Thickness-stiffness trade-off improves lodging resistance in rice.

Lodging of cereal crops significantly reduces grain yield and quality, making lodging resistance a prime target for breeding programs. However, lodging resistance among different rice (Oryza sativa L.) cultivars in the field remains largely unknown, as is the relationship between the major properties of culms such as their morphological and mechanical properties. Here, we investigated the morphological and mechanical properties of 12 rice cultivars by considering different internodes within culms. We detected variation in these two traits among cultivars: one set of cultivars had thicker but softer culms (thickness-type), while the other set of cultivars showed stiffer but thinner culms (stiffness-type). We designate this variation as a thickness-stiffness trade-off. We then constructed a mechanical model to dissect the mechanical and/or morphological constraints of rice culms subjected to their own weight (self-weight load). Through modeling, we discovered that ear weight and the morphology of the highest internode were important for reducing deflection, which may be important factors to achieve higher lodging resistance. The mechanical theory devised in this study could be used to predict the deflection of rice culms and may open new avenues for novel mechanics-based breeding techniques.

Shoot gravitropism and organ straightening cooperate to arrive at a mechanically favorable shape in Arabidopsis.

Gravitropism is the plant organ bending in response to gravity, while a straightening mechanism prevents bending beyond the gravitropic set-point angle. The promotion and prevention of bending occur simultaneously around the inflorescence stem tip. How these two opposing forces work together and what part of the stem they affect are unknown. To understand the mechanical forces involved, we rotated wild type and organ-straightening-deficient mutant (myosin xif xik) Arabidopsis plants to a horizontal position to initiate bending. The mutant stems started to bend before the wild-type stems, which led us to hypothesize that the force preventing bending was weaker in mutant. We modeled the wild-type and mutant stems as elastic rods, and evaluated two parameters: an organ-angle-dependent gravitropic-responsive parameter (ß) and an organ-curvature-dependent proprioceptive-responsive parameter (γ). Our model showed that these two parameters were lower in mutant than in wild type, implying that, unexpectedly, both promotion and prevention of bending are weak in mutant. Subsequently, finite element method simulations revealed that the compressive stress in the middle of the stem was significantly lower in wild type than in mutant. The results of this study show that myosin-XIk-and-XIf-dependent organ straightening adjusts the stress distribution to achieve a mechanically favorable shape.

A mechanical theory of competition between plant root growth and soil pressure reveals a potential mechanism of root penetration.

Root penetration into the soil is essential for plants to access water and nutrients, as well as to mechanically support aboveground structures. This requires a combination of healthy plant growth, adequate soil mechanical properties, and compatible plant-soil interactions. Despite the current knowledge of the static rheology driving the interactions at the root-soil interface, few theoretical approaches have attempted to describe root penetration with dynamic rheology. In this work, we experimentally showed that radish roots in contact with soil of specific density during a specific growth stage fail to penetrate the soil. To explore the mechanism of root penetration into the soil, we constructed a theoretical model to explore the relevant conditions amenable to root entry into the soil. The theory indicates that dimensionless parameters such as root growth anisotropy, static root-soil competition, and dynamic root-soil competition are important for root penetration. The consequent theoretical expectations were supported by finite element analysis, and a potential mechanism of root penetration into the soil is discussed.

Coordinate Normalization of Live-Cell Imaging Data Reveals Growth Dynamics of the Arabidopsis Zygote.

Polarization of the zygote defines the body axis during plant development. In Arabidopsis (Arabidopsis thaliana), the zygote becomes polarized and elongates in the longitudinal direction, ultimately forming the apical-basal axis of the mature plant. Despite its importance, the mechanism for this elongation remains poorly understood. Based on live-cell imaging of the zygote, we developed new image analysis methods, referred to as coordinate normalization, that appropriately fix and align positions in an image, preventing fluctuation across a temporal sequence of images. Using these methods, we discovered that the zygote elongates only at its apical tip region, similar to tip-growing cells such as pollen tubes and root hairs. We also investigated the spatiotemporal dynamics of the apical tip contour of the zygote and observed that the zygote tip retains its isotropic, hemispherical apical shape during cell elongation. By looking at the elliptical fitting of the contour over time, we further discovered that the apical cell tip becomes thinner at first and then thickens, with a transient increase in growth speed that is followed by the first cell division. We performed the same series of analyses using root hairs and established that both the hemispherical tip shape and the changes in growth rate associated with changes in tip size are specific to the zygote. In summary, the Arabidopsis zygote undergoes directional elongation as a tip-growing cell, but its tip retains an unusual isotropic shape, and the manner of growth changes with the developmental stage.

