Auxin-driven patterning with unidirectional fluxes

Developmental timing in plants

Plants exhibit reproducible timing of developmental events at multiple scales, from switches in cell identity to maturation of the whole plant. Control of developmental timing likely evolved for similar reasons that humans invented clocks: to coordinate events. However, whereas clocks are designed to run independently of conditions, plant developmental timing is strongly dependent on growth and environment. Using simplified models to convey key concepts, we review how growth-dependent and inherent timing mechanisms interact with the environment to control cyclical and progressive developmental transitions in plants.

Regulation of tissue growth in plants - A mathematical modeling study on shade avoidance response in Arabidopsis hypocotyls

Introduction

Plant growth is a plastic phenomenon controlled both by endogenous genetic programs and by environmental cues. The embryonic stem, the hypocotyl, is an ideal model system for the quantitative study of growth due to its relatively simple geometry and cellular organization, and to its essentially unidirectional growth pattern. The hypocotyl of Arabidopsis thaliana has been studied particularly well at the molecular-genetic level and at the cellular level, and it is the model of choice for analysis of the shade avoidance syndrome (SAS), a growth reaction that allows plants to compete with neighboring plants for light. During SAS, hypocotyl growth is controlled primarily by the growth hormone auxin, which stimulates cell expansion without the involvement of cell division.

Methods

We assessed hypocotyl growth at cellular resolution in Arabidopsis mutants defective in auxin transport and biosynthesis and we designed a mathematical auxin transport model based on known polar and non-polar auxin transporters (ABCB1, ABCB19, and PINs) and on factors that control auxin homeostasis in the hypocotyl. In addition, we introduced into the model biophysical properties of the cell types based on precise cell wall measurements.

Results and Discussion

Our model can generate the observed cellular growth patterns based on auxin distribution along the hypocotyl resulting from production in the cotyledons, transport along the hypocotyl, and general turnover of auxin. These principles, which resemble the features of mathematical models of animal morphogen gradients, allow to generate robust shallow auxin gradients as they are expected to exist in tissues that exhibit quantitative auxin-driven tissue growth, as opposed to the sharp auxin maxima generated by patterning mechanisms in plant development.

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.

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.

Organ Patterning at the Shoot Apical Meristem (SAM): The Potential Role of the Vascular System

Auxin, which is transported in the outermost cell layer, is one of the major players involved in plant organ initiation and positioning at the shoot apical meristem (SAM). However, recent studies have recognized the role of putative internal signals as an important factor collaborating with the well-described superficial pathway of organogenesis regulation. Different internal signals have been proposed; however, their nature and transport route have not been precisely determined. Therefore, in this mini-review, we aimed to summarize the current knowledge regarding the auxin-dependent regulation of organ positioning at the SAM and to discuss the vascular system as a potential route for internal signals. In addition, as regular organ patterning is a universal phenomenon, we focus on the role of the vasculature in this process in the major lineages of land plants, i.e., bryophytes, lycophytes, ferns, gymnosperms, and angiosperms.

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.

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.

Developmental regulation of leaf venation patterns: monocot versus eudicots and the role of auxin

Organisation and patterning of the vascular network in land plants varies in different taxonomic, developmental and environmental contexts. In leaves, the degree of vascular strand connectivity influences both light and CO₂ harvesting capabilities as well as hydraulic capacity. As such, developmental mechanisms that regulate leaf venation patterning have a direct impact on physiological performance. Development of the leaf venation network requires the specification of procambial cells within the ground meristem of the primordium and subsequent proliferation and differentiation of the procambial lineage to form vascular strands. An understanding of how diverse venation patterns are manifest therefore requires mechanistic insight into how procambium is dynamically specified in a growing leaf. A role for auxin in this process was identified many years ago, but questions remain. In this review we first provide an overview of the diverse venation patterns that exist in land plants, providing an evolutionary perspective. We then focus on the developmental regulation of leaf venation patterns in angiosperms, comparing patterning in eudicots and monocots, and the role of auxin in each case. Although common themes emerge, we conclude that the developmental mechanisms elucidated in eudicots are unlikely to fully explain how parallel venation patterns in monocot leaves are elaborated.

