The genetics of geometry

A 3-component module maintains sepal flatness in Arabidopsis

As in origami, morphogenesis in living systems heavily relies on tissue curving and folding through the interplay between biochemical and biomechanical cues. By contrast, certain organs maintain their flat posture over several days. Here, we identified a pathway that is required for the maintenance of organ flatness, taking the sepal, the outermost floral organ, in Arabidopsis as a model system. Through genetic, cellular, and mechanical approaches, our results demonstrate that the global gene expression regulator VERNALIZATION INDEPENDENCE 4 (VIP4) fine-tunes the mechanical properties of sepal cell walls and maintains balanced growth on both sides of the sepals, mainly by orchestrating the distribution pattern of AUXIN RESPONSE FACTOR 3 (ARF3). vip4 mutation results in softer cell walls and faster cell growth on the adaxial sepal side, which eventually cause sepals to bend outward. Downstream of VIP4, ARF3 works through modulating auxin to downregulate pectin methylesterase VANGUARD1, resulting in decreased cell wall stiffness. Thus, our work unravels a 3-component module that relates hormonal patterns to organ curvature and actively maintains sepal flatness during its growth.

Machine learning-enabled high-throughput industry screening of edible oils

Long-term consumption of mixed fraudulent edible oils increases the risk of developing of chronic diseases which has been a threat to the public health globally. The complicated global supply-chain is making the industry malpractices had often gone undetected. In order to restore the confidence of consumers, traceability (and accountability) of every level in the supply chain is vital. In this work, we shown that machine learning (ML) assisted windowed spectroscopy (e.g., visible-band, infra-red band) produces high-throughput, non-destructive, and label-free authentication of edible oils (e.g., olive oils, sunflower oils), offers the feasibility for rapid analysis of large-scale industrial screening. We report achieving high-level of discriminant (AUC > 0.96) in the large-scale (n ≈ 11,500) of adulteration in olive oils. Notably, high clustering fidelity of 'spectral fingerprints' achieved created opportunity for (hypothesis-free) self-sustaining large database compilation which was never possible without machine learning. (137 words).

Spatiotemporally distinct responses to mechanical forces shape the developing seed of Arabidopsis

Organ morphogenesis depends on mechanical interactions between cells and tissues. These interactions generate forces that can be sensed by cells and affect key cellular processes. However, how mechanical forces, together with biochemical signals, contribute to the shaping of complex organs is still largely unclear. We address this question using the seed of Arabidopsis as a model system. We show that seeds first experience a phase of rapid anisotropic growth that is dependent on the response of cortical microtubule (CMT) to forces, which guide cellulose deposition according to shape-driven stresses in the outermost layer of the seed coat. However, at later stages of development, we show that seed growth is isotropic and depends on the properties of an inner layer of the seed coat that stiffens its walls in response to tension but has isotropic material properties. Finally, we show that the transition from anisotropic to isotropic growth is due to the dampening of cortical microtubule responses to shape-driven stresses. Altogether, our work supports a model in which spatiotemporally distinct mechanical responses control the shape of developing seeds in Arabidopsis.

A mechanical transition from tension to buckling underlies the jigsaw puzzle shape morphogenesis of histoblasts in the Drosophila epidermis

The polygonal shape of cells in proliferating epithelia is a result of the tensile forces of the cytoskeletal cortex and packing geometry set by the cell cycle. In the larval Drosophila epidermis, two cell populations, histoblasts and larval epithelial cells, compete for space as they grow on a limited body surface. They do so in the absence of cell divisions. We report a striking morphological transition of histoblasts during larval development, where they change from a tensed network configuration with straight cell outlines at the level of adherens junctions to a highly folded morphology. The apical surface of histoblasts shrinks while their growing adherens junctions fold, forming deep lobules. Volume increase of growing histoblasts is accommodated basally, compensating for the shrinking apical area. The folded geometry of apical junctions resembles elastic buckling, and we show that the imbalance between the shrinkage of the apical domain of histoblasts and the continuous growth of junctions triggers buckling. Our model is supported by laser dissections and optical tweezer experiments together with computer simulations. Our analysis pinpoints the ability of histoblasts to store mechanical energy to a much greater extent than most other epithelial cell types investigated so far, while retaining the ability to dissipate stress on the hours time scale. Finally, we propose a possible mechanism for size regulation of histoblast apical size through the lateral pressure of the epidermis, driven by the growth of cells on a limited surface. Buckling effectively compacts histoblasts at their apical plane and may serve to avoid physical harm to these adult epidermis precursors during larval life. Our work indicates that in growing nondividing cells, compressive forces, instead of tension, may drive cell morphology.

The Ins and Outs of Homeodomain-Leucine Zipper/Hormone Networks in the Regulation of Plant Development

The generation of complex plant architectures depends on the interactions among different molecular regulatory networks that control the growth of cells within tissues, ultimately shaping the final morphological features of each structure. The regulatory networks underlying tissue growth and overall plant shapes are composed of intricate webs of transcriptional regulators which synergize or compete to regulate the expression of downstream targets. Transcriptional regulation is intimately linked to phytohormone networks as transcription factors (TFs) might act as effectors or regulators of hormone signaling pathways, further enhancing the capacity and flexibility of molecular networks in shaping plant architectures. Here, we focus on homeodomain-leucine zipper (HD-ZIP) proteins, a class of plant-specific transcriptional regulators, and review their molecular connections with hormonal networks in different developmental contexts. We discuss how HD-ZIP proteins emerge as key regulators of hormone action in plants and further highlight the fundamental role that HD-ZIP/hormone networks play in the control of the body plan and plant growth.