Rigidity control mechanism by turgor pressure in plants.

The bodies of herbaceous plants are slender, thin, and soft. These plants support their bodies through the action of turgor pressure associated with their internal water stores. The purpose of this study was to apply the principles of structural mechanics to clarify the underlying mechanism of rigidity control that is responsible for turgor pressure in plants and the reason behind the self-supporting ability of herbaceous plants. We modeled a plant a horizontally oriented thin-walled cylindrical cantilever with closed ends enclosing a cavity filled with water that is acted on by its own weight and by internal tension generated through turgor pressure. We derived an equation describing the plant's consequent deflection, introducing a dimensionless parameter to express the decrease in deflection associated with the action of turgor pressure. We found that the mechanical and physical characteristics of herbaceous plants that would appear to be counter-productive from a superficial perspective increase the deflection decreasing effect of turgor pressure.

Pulvinar slits: Cellulose-deficient and de-methyl-esterified pectin-rich structures in a legume motor cell.

The cortical motor cells (CMCs) in a legume pulvinus execute the reversible deformation in leaf movement that is driven by changes in turgor pressure. In contrast to the underlying osmotic regulation property, the cell wall structure of CMCs that contributes to the movement has yet to be characterized in detail. Here, we report that the cell wall of CMCs has circumferential slits with low levels of cellulose deposition, which are widely conserved among legume species. This structure is unique and distinct from that of any other primary cell walls reported so far; thus, we named them "pulvinar slits." Notably, we predominantly detected de-methyl-esterified homogalacturonan inside pulvinar slits, with a low deposition of highly methyl-esterified homogalacturonan, as with cellulose. In addition, Fourier transform infrared spectroscopy analysis indicated that the cell wall composition of pulvini is different from that of other axial organs, such as petioles or stems. Moreover, monosaccharide analysis showed that pulvini are pectin-rich organs like developing stems and that the amount of galacturonic acid in pulvini is greater than in developing stems. Computer modeling suggested that pulvinar slits facilitate anisotropic extension in the direction perpendicular to the slits in the presence of turgor pressure. When tissue slices of CMCs were transferred to different extracellular osmotic conditions, pulvinar slits altered their opening width, indicating their deformability. In this study, we thus characterized a distinctive cell wall structure of CMCs, adding to our knowledge of repetitive and reversible organ deformation as well as the structural diversity and function of the plant cell wall.

Elastic shell theory for plant cell wall stiffness reveals contributions of cell wall elasticity and turgor pressure in AFM measurement.

The stiffness of a plant cell in response to an applied force is determined not only by the elasticity of the cell wall but also by turgor pressure and cell geometry, which affect the tension of the cell wall. Although stiffness has been investigated using atomic force microscopy (AFM) and Young's modulus of the cell wall has occasionally been estimated using the contact-stress theory (Hertz theory), the existence of tension has made the study of stiffness more complex. Elastic shell theory has been proposed as an alternative method; however, the estimation of elasticity remains ambiguous. Here, we used finite element method simulations to verify the formula of the elastic shell theory for onion (Allium cepa) cells. We applied the formula and simulations to successfully quantify the turgor pressure and elasticity of a cell in the plane direction using the cell curvature and apparent stiffness measured by AFM. We conclude that tension resulting from turgor pressure regulates cell stiffness, which can be modified by a slight adjustment of turgor pressure in the order of 0.1 MPa. This theoretical analysis reveals a path for understanding forces inherent in plant cells.

Exploring the mechanical and morphological rationality of tree branch structure based on 3D point cloud analysis and the finite element method.

Trees are thought to have acquired a mechanically optimized shape through evolution, but a scientific methodology to investigate the mechanical rationality of tree morphology remains to be established. The aim of this study was to develop a new method for 3D reconstruction of actual tree shape and to establish a theoretical formulation for elucidating the structure and function of tree branches. We obtained 3D point cloud data of tree shape of Japanese zelkova (Zelkova serrata) and Japanese larch (Larix kaempferi) using the NavVis Lidar scanner, then applied a cylinder structure extraction from point cloud data with error estimation. We then formulated the mechanical stress of branches under gravity using the elastic theory, and performed finite element method simulations to evaluate the mechanical characteristics. Subsequently, we constructed a mechanics-based theoretical formulation of branch development that ensures constant bending stress produces various branching patterns depending on growth properties. The derived theory recapitulates the trade-off among branch growth anisotropy, stress-gravity length, and branch shape, which may open the quantitative way to evaluate mechanical and morphological rationality of tree branches.

Reduction in organ-organ friction is critical for corolla elongation in morning glory.

