An intracellular partitioning-based framework for tissue cell polarity in plants and animals

Computer models of cell polarity establishment in plants

Plant development is a complex task, and many processes involve changes in the asymmetric subcellular distribution of cell components that strongly depend on cell polarity. Cell polarity regulates anisotropic growth and polar localization of membrane proteins and helps to identify the cell's position relative to its neighbors within an organ. Cell polarity is critical in a variety of plant developmental processes, including embryogenesis, cell division, and response to external stimuli. The most conspicuous downstream effect of cell polarity is the polar transport of the phytohormone auxin, which is the only known hormone transported in a polar fashion in and out of cells by specialized exporters and importers. The biological processes behind the establishment of cell polarity are still unknown, and researchers have proposed several models that have been tested using computer simulations. The evolution of computer models has progressed in tandem with scientific discoveries, which have highlighted the importance of genetic, chemical, and mechanical input in determining cell polarity and regulating polarity-dependent processes such as anisotropic growth, protein subcellular localization, and the development of organ shapes. The purpose of this review is to provide a comprehensive overview of the current understanding of computer models of cell polarity establishment in plants, focusing on the molecular and cellular mechanisms, the proteins involved, and the current state of the field.

Spatial consistency of cell growth direction during organ morphogenesis requires CELLULOSE SYNTHASE INTERACTIVE1

Extracellular matrices contain fibril-like polymers often organized in parallel arrays. Although their role in morphogenesis has been long recognized, it remains unclear how the subcellular control of fibril synthesis translates into organ shape. We address this question using the Arabidopsis sepal as a model organ. In plants, cell growth is restrained by the cell wall (extracellular matrix). Cellulose microfibrils are the main load-bearing wall component, thought to channel growth perpendicularly to their main orientation. Given the key function of CELLULOSE SYNTHASE INTERACTIVE1 (CSI1) in guidance of cellulose synthesis, we investigate the role of CSI1 in sepal morphogenesis. We observe that sepals from csi1 mutants are shorter, although their newest cellulose microfibrils are more aligned compared to wild-type. Surprisingly, cell growth anisotropy is similar in csi1 and wild-type plants. We resolve this apparent paradox by showing that CSI1 is required for spatial consistency of growth direction across the sepal.

Self-organized collective cell behaviors as design principles for synthetic developmental biology

Over the past two decades, molecular cell biology has graduated from a mostly analytic science to one with substantial synthetic capability. This success is built on a deep understanding of the structure and function of biomolecules and molecular mechanisms. For synthetic biology to achieve similar success at the scale of tissues and organs, an equally deep understanding of the principles of development is required. Here, we review some of the central concepts and recent progress in tissue patterning, morphogenesis and collective cell migration and discuss their value for synthetic developmental biology, emphasizing in particular the power of (guided) self-organization and the role of theoretical advances in making developmental insights applicable in synthesis.

The mechanics of plant morphogenesis

Understanding the mechanism by which patterned gene activity leads to mechanical deformation of cells and tissues to create complex forms is a major challenge for developmental biology. Plants offer advantages for addressing this problem because their cells do not migrate or rearrange during morphogenesis, which simplifies analysis. We synthesize results from experimental analysis and computational modeling to show how mechanical interactions between cellulose fibers translate through wall, cell, and tissue levels to generate complex plant tissue shapes. Genes can modify mechanical properties and stresses at each level, though the values and pattern of stresses differ from one level to the next. The dynamic cellulose network provides elastic resistance to deformation while allowing growth through fiber sliding, which enables morphogenesis while maintaining mechanical strength.

Localization of stomatal lineage proteins reveals contrasting planar polarity patterns in Arabidopsis cotyledons

Many plant cells exhibit polarity, revealed by asymmetric localization of specific proteins within each cell.^1,2,3,4,5,6 Polarity is typically coordinated between cells across a tissue, raising the question of how coordination is achieved. One hypothesis is that mechanical stresses provide cues.⁷ This idea gains support from experiments in which cotyledons were mechanically stretched transversely to their midline.⁸ These previously published results showed that without applied tension, the stomatal lineage cell polarity marker, BREVIS RADIX-LIKE 2 (BRXL2), exhibited no significant excess in the transverse orientation. By contrast, 7 h after stretching, BRXL2 polarity distribution exhibited transverse excess, aligned with the stretch direction. These stretching experiments involved statistical comparisons between snapshots of stretched and unstretched cotyledons, with different specimens being imaged in each case.⁸ Here, we image the same cotyledon before and after stretching and find no evidence for reorientation of polarity. Instead, statistical analysis shows that cotyledons contain a pre-existing transverse excess in BRXL2 polarity orientation that is not significantly modified by applied tension. The transverse excess reflects BRLX2 being preferentially localized toward the medial side of the cell, nearer to the cotyledon midline, creating a weak medial bias. A second polarity marker, BREAKING OF ASYMMETRY IN THE STOMATAL LINEAGE (BASL), also exhibits weak medial bias in stomatal lineages, whereas ectopic expression of BASL in non-stomatal cells exhibits strong proximal bias, as previously observed in rosette leaves. This proximal bias is also unperturbed by applied tension. Our findings therefore show that cotyledons contain two near-orthogonal coordinated biases in planar polarity: mediolateral and proximodistal.

