Regulatory role of cell division rules on tissue growth heterogeneity

Stiffness transitions in new walls post-cell division differ between Marchantia polymorpha gemmae and Arabidopsis thaliana leaves

Plant morphogenesis is governed by the mechanics of the cell wall-a stiff and thin polymeric box that encloses the cells. The cell wall is a highly dynamic composite material. New cell walls are added during cell division. As the cells continue to grow, the properties of cell walls are modulated to undergo significant changes in shape and size without breakage. Spatial and temporal variations in cell wall mechanical properties have been observed. However, how they relate to cell division remains an outstanding question. Here, we combine time-lapse imaging with local mechanical measurements via atomic force microscopy to systematically map the cell wall's age and growth, with their stiffness. We make use of two systems, Marchantia polymorpha gemmae, and Arabidopsis thaliana leaves. We first characterize the growth and cell division of M. polymorpha gemmae. We then demonstrate that cell division in M. polymorpha gemmae results in the generation of a temporary stiffer and slower-growing new wall. In contrast, this transient phenomenon is absent in A. thaliana leaves. We provide evidence that this different temporal behavior has a direct impact on the local cell geometry via changes in the junction angle. These results are expected to pave the way for developing more realistic plant morphogenetic models and to advance the study into the impact of cell division on tissue growth.

Patterned proliferation orients tissue-wide stress to control root vascular symmetry in Arabidopsis

Symmetric tissue alignment is pivotal to the functions of plant vascular tissue, such as long-distance molecular transport and lateral organ formation. During the vascular development of the Arabidopsis roots, cytokinins initially determine cell-type boundaries among vascular stem cells and subsequently promote cell proliferation to establish vascular tissue symmetry. Although it is unknown whether and how the symmetry of initially defined boundaries is progressively refined under tissue growth in plants, such boundary shapes in animal tissues are regulated by cell fluidity, e.g., cell migration and intercalation, lacking in plant tissues. Here, we uncover that cell proliferation during vascular development produces anisotropic compressive stress, smoothing, and symmetrizing cell arrangement of the vascular-cell-type boundary. Mechanistically, the GATA transcription factor HANABA-TARANU cooperates with the type-B Arabidopsis response regulators to form an incoherent feedforward loop in cytokinin signaling. The incoherent feedforward loop fine-tunes the position and frequency of vascular cell proliferation, which in turn restricts the source of mechanical stress to the position distal and symmetric to the boundary. By combinatorial analyses of mechanical simulations and laser cell ablation, we show that the spatially constrained environment of vascular tissue efficiently entrains the stress orientation among the cells to produce a tissue-wide stress field. Together, our data indicate that the localized proliferation regulated by the cytokinin signaling circuit is decoded into a globally oriented mechanical stress to shape the vascular tissue symmetry, representing a reasonable mechanism controlling the boundary alignment and symmetry in tissue lacking cell fluidity.

Large-scale analysis and computer modeling reveal hidden regularities behind variability of cell division patterns in Arabidopsis thaliana embryogenesis

Noise plays a major role in cellular processes and in the development of tissues and organs. Several studies have examined the origin, the integration or the accommodation of noise in gene expression, cell growth and elaboration of organ shape. By contrast, much less is known about variability in cell division plane positioning, its origin and links with cell geometry, and its impact on tissue organization. Taking advantage of the first-stereotyped-then-variable division patterns in the embryo of the model plant Arabidopsis thaliana, we combined 3D imaging and quantitative cell shape and cell lineage analysis together with mathematical and computer modeling to perform a large-scale, systematic analysis of variability in division plane orientation. Our results reveal that, paradoxically, variability in cell division patterns of Arabidopsis embryos is accompanied by a progressive reduction of heterogeneity in cell shape topology. The paradox is solved by showing that variability operates within a reduced repertoire of possible division plane orientations that is related to cell geometry. We show that in several domains of the embryo, a recently proposed geometrical division rule recapitulates observed variable patterns, suggesting that variable patterns emerge from deterministic principles operating in a variable geometrical context. Our work highlights the importance of emerging patterns in the plant embryo under iterated division principles, but also reveal domains where deviations between rule predictions and experimental observations point to additional regulatory mechanisms.

Defects in division plane positioning in the root meristematic zone affect cell organization in the differentiation zone

Cell division plane orientation is critical for plant and animal development and growth. TANGLED1 (TAN1) and AUXIN-INDUCED-IN-ROOT-CULTURES9 (AIR9) are division-site localized microtubule-binding proteins required for division plane positioning. tan1 and air9 Arabidopsis thaliana single mutants have minor or no noticeable phenotypes but the tan1 air9 double mutant has synthetic phenotypes including stunted growth, misoriented divisions, and aberrant cell-file rotation in the root differentiation zone. These data suggest that TAN1 plays a role in nondividing cells. To determine whether TAN1 is required in elongating and differentiating cells in the tan1 air9 double mutant, we limited its expression to actively dividing cells using the G2/M-specific promoter of the syntaxin KNOLLE (pKN:TAN1-YFP). Unexpectedly, in addition to rescuing division plane defects, pKN:TAN1-YFP rescued root growth and the root differentiation zone cell file rotation defects in the tan1 air9 double mutant. This suggests that defects that occur in the meristematic zone later affect the organization of elongating and differentiating cells.