A 3-component module maintains sepal flatness in Arabidopsis

As in origami, morphogenesis in living systems heavily relies on tissue curving and folding, through the interplay between biochemical and biomechanical cues. In contrast, certain organs maintain their flat posture over several days. Here we identified a pathway, which is required for the maintenance of organ flatness, taking the sepal, the outermost floral organ, in Arabidopsis as a model system. Through genetic, cellular and mechanical approaches, our results demonstrate that global gene expression regulator VERNALIZATION INDEPENDENCE 4 (VIP4) fine-tunes the mechanical properties of sepal cell walls and maintains balanced growth on both sides of the sepals, mainly by orchestrating the distribution pattern of AUXIN RESPONSE FACTOR 3 (ARF3). vip4 mutation results in softer cell walls and faster cell growth on the adaxial sepal side, which eventually cause sepals to bend outward. Downstream of VIP4, ARF3 works through modulating auxin signaling to down-regulate pectin methylesterase VANGUARD1, resulting in decreased cell wall stiffness. Our work unravels a 3-component module, which relates hormonal patterns to organ curvature, and actively maintains sepal flatness during its growth.

A quantitative morphospace of multicellular organ design in the plant Arabidopsis

Organ function emerges from the interactions between their constituent cells. The investigation of cellular organization can provide insight into organ function following structure-function relationships. Here, we investigate the extent to which properties in cellular organization can arise "for free" as an emergent property of embedding cells in space versus those that are actively generated by patterning processes. Default cellular configurations were established using three-dimensional (3D) digital tissue models. Network-based analysis of these synthetic cellular assemblies established a quantitative topological baseline of cellular organization, granted by virtue of passive spatial packing and the minimal amount of order that emerges for free in tessellated tissues. A 3D cellular-resolution digital tissue atlas for the model plant species Arabidopsis was generated, and the extent to which the organs in this organism conform to the default configurations was established through statistical comparisons with digital tissue models. Cells in different tissues of Arabidopsis do not conform to random packing arrangements to varying degrees. Most closely matching the random models was the undifferentiated shoot apical meristem (SAM) from which aerial organs emanate. By contrast, leaf and sepal tissue showed the greatest deviation from this baseline, suggesting these to be the most "complex" tissues in Arabidopsis. Investigation of the patterning principles responsible for the gap between these tissues and default patterns revealed cell elongation and the introduction of air spaces to contribute toward additional organ patterning complexity. This work establishes a quantitative morphospace to understand the principles of organ construction and its diversity within a single organism.

Axes and polarities in leaf vein formation

For multicellular organisms to develop, cells must grow, divide, and differentiate along preferential or exclusive orientations or directions. Moreover, those orientations, or axes, and directions, or polarities, must be coordinated between cells within and between tissues. Therefore, how axes and polarities are coordinated between cells is a key question in biology. In animals, such coordination mainly depends on cell migration and direct interaction between proteins protruding from the plasma membrane. Both cell movements and direct cell-cell interactions are prevented in plants by cell walls that surround plant cells and keep them apart and in place. Therefore, plants have evolved unique mechanisms to coordinate their cell axes and polarities. Here I will discuss evidence suggesting that understanding how leaf veins form may uncover those unique mechanisms. Indeed, unlike previously thought, the cell-to-cell polar transport of the plant hormone auxin along developing veins cannot account for many features of vein patterning. Instead, those features can be accounted for by models of vein patterning that combine polar auxin transport with auxin diffusion through plasmodesmata along the axis of developing veins. Though it remains unclear whether such a combination of polar transport and axial diffusion of auxin can account for the formation of the variety of vein patterns found in plant leaves, evidence suggests that such a combined mechanism may control plant developmental processes beyond vein patterning.

Interspersed expression of CUP-SHAPED COTYLEDON2 and REDUCED COMPLEXITY shapes Cardamine hirsuta complex leaf form

How genetically regulated growth shapes organ form is a key problem in developmental biology. Here, we investigate this problem using the leaflet-bearing complex leaves of Cardamine hirsuta as a model. Leaflet development requires the action of two growth-repressing transcription factors: REDUCED COMPLEXITY (RCO), a homeodomain protein, and CUP-SHAPED COTYLEDON2 (CUC2), a NAC-domain protein. However, how their respective growth-repressive actions are integrated in space and time to generate complex leaf forms remains unknown. By using live imaging, we show that CUC2 and RCO are expressed in an interspersed fashion along the leaf margin, creating a distinctive striped pattern. We find that this pattern is functionally important because forcing RCO expression in the CUC2 domain disrupts auxin-based marginal patterning and can abolish leaflet formation. By combining genetic perturbations with time-lapse imaging and cellular growth quantifications, we provide evidence that RCO-mediated growth repression occurs after auxin-based leaflet patterning and in association with the repression of cell proliferation. Additionally, through the use of genetic mosaics, we show that RCO is sufficient to repress both cellular growth and proliferation in a cell-autonomous manner. This mechanism of growth repression is different to that of CUC2, which occurs in proliferating cells. Our findings clarify how the two growth repressors RCO and CUC2 coordinate to subdivide developing leaf primordia into distinct leaflets and generate the complex leaf form. They also indicate different relationships between growth repression and cell proliferation in the patterning and post-patterning stages of organogenesis.