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.

Auxin canalization: From speculative models toward molecular players

Among the most fascinated properties of the plant hormone auxin is its ability to promote formation of its own directional transport routes. These gradually narrowing auxin channels form from the auxin source toward the sink and involve coordinated, collective polarization of individual cells. Once established, the channels provide positional information, along which new vascular strands form, for example, during organogenesis, regeneration, or leave venation. The main prerequisite of this still mysterious auxin canalization mechanism is a feedback between auxin signaling and its directional transport. This is manifested by auxin-induced re-arrangements of polar, subcellular localization of PIN-FORMED (PIN) auxin exporters. Immanent open questions relate to how position of auxin source and sink as well as tissue context are sensed and translated into tissue polarization and how cells communicate to polarize coordinately. Recently, identification of the first molecular players opens new avenues into molecular studies of this intriguing example of self-organizing plant development.

Integration of Core Mechanisms Underlying Plant Aerial Architecture

Over the last decade or so important progress has been made in identifying and understanding a set of patterning mechanisms that have the potential to explain many aspects of plant morphology. These include the feedback loop between mechanical stresses and interphase microtubules, the regulation of plant cell polarity and the role of adaxial and abaxial cell type boundaries. What is perhaps most intriguing is how these mechanisms integrate in a combinatorial manner that provides a means to generate a large variety of commonly seen plant morphologies. Here, I review our current understanding of these mechanisms and discuss the links between them.

A coupled mechano-biochemical model for cell polarity guided anisotropic root growth

Plants develop new organs to adjust their bodies to dynamic changes in the environment. How independent organs achieve anisotropic shapes and polarities is poorly understood. To address this question, we constructed a mechano-biochemical model for Arabidopsis root meristem growth that integrates biologically plausible principles. Computer model simulations demonstrate how differential growth of neighboring tissues results in the initial symmetry-breaking leading to anisotropic root growth. Furthermore, the root growth feeds back on a polar transport network of the growth regulator auxin. Model, predictions are in close agreement with in vivo patterns of anisotropic growth, auxin distribution, and cell polarity, as well as several root phenotypes caused by chemical, mechanical, or genetic perturbations. Our study demonstrates that the combination of tissue mechanics and polar auxin transport organizes anisotropic root growth and cell polarities during organ outgrowth. Therefore, a mobile auxin signal transported through immobile cells drives polarity and growth mechanics to coordinate complex organ development.

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.

A Molecular Pinball Machine of the Plasma Membrane Regulates Plant Growth-A New Paradigm

Novel molecular pinball machines of the plasma membrane control cytosolic Ca²⁺ levels that regulate plant metabolism. The essential components involve: 1. an auxin-activated proton pump; 2. arabinogalactan glycoproteins (AGPs); 3. Ca²⁺ channels; 4. auxin-efflux "PIN" proteins. Typical pinball machines release pinballs that trigger various sound and visual effects. However, in plants, "proton pinballs" eject Ca²⁺ bound by paired glucuronic acid residues of numerous glycomodules in periplasmic AGP-Ca²⁺. Freed Ca²⁺ ions flow down the electrostatic gradient through open Ca²⁺ channels into the cytosol, thus activating numerous Ca²⁺-dependent activities. Clearly, cytosolic Ca²⁺ levels depend on the activity of the proton pump, the state of Ca²⁺ channels and the size of the periplasmic AGP-Ca²⁺ capacitor; proton pump activation is a major regulatory focal point tightly controlled by the supply of auxin. Auxin efflux carriers conveniently known as "PIN" proteins (null mutants are pin-shaped) pump auxin from cell to cell. Mechanosensitive Ca²⁺ channels and their activation by reactive oxygen species (ROS) are yet another factor regulating cytosolic Ca²⁺. Cell expansion also triggers proton pump/pinball activity by the mechanotransduction of wall stress via Hechtian adhesion, thus forming a Hechtian oscillator that underlies cycles of wall plasticity and oscillatory growth. Finally, the Ca²⁺ homeostasis of plants depends on cell surface external storage as a source of dynamic Ca²⁺, unlike the internal ER storage source of animals, where the added regulatory complexities ranging from vitamin D to parathormone contrast with the elegant simplicity of plant life. This paper summarizes a sixty-year Odyssey.