Topological properties accurately predict cell division events and organization of shoot apical meristem in Arabidopsis thaliana

Cell division and the resulting changes to the cell organization affect the shape and functionality of all tissues. Thus, understanding the determinants of the tissue-wide changes imposed by cell division is a key question in developmental biology. Here, we use a network representation of live cell imaging data from shoot apical meristems (SAMs) in Arabidopsis thaliana to predict cell division events and their consequences at the tissue level. We show that a support vector machine classifier based on the SAM network properties is predictive of cell division events, with test accuracy of 76%, which matches that based on cell size alone. Furthermore, we demonstrate that the combination of topological and biological properties, including cell size, perimeter, distance and shared cell wall between cells, can further boost the prediction accuracy of resulting changes in topology triggered by cell division. Using our classifiers, we demonstrate the importance of microtubule-mediated cell-to-cell growth coordination in influencing tissue-level topology. Together, the results from our network-based analysis demonstrate a feedback mechanism between tissue topology and cell division in A. thaliana SAMs.

Exogenous 6-Benzyladenine Improves Waterlogging Tolerance in Maize Seedlings by Mitigating Oxidative Stress and Upregulating the Ascorbate-Glutathione Cycle

The synthetic cytokinin 6-benzyladenine (6-BA) regulates plant growth and prevents the negative consequences of various forms of abiotic stress, including waterlogging in crop plants. The present study aimed to investigate the effects of exogenous 6-BA on the growth, oxidative stress, and ascorbate-glutathione (AsA-GSH) cycle system in the inbred SY-MY13 (waterlogging-resistant) and SY-XT1 (waterlogging-sensitive) seedlings of waxy corn in conditions of waterlogging stress. The results demonstrated that waterlogging stress causes chlorosis and necrosis in waxy corn leaves, inhibiting growth and leading to the accumulation of reactive oxygen species (ROS), which induces oxidative stress and, in turn, reduces membrane lipid peroxidation and the disruption of membrane homeostasis. This is specifically manifested in the increased concentrations of superoxide anion radicals ( O 2 - ), hydrogen peroxide (H₂O₂), and malondialdehyde (MDA), in addition to increased relative electrical conductivity (REC%) values. The SY-MY13 strain exhibited growth superior to that of SY-XT1 when waterlogged due to its excellent waterlogging resistance. Thus, exogenous 6-BA was found to be effective in enhancing the growth of plants stressed by waterlogging in terms of the weight of the shoots and roots, shoot height, and leaf area. In addition to this, exogenous 6-BA also reduced the accumulation of O 2 - , H₂O₂, and MDA, increased ascorbate peroxidase (APX), glutathione reductase (GR), dehydroascorbate reductase (DHAR), and monodehydroascorbate reductase (MDHAR) activity, and enhanced ascorbic acid (AsA), and reduced glutathione (GSH) concentration through the regulation of the efficiency of the AsA-GSH cycle system in maize plants. Hence, the application of exogenous 6-BA can alleviate waterlogging-induced damage and improve waterlogging tolerance in waxy corn via the activation of the AsA-GSH cycle system and the elimination of ROS.

Mechanobiology of cell division in plant growth

Cell division in plants is particularly important as cells cannot rearrange. It therefore determines the arrangement of cells (topology) and their size and shape (geometry). Cell division reduces mechanical stress locally by producing smaller cells and alters mechanical properties by reinforcing the mechanical wall network, both of which can alter overall tissue morphology. Division orientation is often regarded as following geometric rules, however recent work has suggested that divisions align with the direction of maximal tensile stress. Mechanical stress has already been shown to feed into many processes of development including those that alter mechanical properties. Such an alignment may enable cell division to selectively reinforce the cell wall network in the direction of maximal tensile stress. Therefore there exists potential feedback between cell division, mechanical stress and growth. Improving our understanding of this topic will help to shed light on the debated role of cell division in organ scale growth.

Epidermal restriction confers robustness to organ shapes

The shape of comparable tissues and organs is consistent among individuals of a given species, but how this consistency or robustness is achieved remains an open question. The interaction between morphogenetic factors determines organ formation and subsequent shaping, which is ultimately a mechanical process. Using a computational approach, we show that the epidermal layer is essential for the robustness of organ geometry control. Specifically, proper epidermal restriction allows organ asymmetry maintenance, and the tensile epidermal layer is sufficient to suppress local variability in growth, leading to shape robustness. The model explains the enhanced organ shape variations in epidermal mutant plants. In addition, differences in the patterns of epidermal restriction may underlie the initial establishment of organ asymmetry. Our results show that epidermal restriction can answer the longstanding question of how cellular growth noise is averaged to produce precise organ shapes, and the findings also shed light on organ asymmetry establishment.

QTL Mapping Using a High-Density Genetic Map to Identify Candidate Genes Associated With Metribuzin Tolerance in Hexaploid Wheat (Triticum aestivum L.)

