Physical models of plant development.

The definition of shape in multicellular organisms is a major issue of developmental biology. It is well established that morphogenesis relies on genetic regulation. However, cells, tissues, and organism behaviors are also bound by the laws of physics, which limit the range of possible deformations organisms can undergo but also define what organisms must do to achieve specific shapes. Besides experiments, theoretical models and numerical simulations of growing tissues are powerful tools to investigate the link between genetic regulation and mechanics. Here, we provide an overview of the main mechanical models of plant morphogenesis developed so far, from subcellular scales to whole tissues. The common concepts and discrepancies between the various models are discussed.

Cytokinin signalling inhibitory fields provide robustness to phyllotaxis.

How biological systems generate reproducible patterns with high precision is a central question in science. The shoot apical meristem (SAM), a specialized tissue producing plant aerial organs, is a developmental system of choice to address this question. Organs are periodically initiated at the SAM at specific spatial positions and this spatiotemporal pattern defines phyllotaxis. Accumulation of the plant hormone auxin triggers organ initiation, whereas auxin depletion around organs generates inhibitory fields that are thought to be sufficient to maintain these patterns and their dynamics. Here we show that another type of hormone-based inhibitory fields, generated directly downstream of auxin by intercellular movement of the cytokinin signalling inhibitor ARABIDOPSIS HISTIDINE PHOSPHOTRANSFER PROTEIN 6 (AHP6), is involved in regulating phyllotactic patterns. We demonstrate that AHP6-based fields establish patterns of cytokinin signalling in the meristem that contribute to the robustness of phyllotaxis by imposing a temporal sequence on organ initiation. Our findings indicate that not one but two distinct hormone-based fields may be required for achieving temporal precision during formation of reiterative structures at the SAM, thus indicating an original mechanism for providing robustness to a dynamic developmental system.

The self-organization of plant microtubules inside the cell volume yields their cortical localization, stable alignment, and sensitivity to external cues.

Many cell functions rely on the ability of microtubules to self-organize as complex networks. In plants, cortical microtubules are essential to determine cell shape as they guide the deposition of cellulose microfibrils, and thus control mechanical anisotropy of the cell wall. Here we analyze how, in turn, cell shape may influence microtubule behavior. Building upon previous models that confined microtubules to the cell surface, we introduce an agent model of microtubules enclosed in a three-dimensional volume. We show that the microtubule network has spontaneous aligned configurations that could explain many experimental observations without resorting to specific regulation. In particular, we find that the preferred cortical localization of microtubules emerges from directional persistence of the microtubules, and their interactions with each other and with the stiff wall. We also identify microtubule parameters that seem relatively insensitive to cell shape, such as length or number. In contrast, microtubule array anisotropy depends on local curvature of the cell surface and global orientation follows robustly the longest axis of the cell. Lastly, we find that geometric cues may be overcome, as the network is capable of reorienting toward weak external directional cues. Altogether our simulations show that the microtubule network is a good transducer of weak external polarity, while at the same time, easily reaching stable global configurations.

Cell division plane orientation based on tensile stress in Arabidopsis thaliana.

Cell geometry has long been proposed to play a key role in the orientation of symmetric cell division planes. In particular, the recently proposed Besson-Dumais rule generalizes Errera's rule and predicts that cells divide along one of the local minima of plane area. However, this rule has been tested only on tissues with rather local spherical shape and homogeneous growth. Here, we tested the application of the Besson-Dumais rule to the divisions occurring in the Arabidopsis shoot apex, which contains domains with anisotropic curvature and differential growth. We found that the Besson-Dumais rule works well in the central part of the apex, but fails to account for cell division planes in the saddle-shaped boundary region. Because curvature anisotropy and differential growth prescribe directional tensile stress in that region, we tested the putative contribution of anisotropic stress fields to cell division plane orientation at the shoot apex. To do so, we compared two division rules: geometrical (new plane along the shortest path) and mechanical (new plane along maximal tension). The mechanical division rule reproduced the enrichment of long planes observed in the boundary region. Experimental perturbation of mechanical stress pattern further supported a contribution of anisotropic tensile stress in division plane orientation. Importantly, simulations of tissues growing in an isotropic stress field, and dividing along maximal tension, provided division plane distributions comparable to those obtained with the geometrical rule. We thus propose that division plane orientation by tensile stress offers a general rule for symmetric cell division in plants.

A novel sensor to map auxin response and distribution at high spatio-temporal resolution.

Auxin is a key plant morphogenetic signal but tools to analyse dynamically its distribution and signalling during development are still limited. Auxin perception directly triggers the degradation of Aux/IAA repressor proteins. Here we describe a novel Aux/IAA-based auxin signalling sensor termed DII-VENUS that was engineered in the model plant Arabidopsis thaliana. The VENUS fast maturing form of yellow fluorescent protein was fused in-frame to the Aux/IAA auxin-interaction domain (termed domain II; DII) and expressed under a constitutive promoter. We initially show that DII-VENUS abundance is dependent on auxin, its TIR1/AFBs co-receptors and proteasome activities. Next, we demonstrate that DII-VENUS provides a map of relative auxin distribution at cellular resolution in different tissues. DII-VENUS is also rapidly degraded in response to auxin and we used it to visualize dynamic changes in cellular auxin distribution successfully during two developmental responses, the root gravitropic response and lateral organ production at the shoot apex. Our results illustrate the value of developing response input sensors such as DII-VENUS to provide high-resolution spatio-temporal information about hormone distribution and response during plant growth and development.