PIN-FORMED1 polarity in the plant shoot epidermis is insensitive to the polarity of neighboring cells

At the Arabidopsis shoot apex, epidermal cells are planar-polarized along an axis marked by the asymmetric localization patterns of several proteins including PIN-FORMED1 (PIN1), which facilitates the directional efflux of the plant hormone auxin to pattern phyllotaxis. While PIN1 polarity is known to be regulated non-cell autonomously via the MONOPTEROS (MP) transcription factor, how this occurs has not been determined. Here, we use mosaic expression of the serine threonine kinase PINOID (PID) to test whether PIN1 polarizes according to the polarity of neighboring cells. Our findings reveal that PIN1 is insensitive to the polarity of PIN1 in neighboring cells arguing against auxin flux or extracellular auxin concentrations acting as a polarity cue, in contrast to previous model proposals.

Tissue-targeted inorganic pyrophosphate hydrolysis in a fugu5 mutant reveals that excess inorganic pyrophosphate triggers developmental defects in a cell-autonomous manner

Excess PPi triggers developmental defects in a cell-autonomous manner. The level of inorganic pyrophosphate (PPi) must be tightly regulated in all kingdoms for the proper execution of cellular functions. In plants, the vacuolar proton pyrophosphatase (H+-PPase) has a pivotal role in PPi homeostasis. We previously demonstrated that the excess cytosolic PPi in the H+-PPase loss-of-function fugu5 mutant inhibits gluconeogenesis from seed storage lipids, arrests cell division in cotyledonary palisade tissue, and triggers a compensated cell enlargement (CCE). Moreover, PPi alters pavement cell (PC) shape, stomatal patterning, and functioning, supporting specific yet broad inhibitory effects of PPi on leaf morphogenesis. Whereas these developmental defects were totally rescued by the expression of the yeast soluble pyrophosphatase IPP1, sucrose supply alone canceled CCE in the palisade tissue but not the epidermal developmental defects. Hence, we postulated that the latter are likely triggered by excess PPi rather than a sucrose deficit. To formally test this hypothesis, we adopted a spatiotemporal approach by constructing and analyzing fugu5-1 PDF1 pro ::IPP1, fugu5-1 CLV1 pro ::IPP1, and fugu5-1 ICL pro ::IPP1, whereby PPi was removed specifically from the epidermis, palisade tissue cells, or during the 4 days following seed imbibition, respectively. It is important to note that whereas PC defects in fugu5-1 PDF1 pro ::IPP1 were completely recovered, those in fugu5-1 CLV1 pro ::IPP1 were not. In addition, phenotypic analyses of fugu5-1 ICL pro ::IPP1 lines demonstrated that the immediate removal of PPi after seed imbibition markedly improved overall plant growth, abolished CCE, but only partially restored the epidermal developmental defects. Next, the impact of spatial and temporal removal of PPi was investigated by capillary electrophoresis time-of-flight mass spectrometry (CE-TOF MS). Our analysis revealed that the metabolic profiles are differentially affected among all the above transgenic lines, and consistent with an axial role of central metabolism of gluconeogenesis in CCE. Taken together, this study provides a conceptual framework to unveil metabolic fluctuations within leaf tissues with high spatio-temporal resolution. Finally, our findings suggest that excess PPi exerts its inhibitory effect in planta in the early stages of seedling establishment in a tissue- and cell-autonomous manner.

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.

Cell biology of the leaf epidermis: Fate specification, morphogenesis, and coordination

As the outermost layer of plants, the epidermis serves as a critical interface between plants and the environment. During leaf development, the differentiation of specialized epidermal cell types, including stomatal guard cells, pavement cells, and trichomes, occurs simultaneously, each providing unique and pivotal functions for plant growth and survival. Decades of molecular-genetic and physiological studies have unraveled key players and hormone signaling specifying epidermal differentiation. However, most studies focus on only one cell type at a time, and how these distinct cell types coordinate as a unit is far from well-comprehended. Here we provide a review on the current knowledge of regulatory mechanisms underpinning the fate specification, differentiation, morphogenesis, and positioning of these specialized cell types. Emphasis is given to their shared developmental origins, fate flexibility, as well as cell cycle and hormonal controls. Furthermore, we discuss computational modeling approaches to integrate how mechanical properties of individual epidermal cell types and entire tissue/organ properties mutually influence each other. We hope to illuminate the underlying mechanisms coordinating the cell differentiation that ultimately generate a functional leaf epidermis.

Shaping the Organ: A Biologist Guide to Quantitative Models of Plant Morphogenesis

Organ morphogenesis is the process of shape acquisition initiated with a small reservoir of undifferentiated cells. In plants, morphogenesis is a complex endeavor that comprises a large number of interacting elements, including mechanical stimuli, biochemical signaling, and genetic prerequisites. Because of the large body of data being produced by modern laboratories, solving this complexity requires the application of computational techniques and analyses. In the last two decades, computational models combined with wet-lab experiments have advanced our understanding of plant organ morphogenesis. Here, we provide a comprehensive review of the most important achievements in the field of computational plant morphodynamics. We present a brief history from the earliest attempts to describe plant forms using algorithmic pattern generation to the evolution of quantitative cell-based models fueled by increasing computational power. We then provide an overview of the most common types of "digital plant" paradigms, and demonstrate how models benefit from diverse techniques used to describe cell growth mechanics. Finally, we highlight the development of computational frameworks designed to resolve organ shape complexity through integration of mechanical, biochemical, and genetic cues into a quantitative standardized and user-friendly environment.