Tolerance to metribuzin, a broad-spectrum herbicide, is an important trait for weed control in wheat breeding. However, the genetics of metribuzin tolerance in relation to the underlying quantitative trait loci (QTL) and genes is limited. This study developed F₈ recombinant inbred lines (RILs) from a cross between a highly resistant genotype (Chuan Mai 25) and highly susceptible genotype (Ritchie), which were used for QTL mapping of metribuzin tolerance. Genotyping was done using a diversity arrays technology sequencing (DArTseq) platform, and phenotyping was done in controlled environments. Herbicide tolerance was measured using three traits, visual score (VS), reduction of chlorophyll content (RCC), and mean value of chlorophyll content for metribuzin-treated plants (MCC). A high-density genetic linkage map was constructed using 2,129 DArTseq markers. Inclusive composite interval mapping (ICIM) identified seven QTL, one each on chromosomes 2A, 2D, 3A, 3B, 4A, 5A, and 6A. Three major QTL-Qrcc.uwa.2AS, Qrcc.uwa.5AL, and Qrcc.uwa.6AL-explained 11.39%, 11.06%, and 11.45% of the phenotypic variation, respectively. The 5A QTL was further validated using kompetitive allele-specific PCR (KASP) assays in an F₃ validation population developed from Chuan Mai 25 × Dagger. Blasting the single-nucleotide polymorphisms (SNPs) flanking the QTL in the wheat reference genome RefV1.0 revealed SNP markers within or very close to annotated genes which could be candidate genes responsible for metribuzin tolerance. Most of the candidate genes were related to metabolic detoxification, especially those of P450 pathway and xenobiotic transmembrane transporter activity, which are reportedly key molecules responsible for herbicide tolerance. This study is the first to use specially developed populations to conduct QTL mapping on the metribuzin tolerance trait. The three major QTL and candidate genes identified in this study could facilitate marker-assisted metribuzin breeding in wheat. The QTL could be fine-mapped to locate the genes responsible for metribuzin tolerance, which could be introgressed into elite wheat cultivars.

Cell Size Control in Plants

The genetic control of the characteristic cell sizes of different species and tissues is a long-standing enigma. Plants are convenient for studying this question in a multicellular context, as their cells do not move and are easily tracked and measured from organ initiation in the meristems to subsequent morphogenesis and differentiation. In this article, we discuss cell size control in plants compared with other organisms. As seen from yeast cells to mammalian cells, size homeostasis is maintained cell autonomously in the shoot meristem. In developing organs, vacuolization contributes to cell size heterogeneity and may resolve conflicts between growth control at the cellular and organ levels. Molecular mechanisms for cell size control have implications for how cell size responds to changes in ploidy, which are particularly important in plant development and evolution. We also discuss comparatively the functional consequences of cell size and their potential repercussions at higher scales, including genome evolution.

Feedback from Tissue Mechanics Self-Organizes Efficient Outgrowth of Plant Organ

Plant organ outgrowth superficially appears like the continuous mechanical deformation of a sheet of cells. Yet, how precisely cells as individual mechanical entities can act to morph a tissue reliably and efficiently into three dimensions during outgrowth is still puzzling, especially when cells are tightly connected as in plant tissue. In plants, the mechanics of cells within a tissue is particularly well-defined because individual cell growth is essentially the mechanical yielding of the cell wall in response to internal turgor pressure. Cell-wall stiffness is controlled by biological signaling, which is impacted by stresses, and hence, cell growth is observed to respond to mechanical stresses building up within a tissue. What is the role of the mechanical feedback during morphing of tissue in three dimensions? Here, we develop a three-dimensional vertex model to investigate tissue mechanics at the onset of organ outgrowth at the tip of a plant shoot. We find that organ height is primarily governed by the ratio of growth rates of faster-growing cells initiating the organ versus slower-growing cells surrounding them. Remarkably, the outgrowth rate is higher when cell growth responds to the tissue-wide mechanical stresses. Our quantitative analysis of simulation data shows that tissue mechanical feedback on cell growth can act via a twofold mechanism. First, the feedback guides patterns of cellular growth. Second, the feedback modifies the stress patterns on the cells, consequently amplifying and propagating growth anisotropies. This mechanism may allow plants to grow organs efficiently out of the meristem by reorganizing the cellular growth rather than inflating growth rates.

Light Regulation of Axillary Bud Outgrowth Along Plant Axes: An Overview of the Roles of Sugars and Hormones

Apical dominance, the process by which the growing apical zone of the shoot inhibits bud outgrowth, involves an intricate network of several signals in the shoot. Auxin originating from plant apical region inhibits bud outgrowth indirectly. This inhibition is in particular mediated by cytokinins and strigolactones, which move from the stem to the bud and that respectively stimulate and repress bud outgrowth. The action of this hormonal network is itself modulated by sugar levels as competition for sugars, caused by the growing apical sugar sink, may deprive buds from sugars and prevents bud outgrowth partly by their signaling role. In this review, we analyze recent findings on the interaction between light, in terms of quantity and quality, and apical dominance regulation. Depending on growth conditions, light may trigger different pathways of the apical dominance regulatory network. Studies pinpoint to the key role of shoot-located cytokinin synthesis for light intensity and abscisic acid synthesis in the bud for R:FR in the regulation of bud outgrowth by light. Our analysis provides three major research lines to get a more comprehensive understanding of light effects on bud outgrowth. This would undoubtedly benefit from the use of computer modeling associated with experimental observations to deal with a regulatory system that involves several interacting signals, feedbacks, and quantitative effects.