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.

Morphogenesis at the shoot meristem

Shoot apical meristems are populations of stem cells which initiate the aerial parts of higher plants. Work during the last decades has revealed a complex network of molecular regulators, which control both meristem maintenance and the production of different types of organs. The behavior of this network in time and space is defined by the local interactions between regulators and also involves hormonal regulation. In particular, auxin and cytokinin are intimately implicated in the coordination of gene expression patterns. To control growth patterns at the shoot meristem the individual components of the network influence directions and rates of cell growth. This requires interference with the mechanical properties of the cells. How this complex multiscale process, characterized by multiple feedbacks, is controlled remains largely an open question. Fortunately, genetics, live imaging, computational modelling and a number of other recently developed tools offer interesting albeit challenging perspectives.

Leaf morphogenesis: The multifaceted roles of mechanics

Plants produce a rich diversity of biological forms, and the diversity of leaves is especially notable. Mechanisms of leaf morphogenesis have been studied in the past two decades, with a growing focus on the interactive roles of mechanics in recent years. Growth of plant organs involves feedback by mechanical stress: growth induces stress, and stress affects growth and morphogenesis. Although much attention has been given to potential stress-sensing mechanisms and cellular responses, the mechanical principles guiding morphogenesis have not been well understood. Here we synthesize the overarching roles of mechanics and mechanical stress in multilevel and multiple stages of leaf morphogenesis, encompassing leaf primordium initiation, phyllotaxis and venation patterning, and the establishment of complex mature leaf shapes. Moreover, the roles of mechanics at multiscale levels, from subcellular cytoskeletal molecules to single cells to tissues at the organ scale, are articulated. By highlighting the role of mechanical buckling in the formation of three-dimensional leaf shapes, this review integrates the perspectives of mechanics and biology to provide broader insights into the mechanobiology of leaf morphogenesis.

Quantitative Live Confocal Imaging in AquilegiaFloral Meristems

In this study, we present a detailed protocol for live imaging and quantitative analysis of floral meristem development in Aquilegia coerulea, a member of the buttercup family (Ranunculaceae). Using confocal microscopy and the image analysis software MorphoGraphX, we were able to examine the cellular growth dynamics during floral organ primordia initiation, and the transition from floral meristem proliferation to termination. This protocol provides a powerful tool to study the development of the meristem and floral organ primordia, and should be easily adaptable to many plant lineages, including other emerging model systems. It will allow researchers to explore questions outside the scope of common model systems.

Looking beyond the gene network - metabolic and mechanical cell drivers of leaf morphogenesis

The above-ground organs in plants display a rich diversity, yet they grow to characteristic sizes and shapes. Organ morphogenesis progresses through a sequence of key events, which are robustly executed spatiotemporally as an emerging property of intrinsic molecular networks while adapting to various environmental cues. This Review focuses on the multiscale control of leaf morphogenesis. Beyond the list of known genetic determinants underlying leaf growth and shape, we focus instead on the emerging novel mechanisms of metabolic and biomechanical regulations that coordinate plant cell growth non-cell-autonomously. This reveals how metabolism and mechanics are not solely passive outcomes of genetic regulation but play instructive roles in leaf morphogenesis. Such an integrative view also extends to fluctuating environmental cues and evolutionary adaptation. This synthesis calls for a more balanced view on morphogenesis, where shapes are considered from the standpoints of geometry, genetics, energy and mechanics, and as emerging properties of the cellular expression of these different properties.

Plant cell walls as mechanical signaling hubs for morphogenesis

The instructive role of mechanical cues during morphogenesis is increasingly being recognized in all kingdoms. Patterns of mechanical stress depend on shape, growth and external factors. In plants, the cell wall integrates these three parameters to function as a hub for mechanical feedback. Plant cells are interconnected by cell walls that provide structural integrity and yet are flexible enough to act as both targets and transducers of mechanical cues. Such cues may act locally at the subcellular level or across entire tissues, requiring tight control of both cell-wall composition and cell-cell adhesion. Here we focus on how changes in cell-wall chemistry and mechanics act in communicating diverse cues to direct growth asymmetries required for plant morphogenesis. We explore the role of cellulose microfibrils, microtubule arrays and pectin methylesterification in the transduction of mechanical cues during morphogenesis. Plant hormones can affect the mechanochemical composition of the cell wall and, in turn, the cell wall can modulate hormone signaling pathways, as well as the tissue-level distribution of these hormones. This also leads us to revisit the position of biochemical growth factors, such as plant hormones, acting both upstream and downstream of mechanical signaling. Finally, while the structure of the cell wall is being elucidated with increasing precision, existing data clearly show that the integration of genetic, biochemical and theoretical studies will be essential for a better understanding of the role of the cell wall as a hub for the mechanical control of plant morphogenesis.

Computational Models of Auxin-Driven Patterning in Shoots

Auxin regulates many aspects of plant development and behavior, including the initiation of new outgrowth, patterning of vascular systems, control of branching, and responses to the environment. Computational models have complemented experimental studies of these processes. We review these models from two perspectives. First, we consider cellular and tissue-level models of interaction between auxin and its transporters in shoots. These models form a coherent body of results exploring different hypotheses pertinent to the patterning of new outgrowth and vascular strands. Second, we consider models operating at the level of plant organs and entire plants. We highlight techniques used to reduce the complexity of these models, which provide a path to capturing the essence of studied phenomena while running simulations efficiently.