Mechanical buckling can pattern the light-diffracting cuticle of Hibiscus trionum

Many species have cuticular striations that play a range of roles, from pollinator attraction to surface wettability. In Hibiscus trionum, the striations span multiple cells at the base of the petal to form a pattern that produces a type of iridescence. It is postulated, using theoretical models, that the pattern of striations could result from mechanical instabilities. By combining the application of mechanical stress with high-resolution imaging, we demonstrate that the cuticle buckles to create a striated pattern. Through mechanical modeling and cryo-SEM fractures, we show that the cuticle behaves like a bilayer system with a stiff film on a compliant substrate. The pattern of buckling aligns with the direction of the stress to create a larger-scale pattern. Our findings contribute to the understanding of the formation of tissue-wide patterns in living organisms.

Leaf Shape Diversity: From Genetic Modules to Computational Models

Plant leaves display considerable variation in shape. Here, we introduce key aspects of leaf development, focusing on the morphogenetic basis of leaf shape diversity. We discuss the importance of the genetic control of the amount, duration, and direction of cellular growth for the emergence of leaf form. We highlight how the combined use of live imaging and computational frameworks can help conceptualize how regulated cellular growth is translated into different leaf shapes. In particular, we focus on the morphogenetic differences between simple and complex leaves and how carnivorous plants form three-dimensional insect traps. We discuss how evolution has shaped leaf diversity in the case of complex leaves, by tinkering with organ-wide growth and local growth repression, and in carnivorous plants, by modifying the relative growth of the lower and upper sides of the leaf primordium to create insect-digesting traps.

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.

A Life Cycle for Modeling Biology at Different Scales

Modeling has become a popular tool for inquiry and discovery across biological disciplines. Models allow biologists to probe complex questions and to guide experimentation. Modeling literacy among biologists, however, has not always kept pace with the rise in popularity of these techniques and the relevant advances in modeling theory. The result is a lack of understanding that inhibits communication and ultimately, progress in data gathering and analysis. In an effort to help bridge this gap, we present a blueprint that will empower biologists to interrogate and apply models in their field. We demonstrate the applicability of this blueprint in two case studies from distinct subdisciplines of biology; developmental-biomechanics and evolutionary biology. The models used in these fields vary from summarizing dynamical mechanisms to making statistical inferences, demonstrating the breadth of the utility of models to explore biological phenomena.

Intrinsic Cell Polarity Coupled to Growth Axis Formation in Tobacco BY-2 Cells

Several plant proteins are preferentially localized to one end of a cell, allowing a polarity to be assigned to the cell. These cell polarity proteins often exhibit coordinated patterns between neighboring cells, termed tissue cell polarity. Tissue cell polarity is widespread in plants and can influence how cells grow, divide, and differentiate [1-5]. However, it is unclear whether cell polarity is established through cell-intrinsic or -extrinsic mechanisms and how polarity is coupled to growth. To address these issues, we analyzed the behavior of a tissue cell polarity protein BASL (BREAKING OF ASYMMETRY IN THE STOMATAL LINEAGE) in the simplifying context of cultured cell filaments and in protoplasts before and during regeneration. We show that BASL is polarly localized when ectopically expressed in tobacco BY-2 cell cultures. Ectopic BASL is found preferentially at the developing tips of cell filaments, likely marking a polarized molecular address. Polarity can shift during the cell cycle and is resistant to treatment with microtubule, actin or auxin transport inhibitors. BASL also exhibits polar localization in spherical protoplasts, in contrast to other polarity proteins so far tested. BASL polarity within protoplasts is dynamic and resistant to auxin transport inhibitors. As protoplasts regenerate, polarity remains dynamic in isotropically growing cells but becomes fixed in anisotropic cells and aligns with the axis of cell growth. Our findings suggest that plant cells have an intrinsic ability to polarize and that environmental or developmental cues may act by biasing the direction of this polarity and thus the orientation of anisotropic growth.

Cellular perspectives for improving mesophyll conductance

After entering the leaf, CO2 faces an intricate pathway to the site of photosynthetic fixation embedded within the chloroplasts. The efficiency of CO2 flux is hindered by a number of structural and biochemical barriers which, together, define the ease of flow of the gas within the leaf, termed mesophyll conductance. Previous authors have identified the key elements of this pathway, raising the prospect of engineering the system to improve CO2 flux and, thus, to increase leaf photosynthetic efficiency. In this review, we provide a perspective on the potential for improving the individual elements that contribute to this complex parameter. We lay particular emphasis on generation of the cellular architecture of the leaf which sets the initial boundaries of a number of mesophyll conductance parameters, incorporating an overview of the molecular transport processes which have been proposed as major facilitators of CO2 flux across structural boundaries along the pathway. The review highlights the research areas where future effort might be invested to increase our fundamental understanding of mesophyll conductance and leaf function and, consequently, to enable translation of these findings to improve the efficiency of crop photosynthesis.