What remains of the evidence for auxin feedback on PIN polarity patterns?

In light of recent findings, the feedback between auxin and PIN that plays a major role in models for self-organized auxin patterning requires revisiting.

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.

Auxin biosynthesis and cellular efflux act together to regulate leaf vein patterning

Our current understanding of vein development in leaves is based on canalization of the plant hormone auxin into self-reinforcing streams which determine the sites of vascular cell differentiation. By comparison, how auxin biosynthesis affects leaf vein patterning is less well understood. Here, after observing that inhibiting polar auxin transport rescues the sparse leaf vein phenotype in auxin biosynthesis mutants, we propose that the processes of auxin biosynthesis and cellular auxin efflux work in concert during vein development. By using computational modeling, we show that localized auxin maxima are able to interact with mechanical forces generated by the morphological constraints which are imposed during early primordium development. This interaction is able to explain four fundamental characteristics of midvein morphology in a growing leaf: (i) distal cell division; (ii) coordinated cell elongation; (iii) a midvein positioned in the center of the primordium; and (iv) a midvein which is distally branched. Domains of auxin biosynthetic enzyme expression are not positioned by auxin canalization, as they are observed before auxin efflux proteins polarize. This suggests that the site-specific accumulation of auxin, as regulated by the balanced action of cellular auxin efflux and local auxin biosynthesis, is crucial for leaf vein formation.

The canalization hypothesis - challenges and alternatives

The 'canalization hypothesis' was suggested 50 years ago by Tsvi Sachs to account for the formation of vascular strands in response to wounding or auxin application. The hypothesis proposes that positive feedback between auxin movement through a cell and the cell's auxin conductivity leads to the gradual selection of narrow 'canals' of polar auxin transport that will differentiate into vascular strands. Though the hypothesis has provided an invaluable conceptual framework to understand the patterned formation of vascular strands, evidence has been accumulating that seems to be incompatible with the hypothesis. We suggest that the challenging evidence is incompatible with current interpretations of the hypothesis but not with the concept at the core of the hypothesis' original formulation.

Auxin canalization and vascular tissue formation by TIR1/AFB-mediated auxin signaling in Arabidopsis

Plant survival depends on vascular tissues, which originate in a self-organizing manner as strands of cells co-directionally transporting the plant hormone auxin. The latter phenomenon (also known as auxin canalization) is classically hypothesized to be regulated by auxin itself via the effect of this hormone on the polarity of its own intercellular transport. Correlative observations supported this concept, but molecular insights remain limited. In the current study, we established an experimental system based on the model Arabidopsis thaliana, which exhibits auxin transport channels and formation of vasculature strands in response to local auxin application. Our methodology permits the genetic analysis of auxin canalization under controllable experimental conditions. By utilizing this opportunity, we confirmed the dependence of auxin canalization on a PIN-dependent auxin transport and nuclear, TIR1/AFB-mediated auxin signaling. We also show that leaf venation and auxin-mediated PIN repolarization in the root require TIR1/AFB signaling. Further studies based on this experimental system are likely to yield better understanding of the mechanisms underlying auxin transport polarization in other developmental contexts.