Live-imaging provides an atlas of cellular growth dynamics in the stamen

Development of multicellular organisms is a complex process involving precise coordination of growth among individual cells. Understanding organogenesis requires measurements of cellular behaviors over space and time. In plants, such a quantitative approach has been successfully used to dissect organ development in both leaves and external floral organs, such as sepals. However, the observation of floral reproductive organs is hampered as they develop inside tightly closed floral buds, and are therefore difficult to access for imaging. We developed a confocal time-lapse imaging method, applied here to Arabidopsis (Arabidopsis thaliana), which allows full quantitative characterization of the development of stamens, the male reproductive organs. Our lineage tracing reveals the early specification of the filament and the anther. Formation of the anther lobes is associated with a temporal increase of growth at the lobe surface that correlates with intensive growth of the developing locule. Filament development is very dynamic and passes through three distinct phases: (1) initial intense, anisotropic growth, and high cell proliferation; (2) restriction of growth and proliferation to the filament proximal region; and (3) resumption of intense and anisotropic growth, displaced to the distal portion of the filament, without cell proliferation. This quantitative atlas of cellular growth dynamics provides a solid framework for future studies into stamen development.

Measuring Intercellular Interface Area in Plant Tissues Using Quantitative 3D Image Analysis

The cells which make up plant tissues remain fixed together through shared cell walls. Cell-to-cell communication principally takes place through these shared interfaces through a combination of plasmodesmata, transporters, and the apoplastic space. To better understand the capacity for intercellular communication in plant tissues, this chapter outlines a method which can be used to quantify the surface area of shared intercellular interfaces using whole mount imaging and quantitative 3D image analysis. This method allows the potential for intercellular communication as prescribed by cellular architecture to be measured at single cell resolution.

Sculpting the surface: Structural patterning of plant epidermis

Plant epidermis are multifunctional surfaces that directly affect how plants interact with animals or microorganisms and influence their ability to harvest or protect from abiotic factors. To do this, plants rely on minuscule structures that confer remarkable properties to their outer layer. These microscopic features emerge from the hierarchical organization of epidermal cells with various shapes and dimensions combined with different elaborations of the cuticle, a protective film that covers plant surfaces. Understanding the properties and functions of those tridimensional elements as well as disentangling the mechanisms that control their formation and spatial distribution warrant a multidisciplinary approach. Here we show how interdisciplinary efforts of coupling modern tools of experimental biology, physics, and chemistry with advanced computational modeling and state-of-the art microscopy are yielding broad new insights into the seemingly arcane patterning processes that sculpt the outer layer of plants.

The root meristem is shaped by brassinosteroid control of cell geometry

Growth extent and direction determine cell and whole-organ architecture. How they are spatio-temporally modulated to control size and shape is not well known. Here we tackled this question by studying the effect of brassinosteroid (BR) signalling on the structure of the root meristem. Quantification of the three-dimensional geometry of thousands of individual meristematic cells across different tissue types showed that the modulation of BR signalling yields distinct changes in growth rate and anisotropy, which affects the time that cells spend in the meristem and has a strong impact on the final root form. By contrast, the hormone effect on cell volume was minor, establishing cell volume as invariant to the effect of BR. Thus, BR has the highest effect on cell shape and growth anisotropy, regulating the overall longitudinal and radial growth of the meristem, while maintaining a coherent distribution of cell sizes. Moving from single-cell quantification to the whole organ, we developed a computational model of radial growth. The simulation demonstrates how differential BR-regulated growth between the inner and outer tissues shapes the meristem and thus explains the non-intuitive outcomes of tissue-specific perturbation of BR signalling. The combined experimental data and simulation suggest that the inner and outer tissues have distinct but coordinated roles in growth regulation.

Plant growth: the What, the How, and the Why

Growth is a widely used term in plant science and ecology, but it can have different meanings depending on the context and the spatiotemporal scale of analysis. At the meristem level, growth is associated with the production of cells and initiation of new organs. At the organ or plant scale and over short time periods, growth is often used synonymously with tissue expansion, while over longer time periods the increase in biomass is a common metric. At even larger temporal and spatial scales, growth is mostly described as net primary production. Here, we first address the question 'what is growth?'. We propose a general framework to distinguish between the different facets of growth, and the corresponding physiological processes, environmental drivers and mathematical formalisms. Based on these different definitions, we then review how plant growth can be measured and analysed at different organisational, spatial and temporal scales. We conclude by discussing why gaining a better understanding of the different facets of plant growth is essential to disentangle genetic and environmental effects on the phenotype, and to uncover the causalities around source or sink limitations of plant growth.

A multiscale analysis of early flower development in Arabidopsis provides an integrated view of molecular regulation and growth control

We have analyzed the link between the gene regulation and growth during the early stages of flower development in Arabidopsis. Starting from time-lapse images, we generated a 4D atlas of early flower development, including cell lineage, cellular growth rates, and the expression patterns of regulatory genes. This information was introduced in MorphoNet, a web-based platform. Using computational models, we found that the literature-based molecular network only explained a minority of the gene expression patterns. This was substantially improved by adding regulatory hypotheses for individual genes. Correlating growth with the combinatorial expression of multiple regulators led to a set of hypotheses for the action of individual genes in morphogenesis. This identified the central factor LEAFY as a potential regulator of heterogeneous growth, which was supported by quantifying growth patterns in a leafy mutant. By providing an integrated view, this atlas should represent a fundamental step toward mechanistic models of flower development.