The role of intracellular interactions in the collective polarization of tissues and its interplay with cellular geometry

Planar cell polarity (PCP), the long-range in-plane polarization of epithelial tissues, provides directional information that guides a multitude of developmental processes at cellular and tissue levels. While it is manifest that cells utilize both intracellular and intercellular interactions, the coupling between the two modules, essential to the coordination of collective polarization, remains an active area of investigation. We propose a generalized reaction-diffusion model to study the role of intracellular interactions in the emergence of long-range polarization, and show that the nonlocality of cytoplasmic interactions, i.e. coupling of membrane proteins localized on different cell-cell junctions, is of vital importance to the faithful detection of weak directional signals, and becomes increasingly more crucial to the stability of polarization against the deleterious effects of large geometric irregularities. We demonstrate that nonlocal interactions are necessary for geometric information to become accessible to the PCP components. The prediction of the model regarding polarization in elongated tissues, is shown to be in agreement with experimental observations, where the polarity emerges perpendicular to the axis of elongation. Core PCP is adopted as a model pathway, in term of which we interpret the model parameters. To this end, we introduce three distinct classes of mutations, (I) in membrane proteins, (II) in cytoplasmic proteins, and (III) local enhancement of geometric disorder. Comparing the in silico and in vivo phenotypes, we show that our model successfully recapitulates the salient phenotypic features of these mutations. Exploring the parameter space helps us shed light on the role of cytoplasmic proteins in cell-cell communications, and make falsifiable predictions regarding the cooperation of cytoplasmic and membrane proteins in the establishment of long-range polarization.

Planar cell polarity (PCP) is an indispensable and conserved pathway in morphogenesis. In spite of the advances in understanding the different modules of PCP, a comprehensive picture of the intracellular protein-protein interactions necessary for the emergence of long-range tissue polarity is still lacking. In order to address this question, we devised a generalized reaction-diffusion model, through which we investigated the role of cytoplasmic interactions in PCP pathways. The length scale of intracellular interactions is demonstrated to be crucial to the stability of the cytoplasmic segregation of membrane proteins in disordered tissues, as well as the capacity of polarization field for detecting the gradient and geometrical cues. Finally, three classes of mutants are investigated within the context of our model. Comparison with the in vivo observations allows us to infer the major contributions of cytoplasmic proteins to the emergence of tissue polarity, and make testable predictions regarding the cooperation of cytoplasmic and membrane proteins in the coordination of collective polarization.

Evolution of carnivorous traps from planar leaves through simple shifts in gene expression

Leaves vary from planar sheets and needle-like structures to elaborate cup-shaped traps. Here, we show that in the carnivorous plant Utricularia gibba, the upper leaf (adaxial) domain is restricted to a small region of the primordium that gives rise to the trap’s inner layer. This restriction is necessary for trap formation, because ectopic adaxial activity at early stages gives radialized leaves and no traps. We present a model that accounts for the formation of both planar and nonplanar leaves through adaxial-abaxial domains of gene activity establishing a polarity field that orients growth. In combination with an orthogonal proximodistal polarity field, this system can generate diverse leaf forms and account for the multiple evolutionary origins of cup-shaped leaves through simple shifts in gene expression.

Shaping of a three-dimensional carnivorous trap through modulation of a planar growth mechanism

Leaves display a remarkable range of forms, from flat sheets with simple outlines to cup-shaped traps. Although much progress has been made in understanding the mechanisms of planar leaf development, it is unclear whether similar or distinctive mechanisms underlie shape transformations during development of more complex curved forms. Here, we use 3D imaging and cellular and clonal analysis, combined with computational modelling, to analyse the development of cup-shaped traps of the carnivorous plant Utricularia gibba. We show that the transformation from a near-spherical form at early developmental stages to an oblate spheroid with a straightened ventral midline in the mature form can be accounted for by spatial variations in rates and orientations of growth. Different hypotheses regarding spatiotemporal control predict distinct patterns of cell shape and size, which were tested experimentally by quantifying cellular and clonal anisotropy. We propose that orientations of growth are specified by a proximodistal polarity field, similar to that hypothesised to account for Arabidopsis leaf development, except that in Utricularia, the field propagates through a highly curved tissue sheet. Independent evidence for the polarity field is provided by the orientation of glandular hairs on the inner surface of the trap. Taken together, our results show that morphogenesis of complex 3D leaf shapes can be accounted for by similar mechanisms to those for planar leaves, suggesting that simple modulations of a common growth framework underlie the shaping of a diverse range of morphologies.

Many plant and animal organs derive from tissue sheets, but how are they shaped to create the diversity of forms observed in nature? This study uses a combination of imaging and mathematical modelling to show how carnivorous plant traps shape themselves in 3D by a growth framework oriented by tissue polarity, similar to that found in planar leaves.

Development: Cell Polarity Is Coordinated over an Entire Plant Leaf

Models of leaf development have long predicted the existence of an organ-wide polarity field. Now, a robust analysis in a developing Arabidopsis leaf reveals the presence of a general and persistent cell polarity coordinated over the entire leaf.