Matching Patterns of Gene Expression to Mechanical Stiffness at Cell Resolution through Quantitative Tandem Epifluorescence and Nanoindentation.

Cell differentiation has been associated with changes in mechanical stiffness in single-cell systems, yet it is unknown whether this association remains true in a multicellular context, particularly in developing tissues. In order to address such questions, we have developed a methodology, termed quantitative tandem epifluorescence and nanoindentation, wherein we sequentially determine cellular genetic identity with confocal microscopy and mechanical properties with atomic force microscopy. We have applied this approach to examine cellular stiffness at the shoot apices of Arabidopsis (Arabidopsis thaliana) plants carrying a fluorescent reporter for the CLAVATA3 (CLV3) gene, which encodes a secreted glycopeptide involved in the regulation of the centrally located stem cell zone in inflorescence and floral meristems. We found that these CLV3-expressing cells are characterized by an enhanced stiffness. Additionally, by tracking cells in young flowers before and after the onset of GREEN FLUORESCENT PROTEIN expression, we observed that an increase in stiffness coincides with this onset. This work illustrates how quantitative tandem epifluorescence and nanoindentation can reveal the spatial and temporal dynamics of both gene expression and cell mechanics at the shoot apex and, by extension, in the epidermis of any thick tissue.

Meristem size contributes to the robustness of phyllotaxis in Arabidopsis.

Using the plant model Arabidopsis, the relationship between day length, the size of the shoot apical meristem, and the robustness of phyllotactic patterns were analysed. First, it was found that reducing day length leads to an increased meristem size and an increased number of alterations in the final positions of organs along the stem. Most of the phyllotactic defects could be related to an altered tempo of organ emergence, while not affecting the spatial positions of organ initiations at the meristem. A correlation was also found between meristem size and the robustness of phyllotaxis in two accessions (Col-0 and WS-4) and a mutant (clasp-1), independent of growth conditions. A reduced meristem size in clasp-1 was even associated with an increased robustness of the phyllotactic pattern, beyond what is observed in the wild type. Interestingly it was also possible to modulate the robustness of phyllotaxis in these different genotypes by changing day length. To conclude, it is shown first that robustness of the phyllotactic pattern is not maximal in the wild type, suggesting that, beyond its apparent stereotypical order, the robustness of phyllotaxis is regulated. Secondly, a role for day length in the robustness of the phyllotaxis was also identified, thus providing a new example of a link between patterning and environment in plants. Thirdly, the experimental results validate previous model predictions suggesting a contribution of meristem size in the robustness of phyllotaxis via the coupling between the temporal sequence and spatial pattern of organ initiations.

Imaging plant growth in 4D: robust tissue reconstruction and lineaging at cell resolution.

Quantitative information on growing organs is required to better understand morphogenesis in both plants and animals. However, detailed analyses of growth patterns at cellular resolution have remained elusive. We developed an approach, multiangle image acquisition, three-dimensional reconstruction and cell segmentation-automated lineage tracking (MARS-ALT), in which we imaged whole organs from multiple angles, computationally merged and segmented these images to provide accurate cell identification in three dimensions and automatically tracked cell lineages through multiple rounds of cell division during development. Using these methods, we quantitatively analyzed Arabidopsis thaliana flower development at cell resolution, which revealed differential growth patterns of key regions during early stages of floral morphogenesis. Lastly, using rice roots, we demonstrated that this approach is both generic and scalable.

Noise and robustness in phyllotaxis.

A striking feature of vascular plants is the regular arrangement of lateral organs on the stem, known as phyllotaxis. The most common phyllotactic patterns can be described using spirals, numbers from the Fibonacci sequence and the golden angle. This rich mathematical structure, along with the experimental reproduction of phyllotactic spirals in physical systems, has led to a view of phyllotaxis focusing on regularity. However all organisms are affected by natural stochastic variability, raising questions about the effect of this variability on phyllotaxis and the achievement of such regular patterns. Here we address these questions theoretically using a dynamical system of interacting sources of inhibitory field. Previous work has shown that phyllotaxis can emerge deterministically from the self-organization of such sources and that inhibition is primarily mediated by the depletion of the plant hormone auxin through polarized transport. We incorporated stochasticity in the model and found three main classes of defects in spiral phyllotaxis--the reversal of the handedness of spirals, the concomitant initiation of organs and the occurrence of distichous angles--and we investigated whether a secondary inhibitory field filters out defects. Our results are consistent with available experimental data and yield a prediction of the main source of stochasticity during organogenesis. Our model can be related to cellular parameters and thus provides a framework for the analysis of phyllotactic mutants at both cellular and tissular levels. We propose that secondary fields associated with organogenesis, such as other biochemical signals or mechanical forces, are important for the robustness of phyllotaxis. More generally, our work sheds light on how a target pattern can be achieved within a noisy background.

