Auxin transport-feedback models of patterning 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.

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.

Leaf vein patterning is regulated by the aperture of plasmodesmata intercellular channels

To form tissue networks, animal cells migrate and interact through proteins protruding from their plasma membranes. Plant cells can do neither, yet plants form vein networks. How plants do so is unclear, but veins are thought to form by the coordinated action of the polar transport and signal transduction of the plant hormone auxin. However, plants inhibited in both pathways still form veins. Patterning of vascular cells into veins is instead prevented in mutants lacking the function of the GNOM (GN) regulator of auxin transport and signaling, suggesting the existence of at least one more GN-dependent vein-patterning pathway. Here we show that in Arabidopsis such a pathway depends on the movement of auxin or an auxin-dependent signal through plasmodesmata (PDs) intercellular channels. PD permeability is high where veins are forming, lowers between veins and nonvascular tissues, but remains high between vein cells. Impaired ability to regulate PD aperture leads to defects in auxin transport and signaling, ultimately leading to vein patterning defects that are enhanced by inhibition of auxin transport or signaling. GN controls PD aperture regulation, and simultaneous inhibition of auxin signaling, auxin transport, and regulated PD aperture phenocopies null gn mutants. Therefore, veins are patterned by the coordinated action of three GN-dependent pathways: auxin signaling, polar auxin transport, and movement of auxin or an auxin-dependent signal through PDs. Such a mechanism of tissue network formation is unprecedented in multicellular organisms.

How do plants form vein networks, in the absence of cellular migration or direct cell-cell interaction? This study shows that a GNOM-dependent combination of polar auxin transport, auxin signal transduction, and movement of an auxin signal through plasmodesmata patterns leaf vascular cells into veins.

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.

Transcriptome Analysis of Developing Wheat Grains at Rapid Expanding Phase Reveals Dynamic Gene Expression Patterns

Simple Summary

Understanding the regulatory mechanism underlying grain development is essential for wheat improvement. The early grain expanding phase boasts critical biological events like embryogenesis and initiation of grain filling. RNA sequencing analysis of this developmental stage revealed dynamic expressions of genes related to cell division, starch biosynthesis, and hormone biosynthesis. An unbalanced expression among triads may play critical roles as shown by multiple enriched metabolic pathways. Our work demonstrated complex regulation mechanisms in early grain development and provided useful information for future wheat improvement.

Abstract

Grain development, as a vital process in the crop’s life cycle, is crucial for determining crop quality and yield. The wheat grain expanding phase is the early process involving the rapid morphological changes and initiation of grain filling. However, little is known about the molecular basis of grain development at this stage. Here, we provide a time-series transcriptome profile of developing wheat grain at 0, 2, 4, 6, 8, and 10 days after pollination of the wheat landrace Chinese Spring. A total of 26,892 differentially expressed genes, including 1468 transcription factors, were found between adjacent time points. Co-expression cluster analysis and Gene Ontology enrichment revealed dynamic expressions of cell division and starch biosynthesis related structural genes and transcription factors. Moreover, diverse, differential and drastically varied expression trends of the key genes related to hormone metabolism were identified. Furthermore, ~30% of triads showed unbalanced expression patterns enriching for genes in multiple pivotal metabolic pathways. Hormone metabolism related genes, such as YUC10 (YUCCA flavin-containing monooxygenase 10), AOS2 (allene oxide synthase 2), CYP90D2 (cytochrome P450 90D2), and CKX1 (cytokinin dehydrogenase 1), were dominantly contributed by A or D homoeologs of the triads. Our study provided a systematic picture of transcriptional regulation of wheat grains at the early grain expanding phase which should deepen our understanding of wheat grain development and help in wheat yield improvement.

Electrophysiological study of Arabidopsis ABCB4 and PIN2 auxin transporters: Evidence of auxin activation and interaction enhancing auxin selectivity

Polar auxin transport through plant tissue strictly requires polarly localized PIN proteins and uniformly distributed ABCB proteins. A functional synergy between the two types of membrane protein where their localizations overlap may create the degree of asymmetric auxin efflux required to produce polar auxin transport. We investigated this possibility by expressing ABCB4 and PIN2 in human embryonic kidney cells and measuring whole-cell ionic currents with the patch-clamp technique and CsCl-based electrolytes. ABCB4 activity was 1.81-fold more selective for Cl- over Cs+ and for PIN2 the value was 2.95. We imposed auxin gradients and determined that ABCB4 and PIN2 were 12-fold more permeable to the auxin anion (IAA-) than Cl-. This measure of the intrinsic selectivity of the transport pathway was 21-fold when ABCB4 and PIN2 were co-expressed. If this increase occurs in plants, it could explain why asymmetric PIN localization is not sufficient to create polar auxin flow. Some form of co-action or synergy between ABCB4 and PIN2 that increases IAA- selectivity at the cell face where both occur may be important. We also found that auxin stimulated ABCB4 activity, which may contribute to a self-reinforcement of auxin transport known as canalization.