Long-read genome assembly and genetic architecture of fruit shape in the bottle gourd

The bottle gourd (Lagenaria siceraria, Cucurbitaceae) is an important horticultural crop exhibiting tremendous diversity in fruit shape. The genetic architecture of fruit shape variation in this species remains unknown. We assembled a long-read-based, high-quality reference genome (ZAAS_Lsic_2.0) with a contig N50 value over 390-fold greater than the existing reference genomes. We then focused on dissection of fruit shape using a one-step geometric morphometrics-based functional mapping approach. We identified 11 quantitative trait loci (QTLs) responsible for fruit shape (fsQTLs), reconstructed their visible effects and revealed syntenic relationships of bottle gourd fsQTLs with 12 fsQTLs previously reported in cucumber, melon or watermelon. Homologs of several well-known and newly identified fruit shape genes, including SUN, OFP, AP2 and auxin transporters, were comapped with bottle gourd QTLs.

What shoots can teach about theories of plant form

Plants generate a large variety of shoot forms with regular geometries. These forms emerge primarily from the activity of a stem cell niche at the shoot tip. Recent efforts have established a theoretical framework of form emergence at the shoot tip, which has empowered the use of modelling in conjunction with biological approaches to begin to disentangle the biochemical and physical mechanisms controlling form development at the shoot tip. Here, we discuss how these advances get us closer to identifying the construction principles of plant shoot tips. Considering the current limits of our knowledge, we propose a roadmap for developing a general theory of form development at the shoot tip.

Of Cells, Strands, and Networks: Auxin and the Patterned Formation of the Vascular System

Throughout plant development, vascular cells continually form from within a population of seemingly equivalent cells. Vascular cells connect end to end to form continuous strands, and vascular strands connect at both or either end to form networks of exquisite complexity and mesmerizing beauty. Here we argue that experimental evidence gained over the past few decades implicates the plant hormone auxin-its production, transport, perception, and response-in all the steps that lead to the patterned formation of the plant vascular system, from the formation of vascular cells to their connection into vascular networks. We emphasize the organizing principles of the cell- and tissue-patterning process, rather than its molecular subtleties. In the picture that emerges, cells compete for an auxin-dependent, cell-polarizing signal; positive feedback between cell polarization and cell-to-cell movement of the polarizing signal leads to gradual selection of cell files; and selected cell files differentiate into vascular strands that drain the polarizing signal from the neighboring cells. Although the logic of the patterning process has become increasingly clear, the molecular details remain blurry; the future challenge will be to bring them into razor-sharp focus.

Organ geometry channels reproductive cell fate in the Arabidopsis ovule primordium

In multicellular organisms, sexual reproduction requires the separation of the germline from the soma. In flowering plants, the female germline precursor differentiates as a single spore mother cell (SMC) as the ovule primordium forms. Here, we explored how organ growth contributes to SMC differentiation. We generated 92 annotated 3D images at cellular resolution in Arabidopsis. We identified the spatio-temporal pattern of cell division that acts in a domain-specific manner as the primordium forms. Tissue growth models uncovered plausible morphogenetic principles involving a spatially confined growth signal, differential mechanical properties, and cell growth anisotropy. Our analysis revealed that SMC characteristics first arise in more than one cell but SMC fate becomes progressively restricted to a single cell during organ growth. Altered primordium geometry coincided with a delay in the fate restriction process in katanin mutants. Altogether, our study suggests that tissue geometry channels reproductive cell fate in the Arabidopsis ovule primordium.

How Mechanical Forces Shape Plant Organs

Plants produce organs of various shapes and sizes. While much has been learned about genetic regulation of organogenesis, the integration of mechanics in the process is also gaining attention. Here, we consider the role of forces as instructive signals in organ morphogenesis. Turgor pressure is the primary cause of mechanical signals in developing organs. Because plant cells are glued to each other, mechanical signals act, in essence, at multiple scales, through cell wall contiguity and water flux. In turn, cells use such signals to resist mechanical stress, for instance, by reinforcing their cell walls. We show that the three elemental shapes behind plant organs - spheres, cylinders and lamina - can be actively maintained by such a mechanical feedback. Combinations of this 3-letter alphabet can generate more complex shapes. Furthermore, mechanical conflicts emerge at the boundary between domains exhibiting different growth rates or directions. These secondary mechanical signals contribute to three other organ shape features - folds, shape reproducibility and growth arrest. The further integration of mechanical signals with the molecular network offers many fruitful prospects for the scientific community, including the role of proprioception in organ shape robustness or the definition of cell and organ identities as a result of an interplay between biochemical and mechanical signals.