Experimental and Theoretical Evidence for Bidirectional Signaling via Core Planar Polarity Protein Complexes in Drosophila

In developing tissues, sheets of cells become planar polarized, enabling coordination of cell behaviors. It has been suggested that "signaling" of polarity information between cells may occur either bidirectionally or monodirectionally between the molecules Frizzled (Fz) and Van Gogh (Vang). Using computational modeling we find that both bidirectional and monodirectional signaling models reproduce known non-autonomous phenotypes derived from patches of mutant tissue of key molecules but predict different phenotypes from double mutant tissue, which have previously given conflicting experimental results. Furthermore, we re-examine experimental phenotypes in the Drosophila wing, concluding that signaling is most likely bidirectional. Our modeling suggests that bidirectional signaling can be mediated either indirectly via bidirectional feedbacks between asymmetric intercellular protein complexes or directly via different affinities for protein binding in intercellular complexes, suggesting future avenues for investigation. Our findings offer insight into mechanisms of juxtacrine cell signaling and how tissue-scale properties emerge from individual cell behaviors.

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.

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.

Patterns of Polar Domains in a Spatiotemporal Model of Interacting Polarities

Polarity fields are known to exhibit long distance patterns, in both physical and biological systems. The mechanisms behind such patterns are poorly understood. Here, we describe the dynamics of polarity fields using an original physical model that generalizes classical spin models on a lattice by incorporating effective transport of polarity molecules between neighboring sites. We account for an external field and for ferromagnetic interactions between sites and prescribe the time evolution of the system using two distinct dissipative classes for nonconserved and conserved variables representing polarity orientation and magnitude, respectively. We observe two main types of steady-state configurations-disordered configurations and patterns of highly polar spots surrounded by regions with low polarity-and we characterize patterns and transitions between configurations. Our results may provide alternative pattern-generating mechanisms for materials endowed with polarity fields.

Systems Biology Approach Pinpoints Minimum Requirements for Auxin Distribution during Fruit Opening

The phytohormone auxin is implied in steering various developmental decisions during plant morphogenesis in a concentration-dependent manner. Auxin maxima have been shown to maintain meristematic activity, for example, of the root apical meristem, and position new sites of outgrowth, such as during lateral root initiation and phyllotaxis. More recently, it has been demonstrated that sites of auxin minima also provide positional information. In the developing Arabidopsis fruit, auxin minima are required for correct differentiation of the valve margin. It remains unclear, however, how this auxin minimum is generated and maintained. Here, we employ a systems biology approach to model auxin transport based on experimental observations. This allows us to determine the minimal requirements for its establishment. Our simulations reveal that two alternative processes-which we coin "flux-barrier" and "flux-passage"-are both able to generate an auxin minimum, but under different parameter settings. Both models are in principle able to yield similar auxin profiles but present qualitatively distinct patterns of auxin flux. The models were tested by tissue-specific inducible ablation, revealing that the auxin minimum in the fruit is most likely generated by a flux-passage process. Model predictions were further supported through 3D PIN localization imaging and implementing experimentally observed transporter localization. Through such an experimental-modeling cycle, we predict how the auxin minimum gradually matures during fruit development to ensure timely fruit opening and seed dispersal.

Toward a 3D model of phyllotaxis based on a biochemically plausible auxin-transport mechanism

Polar auxin transport lies at the core of many self-organizing phenomena sustaining continuous plant organogenesis. In angiosperms, the shoot apical meristem is a potentially unique system in which the two main modes of auxin-driven patterning—convergence and canalization—co-occur in a coordinated manner and in a fully three-dimensional geometry. In the epidermal layer, convergence points form, from which auxin is canalized towards inner tissue. Each of these two patterning processes has been extensively investigated separately, but the integration of both in the shoot apical meristem remains poorly understood. We present here a first attempt of a three-dimensional model of auxin-driven patterning during phyllotaxis. We base our simulations on a biochemically plausible mechanism of auxin transport proposed by Cieslak et al. (2015) which generates both convergence and canalization patterns. We are able to reproduce most of the dynamics of PIN1 polarization in the meristem, and we explore how the epidermal and inner cell layers act in concert during phyllotaxis. In addition, we discuss the mechanism by which initiating veins connect to the already existing vascular system.

The regularity of leaf arrangement around stems has long puzzled scientists. The key role played by the plant hormone auxin is now well established. On the surface of the tissue responsible for leaf formation, auxin accumulates at several points, from which new leaves eventually emerge. Auxin also guides the progression of new veins from the nascent leaves to the vascular system of the plant. Models of auxin transport have been developed to explain either auxin accumulation or auxin-driven venation. We propose the first three-dimensional model embracing both phenomena using a unifying mechanism of auxin transport. This integrative approach allows an assessment of our present knowledge on how auxin contributes to the early development of leaves. Our model reproduces many observations of auxin dynamics. It highlights how the inner and epidermal tissues act together to position new leaves. We also show that an additional, yet unknown, mechanism is required to attract new developing veins towards the main vasculature of the plant.

A theoretical framework for planar polarity establishment through interpretation of graded cues by molecular bridges

Planar polarity is a widespread phenomenon found in many tissues, allowing cells to coordinate morphogenetic movements and function. A common feature of animal planar polarity systems is the formation of molecular bridges between cells, which become polarised along a tissue axis. We propose that these bridges provide a general mechanism by which cells interpret different forms of tissue gradients to coordinate directional information. We illustrate this using a generalised and consistent modelling framework, providing a conceptual basis for understanding how different mechanisms of gradient function can generate planar polarity. We make testable predictions of how different gradient mechanisms can influence polarity direction.