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.

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.

Dynamics of Auxin and Cytokinin Metabolism during Early Root and Hypocotyl Growth in Theobroma cacao

The spatial location and timing of plant developmental events are largely regulated by the well balanced effects of auxin and cytokinin phytohormone interplay. Together with transport, localized metabolism regulates the concentration gradients of their bioactive forms, ultimately eliciting growth responses. In order to explore the dynamics of auxin and cytokinin metabolism during early seedling growth in Theobroma cacao (cacao), we have performed auxin and cytokinin metabolite profiling in hypocotyls and root developmental sections at different times by using ultra-high-performance liquid chromatography-electrospray tandem mass spectrometry (UHPLC-MS/MS). Our work provides quantitative characterization of auxin and cytokinin metabolites throughout early root and hypocotyl development and identifies common and distinctive features of auxin and cytokinin metabolism during cacao seedling development.

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.

Phenotypes of Vascular Flow Networks

Complex distribution networks are pervasive in biology. Examples include nutrient transport in the slime mold Physarum polycephalum as well as mammalian and plant venation. Adaptive rules are believed to guide development of these networks and lead to a reticulate, hierarchically nested topology that is both efficient and resilient against perturbations. However, as of yet, no mechanism is known that can generate such networks on all scales. We show how hierarchically organized reticulation can be constructed and maintained through spatially correlated load fluctuations on a particular length scale. We demonstrate that the network topologies generated represent a trade-off between optimizing transport efficiency, construction cost, and damage robustness and identify the Pareto-efficient front that evolution is expected to favor and select for. We show that the typical fluctuation length scale controls the position of the networks on the Pareto front and thus on the spectrum of venation phenotypes.

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.

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.

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.

Global Optimization, Local Adaptation, and the Role of Growth in Distribution Networks

Highly optimized complex transport networks serve crucial functions in many man-made and natural systems such as power grids and plant or animal vasculature. Often, the relevant optimization functional is nonconvex and characterized by many local extrema. In general, finding the global, or nearly global optimum is difficult. In biological systems, it is believed that such an optimal state is slowly achieved through natural selection. However, general coarse grained models for flow networks with local positive feedback rules for the vessel conductivity typically get trapped in low efficiency, local minima. In this work we show how the growth of the underlying tissue, coupled to the dynamical equations for network development, can drive the system to a dramatically improved optimal state. This general model provides a surprisingly simple explanation for the appearance of highly optimized transport networks in biology such as leaf and animal vasculature.

Staying Tight: Plasmodesmal Membrane Contact Sites and the Control of Cell-to-Cell Connectivity in Plants

Multicellularity differs in plants and animals in that the cytoplasm, plasma membrane, and endomembrane of plants are connected between cells through plasmodesmal pores. Plasmodesmata (PDs) are essential for plant life and serve as conduits for the transport of proteins, small RNAs, hormones, and metabolites during developmental and defense signaling. They are also the only pathways available for viruses to spread within plant hosts. The membrane organization of PDs is unique, characterized by the close apposition of the endoplasmic reticulum and the plasma membrane and spoke-like filamentous structures linking the two membranes, which define PDs as membrane contact sites (MCSs). This specialized membrane arrangement is likely critical for PD function. Here, we review how PDs govern developmental and defensive signaling in plants, compare them with other types of MCSs, and discuss in detail the potential functional significance of the MCS nature of PDs.

Rules and Self-Organizing Properties of Post-embryonic Plant Organ Cell Division Patterns

Plants form new organs with patterned tissue organization throughout their lifespan. It is unknown whether this robust post-embryonic organ formation results from stereotypic dynamic processes, in which the arrangement of cells follows rigid rules. Here, we combine modeling with empirical observations of whole-organ development to identify the principles governing lateral root formation in Arabidopsis. Lateral roots derive from a small pool of founder cells in which some take a dominant role as seen by lineage tracing. The first division of the founders is asymmetric, tightly regulated, and determines the formation of a layered structure. Whereas the pattern of subsequent cell divisions is not stereotypic between different samples, it is characterized by a regular switch in division plane orientation. This switch is also necessary for the appearance of patterned layers as a result of the apical growth of the primordium. Our data suggest that lateral root morphogenesis is based on a limited set of rules. They determine cell growth and division orientation. The organ-level coupling of the cell behavior ensures the emergence of the lateral root's characteristic features. We propose that self-organizing, non-deterministic modes of development account for the robustness of plant organ morphogenesis.

Control of vein network topology by auxin transport

Background

Tissue networks such as the vascular networks of plant and animal organs transport signals and nutrients in most multicellular organisms. The transport function of tissue networks depends on topological features such as the number of networks’ components and the components’ connectedness; yet what controls tissue network topology is largely unknown, partly because of the difficulties in quantifying the effects of genes on tissue network topology. We address this problem for the vein networks of plant leaves by introducing biologically motivated descriptors of vein network topology; we combine these descriptors with cellular imaging and molecular genetic analysis; and we apply this combination of approaches to leaves of Arabidopsis thaliana that lack function of, overexpress or misexpress combinations of four PIN-FORMED (PIN) genes—PIN1, PIN5, PIN6, and PIN8—which encode transporters of the plant signal auxin and are known to control vein network geometry.

