morphogenesis, it has become clear that mechanics contributes to anisotropic forms in a subtle interaction with various molecular actors. Here, we consider plants, fungi, oomycetes, and bacteria, and we review the mechanisms by which elongated shapes are generated and maintained. We focus on theoretical models of the interplay between growth and mechanics, in relation with experimental data, and discuss how models may help us improve our understanding of the underlying biological mechanisms.

Clones of cells switch from reduction to enhancement of size variability in Arabidopsis sepals

Organs form with remarkably consistent sizes and shapes during development, whereas a high variability in growth is observed at the cell level. Given this contrast, it is unclear how such consistency in organ scale can emerge from cellular behavior. Here, we examine an intermediate scale, the growth of clones of cells in Arabidopsis sepals. Each clone consists of the progeny of a single progenitor cell. At early stages, we find that clones derived from a small progenitor cell grow faster than those derived from a large progenitor cell. This results in a reduction in clone size variability, a phenomenon we refer to as size uniformization. By contrast, at later stages of clone growth, clones change their growth pattern to enhance size variability, when clones derived from larger progenitor cells grow faster than those derived from smaller progenitor cells. Finally, we find that, at early stages, fast growing clones exhibit greater cell growth heterogeneity. Thus, cellular variability in growth might contribute to a decrease in the variability of clones throughout the sepal.

Summary: Growth analyses of Arabidopsis sepals identify a tipping point in organ development, at which clones of cells change their growth pattern from size uniformization to size variability enhancement.

Virus mutations and their impact on vaccination against infectious bursal disease (Gumboro disease)

Infectious bursal disease (also known as Gumboro disease) is an immunosuppressive viral disease specific to chickens. In spite of all the information amassed on the antigenic and immunological characteristics of the virus, the disease has not yet been brought fully under control. It is still prevalent in properly vaccinated flocks carrying specific antibodies at levels normally high enough to prevent the disease. Common causes apart, failure of vaccination against infectious bursal disease is associated mainly with early vaccination in flocks of unknown immune status and with the evolution of viruses circulating in the field, leading to antigenic drift and a sharp rise in pathogenicity. Various highly sensitive molecular techniques have clarified the viral determinants of antigenicity and pathogenicity of the infectious bursal disease virus. However, these markers are not universally recognised and tend to be considered as evolutionary markers. Antigenic variants of the infectious bursal disease virus possess modified neutralising epitopes that allow them to evade the action of maternally-derived or vaccine-induced antibodies. Autogenous or multivalent vaccines are required to control antigenic variants in areas where classical and variant virus strains coexist. Pathotypic variants (very virulent viruses) remain antigenically related to classical viruses. The difficulty in controlling pathotypic variants is linked to the difficulty of eliciting an early immune response, because of the risk of the vaccine virus being neutralised by maternal antibodies. Mathematical calculation of the optimal vaccination time and the use of vaccines resistant to maternally-derived antibodies have improved the control of very virulent viruses.

Variations in basement membrane mechanics are linked to epithelial morphogenesis

The regulation of morphogenesis by the basement membrane (BM) may rely on changes in its mechanical properties. To test this, we developed an atomic force microscopy-based method to measure BM mechanical stiffness during two key processes in Drosophila ovarian follicle development. First, follicle elongation depends on epithelial cells that collectively migrate, secreting BM fibrils perpendicularly to the anteroposterior axis. Our data show that BM stiffness increases during this migration and that fibril incorporation enhances BM stiffness. In addition, stiffness heterogeneity, due to oriented fibrils, is important for egg elongation. Second, epithelial cells change their shape from cuboidal to either squamous or columnar. We prove that BM softens around the squamous cells and that this softening depends on the TGFβ pathway. We also demonstrate that interactions between BM constituents are necessary for cell flattening. Altogether, these results show that BM mechanical properties are modified during development and that, in turn, such mechanical modifications influence both cell and tissue shapes.