In complex structures such as flowers, organ-organ interactions are critical for morphogenesis. The corolla plays a central role in attracting pollinators: thus, its proper development is important in nature, agriculture, and horticulture. Although the intraorgan mechanism of corolla development has been studied, the importance of organ-organ interactions during development remains unknown. Here, using corolla mutants of morning glory described approximately 200 years ago, we show that glandular secretory trichomes (GSTs) regulate floral organ interactions needed for corolla morphogenesis. Defects in GST development in perianth organs result in folding of the corolla tube, and release of mechanical stress by sepal removal restores corolla elongation. Computational modeling shows that the folding occurs because of buckling caused by mechanical stress from friction at the distal side of the corolla. Our results suggest a novel function of GSTs in regulating the physical interaction of floral organs for macroscopic morphogenesis of the corolla.

Tissue growth constrains root organ outlines into an isometrically scalable shape.

Organ morphologies are diverse but also conserved under shared developmental constraints among species. Any geometrical similarities in the shape behind diversity and the underlying developmental constraints remain unclear. Plant root tip outlines commonly exhibit a dome shape, which likely performs physiological functions, despite the diversity in size and cellular organization among distinct root classes and/or species. We carried out morphometric analysis of the primary roots of ten angiosperm species and of the lateral roots (LRs) of Arabidopsis, and found that each root outline was isometrically scaled onto a parameter-free catenary curve, a stable structure adopted for arch bridges. Using the physical model for bridges, we analogized that localized and spatially uniform occurrence of oriented cell division and expansion force the LR primordia (LRP) tip to form a catenary curve. These growth rules for the catenary curve were verified by tissue growth simulation of developing LRP development based on time-lapse imaging. Consistently, LRP outlines of mutants compromised in these rules were found to deviate from catenary curves. Our analyses demonstrate that physics-inspired growth rules constrain plant root tips to form isometrically scalable catenary curves.

Cortical tension overrides geometrical cues to orient microtubules in confined protoplasts.

In plant cells, cortical microtubules (CMTs) generally control morphogenesis by guiding cellulose synthesis. CMT alignment has been proposed to depend on geometrical cues, with microtubules aligning with the cell long axis in silico and in vitro. Yet, CMTs are usually transverse in vivo, i.e., along predicted maximal tension, which is transverse for cylindrical pressurized vessels. Here, we adapted a microwell setup to test these predictions in a single-cell system. We confined protoplasts laterally to impose a curvature ratio and modulated pressurization through osmotic changes. We find that CMTs can be longitudinal or transverse in wallless protoplasts and that the switch in CMT orientation depends on pressurization. In particular, longitudinal CMTs become transverse when cortical tension increases. This explains the dual behavior of CMTs in planta: CMTs become longitudinal when stress levels become low, while stable transverse CMT alignments in tissues result from their autonomous response to tensile stress fluctuations.

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.

Root shape adaptation to mechanical stress derived from unidirectional vibrations in Populus nigra.

While it is known that plant roots can change their shapes to the stress direction, it remains unclear if the root orientation can change as a means for mechanical reinforcement. When stress in form of a unidirectional vibration is applied to cuttings of Populus nigra for 5 min a day over a period of 20 days, the root system architecture changes. The contribution of roots with a diameter larger than 0.04 cm increases, while the allocation to roots smaller than 0.03 cm decreases. In addition to the root diameter allocation, the root orientation in the stem proximity was analyzed by appearance and with a nematic tensor analysis in an attempt to calculate the average root orientation. The significant different allocation to roots with a larger diameter, and the tendency of roots to align in the vicinity of the stress axis (not significantly different), are indicating a mechanical reinforcement to cope with the received strain. This work indicates an adaptive root system architecture and a possible adaptive root orientation for mechanical reinforcement.

Spatio-temporal kinematic analysis of shoot gravitropism in Arabidopsis thaliana.

Plant shoots can bend upward against gravity, a behavior known as shoot gravitropism. The conventional quantification of shoot bending has been restricted to measurements of shoot tip angle, which cannot fully describe the spatio-temporal bending process. Recently, however, advanced imaging analyses have been developed to quantify in detail the spatio-temporal changes in inclination angle and curvature of the shoot. We used one such method (KymoRod) to analyze the gravitropism of the Arabidopsis thaliana inflorescence stem, and successfully extracted characteristics that capture when and where bending occurs. Furthermore, we implemented an elastic spring theoretical model and successfully determined best fitted parameters that may explain typical bending behaviors of the inflorescence stem. Overall, we propose a data-model combined framework to quantitatively investigate shoot gravitropism in plants.