Summary: This Hypothesis uses a theoretical framework to explore how molecular bridges provide a general mechanism to interpret different forms of tissue gradients to establish planar polarity.

Emergence of robust patterns from local rules during plant development

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

Mechanics, geometry and genetics of epidermal cell shape regulation: different pieces of the same puzzle

Pavement cells in the leaf epidermis of many plant species have intricate shapes that fit together much like the pieces of a jigsaw puzzle. They provide an accessible system to understand the development of complex cell shape. Since a protrusion in one cell must fit into the indentation in its neighbor, puzzle cells are also a good system to study how cell shape is coordinated across a plant tissue. Although molecular mechanisms have been proposed for both the patterning and coordination of puzzle cells, evidence is accumulating that mechanical and/or geometric cues may play a more significant role than previously thought.

Drawing a Line: Grasses and Boundaries

Delineation between distinct populations of cells is essential for organ development. Boundary formation is necessary for the maintenance of pluripotent meristematic cells in the shoot apical meristem (SAM) and differentiation of developing organs. Boundaries form between the meristem and organs, as well as between organs and within organs. Much of the research into the boundary gene regulatory network (GRN) has been carried out in the eudicot model Arabidopsis thaliana. This work has identified a dynamic network of hormone and gene interactions. Comparisons with other eudicot models, like tomato and pea, have shown key conserved nodes in the GRN and species-specific alterations, including the recruitment of the boundary GRN in leaf margin development. How boundaries are defined in monocots, and in particular the grass family which contains many of the world’s staple food crops, is not clear. In this study, we review knowledge of the grass boundary GRN during vegetative development. We particularly focus on the development of a grass-specific within-organ boundary, the ligule, which directly impacts leaf architecture. We also consider how genome engineering and the use of natural diversity could be leveraged to influence key agronomic traits relative to leaf and plant architecture in the future, which is guided by knowledge of boundary GRNs.

Spatiotemporal coordination of cell division and growth during organ morphogenesis

A developing plant organ exhibits complex spatiotemporal patterns of growth, cell division, cell size, cell shape, and organ shape. Explaining these patterns presents a challenge because of their dynamics and cross-correlations, which can make it difficult to disentangle causes from effects. To address these problems, we used live imaging to determine the spatiotemporal patterns of leaf growth and division in different genetic and tissue contexts. In the simplifying background of the speechless (spch) mutant, which lacks stomatal lineages, the epidermal cell layer exhibits defined patterns of division, cell size, cell shape, and growth along the proximodistal and mediolateral axes. The patterns and correlations are distinctive from those observed in the connected subepidermal layer and also different from the epidermal layer of wild type. Through computational modelling we show that the results can be accounted for by a dual control model in which spatiotemporal control operates on both growth and cell division, with cross-connections between them. The interactions between resulting growth and division patterns lead to a dynamic distributions of cell sizes and shapes within a deforming leaf. By modulating parameters of the model, we illustrate how phenotypes with correlated changes in cell size, cell number, and organ size may be generated. The model thus provides an integrated view of growth and division that can act as a framework for further experimental study.

Organ morphogenesis involves two coordinated processes: growth of tissue and increase in cell number through cell division. Both processes have been analysed individually in many systems and shown to exhibit complex patterns in space and time. However, it is unclear how these patterns of growth and cell division are coordinated in a growing leaf that is undergoing shape changes. We have addressed this problem using live imaging to track growth and cell division in the developing leaf of the mustard plant Arabidopsis thaliana. Using subsequent computational modelling, we propose an integrated model of leaf growth and cell division, which generates dynamic distributions of cell size and shape in different tissue layers, closely matching those observed experimentally. A key aspect of the model is dual control of spatiotemporal patterns of growth and cell division parameters. By modulating parameters in the model, we illustrate how phenotypes may correlate with changes in cell size, cell number, and organ size.

Ectopic BASL Reveals Tissue Cell Polarity throughout Leaf Development in Arabidopsis thaliana

Tissue-wide polarity fields, in which cell polarity is coordinated across the tissue, have been described for planar organs such as the Drosophila wing and are considered important for coordinating growth and differentiation [1]. In planar plant organs, such as leaves, polarity fields have been identified for subgroups of cells, such as stomatal lineages [2], trichomes [3, 4], serrations [5], or early developmental stages [6]. Here, we show that ectopic induction of the stomatal protein BASL (BREAKING OF ASYMMETRY IN THE STOMATAL LINEAGE) reveals a tissue-wide epidermal polarity field in leaves throughout development. Ectopic GFP-BASL is typically localized toward the proximal end of cells and to one lobe of mature pavement cells, revealing a polarity field that aligns with the proximodistal axis of the leaf (base to tip). The polarity field is largely parallel to the midline of the leaf but diverges in more lateral positions, particularly at later stages in development, suggesting it may be deformed during growth. The polarity field is observed in the speechless mutant, showing that it is independent of stomatal lineages, and is observed in isotropic cells, showing that cell shape anisotropy is not required for orienting polarity. Ectopic BASL forms convergence and divergence points at serrations, mirroring epidermal PIN polarity patterns, suggesting a common underlying polarity mechanism. Thus, we show that similar to the situation in animals, planar plant organs have a tissue-wide cell polarity field, and this may provide a general cellular mechanism for guiding growth and differentiation.