Extracting Subcellular Fibrillar Alignment with Error Estimation: Application to Microtubules

The order and orientation of cortical microtubule (CMT) arrays and their dynamics play an essential role in plant morphogenesis. To extract detailed CMT alignment structures in an objective, local, and accurate way, we propose an error-based extraction method that applies to general fluorescence intensity data on three-dimensional cell surfaces. Building on previous techniques to quantify alignments, our method can determine the statistical error for specific local regions, or the minimal scales of local regions for a desired accuracy goal. After validating our method with synthetic images with known alignments, we demonstrate the ability of our method to quantify subcellular CMT alignments on images with microtubules marked with green fluorescent protein in various cell types. Our method could also be applied to detect alignment structures in other fibrillar elements, such as actin filaments, cellulose, and collagen.

Segmentation of 3D images of plant tissues at multiple scales using the level set method

BACKGROUND

Developmental biology has made great strides in recent years towards the quantification of cellular properties during development. This requires tissues to be imaged and segmented to generate computerised versions that can be easily analysed. In this context, one of the principal technical challenges remains the faithful detection of cellular contours, principally due to variations in image intensity throughout the tissue. Watershed segmentation methods are especially vulnerable to these variations, generating multiple errors due notably to the incorrect detection of the outer surface of the tissue.

RESULTS

We use the level set method (LSM) to improve the accuracy of the watershed segmentation in different ways. First, we detect the outer surface of the tissue, reducing the impact of low and variable contrast at the surface during imaging. Second, we demonstrate a new edge function for a level set, based on second order derivatives of the image, to segment individual cells. Finally, we also show that the LSM can be used to segment nuclei within the tissue.

CONCLUSION

The watershed segmentation of the outer cell layer is demonstrably improved when coupled with the LSM-based surface detection step. The tool can also be used to improve watershed segmentation at cell-scale, as well as to segment nuclei within a tissue. The improved segmentation increases the quality of analysis, and the surface detected by our algorithm may be used to calculate local curvature or adapted for other uses, such as mathematical simulations.

The Developmental Regulator SEEDSTICK Controls Structural and Mechanical Properties of the Arabidopsis Seed Coat

Although many transcription factors involved in cell wall morphogenesis have been identified and studied, it is still unknown how genetic and molecular regulation of cell wall biosynthesis is integrated into developmental programs. We demonstrate by molecular genetic studies that SEEDSTICK (STK), a transcription factor controlling ovule and seed integument identity, directly regulates PMEI6 and other genes involved in the biogenesis of the cellulose-pectin matrix of the cell wall. Based on atomic force microscopy, immunocytochemistry, and chemical analyses, we propose that structural modifications of the cell wall matrix in the stk mutant contribute to defects in mucilage release and seed germination under water-stress conditions. Our studies reveal a molecular network controlled by STK that regulates cell wall properties of the seed coat, demonstrating that developmental regulators controlling organ identity also coordinate specific aspects of cell wall characteristics.

The impact of mechanical compression on cortical microtubules in Arabidopsis: a quantitative pipeline

Exogenous mechanical perturbations on living tissues are commonly used to investigate whether cell effectors can respond to mechanical cues. However, in most of these experiments, the applied mechanical stress and/or the biological response are described only qualitatively. We developed a quantitative pipeline based on microindentation and image analysis to investigate the impact of a controlled and prolonged compression on microtubule behaviour in the Arabidopsis shoot apical meristem, using microtubule fluorescent marker lines. We found that a compressive stress, in the order of magnitude of turgor pressure, induced apparent microtubule bundling. Importantly, that response could be reversed several hours after the release of compression. Next, we tested the contribution of microtubule severing to compression-induced bundling: microtubule bundling seemed less pronounced in the katanin mutant, in which microtubule severing is dramatically reduced. Conversely, some microtubule bundles could still be observed 16 h after the release of compression in the spiral2 mutant, in which severing rate is instead increased. To quantify the impact of mechanical stress on anisotropy and orientation of microtubule arrays, we used the nematic tensor based FibrilTool ImageJ/Fiji plugin. To assess the degree of apparent bundling of the network, we developed several methods, some of which were borrowed from geostatistics. The final microtubule bundling response could notably be related to tissue growth velocity that was recorded by the indenter during compression. Because both input and output are quantified, this pipeline is an initial step towards correlating more precisely the cytoskeleton response to mechanical stress in living tissues.