Mathematical Modelling of Auxin Transport in Plant Tissues: Flux Meets Signalling and Growth

Plant hormone auxin has critical roles in plant growth, dependent on its heterogeneous distribution in plant tissues. Exactly how auxin transport and developmental processes such as growth coordinate to achieve the precise patterns of auxin observed experimentally is not well understood. Here we use mathematical modelling to examine the interplay between auxin dynamics and growth and their contribution to formation of patterns in auxin distribution in plant tissues. Mathematical models describing the auxin-related signalling pathway, PIN and AUX1 dynamics, auxin transport, and cell growth in plant tissues are derived. A key assumption of our models is the regulation of PIN proteins by the auxin-responsive ARF-Aux/IAA signalling pathway, with upregulation of PIN biosynthesis by ARFs. Models are analysed and solved numerically to examine the long-time behaviour and auxin distribution. Changes in auxin-related signalling processes are shown to be able to trigger transition between passage- and spot-type patterns in auxin distribution. The model was also shown to be able to generate isolated cells with oscillatory dynamics in levels of components of the auxin signalling pathway which could explain oscillations in levels of ARF targets that have been observed experimentally. Cell growth was shown to have influence on PIN polarisation and determination of auxin distribution patterns. Numerical simulation results indicate that auxin-related signalling processes can explain the different patterns in auxin distributions observed in plant tissues, whereas the interplay between auxin transport and growth can explain the ‘reverse-fountain’ pattern in auxin distribution observed at plant root tips.

Coordination of tissue cell polarity by auxin transport and signaling

Plants coordinate the polarity of hundreds of cells during vein formation, but how they do so is unclear. The prevailing hypothesis proposes that GNOM, a regulator of membrane trafficking, positions PIN-FORMED auxin transporters to the correct side of the plasma membrane; the resulting cell-to-cell, polar transport of auxin would coordinate tissue cell polarity and induce vein formation. Contrary to predictions of the hypothesis, we find that vein formation occurs in the absence of PIN-FORMED or any other intercellular auxin-transporter; that the residual auxin-transport-independent vein-patterning activity relies on auxin signaling; and that a GNOM-dependent signal acts upstream of both auxin transport and signaling to coordinate tissue cell polarity and induce vein formation. Our results reveal synergism between auxin transport and signaling, and their unsuspected control by GNOM in the coordination of tissue cell polarity during vein patterning, one of the most informative expressions of tissue cell polarization in plants.

Plants, animals and other living things grow and develop over their lifetimes: for example, oak trees come from acorns and chickens begin their lives as eggs. To achieve these transformations, the cells in those living things must grow, divide and change their shape and other features.

Plants and animals specify the directions in which their cells will grow and develop by gathering specific proteins to one side of the cells. This makes one side different from all the other sides, which the cells use as an internal compass that points in one direction. To align their internal compasses, animal cells touch one another and often move around inside the body. Plant cells, on the other hand, are surrounded by a wall that keeps them apart and prevents them from moving around. So how do plant cells align their internal compasses?

Scientists have long thought that a protein called GNOM aligns the internal compasses of plant cells. The hypothesis proposes that GNOM gathers another protein, called PIN1, to one side of a cell. PIN1 would then pump a plant hormone known as auxin out of this first cell and, in doing so, would also drain auxin away from the cell on the opposite side. In this second cell, GNOM would then gather PIN1 to the side facing the first cell, and this process would repeat until all the cells' compasses were aligned.

To test this hypothesis, Verna et al. combined microscopy with genetic approaches to study how cells' compasses are aligned in the leaves of a plant called Arabidopsis thaliana. The experiments revealed that auxin needs to move from cell-to-cell to align the cells’ compasses. However, contrary to the above hypothesis, this movement of auxin was not sufficient: the cells also needed to be able to detect and respond to the auxin that entered them. Along with controlling how auxin moved between the cells, GNOM also regulated how the cells responded to the auxin.

These findings reveal how plants specify which directions their cells grow and develop. In the future, this knowledge may eventually aid efforts to improve crop yields by controlling the growth and development of crop plants.