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Ectopic expression of BASL in Arabidopsis leaves reveals coordinated polarity

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The ectopic BASL polarity field is independent of the stomatal lineage

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The polarity field reorients around serrations, mirroring PIN1 polarity

Heterogeneity and Robustness in Plant Morphogenesis: From Cells to Organs

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

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

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

Why plants make puzzle cells, and how their shape emerges

The shape and function of plant cells are often highly interdependent. The puzzle-shaped cells that appear in the epidermis of many plants are a striking example of a complex cell shape, however their functional benefit has remained elusive. We propose that these intricate forms provide an effective strategy to reduce mechanical stress in the cell wall of the epidermis. When tissue-level growth is isotropic, we hypothesize that lobes emerge at the cellular level to prevent formation of large isodiametric cells that would bulge under the stress produced by turgor pressure. Data from various plant organs and species support the relationship between lobes and growth isotropy, which we test with mutants where growth direction is perturbed. Using simulation models we show that a mechanism actively regulating cellular stress plausibly reproduces the development of epidermal cell shape. Together, our results suggest that mechanical stress is a key driver of cell-shape morphogenesis.

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

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

Plants exhibit an astonishing diversity in architecture and morphology. A key to such diversity is the ability of their cells to coordinate and grow to reach a broad spectrum of sizes and shapes. Cell growth in plants is guided by the microtubule cytoskeleton. Here, we seek to understand how microtubules self-organize close to the cell surface. We build upon previous two-dimensional models and we consider microtubules as lines growing in three dimensions, accounting for interactions between microtubules or between microtubules and the cell surface. We show that microtubule arrays are able to adapt to various cell shapes and to reorient in response to external signals. Altogether, our results help to understand how the microtubule cytoskeleton contributes to the diversity of plant shapes and to how these shapes adapt to environment.

Self-organizing periodicity in development: organ positioning in plants

Periodic patterns during development often occur spontaneously through a process of self-organization. While reaction-diffusion mechanisms are often invoked, other types of mechanisms that involve cell-cell interactions and mechanical buckling have also been identified. Phyllotaxis, or the positioning of plant organs, has emerged as an excellent model system to study the self-organization of periodic patterns. At the macro scale, the regular spacing of organs on the growing plant shoot gives rise to the typical spiral and whorled arrangements of plant organs found in nature. In turn, this spacing relies on complex patterns of cell polarity that involve feedback between a signaling molecule - the plant hormone auxin - and its polar, cell-to-cell transport. Here, we review recent progress in understanding phyllotaxis and plant cell polarity and highlight the development of new tools that can help address the remaining gaps in our understanding.

Developmental cartography: coordination via hormonal and genetic interactions during gynoecium formation

Development in multicellular organisms requires the establishment of tissue identity through polarity cues. The Arabidopsis gynoecium presents an excellent model to study this coordination, as it comprises a complex tissue structure which is established through multiple polarity systems. The gynoecium is derived from the fusion of two carpels and forms in the centre of the flower. Many regulators of carpel development also have roles in leaf development, emphasizing the evolutionary origin of carpels as modified leaves. The gynoecium can therefore be considered as having evolved from a simple setup followed by adjustment in tissue polarity to facilitate efficient reproduction. Here, we discuss concepts to understand how hormonal and genetic systems interact to pattern the gynoecium.

On genes and form

The mechanisms by which organisms acquire their sizes and shapes through growth was a major focus of D'Arcy Thompson's book On Growth and Form. By applying mathematical and physical principles to a range of biological forms, Thompson achieved fresh insights, such as the notion that diverse biological shapes could be related through simple deformations of a coordinate system. However, Thompson considered genetics to lie outside the scope of his work, even though genetics was a growing discipline at the time the book was published. Here, we review how recent advances in cell, developmental, evolutionary and computational biology allow Thompson's ideas to be integrated with genes and the processes they influence to provide a deeper understanding of growth and morphogenesis. We consider how genes interact with subcellular-, cellular- and tissue-level processes in plants to yield patterns of growth that underlie the developmental and evolutionary shape transformations Thompson so eloquently described.

Pavement cells and the topology puzzle

D'Arcy Thompson emphasised the importance of surface tension as a potential driving force in establishing cell shape and topology within tissues. Leaf epidermal pavement cells grow into jigsaw-piece shapes, highly deviating from such classical forms. We investigate the topology of developing Arabidopsis leaves composed solely of pavement cells. Image analysis of around 50,000 cells reveals a clear and unique topological signature, deviating from previously studied epidermal tissues. This topological distribution is established early during leaf development, already before the typical pavement cell shapes emerge, with topological homeostasis maintained throughout growth and unaltered between division and maturation zones. Simulating graph models, we identify a heuristic cellular division rule that reproduces the observed topology. Our parsimonious model predicts how and when cells effectively place their division plane with respect to their neighbours. We verify the predicted dynamics through in vivo tracking of 800 mitotic events, and conclude that the distinct topology is not a direct consequence of the jigsaw piece-like shape of the cells, but rather owes itself to a strongly life history-driven process, with limited impact from cell-surface mechanics.