Turing conditions for pattern forming systems on evolving manifolds

The study of pattern-forming instabilities in reaction-diffusion systems on growing or otherwise time-dependent domains arises in a variety of settings, including applications in developmental biology, spatial ecology, and experimental chemistry. Analyzing such instabilities is complicated, as there is a strong dependence of any spatially homogeneous base states on time, and the resulting structure of the linearized perturbations used to determine the onset of instability is inherently non-autonomous. We obtain general conditions for the onset and structure of diffusion driven instabilities in reaction-diffusion systems on domains which evolve in time, in terms of the time-evolution of the Laplace-Beltrami spectrum for the domain and functions which specify the domain evolution. Our results give sufficient conditions for diffusive instabilities phrased in terms of differential inequalities which are both versatile and straightforward to implement, despite the generality of the studied problem. These conditions generalize a large number of results known in the literature, such as the algebraic inequalities commonly used as a sufficient criterion for the Turing instability on static domains, and approximate asymptotic results valid for specific types of growth, or specific domains. We demonstrate our general Turing conditions on a variety of domains with different evolution laws, and in particular show how insight can be gained even when the domain changes rapidly in time, or when the homogeneous state is oscillatory, such as in the case of Turing-Hopf instabilities. Extensions to higher-order spatial systems are also included as a way of demonstrating the generality of the approach.

Multiscale integration of environmental stimuli in plant tropism produces complex behaviors

Plant tropism refers to the directed movement of an organ or organism in response to external stimuli. Typically, these stimuli induce hormone transport that triggers cell growth or deformation. In turn, these local cellular changes create mechanical forces on the plant tissue that are balanced by an overall deformation of the organ, hence changing its orientation with respect to the stimuli. This complex feedback mechanism takes place in a three-dimensional growing plant with varying stimuli depending on the environment. We model this multiscale process in filamentary organs for an arbitrary stimulus by explicitly linking hormone transport to local tissue deformation leading to the generation of mechanical forces and the deformation of the organ in three dimensions. We show, as examples, that the gravitropic, phototropic, nutational, and thigmotropic dynamic responses can be easily captured by this framework. Further, the integration of evolving stimuli and/or multiple contradictory stimuli can lead to complex behavior such as sun following, canopy escape, and plant twining.

Linking Genes to Shape in Plants Using Morphometrics

A transition from qualitative to quantitative descriptors of morphology has been facilitated through the growing field of morphometrics, representing the conversion of shapes and patterns into numbers. The analysis of plant form at the macromorphological scale using morphometric approaches quantifies what is commonly referred to as a phenotype. Quantitative phenotypic analysis of individuals with contrasting genotypes in turn provides a means to establish links between genes and shapes. The path from a gene to a morphological phenotype is, however, not direct, with instructive information progressing both across multiple scales of biological complexity and through nonintuitive feedback, such as mechanical signals. In this review, we explore morphometric approaches used to perform whole-plant phenotyping and quantitative approaches in capture processes in the mesoscales, which bridge the gaps between genes and shapes in plants. Quantitative frameworks involving both the computational simulation and the discretization of data into networks provide a putative path to predicting emergent shape from underlying genetic programs.

The development of body and organ shape

Background

Organisms show an incredibly diverse array of body and organ shapes that are both unique to their taxon and important for adapting to their environment. Achieving these specific shapes involves coordinating the many processes that transform single cells into complex organs, and regulating their growth so that they can function within a fully-formed body.

Main text

Conceptually, body and organ shape can be separated in two categories, although in practice these categories need not be mutually exclusive. Body shape results from the extent to which organs, or parts of organs, grow relative to each other. The patterns of relative organ size are characterized using allometry. Organ shape, on the other hand, is defined as the geometric features of an organ’s component parts excluding its size. Characterization of organ shape is frequently described by the relative position of homologous features, known as landmarks, distributed throughout the organ. These descriptions fall into the domain of geometric morphometrics.

Conclusion

In this review, we discuss the methods of characterizing body and organ shape, the developmental programs thought to underlie each, highlight when and how the mechanisms regulating body and organ shape might overlap, and provide our perspective on future avenues of research.

Studying cell wall mechanics using an automated confocal micro-extensometer

Recently there has been a lot of interest in quantifying mechanical properties and responses to mechanical stress. This type of data can provide insight into how growth is regulated, the processes that enable it to occur and how stresses that build up during development feedback onto development itself. However, quantifying mechanical properties of plant cell walls is difficult as the material is heterogeneous, anisotropic and shows complex time-dependent properties as well as being subject to the complex geometries of plant tissues. It is therefore necessary to have a range of methods to enable the quantification of these properties at different resolutions and time-scales. Here we provide a guide to quantifying mechanical properties in Arabidopsis thaliana hypocotyls using a tensile testing device an automated confocal micro-extensometer (ACME). In contrast to indentation methods, tensile testing provides information on the tissue as a whole and in the plane of the sample. We also detail how to adapt the method to use it for quantifying responses to mechanical stress.

Shaping Organs: Shared Structural Principles Across Kingdoms

Development encapsulates the morphogenesis of an organism from a single fertilized cell to a functional adult. A critical part of development is the specification of organ forms. Beyond the molecular control of morphogenesis, shape in essence entails structural constraints and thus mechanics. Revisiting recent results in biophysics and development, and comparing animal and plant model systems, we derive key overarching principles behind the formation of organs across kingdoms. In particular, we highlight how growing organs are active rather than passive systems and how such behavior plays a role in shaping the organ. We discuss the importance of considering different scales in understanding how organs form. Such an integrative view of organ development generates new questions while calling for more cross-fertilization between scientific fields and model system communities.