The dynamic mosaic phenotypes of flowering plants

Ecological interaction and adaptation both depend on phenotypic characteristics. In contrast with the common conception of the 'adult' phenotype, plant bodies develop continuously during their lives. Furthermore, the different units (metamers) that comprise plant bodies are not identical copies, but vary extensively within individuals. These characteristics foster recognition of plant phenotypes as dynamic mosaics. We elaborate this conception based largely on a wide-ranging review of developmental, ecological and evolutionary studies of plant reproduction, and identify its utility in the analysis of plant form, function and diversification. An expanded phenotypic conception is warranted because dynamic mosaic features affect plant performance and evolve. Evidence demonstrates that dynamic mosaic phenotypes enable functional ontogeny, division of labour, resource and mating efficiency. In addition, dynamic mosaic features differ between individuals and experience phenotypic selection. Investigation of the characteristics and roles of dynamic and mosaic features of plant phenotypes benefits from considering within-individual variation as a function-valued trait that can be analysed with functional data methods. Phenotypic dynamics and within-individual variation arise despite an individual's genetic uniformity, and develop largely by heterogeneous gene expression and associated hormonal control. These characteristics can be heritable, so that dynamic mosaic phenotypes can evolve and diversify by natural selection.

Auxin transport model for leaf venation

The plant hormone auxin controls many aspects of the development of plants. One striking dynamical feature is the self-organization of leaf venation patterns which is driven by high levels of auxin within vein cells. The auxin transport is mediated by specialized membrane-localized proteins. Many venation models have been based on polarly localized efflux-mediator proteins of the PIN family. Here, we investigate a modelling framework for auxin transport with a positive feedback between auxin fluxes and transport capacities that are not necessarily polar, i.e. directional across a cell wall. Our approach is derived from a discrete graph-based model for biological transportation networks, where cells are represented by graph nodes and intercellular membranes by edges. The edges are not a priori oriented and the direction of auxin flow is determined by its concentration gradient along the edge. We prove global existence of solutions to the model and the validity of Murray's Law for its steady states. Moreover, we demonstrate with numerical simulations that the model is able connect an auxin source-sink pair with a mid-vein and that it can also produce branching vein patterns. A significant innovative aspect of our approach is that it allows the passage to a formal macroscopic limit which can be extended to include network growth. We perform mathematical analysis of the macroscopic formulation, showing the global existence of weak solutions for an appropriate parameter range.

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.

The Role of the Primary Cell Wall in Plant Morphogenesis

Morphogenesis remains a riddle, wrapped in a mystery, inside an enigma. It remains a formidable problem viewed from many different perspectives of morphology, genetics, and computational modelling. We propose a biochemical reductionist approach that shows how both internal and external physical forces contribute to plant morphogenesis via mechanical stress⁻strain transduction from the primary cell wall tethered to the plasma membrane by a specific arabinogalactan protein (AGP). The resulting stress vector, with direction defined by Hechtian adhesion sites, has a magnitude of a few piconewtons amplified by a hypothetical Hechtian growth oscillator. This paradigm shift involves stress-activated plasma membrane Ca2+ channels and auxin-activated H⁺-ATPase. The proton pump dissociates periplasmic AGP-glycomodules that bind Ca2+. Thus, as the immediate source of cytosolic Ca2+, an AGP-Ca2+ capacitor directs the vectorial exocytosis of cell wall precursors and auxin efflux (PIN) proteins. In toto, these components comprise the Hechtian oscillator and also the gravisensor. Thus, interdependent auxin and Ca2+ morphogen gradients account for the predominance of AGPs. The size and location of a cell surface AGP-Ca2+ capacitor is essential to differentiation and explains AGP correlation with all stages of morphogenetic patterning from embryogenesis to root and shoot. Finally, the evolutionary origins of the Hechtian oscillator in the unicellular Chlorophycean algae reflect the ubiquitous role of chemiosmotic proton pumps that preceded DNA at the dawn of life.

Spatial regularity control of phyllotaxis pattern generated by the mutual interaction between auxin and PIN1