Coupling water fluxes with cell wall mechanics in a multicellular model of plant development

The growth of plant organs is a complex process powered by osmosis that attracts water inside the cells; this influx induces simultaneously an elastic extension of the walls and pressure in the cells, called turgor pressure; above a threshold, the walls yield and the cells grow. Based on Lockhart's seminal work, various models of plant morphogenesis have been proposed, either for single cells, or focusing on the wall mechanical properties. However, the synergistic coupling of fluxes and wall mechanics has not yet been fully addressed in a multicellular model. This work lays the foundations of such a model, by simplifying as much as possible each process and putting emphasis on the coupling itself. Its emergent properties are rich and can help to understand plant morphogenesis. In particular, we show that the model can display a new type of lateral inhibitory mechanism that amplifies growth heterogeneities due e.g to cell wall loosening.

Statistics of noisy growth with mechanical feedback in elastic tissues

Tissue growth is a fundamental aspect of development and is intrinsically noisy. Stochasticity has important implications for morphogenesis, precise control of organ size, and regulation of tissue composition and heterogeneity. However, the basic statistical properties of growing tissues, particularly when growth induces mechanical stresses that can in turn affect growth rates, have received little attention. Here, we study the noisy growth of elastic sheets subject to mechanical feedback. Considering both isotropic and anisotropic growth, we find that the density-density correlation function shows power law scaling. We also consider the dynamics of marked, neutral clones of cells. We find that the areas (but not the shapes) of two clones are always statistically independent, even when they are adjacent. For anisotropic growth, we show that clone size variance scales like the average area squared and that the mode amplitudes characterizing clone shape show a slow [Formula: see text] decay, where n is the mode index. This is in stark contrast to the isotropic case, where relative variations in clone size and shape vanish at long times. The high variability in clone statistics observed in anisotropic growth is due to the presence of two soft modes-growth modes that generate no stress. Our results lay the groundwork for more in-depth explorations of the properties of noisy tissue growth in specific biological contexts.

Cell geometry determines symmetric and asymmetric division plane selection in Arabidopsis early embryos

Plant tissue architecture and organ morphogenesis rely on the proper orientation of cell divisions. Previous attempts to predict division planes from cell geometry in plants mostly focused on 2D symmetric divisions. Using the stereotyped division patterns of Arabidopsis thaliana early embryogenesis, we investigated geometrical principles underlying plane selection in symmetric and in asymmetric divisions within complex 3D cell shapes. Introducing a 3D computational model of cell division, we show that area minimization constrained on passing through the cell centroid predicts observed divisions. Our results suggest that the positioning of division planes ensues from cell geometry and gives rise to spatially organized cell types with stereotyped shapes, thus underlining the role of self-organization in the developing architecture of the embryo. Our data further suggested the rule could be interpreted as surface minimization constrained by the nucleus position, which was validated using live imaging of cell divisions in the stomatal cell lineage.

The proper positioning of division planes is key for correct development and morphogenesis of organs, in particular in plants were cellular walls prevent cell rearrangements. Elucidating how division planes are selected is therefore essential to decipher the cellular bases of plant morphogenesis. Previous attempts to identify geometrical rules relating cell shape and division plane positioning in plants mostly focused on symmetric divisions in tissues reduced to 2D geometries. Here, we combined 3D quantitative image analysis and a new 3D cell division model to evaluate the existence of geometrical rules in asymmetrical and symmetrical divisions of complex cell shapes. We show that in the early embryo of the model plant Arabidopsis thaliana, which presents stereotyped but complex cell division patterns, a single geometrical rule (area minimization constrained on passing through the cell centroid) recapitulates the complete sequence of division events. This new rule, valid for both symmetrical and asymmetrical divisions, generalizes previously proposed cell division rules and can be interpreted based on the dynamics of the cytoskeleton and on the positioning of the nucleus, a hypothesis that we validated using leaf cell division patterns. This work highlights the importance of self-organization in plant early morphogenesis and the emergence of robust cellular organizations based on geometrical feedback loops between cell geometry and division plane selection.