Turing and Benjamin–Feir instability mechanisms in non-autonomous systems

The Turing and Benjamin–Feir instabilities are two of the primary instability mechanisms useful for studying the transition from homogeneous states to heterogeneous spatial or spatio-temporal states in reaction–diffusion systems. We consider the case when the underlying reaction–diffusion system is non-autonomous or has a base state which varies in time, as in this case standard approaches, which rely on temporal eigenvalues, break down. We are able to establish respective criteria for the onset of each instability using comparison principles, obtaining inequalities which involve the in general time-dependent model parameters and their time derivatives. In the autonomous limit where the base state is constant in time, our results exactly recover the respective Turing and Benjamin–Feir conditions known in the literature. Our results make the Turing and Benjamin–Feir analysis amenable for a wide collection of applications, and allow one to better understand instabilities emergent due to a variety of non-autonomous mechanisms, including time-varying diffusion coefficients, time-varying reaction rates, time-dependent transitions between reaction kinetics and base states which change in time (such as heteroclinic connections between unique steady states, or limit cycles), to name a few examples.

Floral organ development goes live

The chance to watch floral organs develop live is not to be missed! Here, we outline reasons why quantitative, live-cell imaging is an important approach to study floral morphogenesis, and provide a basic workflow of how to get started. We highlight key advances in morphodynamics of lateral organ development, and discuss recent work that uses live confocal imaging to address the regulation of floral organ number, its robustness, and patterning mechanisms that exploit stochasticity.

Plant Biology: Bending of Plant Organs

Tissue folding allows for the development of complex three-dimensional morphologies necessary for various functions. A new study provides novel mechanistic insights linking plant cell wall and hormonal pathways involved in bending of plant tissue through regulation of differential growth.

Interplay between Cell Wall and Auxin Mediates the Control of Differential Cell Elongation during Apical Hook Development

Differential growth plays a crucial role during morphogenesis [1-3]. In plants, development occurs within mechanically connected tissues, and local differences in cell expansion lead to deformations at the organ level, such as buckling or bending [4, 5]. During early seedling development, bending of hypocotyl by differential cell elongation results in apical hook structure that protects the shoot apical meristem from being damaged during emergence from the soil [6, 7]. Plant hormones participate in apical hook development, but not how they mechanistically drive differential growth [8]. Here, we present evidence of interplay between hormonal signals and cell wall in auxin-mediated differential cell elongation using apical hook development as an experimental model. Using genetic and cell biological approaches, we show that xyloglucan (a major primary cell wall component) mediates asymmetric mechanical properties of epidermal cells required for hook development. The xxt1 xxt2 mutant, deficient in xyloglucan [9], displays severe defects in differential cell elongation and hook development. Analysis of xxt1 xxt2 mutant reveals a link between cell wall and transcriptional control of auxin transporters PINFORMEDs (PINs) and AUX1 crucial for establishing the auxin response maxima required for preferential repression of elongation of the cells on the inner side of the hook. Genetic evidence identifies auxin response factor ARF2 as a negative regulator acting downstream of xyloglucan-dependent control of hook development and transcriptional control of polar auxin transport. Our results reveal a crucial feedback process between the cell wall and transcriptional control of polar auxin transport, underlying auxin-dependent control of differential cell elongation in plants.

Water Affects Morphogenesis of Growing Aquatic Plant Leaves

Lotus leaves floating on water usually experience short-wavelength edge wrinkling that decays toward the center, while the leaves growing above water normally morph into a global bending cone shape with long rippled waves near the edge. Observations suggest that the underlying water (liquid substrate) significantly affects the morphogenesis of leaves. To understand the biophysical mechanism under such phenomena, we develop mathematical models that can effectively account for inhomogeneous differential growth of floating and freestanding leaves to quantitatively predict formation and evolution of their morphology. We find, both theoretically and experimentally, that the short-wavelength buckled configuration is energetically favorable for growing membranes lying on liquid, while the global buckling shape is more preferable for suspended ones. Other influencing factors such as the stem or vein, heterogeneity, and dimension are also investigated. Our results provide a fundamental insight into a variety of plant morphogenesis affected by water foundation and suggest that such surface instabilities can be harnessed for morphology control of biomimetic deployable structures using substrate or edge actuation.

Arabidopsis IPGA1 is a microtubule-associated protein essential for cell expansion during petal morphogenesis

Unlike animal cells, plant cells do not possess centrosomes that serve as microtubule organizing centers; how microtubule arrays are organized throughout plant morphogenesis remains poorly understood. We report here that Arabidopsis INCREASED PETAL GROWTH ANISOTROPY 1 (IPGA1), a previously uncharacterized microtubule-associated protein, regulates petal growth and shape by affecting cortical microtubule organization. Through a genetic screen, we showed that IPGA1 loss-of-function mutants displayed a phenotype of longer and narrower petals, as well as increased anisotropic cell expansion of the petal epidermis in the late phases of flower development. Map-based cloning studies revealed that IPGA1 encodes a previously uncharacterized protein that colocalizes with and directly binds to microtubules. IPGA1 plays a negative role in the organization of cortical microtubules into parallel arrays oriented perpendicular to the axis of cell elongation, with the ipga1-1 mutant displaying increased microtubule ordering in petal abaxial epidermal cells. The IPGA1 family is conserved among land plants and its homologs may have evolved to regulate microtubule organization. Taken together, our findings identify IPGA1 as a novel microtubule-associated protein and provide significant insights into IPGA1-mediated microtubule organization and petal growth anisotropy.