Phyllotaxis, the arrangement of leaves on a plant stem, is well known because of its beautiful geometric configuration, which is derived from the constant spacing between leaf primordia. This phyllotaxis is established by mutual interaction between a diffusible plant hormone auxin and its efflux carrier PIN1, which cooperatively generate a regular pattern of auxin maxima, small regions with high auxin concentrations, leading to leaf primordia. However, the molecular mechanism of the regular pattern of auxin maxima is still largely unknown. To better understand how the phyllotaxis pattern is controlled, we investigated mathematical models based on the auxin-PIN1 interaction through linear stability analysis and numerical simulations, focusing on the spatial regularity control of auxin maxima. As in previous reports, we first confirmed that this spatial regularity can be reproduced by a highly simplified and abstract model. However, this model lacks the extracellular region and is not appropriate for considering the molecular mechanism. Thus, we investigated how auxin maxima patterns are affected under more realistic conditions. We found that the spatial regularity is eliminated by introducing the extracellular region, even in the presence of direct diffusion between cells or between extracellular spaces, and this strongly suggests the existence of an unknown molecular mechanism. To unravel this mechanism, we assumed a diffusible molecule to verify various feedback interactions with auxin-PIN1 dynamics. We revealed that regular patterns can be restored by a diffusible molecule that mediates the signaling from auxin to PIN1 polarization. Furthermore, as in the one-dimensional case, similar results are observed in the two-dimensional space. These results provide a great insight into the theoretical and molecular basis for understanding the phyllotaxis pattern. Our theoretical analysis strongly predicts a diffusible molecule that is pivotal for the phyllotaxis pattern but is yet to be determined experimentally.

Coordination of cell polarity and the patterning of leaf vein networks

During development, the behavior of cells in tissues is coordinated along specific orientations or directions by coordinating the polar localization of components in those cells. The coordination of such cell polarity is perhaps nowhere more spectacular than in developing leaves, where the polarity of hundreds of cells is coordinated in the leaf epidermis and inner tissue to pattern vein networks. Available evidence suggests that the spectacular coordination of cell polarity that patterns vein networks is controlled by auxin transport and levels, and by genes that have been implicated in the polar localization of auxin transporters.

WRKY23 is a component of the transcriptional network mediating auxin feedback on PIN polarity

Auxin is unique among plant hormones due to its directional transport that is mediated by the polarly distributed PIN auxin transporters at the plasma membrane. The canalization hypothesis proposes that the auxin feedback on its polar flow is a crucial, plant-specific mechanism mediating multiple self-organizing developmental processes. Here, we used the auxin effect on the PIN polar localization in Arabidopsis thaliana roots as a proxy for the auxin feedback on the PIN polarity during canalization. We performed microarray experiments to find regulators of this process that act downstream of auxin. We identified genes that were transcriptionally regulated by auxin in an AXR3/IAA17- and ARF7/ARF19-dependent manner. Besides the known components of the PIN polarity, such as PID and PIP5K kinases, a number of potential new regulators were detected, among which the WRKY23 transcription factor, which was characterized in more detail. Gain- and loss-of-function mutants confirmed a role for WRKY23 in mediating the auxin effect on the PIN polarity. Accordingly, processes requiring auxin-mediated PIN polarity rearrangements, such as vascular tissue development during leaf venation, showed a higher WRKY23 expression and required the WRKY23 activity. Our results provide initial insights into the auxin transcriptional network acting upstream of PIN polarization and, potentially, canalization-mediated plant development.

The plant hormone auxin belongs to the major plant-specific developmental regulators. It mediates or modifies almost all aspects of plant life. One of the fascinating features of the auxin action is its directional movement between cells, whose direction can be regulated by auxin signaling itself. This plant-specific feedback regulation has been proposed decades ago and allows for the self-organizing formation of distinct auxin channels shown to be crucial for processes, such as the regular pattern formation of leaf venation, organ formation, and regeneration of plant tissues. Despite the prominent importance of this so called auxin canalization process, the insight into the underlying molecular mechanism is very limited. Here, we identified a number of genes that are transcriptionally regulated and act downstream of the auxin signaling to mediate the auxin feedback on the polarized auxin transport. One of them is the WRKY23 transcription factor that has previously been unsuspected to play a role in this process. Our work provides the first insights into the transcriptional regulation of the auxin canalization and opens multiple avenues to further study this crucial process.

Auxin Signaling

Auxin triggers diverse responses in plants, and this is reflected in quantitative and qualitative diversity in the auxin signaling machinery.

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.