Modulation of tissue growth heterogeneity by responses to mechanical stress

Morphogenesis often yields organs with robust size and shapes, whereas cell growth and deformation feature significant spatiotemporal variability. Here, we investigate whether tissue responses to mechanical signals contribute to resolve this apparent paradox. We built a model of growing tissue made of fiber-like material, which may account for the cytoskeleton, polar cell-cell adhesion, or the extracellular matrix in animals and for the cell wall in plants. We considered the synthesis and remodeling of this material, as well as the modulation of synthesis by isotropic and anisotropic response to mechanical stress. Formally, our model describes an expanding, mechanoresponsive, nematic, and active fluid. We show that mechanical responses buffer localized perturbations, with two possible regimes-hyporesponsive and hyperresponsive-and the transition between the two corresponds to a minimum value of the relaxation time. Whereas robustness of shapes suggests that growth fluctuations are confined to small scales, our model yields growth fluctuations that have long-range correlations. This indicates that growth fluctuations are a significant source of heterogeneity in development. Nevertheless, we find that mechanical responses may dampen such fluctuations, with a specific magnitude of anisotropic response that minimizes heterogeneity of tissue contours. We finally discuss how our predictions might apply to the development of plants and animals. Altogether, our results call for the systematic quantification of fluctuations in growing tissues.

Neurokinin-3 receptor activation selectively prolongs atrial refractoriness by inhibition of a background K+ channel

The cardiac autonomic nervous system (ANS) controls normal atrial electrical function. The cardiac ANS produces various neuropeptides, among which the neurokinins, whose actions on atrial electrophysiology are largely unknown. We here demonstrate that the neurokinin substance-P (Sub-P) activates a neurokinin-3 receptor (NK-3R) in rabbit, prolonging action potential (AP) duration through inhibition of a background potassium current. In contrast, ventricular AP duration was unaffected by NK-3R activation. NK-3R stimulation lengthened atrial repolarization in intact rabbit hearts and consequently suppressed arrhythmia duration and occurrence in a rabbit isolated heart model of atrial fibrillation (AF). In human atrial appendages, the phenomenon of NK-3R mediated lengthening of atrial repolarization was also observed. Our findings thus uncover a pathway to selectively modulate atrial AP duration by activation of a hitherto unidentified neurokinin-3 receptor in the membrane of atrial myocytes. NK-3R stimulation may therefore represent an anti-arrhythmic concept to suppress re-entry-based atrial tachyarrhythmias, including AF.

The cardiac autonomic nervous system produces various neuropeptides, such as neurokinin substance-P (Sub-P), whose function remains largely unclear. Here, authors show that Sub-P causes a receptor-mediated prolongation of the atrial action potential through a reduced background potassium current, and prevents atrial fibrillation.

Possible roles of mechanical cell elimination intrinsic to growing tissues from the perspective of tissue growth efficiency and homeostasis

Cell competition is a phenomenon originally described as the competition between cell populations with different genetic backgrounds; losing cells with lower fitness are eliminated. With the progress in identification of related molecules, some reports described the relevance of cell mechanics during elimination. Furthermore, recent live imaging studies have shown that even in tissues composed of genetically identical cells, a non-negligible number of cells are eliminated during growth. Thus, mechanical cell elimination (MCE) as a consequence of mechanical cellular interactions is an unavoidable event in growing tissues and a commonly observed phenomenon. Here, we studied MCE in a genetically-homogeneous tissue from the perspective of tissue growth efficiency and homeostasis. First, we propose two quantitative measures, cell and tissue fitness, to evaluate cellular competitiveness and tissue growth efficiency, respectively. By mechanical tissue simulation in a pure population where all cells have the same mechanical traits, we clarified the dependence of cell elimination rate or cell fitness on different mechanical/growth parameters. In particular, we found that geometrical (specifically, cell size) and mechanical (stress magnitude) heterogeneities are common determinants of the elimination rate. Based on these results, we propose possible mechanical feedback mechanisms that could improve tissue growth efficiency and density/stress homeostasis. Moreover, when cells with different mechanical traits are mixed (e.g., in the presence of phenotypic variation), we show that MCE could drive a drastic shift in cell trait distribution, thereby improving tissue growth efficiency through the selection of cellular traits, i.e. intra-tissue "evolution". Along with the improvement of growth efficiency, cell density, stress state, and phenotype (mechanical traits) were also shown to be homogenized through growth. More theoretically, we propose a mathematical model that approximates cell competition dynamics, by which the time evolution of tissue fitness and cellular trait distribution can be predicted without directly simulating a cell-based mechanical model.

A method to generate the surface cell layer of the 3D virtual shoot apex from apical initials

BACKGROUND

The development of cell pattern in the surface cell layer of the shoot apex can be investigated in vivo by use of a time-lapse confocal images, showing naked meristem in 3D in successive times. However, how this layer is originated from apical initials and develops as a result of growth and divisions of their descendants, remains unknown. This is an open area for computer modelling. A method to generate the surface cell layer is presented on the example of the 3D paraboloidal shoot apical dome. In the used model the layer originates from three apical initials that meet at the dome summit and develops through growth and cell divisions under the isotropic surface growth, defined by the growth tensor. The cells, which are described by polyhedrons, divide anticlinally with the smallest division plane that passes depending on the used mode through the cell center, or the point found randomly near this center. The formation of the surface cell pattern is described with the attention being paid to activity of the apical initials and fates of their descendants.