Leaf growth is conformal

Growth pattern dynamics lie at the heart of morphogenesis. Here, we investigate the growth of plant leaves. We compute the conformal transformation that maps the contour of a leaf at a given stage onto the contour of the same leaf at a later stage. Based on the mapping we predict the local displacement field in the leaf blade and find it to agree with the experimentally measured displacement field to 92%. This approach is applicable to any two-dimensional system with locally isotropic growth, enabling the deduction of the whole growth field just from observation of the tissue contour.

Multiscale quantification of morphodynamics: MorphoLeaf software for 2D shape analysis

A major challenge in morphometrics is to analyse complex biological shapes formed by structures at different scales. Leaves exemplify this challenge as they combine differences in their overall shape with smaller shape variations at their margin, leading to lobes or teeth. Current methods based on contour or on landmark analysis are successful in quantifying either overall leaf shape or leaf margin dissection, but fail in combining the two. Here, we present a comprehensive strategy and its associated freely available platform for the quantitative, multiscale analysis of the morphology of leaves with different architectures. For this, biologically relevant landmarks are automatically extracted and hierarchised, and used to guide the reconstruction of accurate average contours that properly represent both global and local features. Using this method, we establish a quantitative framework of the developmental trajectory of Arabidopsis leaves of different ranks and retrace the origin of leaf heteroblasty. When applied to different mutant forms, our method can contribute to a better understanding of gene function, as we show here for the role of CUC2 during Arabidopsis leaf serration. Finally, we illustrate the wider applicability of our tool by analysing hand morphometrics.

Endosperm turgor pressure decreases during early Arabidopsis seed development

In Arabidopsis, rapid expansion of the coenocytic endosperm after fertilisation has been proposed to drive early seed growth, which is in turn constrained by the seed coat. This hypothesis implies physical heterogeneity between the endosperm and seed coat compartments during early seed development, which to date has not been demonstrated. Here, we combine tissue indentation with modelling to show that the physical properties of the developing seed are consistent with the hypothesis that elevated endosperm-derived turgor pressure drives early seed expansion. We provide evidence that whole-seed turgor is generated by the endosperm at early developmental stages. Furthermore, we show that endosperm cellularisation and seed growth arrest are associated with a drop in endosperm turgor pressure. Finally, we demonstrate that this decrease is perturbed when the function of POLYCOMB REPRESSIVE COMPLEX 2 is lost, suggesting that turgor pressure changes could be a target of genomic imprinting. Our results indicate a developmental role for changes in endosperm turgor pressure in the Arabidopsis seed.

A Mechanical Feedback Restricts Sepal Growth and Shape in Arabidopsis

How organs reach their final shape is a central yet unresolved question in developmental biology. Here we investigate whether mechanical cues contribute to this process. We analyze the epidermal cells of the Arabidopsis sepal, focusing on cortical microtubule arrays, which align along maximal tensile stresses and restrict growth in that direction through their indirect impact on the mechanical anisotropy of cell walls. We find a good match between growth and microtubule orientation throughout most of the development of the sepal. However, at the sepal tip, where organ maturation initiates and growth slows down in later stages, microtubules remain in a configuration consistent with fast anisotropic growth, i.e., transverse, and the anisotropy of their arrays even increases. To understand this apparent paradox, we built a continuous mechanical model of a growing sepal. The model demonstrates that differential growth in the sepal can generate transverse tensile stress at the tip. Consistently, microtubules respond to mechanical perturbations and align along maximal tension at the sepal tip. Including this mechanical feedback in our growth model of the sepal, we predict an impact on sepal shape that is validated experimentally using mutants with either increased or decreased microtubule response to stress. Altogether, this suggests that a mechanical feedback loop, via microtubules acting both as stress sensor and growth regulator, channels the growth and shape of the sepal tip. We propose that this proprioception mechanism is a key step leading to growth arrest in the whole sepal in response to its own growth.