Cross-species functional diversity within the PIN auxin efflux protein family

In Arabidopsis, development during flowering is coordinated by transport of the hormone auxin mediated by polar-localized PIN-FORMED1 (AtPIN1). However Arabidopsis has lost a PIN clade sister to AtPIN1, Sister-of-PIN1 (SoPIN1), which is conserved in flowering plants. We previously proposed that the AtPIN1 organ initiation and vein patterning functions are split between the SoPIN1 and PIN1 clades in grasses. Here we show that in the grass Brachypodium sopin1 mutants have organ initiation defects similar to Arabidopsis atpin1, while loss of PIN1 function in Brachypodium has little effect on organ initiation but alters stem growth. Heterologous expression of Brachypodium SoPIN1 and PIN1b in Arabidopsis provides further evidence of functional specificity. SoPIN1 but not PIN1b can mediate flower formation in null atpin1 mutants, although both can complement a missense allele. The behavior of SoPIN1 and PIN1b in Arabidopsis illustrates how membrane and tissue-level accumulation, transport activity, and interaction contribute to PIN functional specificity.

Cross-species functional diversity within the PIN auxin efflux protein family

In Arabidopsis, development during flowering is coordinated by transport of the hormone auxin mediated by polar-localized PIN-FORMED1 (AtPIN1). However Arabidopsis has lost a PIN clade sister to AtPIN1, Sister-of-PIN1 (SoPIN1), which is conserved in flowering plants. We previously proposed that the AtPIN1 organ initiation and vein patterning functions are split between the SoPIN1 and PIN1 clades in grasses. Here we show that in the grass Brachypodium sopin1 mutants have organ initiation defects similar to Arabidopsis atpin1, while loss of PIN1 function in Brachypodium has little effect on organ initiation but alters stem growth. Heterologous expression of Brachypodium SoPIN1 and PIN1b in Arabidopsis provides further evidence of functional specificity. SoPIN1 but not PIN1b can mediate flower formation in null atpin1 mutants, although both can complement a missense allele. The behavior of SoPIN1 and PIN1b in Arabidopsis illustrates how membrane and tissue-level accumulation, transport activity, and interaction contribute to PIN functional specificity.

A common developmental program can produce diverse leaf shapes

Eudicot leaves have astoundingly diverse shapes. The central problem addressed in this paper is the developmental origin of this diversity. To investigate this problem, we propose a computational model of leaf development that generalizes the largely conserved molecular program for the reference plants Arabidopsis thaliana, Cardamine hirsuta and Solanum lycopersicum. The model characterizes leaf development as a product of three interwoven processes: the patterning of serrations, lobes and/or leaflets on the leaf margin; the patterning of the vascular system; and the growth of the leaf blade spanning the main veins. The veins play a significant morphogenetic role as a local determinant of growth directions. We show that small variations of this model can produce diverse leaf shapes, from simple to lobed to compound. It is thus plausible that diverse shapes of eudicot leaves result from small variations of a common developmental program.

A recovery principle provides insight into auxin pattern control in the Arabidopsis root

Regulated auxin patterning provides a key mechanism for controlling root growth and development. We have developed a data-driven mechanistic model using realistic root geometry and formulated a principle to theoretically investigate quantitative auxin pattern recovery following auxin transport perturbation. This principle reveals that auxin patterning is potentially controlled by multiple combinations of interlinked levels and localisation of influx and efflux carriers. We demonstrate that (1) when efflux carriers maintain polarity but change levels, maintaining the same auxin pattern requires non-uniform and polar distribution of influx carriers; (2) the emergence of the same auxin pattern, from different levels of influx carriers with the same nonpolar localisation, requires simultaneous modulation of efflux carrier level and polarity; and (3) multiple patterns of influx and efflux carriers for maintaining an auxin pattern do not have spatially proportional correlation. This reveals that auxin pattern formation requires coordination between influx and efflux carriers. We further show that the model makes various predictions that can be experimentally validated.