RESULTS

The computer generated surface layer that included about 350 cells required about 1200 divisions of the apical initials and their derivatives. The derivatives were arranged into three more or less equal clonal sectors composed of cellular clones at different age. Each apical initial renewed itself 7-8 times to produce the sector. In the shape and location and the cellular clones the following divisions of the initial were manifested. The application of the random factor resulted in more realistic cell pattern in comparison to the pure mode. The cell divisions were analyzed statistically on the top view. When all of the division walls were considered, their angular distribution was uniform, whereas in the distribution that was limited to apical initials only, some preferences related to their arrangement at the dome summit were observed.

CONCLUSIONS

The realistic surface cell pattern was obtained. The present method is a useful tool to generate surface cell layer, study activity of initial cells and their derivatives, and how cell expansion and division are coordinated during growth. We expect its further application to clarify the question of a number and permanence or impermanence of initial cells, and possible relationship between their shape and oriented divisions, both on the ground of the growth tensor approach.

Coordination of plant cell growth and division: collective control or mutual agreement?

Plant tissue growth requires the interdependent cellular processes of cytoplasmic growth, cell wall extension and cell division, but the feedbacks that link these processes are poorly understood. Recent papers have revealed developmentally regulated coupling between plant cell growth and progression through both mitotic cycles and endocycles. Modeling has given insight into the effects of cell geometry and tissue mechanics on the orientation of cell divisions. Developmental inputs by auxin have been highlighted in the control of cell turgor, vacuole function and the microtubule dynamics that underlies oriented growth and division. Overall, recent work emphasizes growth and proliferation as processes that are negotiated within and between cells, rather than imposed on cells across tissues.

A continuous growth model for plant tissue

Morphogenesis in plants and animals involves large irreversible deformations. In plants, the response of the cell wall material to internal and external forces is determined by its mechanical properties. An appropriate model for plant tissue growth must include key features such as anisotropic and heterogeneous elasticity and cell dependent evaluation of mechanical variables such as turgor pressure, stress and strain. In addition, a growth model needs to cope with cell divisions as a necessary part of the growth process. Here we develop such a growth model, which is capable of employing not only mechanical signals but also morphogen signals for regulating growth. The model is based on a continuous equation for updating the resting configuration of the tissue. Simultaneously, material properties can be updated at a different time scale. We test the stability of our model by measuring convergence of growth results for a tissue under the same mechanical and material conditions but with different spatial discretization. The model is able to maintain a strain field in the tissue during re-meshing, which is of particular importance for modeling cell division. We confirm the accuracy of our estimations in two and three-dimensional simulations, and show that residual stresses are less prominent if strain or stress is included as input signal to growth. The approach results in a model implementation that can be used to compare different growth hypotheses, while keeping residual stresses and other mechanical variables updated and available for feeding back to the growth and material properties.

Relationship between the species-representative phenotype and intraspecific variation in Ranunculaceae floral organ and Asteraceae flower numbers

BACKGROUND AND AIMS

Phenotypic variation in floral morphologies contributes to speciation by testing various morphologies that might have higher adaptivity, leading eventually to phylogenetic diversity. Species diversity has been recognized, however, by modal morphologies where the variation is averaged out, so little is known about the relationship between the variation and the diversity.

METHODS

We analysed quantitatively the intraspecific variation of the organ numbers within flowers of Ranunculaceae, a family which branched near the monocot-eudicot separation, and the numbers of flowers within the capitula of Asteraceae, one of the most diverse families of eudicots. We used four elementary statistical quantities: mean, standard deviation (s.d.), degree of symmetry (skewness) and steepness (kurtosis).

KEY RESULTS

While these four quantities vary among populations, we found a common relationship between s.d. and the mean number of petals and sepals in Ranunculaceae and number of flowers per capitulum in Asteraceae. The s.d. is equal to the square root of the difference between the mean and specific number, showing robustness: for example, 3 in Ficaria sepals, 5 in Ranunculus petals and Anemone tepals, and 13 in Farfugium ray florets. This square-root relationship was not applicable to Eranthis petals which show little correlation between the s.d. and mean, and the stamens and carpels of Ranunculaceae whose s.d. is proportional to the mean. The specific values found in the square-root relationship provide a novel way to find the species-representative phenotype among varied morphologies.

CONCLUSIONS

The representative phenotype is, in most cases, unique to the species or genus level, despite intraspecific differences of average phenotype among populations. The type of variation shown by the statistical quantities indicates not only the robustness of the morphologies but also how flowering plants changed during evolution among representative phenotypes that eventually led to phylogenetic diversification.

Multiscale models in the biomechanics of plant growth

Plant growth occurs through the coordinated expansion of tightly adherent cells, driven by regulated softening of cell walls. It is an intrinsically multiscale process, with the integrated properties of multiple cell walls shaping the whole tissue. Multiscale models encode physical relationships to bring new understanding to plant physiology and development.