A Dual Function for Prickle in Regulating Frizzled Stability during Feedback-Dependent Amplification of Planar Polarity

The core planar polarity pathway coordinates epithelial cell polarity during animal development, and loss of its activity gives rise to a range of defects, from aberrant morphogenetic cell movements to failure to correctly orient structures, such as hairs and cilia. The core pathway functions via a mechanism involving segregation of its protein components to opposite cells ends, where they form asymmetric intracellular complexes that couple cell-cell polarity. This segregation is a self-organizing process driven by feedback interactions between the core proteins themselves. Despite intense efforts, the molecular pathways underlying feedback have proven difficult to elucidate using conventional genetic approaches. Here we investigate core protein function during planar polarization of the Drosophila wing by combining quantitative measurements of protein dynamics with loss-of-function genetics, mosaic analysis, and temporal control of gene expression. Focusing on the key core protein Frizzled, we show that its stable junctional localization is promoted by the core proteins Strabismus, Dishevelled, Prickle, and Diego. In particular, we show that the stabilizing function of Prickle on Frizzled requires Prickle activity in neighboring cells. Conversely, Prickle in the same cell has a destabilizing effect on Frizzled. This destabilizing activity is dependent on the presence of Dishevelled and blocked in the absence of Dynamin and Rab5 activity, suggesting an endocytic mechanism. Overall, our approach reveals for the first time essential in vivo stabilizing and destabilizing interactions of the core proteins required for self-organization of planar polarity.

Mechanical regulation of organ asymmetry in leaves

How appendages, such as plant leaves or animal limbs, develop asymmetric shapes remains a fundamental question in biology. Although ongoing research has revealed the genetic regulation of organ pattern formation, how gene activity ultimately directs organ shape remains unclear. Here, we show that leaf dorsoventral (adaxial-abaxial) polarity signals lead to mechanical heterogeneity of the cell wall, related to the methyl-esterification of cell-wall pectins in tomato and Arabidopsis. Numerical simulations predicate that mechanical heterogeneity is sufficient to produce the asymmetry seen in planar leaves. Experimental tests that alter pectin methyl-esterification, and therefore cell wall mechanical properties, support this model and lead to polar changes in gene expression, suggesting the existence of a feedback mechanism for mechanical signals in morphogenesis. Thus, mechanical heterogeneity within tissue may underlie organ shape asymmetry.

A synthetic planar cell polarity system reveals localized feedback on Fat4-Ds1 complexes

The atypical cadherins Fat and Dachsous (Ds) have been found to underlie planar cell polarity (PCP) in many tissues. Theoretical models suggest that polarity can arise from localized feedbacks on Fat-Ds complexes at the cell boundary. However, there is currently no direct evidence for the existence or mechanism of such feedbacks. To directly test the localized feedback model, we developed a synthetic biology platform based on mammalian cells expressing the human Fat4 and Ds1. We show that Fat4-Ds1 complexes accumulate on cell boundaries in a threshold-like manner and exhibit dramatically slower dynamics than unbound Fat4 and Ds1. This suggests a localized feedback mechanism based on enhanced stability of Fat4-Ds1 complexes. We also show that co-expression of Fat4 and Ds1 in the same cells is sufficient to induce polarization of Fat4-Ds1 complexes. Together, these results provide direct evidence that localized feedbacks on Fat4-Ds1 complexes can give rise to PCP.

Resolving Conflicts: Modeling Genetic Control of Plant Morphogenesis

Computational modeling of tissue morphogenesis reveals how spatiotemporal patterns of gene activity control tissue shape by introducing several types of tissue conflict. These conflicts reflect genetic modulation of processes that influence the cellular mechanical properties and may underlie the enormous diversity of forms that have evolved in plants and animals.

Virtual Plant Tissue: Building Blocks for Next-Generation Plant Growth Simulation

Motivation: Computational modeling of plant developmental processes is becoming increasingly important. Cellular resolution plant tissue simulators have been developed, yet they are typically describing physiological processes in an isolated way, strongly delimited in space and time. Results: With plant systems biology moving toward an integrative perspective on development we have built the Virtual Plant Tissue (VPTissue) package to couple functional modules or models in the same framework and across different frameworks. Multiple levels of model integration and coordination enable combining existing and new models from different sources, with diverse options in terms of input/output. Besides the core simulator the toolset also comprises a tissue editor for manipulating tissue geometry and cell, wall, and node attributes in an interactive manner. A parameter exploration tool is available to study parameter dependence of simulation results by distributing calculations over multiple systems. Availability: Virtual Plant Tissue is available as open source (EUPL license) on Bitbucket (https://bitbucket.org/vptissue/vptissue). The project has a website https://vptissue.bitbucket.io.

Mechanisms of Cell Polarization

Cell polarization is a key step in the migration, development, and organization of eukaryotic cells, both at the single cell and multicellular level. Research on the mechanisms that give rise to polarization of a given cell, and organization of polarity within a tissue has led to new understanding across cellular and developmental biology. In this review, we describe some of the history of theoretical and experimental aspects of the field, as well as some interesting questions and challenges for the future.