Mechanical Stress Induces Remodeling of Vascular Networks in Growing Leaves

Differentiation into well-defined patterns and tissue growth are recognized as key processes in organismal development. However, it is unclear whether patterns are passively, homogeneously dilated by growth or whether they remodel during tissue expansion. Leaf vascular networks are well-fitted to investigate this issue, since leaves are approximately two-dimensional and grow manyfold in size. Here we study experimentally and computationally how vein patterns affect growth. We first model the growing vasculature as a network of viscoelastic rods and consider its response to external mechanical stress. We use the so-called texture tensor to quantify the local network geometry and reveal that growth is heterogeneous, resembling non-affine deformations in composite materials. We then apply mechanical forces to growing leaves after veins have differentiated, which respond by anisotropic growth and reorientation of the network in the direction of external stress. External mechanical stress appears to make growth more homogeneous, in contrast with the model with viscoelastic rods. However, we reconcile the model with experimental data by incorporating randomness in rod thickness and a threshold in the rod growth law, making the rods viscoelastoplastic. Altogether, we show that the higher stiffness of veins leads to their reorientation along external forces, along with a reduction in growth heterogeneity. This process may lead to the reinforcement of leaves against mechanical stress. More generally, our work contributes to a framework whereby growth and patterns are coordinated through the differences in mechanical properties between cell types.

A Mechanical Model to Interpret Cell-Scale Indentation Experiments on Plant Tissues in Terms of Cell Wall Elasticity and Turgor Pressure

Morphogenesis in plants is directly linked to the mechanical elements of growing tissues, namely cell wall and inner cell pressure. Studies of these structural elements are now often performed using indentation methods such as atomic force microscopy. In these methods, a probe applies a force to the tissue surface at a subcellular scale and its displacement is monitored, yielding force-displacement curves that reflect tissue mechanics. However, the interpretation of these curves is challenging as they may depend not only on the cell probed, but also on neighboring cells, or even on the whole tissue. Here, we build a realistic three-dimensional model of the indentation of a flower bud using SOFA (Simulation Open Framework Architecture), in order to provide a framework for the analysis of force-displacement curves obtained experimentally. We find that the shape of indentation curves mostly depends on the ratio between cell pressure and wall modulus. Hysteresis in force-displacement curves can be accounted for by a viscoelastic behavior of the cell wall. We consider differences in elastic modulus between cell layers and we show that, according to the location of indentation and to the size of the probe, force-displacement curves are sensitive with different weights to the mechanical components of the two most external cell layers. Our results confirm most of the interpretations of previous experiments and provide a guide to future experimental work.

Mechanical stress mediated by both endosperm softening and embryo growth underlies endosperm elimination in Arabidopsis seeds

Seed development in angiosperms demands the tightly co-ordinated development of three genetically distinct structures. The embryo is surrounded by the endosperm, which is in turn enclosed within the maternally derived seed coat. In Arabidopsis final seed size is determined by early expansion of the coenocytic endosperm, which then cellularizes and subsequently undergoes developmental Programmed Cell Death, breaking down as the embryo grows. Endosperm breakdown requires the endosperm-specific basic Helix Loop Helix transcription factor ZHOUPI. However, to date the mechanism underlying the Arabidopsis endosperm breakdown process has not been elucidated. Here we provide evidence that ZHOUPI does not induce the developmental Programmed Cell Death of the endosperm directly. Instead ZHOUPI indirectly triggers cell death by regulating the expression of cell wall modifying enzymes, thus altering the physical properties of the endosperm to condition a mechanical environment permitting the compression of the cellularized endosperm by the developing embryo.

Mechanical stress contributes to the expression of the STM homeobox gene in Arabidopsis shoot meristems

The role of mechanical signals in cell identity determination remains poorly explored in tissues. Furthermore, because mechanical stress is widespread, mechanical signals are difficult to uncouple from biochemical-based transduction pathways. Here we focus on the homeobox gene SHOOT MERISTEMLESS (STM), a master regulator and marker of meristematic identity in Arabidopsis. We found that STM expression is quantitatively correlated to curvature in the saddle-shaped boundary domain of the shoot apical meristem. As tissue folding reflects the presence of mechanical stress, we test and demonstrate that STM expression is induced after micromechanical perturbations. We also show that STM expression in the boundary domain is required for organ separation. While STM expression correlates with auxin depletion in this domain, auxin distribution and STM expression can also be uncoupled. STM expression and boundary identity are thus strengthened through a synergy between auxin depletion and an auxin-independent mechanotransduction pathway at the shoot apical meristem.