Analysis of cell division patterns in the Arabidopsis shoot apical meristem

The stereotypic pattern of cell shapes in the Arabidopsis shoot apical meristem (SAM) suggests that strict rules govern the placement of new walls during cell division. When a cell in the SAM divides, a new wall is built that connects existing walls and divides the cytoplasm of the daughter cells. Because features that are determined by the placement of new walls such as cell size, shape, and number of neighbors are highly regular, rules must exist for maintaining such order. Here we present a quantitative model of these rules that incorporates different observed features of cell division. Each feature is incorporated into a "potential function" that contributes a single term to a total analog of potential energy. New cell walls are predicted to occur at locations where the potential function is minimized. Quantitative terms that represent the well-known historical rules of plant cell division, such as those given by Hofmeister, Errera, and Sachs are developed and evaluated against observed cell divisions in the epidermal layer (L1) of Arabidopsis thaliana SAM. The method is general enough to allow additional terms for nongeometric properties such as internal concentration gradients and mechanical tensile forces.

A plant cell division algorithm based on cell biomechanics and ellipse-fitting

BACKGROUND AND AIMS

The importance of cell division models in cellular pattern studies has been acknowledged since the 19th century. Most of the available models developed to date are limited to symmetric cell division with isotropic growth. Often, the actual growth of the cell wall is either not considered or is updated intermittently on a separate time scale to the mechanics. This study presents a generic algorithm that accounts for both symmetrically and asymmetrically dividing cells with isotropic and anisotropic growth. Actual growth of the cell wall is simulated simultaneously with the mechanics.

METHODS

The cell is considered as a closed, thin-walled structure, maintained in tension by turgor pressure. The cell walls are represented as linear elastic elements that obey Hooke's law. Cell expansion is induced by turgor pressure acting on the yielding cell-wall material. A system of differential equations for the positions and velocities of the cell vertices as well as for the actual growth of the cell wall is established. Readiness to divide is determined based on cell size. An ellipse-fitting algorithm is used to determine the position and orientation of the dividing wall. The cell vertices, walls and cell connectivity are then updated and cell expansion resumes. Comparisons are made with experimental data from the literature.

KEY RESULTS

The generic plant cell division algorithm has been implemented successfully. It can handle both symmetrically and asymmetrically dividing cells coupled with isotropic and anisotropic growth modes. Development of the algorithm highlighted the importance of ellipse-fitting to produce randomness (biological variability) even in symmetrically dividing cells. Unlike previous models, a differential equation is formulated for the resting length of the cell wall to simulate actual biological growth and is solved simultaneously with the position and velocity of the vertices.

CONCLUSIONS

The algorithm presented can produce different tissues varying in topological and geometrical properties. This flexibility to produce different tissue types gives the model great potential for use in investigations of plant cell division and growth in silico.

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.

COMPARISON OF EMPIRICAL RULES DESCRIBING CELL PLATE FORMATION IN 2D COMPUTER SIMULATIONS OF APICAL MERISTEM IN PLANTS

There are two families of lines describing the cell wall pattern in root and shoot apices; periclines and anticlines. The lines of these two families are mutually orthogonal and steady during apex growth. They approximate orientation of cell walls in the apices. These lines are preserved in the growing organ. The direction of periclines and anticlines is regulated at the organ level. This paper focuses on the question: how is the pattern of periclines and anticlines maintained? There are a number of rules, which deal with the problem of the orientation of a new cell wall. We test three of them: Errera rule (the smallest possible area of a new cell wall that divides the mother cell into equal portions is chosen), Sachs rule (the new wall is perpendicular to the nearest wall from the geometric center where it is inserted) and Hejnowicz postulate (the new cell wall is perpendicular to one of the principal directions of growth rate). We tested these rules in the computer simulation of the organ growth and cell divisions.

Growth and cellular patterns in the petal epidermis of Antirrhinum majus: empirical studies

BACKGROUND AND AIMS

Analysis of cellular patterns in plant organs provides information about the orientation of cell divisions and predominant growth directions. Such an approach was employed in the present study in order to characterize growth of the asymmetrical wild-type dorsal petal and the symmetrical dorsalized petal of the backpetals mutant in Antirrhinum majus. The aims were to determine how growth in an initially symmetrical petal primordium leads to the development of mature petals differing in their symmetry, and to determine how specific cellular patterns in the petal epidermis are formed.

METHODS

Cellular patterns in the epidermis in both petal types over consecutive developmental stages were visualized and characterized quantitatively in terms of cell wall orientation and predominant types of four-cell packets. The data obtained were interpreted in terms of principal directions of growth (PDGs).

KEY RESULTS

Both petal types grew predominantly along the proximo-distal axis. Anticlinal cell walls in the epidermis exhibited a characteristic fountain-like pattern that was only slightly modified in time. New cell walls were mostly perpendicular to PDG trajectories, but this alignment could change with wall age.

CONCLUSIONS

The results indicate that the predominant orientation of cell division planes and the fountain-like cellular pattern observed in both petal types may be related to PDGs. The difference in symmetry between the two petal types arises because PDG trajectories in the field of growth rates (growth field) controlling petal growth undergo gradual redefinition. This redefinition probably takes place in both petal types but only in the wild-type does it eventually lead to asymmetry in the growth field. Two scenarios of how redefinition of PDGs may contribute to this asymmetry are considered.