Developmental mechanisms involved in the diversification of flowers

We all appreciate the fantastic diversity of flowers. How flowers diversified, however, remains largely enigmatic. The mechanisms underlying the diversification of flowers are complex because the overall appearance of a flower is determined by many factors, such as the shape and size of its receptacle, and the arrangement, number, type, shape and colour of floral organs. Modifications of the developmental trajectories of a flower and its components, therefore, can lead to the generation of new floral types. In this Review, by summarizing the recent progress in studying the initiation, identity determination, morphogenesis and maturation of floral organs, we present our current understanding of the mechanisms underlying the diversification of flowers.

Connected through the force: mechanical signals in plant development

As multicellular organisms, plants acquire characteristic shapes through a complex set of biological processes known as morphogenesis. Biochemical signalling underlies much of development, as it allows cells to acquire specific identities based on their position within tissues and organs. However, as growing physical structures, plants, and their constituent cells, also experience internal and external physical forces that can be perceived and can influence key processes such as growth, polarity, and gene expression. This process, which adds another layer of control to growth and development, has important implications for plant morphogenesis. This review provides an overview of recent research into the role of mechanical signals in plant development and aims to show how mechanical signalling can be used, in concert with biochemical signals, as a cue allowing cells and tissues to coordinate their behaviour and to add robustness to developmental processes.

Growth and biomechanics of shoot organs

Plant organs arise through complex interactions between biological and physical factors that control morphogenesis. While there has been tremendous progress in the understanding of the genetics behind development, we know much less about how mechanical forces control growth in plants. In recent years, new multidisciplinary research combining genetics, live-imaging, physics, and computational modeling has begun to fill this gap by revealing the crucial role of biomechanics in the establishment of plant organs. In this review, we provide an overview of our current understanding of growth during initiation, patterning, and expansion of shoot lateral organs. We discuss how growth is controlled by physical forces, and how mechanical stresses generated during growth can control morphogenesis at the level of both cells and tissues. Understanding the mechanical basis of growth and morphogenesis in plants is in its early days, and many puzzling facts are yet to be deciphered.

Formal description of plant morphogenesis

Plant morphogenesis may be characterized by complex feedback mechanisms between signals specifying growth and by the growth of the plant body itself. Comprehension of such feedback mechanisms is an ongoing research task and can be aided with formal descriptions of morphogenesis. In this review, we present a number of established mathematical paradigms that are useful to the formal representation of plant shape, and of biomechanical and biochemical signaling. Specifically, we discuss work from a range of research areas including plant biology, material sciences, fluid dynamics, and computer graphics. Treating plants as organized systems of information processing allows us to compare these different mathematical methods in terms of their expressive power of biological hypotheses. This is an attempt to bring together a large number of computational modeling concepts and make them accessible to the analytical as well as empirical student of plant morphogenesis.

Plant behaviour in response to the environment: information processing in the solid state

Information processing and storage underpins many biological processes of vital importance to organism survival. Like animals, plants also acquire, store and process environmental information relevant to their fitness, and this is particularly evident in their decision-making. The control of plant organ growth and timing of their developmental transitions are carefully orchestrated by the collective action of many connected computing agents, the cells, in what could be addressed as distributed computation. Here, we discuss some examples of biological information processing in plants, with special interest in the connection to formal computational models drawn from theoretical frameworks. Research into biological processes with a computational perspective may yield new insights and provide a general framework for information processing across different substrates. This article is part of the theme issue 'Liquid brains, solid brains: How distributed cognitive architectures process information'.

Multicellular Systems Biology: Quantifying Cellular Patterning and Function in Plant Organs Using Network Science

Organ function is at least partially shaped and constrained by the organization of their constituent cells. Extensive investigation has revealed mechanisms explaining how these patterns are generated, with less being known about their functional relevance. In this paper, a methodology to discretize and quantitatively analyze cellular patterning is described. By performing global organ-scale cellular interaction mapping, the organization of cells can be extracted and analyzed using network science. This provides a means to take the developmental analysis of cellular organization in complex organisms beyond qualitative descriptions and provides data-driven approaches to inferring cellular function. The bridging of a structure-function relationship in hypocotyl epidermal cell patterning through global topological analysis provides support for this approach. The analysis of cellular topologies from patterning mutants further enables the contribution of gene activity toward the organizational properties of tissues to be linked, bridging molecular and tissue scales. This systems-based approach to investigate multicellular complexity paves the way to uncovering the principles of complex organ design and achieving predictive genotype-phenotype mapping.

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.

Volumetric finite-element modelling of biological growth

Differential growth is the driver of tissue morphogenesis in plants, and also plays a fundamental role in animal development. Although the contributions of growth to shape change have been captured through modelling tissue sheets or isotropic volumes, a framework for modelling both isotropic and anisotropic volumetric growth in three dimensions over large changes in size and shape has been lacking. Here, we describe an approach based on finite-element modelling of continuous volumetric structures, and apply it to a range of forms and growth patterns, providing mathematical validation for examples that admit analytic solution. We show that a major difference between sheet and bulk tissues is that the growth of bulk tissue is more constrained, reducing the possibility of tissue conflict resolution through deformations such as buckling. Tissue sheets or cylinders may be generated from bulk shapes through anisotropic specified growth, oriented by a polarity field. A second polarity field, orthogonal to the first, allows sheets with varying lengths and widths to be generated, as illustrated by the wide range of leaf shapes observed in nature. The framework we describe thus provides a key tool for developing hypotheses for plant morphogenesis and is also applicable to other tissues that deform through differential growth or contraction.