Experimental and Theoretical Methods to Approach the Study of Vascular Patterning in the Plant Shoot

The plant vascular system provides transport and mechanical support functions that are essential for suitable plant growth and development. In Arabidopsis thaliana (Arabidopsis), the vascular tissues at the shoot inflorescence stems are disposed in organized vascular bundles. The vascular patterning emergence and development within the shoot inflorescence stems is under the control of plant growth regulators (De Rybel et al., Nat Rev Mol Cell Biol 17:30-40, 2016; Caño-Delgado et al., Annu Rev Cell Dev Biol 26:605-637, 2010). By using a combined approach of experimental methods for vascular tissues visualization and quantification together with theoretical methods through mathematical and computational modeling, we have reported that auxin transport and brassinosteroid signaling play complementary roles in the formation of the periodic vascular patterning in the shoot (Ibañes et al., Proc Natl Acad Sci U S A 106:13630-13635, 2009; Fàbregas et al., Plant Signal Behav 5:903-906, 2010; Fàbregas et al., PLoS Genet 11:e1005183, 2015). Here, we report the methodology for the interdisciplinary analysis of the shoot vascular patterning in the plant model Arabidopsis into a handle procedure for visualization, quantification, data analysis, and modeling implementation.

Formation of polarity convergences underlying shoot outgrowths

The development of outgrowths from plant shoots depends on formation of epidermal sites of cell polarity convergence with high intracellular auxin at their centre. A parsimonious model for generation of convergence sites is that cell polarity for the auxin transporter PIN1 orients up auxin gradients, as this spontaneously generates convergent alignments. Here we test predictions of this and other models for the patterns of auxin biosynthesis and import. Live imaging of outgrowths from kanadi1 kanadi2 Arabidopsis mutant leaves shows that they arise by formation of PIN1 convergence sites within a proximodistal polarity field. PIN1 polarities are oriented away from regions of high auxin biosynthesis enzyme expression, and towards regions of high auxin importer expression. Both expression patterns are required for normal outgrowth emergence, and may form part of a common module underlying shoot outgrowths. These findings are more consistent with models that spontaneously generate tandem rather than convergent alignments.

DOI:http://dx.doi.org/10.7554/eLife.18165.001

Plants, unlike animals, are able to grow and develop throughout their lives. New leaves and flowers are made from outgrowths that constantly form at the tip of growing shoots. Groups of cells in the outer layer of the shoot tip arrange a protein called PIN1 so that it is more abundant on the cell surfaces that face towards the centre of the group. PIN1 transports a hormone called auxin out of plant cells and this “convergent” arrangement of PIN1 increases the levels of auxin in cells at the centre of the group, leading to the formation of a new outgrowth. However, it is not clear what causes these cells to position their PIN1 proteins in this way.

Several hypotheses have been proposed to explain how convergent patterns of PIN1 form. For example, according to the “up-the-gradient” hypothesis, PIN1 is allocated to the end of a cell that is next to a cell with a higher level of auxin. Abley et al. have now compared predictions from computer models with new experimental data from a plant called Arabidopsis to evaluate three hypotheses for how convergent PIN1 patterns form. A computer model based on the up-the-gradient hypothesis naturally creates convergent PIN1 patterns, even if each cell starts off with the same level of auxin. On the other hand, models based on two other hypotheses generate tandem alignments of PIN1 so that auxin is transported in the same direction along lines of cells.

Next, Abley et al. tested these models using mutant Arabidopsis plants that develop outgrowths from the lower surface of their leaves. These outgrowths form in a similar way to outgrowths at the growing shoot tip, but in a simpler context. The experiments show that the patterns of where auxin is produced in growing leaves were more compatible with the tandem alignment models than the up-the-gradient model. This suggests that plants use a tandem alignment mechanism to form convergences of PIN1 proteins that generate the local increases in auxin needed to make new outgrowths.

This study only examined a single layer of cells on the plant surface. Other cell layers also show highly organised patterns of PIN1 proteins, so a future challenge is to extend the approach to study the entire 3D structure of new shoot outgrowths.

DOI:http://dx.doi.org/10.7554/eLife.18165.002