NanoIndentation, an ImageJ Plugin for the Quantification of Cell Mechanics.

Growth and morphogenesis in plants depend on cell wall mechanics and on turgor pressure. Nanoindentation methods, such as atomic force microscopy (AFM), enable measurements of mechanical properties of a tissue at subcellular resolution, while confocal microscopy of tissues expressing fluorescent reporters indicates cell identity. Associating mechanical data with specific cells is essential to reveal the links between cell identity and cell mechanics. Here we describe an image analysis protocol that allows us to segment AFM scans containing information on tissue topography and/or mechanics, to stitch several scans in order to reconstitute an entire region of the tissue investigated, to segment the scans and label cells, and to associate labeled cells to the projection of confocal images. Thus all mechanical data can be mapped to the corresponding cells and to their identity. This protocol is implemented using NanoIndentation, a plugin that we are developing in the Fiji distribution of ImageJ.

Cellular Heterogeneity in Pressure and Growth Emerges from Tissue Topology and Geometry.

Cell-to-cell heterogeneity prevails in many systems, as exemplified by cell growth, although the origin and function of such heterogeneity are often unclear. In plants, growth is physically controlled by cell wall mechanics and cell hydrostatic pressure, alias turgor pressure. Whereas cell wall heterogeneity has received extensive attention, the spatial variation of turgor pressure is often overlooked. Here, combining atomic force microscopy and a physical model of pressurized cells, we show that turgor pressure is heterogeneous in the Arabidopsis shoot apical meristem, a population of stem cells that generates all plant aerial organs. In contrast with cell wall mechanical properties that appear to vary stochastically between neighboring cells, turgor pressure anticorrelates with cell size and cell neighbor number (local topology), in agreement with the prediction by our model of tissue expansion, which couples cell wall mechanics and tissue hydraulics. Additionally, our model predicts two types of correlations between pressure and cellular growth rate, where high pressure may lead to faster- or slower-than-average growth, depending on cell wall extensibility, yield threshold, osmotic pressure, and hydraulic conductivity. The meristem exhibits one of these two regimes, depending on conditions, suggesting that, in this tissue, water conductivity may contribute to growth control. Our results unravel cell pressure as a source of patterned heterogeneity and illustrate links between local topology, cell mechanical state, and cell growth, with potential roles in tissue homeostasis.

Robust organ size requires robust timing of initiation orchestrated by focused auxin and cytokinin signalling.

Organ size and shape are precisely regulated to ensure proper function. The four sepals in each Arabidopsis thaliana flower must maintain the same size throughout their growth to continuously enclose and protect the developing bud. Here we show that DEVELOPMENT RELATED MYB-LIKE 1 (DRMY1) is required for both timing of organ initiation and proper growth, leading to robust sepal size in Arabidopsis. Within each drmy1 flower, the initiation of some sepals is variably delayed. Late-initiating sepals in drmy1 mutants remain smaller throughout development, resulting in variability in sepal size. DRMY1 focuses the spatiotemporal signalling patterns of the plant hormones auxin and cytokinin, which jointly control the timing of sepal initiation. Our findings demonstrate that timing of organ initiation, together with growth and maturation, contribute to robust organ size.

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.

Analysis of 3D gene expression patterns in plants using whole-mount RNA in situ hybridization.

In situ mRNA hybridization is one of the most powerful techniques for analyzing patterns of gene expression. However, its usefulness is limited in complex plant tissues by the need to fix, embed and section samples before localizing the desired mRNA. Here we present a robust whole-mount in situ hybridization method that allows easy access to patterns of gene expression in intact, complex tissues, such as the inflorescence apex of Arabidopsis thaliana. The tissue is first fixed and then permeabilized by treatment with a cocktail of cell wall-digesting enzymes that has been optimized to preserve the integrity of tissue structures, while also permitting the detection of expression patterns in deep tissues. In addition to colorimetric staining, fluorimetric staining that can be imaged by confocal microscopy can also be used with this protocol, thus providing full 3D resolution. The entire procedure can take <3 d from tissue preparation to image acquisition.

The role of mechanical forces in plant morphogenesis.

The shape of an organism relies on a complex network of genetic regulations and on the homeostasis and distribution of growth factors. In parallel to the molecular control of growth, shape changes also involve major changes in structure, which by definition depend on the laws of mechanics. Thus, to understand morphogenesis, scientists have turned to interdisciplinary approaches associating biology and physics to investigate the contribution of mechanical forces in morphogenesis, sometimes re-examining theoretical concepts that were laid out by early physiologists. Major advances in the field have notably been possible thanks to the development of computer simulations and live quantitative imaging protocols in recent years. Here, we present the mechanical basis of shape changes in plants, focusing our discussion on undifferentiated tissues. How can growth be translated into a quantified geometrical output? What is the mechanical basis of cell and tissue growth? What is the contribution of mechanical forces in patterning?