Laser micromarking technique in studying the negative gravitropism in pea stem.

A laser micromarking technique on plant epidermis was developed to study how a plant can reduce the stress in bending behavior by controlling the growth and morphogenesis. The negative gravitropism in a pea seedling (Pisum sativum L.) was discussed based on the time-dependent displacement of laser marking points which were formed by spatially-selective laser ablation of the cuticle layer that covers the outer surface of a plant. The elongation of the stem in the horizontal direction was remarkable in the first half of the gravitropism. The elongation percentages of the stem length between laser-marking points at around upper surface, middle, and bottom surface were evaluated to be 2.57, 4.87, and 7.70%, respectively. The characteristic feature of the stem bending in gravitropism is the elongation even at the upper surface region, that is, inside of the bending. This is a different feature from cantilever beams for structural materials like metals and polymers, where the compression of the upper surface and elongation of the bottom surface are caused by bending. Another laser micromarking technique was developed to improve the resolution of a dot-matrix pattern by fluorescent material transfer to a plant through a masking film with a micro-hole matrix pattern. Similar time-dependent displacement behavior was observed for a fluorescent dot-marked stem showing a feedback control loop in the mechanical optimization. These results suggested that plants solve the problem of the stress in stem bending through growth. The laser micromarking is an effective method for studying the mechanical optimization in plants.

A mathematical model explores the contributions of bending and stretching forces to shoot gravitropism in Arabidopsis.

Plant shoot gravitropism is a complex phenomenon resulting from gravity sensing, curvature sensing (proprioception), the ability to uphold self-weight and growth. Although recent data analysis and modelling have revealed the detailed morphology of shoot bending, the relative contribution of bending force (derived from the gravi-proprioceptive response) and stretching force (derived from shoot axial growth) behind gravitropism remains poorly understood. To address this gap, we combined morphological data with a theoretical model to analyze shoot bending in wild-type and lazy1-like 1 mutant Arabidopsis thaliana. Using data from actual bending events, we searched for model parameters that minimized discrepancies between the data and mathematical model. The resulting model suggests that both the bending force and the stretching force differ significantly between the wild type and mutant. We discuss the implications of the mechanical forces associated with differential cell growth and present a plausible mechanical explanation of shoot gravitropism.

Suppression of soft spots and excited modes in the shape deformation model with spatio-temporal growth noise.

The shapes of plant organs such as sepals are precise and reproducible, although the cells composing these organs are highly heterogeneous. We investigate the collective behavior of a shape deformation model with spatio-temporal fluctuations in elasticity (Hong et al., Dev. Cell, 38, 15, 2016). It is shown that the spatio-temporal growth noise has two opposing effect: the temporal noise promotes the reproducibility of the organ shape, whereas the spatial noise disturbs it, leading to the organ undergoing an abnormal shape deformation. To understand how such abnormality can emerge, we study the eigenvectors of the correlation matrix of the growth velocity. It is revealed that the anomalous shape deformations can be created by two independent factors: (1) excited modes where the orientations of the eigenvectors with m ≥ 2 are spatially correlated, and/or (2) soft spots where spot structures with high fluctuations in the magnitudes of the eigenvectors appear non-uniformly.

A Rho-based reaction-diffusion system governs cell wall patterning in metaxylem vessels.

Rho GTPases play crucial roles in cell polarity and pattern formation. ROPs, Rho of plant GTPases, are widely involved in cell wall patterning in plants, yet the molecular mechanism underlying their action remains unknown. Arabidopsis ROP11 is locally activated to form plasma membrane domains, which direct formation of cell wall pits in metaxylem vessel cells through interaction with cortical microtubules. Here, we show that the pattern formation of cell wall pits is governed by ROP activation via a reaction-diffusion mechanism. Genetic analysis and reconstructive assays revealed that ROPGEF4/7 and ROPGAP3/4, which encode ROP activators and inactivators, respectively, regulated the formation of ROP-activated domains; these in turn determined the pattern of cell wall pits. Mathematical modelling showed that ROP-activation cycle generated ROP domains by reaction-diffusion mechanism. The model predicted that a positive feedback and slow diffusion of ROP11-ROPGEF4 complex were required to generate ROP-activated domains. ROPGEF4 formed a dimer that interacted with activated ROP11 in vivo, which could provide positive feedback for ROP activation. ROPGEF4 was highly stable on the plasma membrane and inhibited ROP11 diffusion. Our study indicated that ROP-based reaction-diffusion system self-organizes ROP-activated domains, thereby determines the pit pattern of metaxylem vessels.

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.

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.