A developmental basis for stochasticity in floral organ numbers

Stochasticity ubiquitously inevitably appears at all levels from molecular traits to multicellular, morphological traits. Intrinsic stochasticity in biochemical reactions underlies the typical intercellular distributions of chemical concentrations, e.g., morphogen gradients, which can give rise to stochastic morphogenesis. While the universal statistics and mechanisms underlying the stochasticity at the biochemical level have been widely analyzed, those at the morphological level have not. Such morphological stochasticity is found in foral organ numbers. Although the floral organ number is a hallmark of floral species, it can distribute stochastically even within an individual plant. The probability distribution of the floral organ number within a population is usually asymmetric, i.e., it is more likely to increase rather than decrease from the modal value, or vice versa. We combined field observations, statistical analysis, and mathematical modeling to study the developmental basis of the variation in floral organ numbers among 50 species mainly from Ranunculaceae and several other families from core eudicots. We compared six hypothetical mechanisms and found that a modified error function reproduced much of the asymmetric variation found in eudicot floral organ numbers. The error function is derived from mathematical modeling of floral organ positioning, and its parameters represent measurable distances in the floral bud morphologies. The model predicts two developmental sources of the organ-number distributions: stochastic shifts in the expression boundaries of homeotic genes and a semi-concentric (whorled-type) organ arrangement. Other models species- or organ-specifically reproduced different types of distributions that reflect different developmental processes. The organ-number variation could be an indicator of stochasticity in organ fate determination and organ positioning.

The simulation model of growth and cell divisions for the root apex with an apical cell in application to Azolla pinnata

In contrast to seed plants, the roots of most ferns have a single apical cell which is the ultimate source of all cells in the root. The apical cell has a tetrahedral shape and divides asymmetrically. The root cap derives from the distal division face, while merophytes derived from three proximal division faces contribute to the root proper. The merophytes are produced sequentially forming three sectors along a helix around the root axis. During development, they divide and differentiate in a predictable pattern. Such growth causes cell pattern of the root apex to be remarkably regular and self-perpetuating. The nature of this regularity remains unknown. This paper shows the 2D simulation model for growth of the root apex with the apical cell in application to Azolla pinnata. The field of growth rates of the organ, prescribed by the model, is of a tensor type (symplastic growth) and cells divide taking principal growth directions into account. The simulations show how the cell pattern in a longitudinal section of the apex develops in time. The virtual root apex grows realistically and its cell pattern is similar to that observed in anatomical sections. The simulations indicate that the cell pattern regularity results from cell divisions which are oriented with respect to principal growth directions. Such divisions are essential for maintenance of peri-anticlinal arrangement of cell walls and coordinated growth of merophytes during the development. The highly specific division program that takes place in merophytes prior to differentiation seems to be regulated at the cellular level.

Vertex-element models for anisotropic growth of elongated plant organs

New tools are required to address the challenge of relating plant hormone levels, hormone responses, wall biochemistry and wall mechanical properties to organ-scale growth. Current vertex-based models (applied in other contexts) can be unsuitable for simulating the growth of elongated organs such as roots because of the large aspect ratio of the cells, and these models fail to capture the mechanical properties of cell walls in sufficient detail. We describe a vertex-element model which resolves individual cells and includes anisotropic non-linear viscoelastic mechanical properties of cell walls and cell division whilst still being computationally efficient. We show that detailed consideration of the cell walls in the plane of a 2D simulation is necessary when cells have large aspect ratio, such as those in the root elongation zone of Arabidopsis thaliana, in order to avoid anomalous transverse swelling. We explore how differences in the mechanical properties of cells across an organ can result in bending and how cellulose microfibril orientation affects macroscale growth. We also demonstrate that the model can be used to simulate growth on realistic geometries, for example that of the primary root apex, using moderate computational resources. The model shows how macroscopic root shape can be sensitive to fine-scale cellular geometries.

Galacturonosyltransferase 4 silencing alters pectin composition and carbon partitioning in tomato

Pectin is a main component of the plant cell wall and is the most complex family of polysaccharides in nature. Its composition is essential for the normal growth and morphology pattern, as demonstrated by pectin-defective mutant phenotypes. Besides this basic role in plant physiology, in tomato, pectin structure contributes to very important quality traits such as fruit firmness. Sixty-seven different enzymatic activities have been suggested to be required for pectin biosynthesis, but only a few genes have been identified and studied so far. This study characterized the tomato galacturonosyltransferase (GAUT) family and performed a detailed functional study of the GAUT4 gene. The tomato genome harbours all genes orthologous to those described previously in Arabidopsis thaliana, and a transcriptional profile revealed that the GAUT4 gene was expressed at higher levels in developing organs. GAUT4-silenced tomato plants exhibited an increment in vegetative biomass associated with palisade parenchyma enlargement. Silenced fruits showed an altered pectin composition and accumulated less starch along with a reduced amount of pectin, which coincided with an increase in firmness. Moreover, the harvest index was dramatically reduced as a consequence of the reduction in the fruit weight and number. Altogether, these results suggest that, beyond its role in pectin biosynthesis, GAUT4 interferes with carbon metabolism, partitioning, and allocation. Hence, this cell-wall-related gene seems to be key in determining plant growth and fruit production in tomato.