Results

We find that PIN1 inhibits vein formation and connection, and that PIN6 acts redundantly to PIN1 in these processes; however, the functions of PIN6 in vein formation are nonhomologous to those of PIN1, while the functions of PIN6 in vein connection are homologous to those of PIN1. We further find that PIN8 provides functions redundant and homologous to those of PIN6 in PIN1-dependent inhibition of vein formation, but that PIN8 has no functions in PIN1/PIN6-dependent inhibition of vein connection. Finally, we find that PIN5 promotes vein formation; that all the vein-formation-promoting functions of PIN5 are redundantly inhibited by PIN6 and PIN8; and that these functions of PIN5, PIN6, and PIN8 are independent of PIN1.

Conclusions

Our results suggest that PIN-mediated auxin transport controls the formation of veins and their connection into networks.

Electronic supplementary material

The online version of this article (doi:10.1186/s12915-015-0208-3) contains supplementary material, which is available to authorized users.

Auxin influx carriers control vascular patterning and xylem differentiation in Arabidopsis thaliana

Auxin is an essential hormone for plant growth and development. Auxin influx carriers AUX1/LAX transport auxin into the cell, while auxin efflux carriers PIN pump it out of the cell. It is well established that efflux carriers play an important role in the shoot vascular patterning, yet the contribution of influx carriers to the shoot vasculature remains unknown. Here, we combined theoretical and experimental approaches to decipher the role of auxin influx carriers in the patterning and differentiation of vascular tissues in the Arabidopsis inflorescence stem. Our theoretical analysis predicts that influx carriers facilitate periodic patterning and modulate the periodicity of auxin maxima. In agreement, we observed fewer and more spaced vascular bundles in quadruple mutants plants of the auxin influx carriers aux1lax1lax2lax3. Furthermore, we show AUX1/LAX carriers promote xylem differentiation in both the shoot and the root tissues. Influx carriers increase cytoplasmic auxin signaling, and thereby differentiation. In addition to this cytoplasmic role of auxin, our computational simulations propose a role for extracellular auxin as an inhibitor of xylem differentiation. Altogether, our study shows that auxin influx carriers AUX1/LAX regulate vascular patterning and differentiation in plants.

Molecular systems governing leaf growth: from genes to networks

Arabidopsis leaf growth consists of a complex sequence of interconnected events involving cell division and cell expansion, and requiring multiple levels of genetic regulation. With classical genetics, numerous leaf growth regulators have been identified, but the picture is far from complete. With the recent advances made in quantitative phenotyping, the study of the quantitative, dynamic, and multifactorial features of leaf growth is now facilitated. The use of high-throughput phenotyping technologies to study large numbers of natural accessions or mutants, or to screen for the effects of large sets of chemicals will allow for further identification of the additional players that constitute the leaf growth regulatory networks. Only a tight co-ordination between these numerous molecular players can support the formation of a functional organ. The connections between the components of the network and their dynamics can be further disentangled through gene-stacking approaches and ultimately through mathematical modelling. In this review, we describe these different approaches that should help to obtain a holistic image of the molecular regulation of organ growth which is of high interest in view of the increasing needs for plant-derived products.

A division in PIN-mediated auxin patterning during organ initiation in grasses

The hormone auxin plays a crucial role in plant morphogenesis. In the shoot apical meristem, the PIN-FORMED1 (PIN1) efflux carrier concentrates auxin into local maxima in the epidermis, which position incipient leaf or floral primordia. From these maxima, PIN1 transports auxin into internal tissues along emergent paths that pattern leaf and stem vasculature. In Arabidopsis thaliana, these functions are attributed to a single PIN1 protein. Using phylogenetic and gene synteny analysis we identified an angiosperm PIN clade sister to PIN1, here termed Sister-of-PIN1 (SoPIN1), which is present in all sampled angiosperms except for Brassicaceae, including Arabidopsis. Additionally, we identified a conserved duplication of PIN1 in the grasses: PIN1a and PIN1b. In Brachypodium distachyon, SoPIN1 is highly expressed in the epidermis and is consistently polarized toward regions of high expression of the DR5 auxin-signaling reporter, which suggests that SoPIN1 functions in the localization of new primordia. In contrast, PIN1a and PIN1b are highly expressed in internal tissues, suggesting a role in vascular patterning. PIN1b is expressed in broad regions spanning the space between new primordia and previously formed vasculature, suggesting a role in connecting new organs to auxin sinks in the older tissues. Within these regions, PIN1a forms narrow canals that likely pattern future veins. Using a computer model, we reproduced the observed spatio-temporal expression and localization patterns of these proteins by assuming that SoPIN1 is polarized up the auxin gradient, and PIN1a and PIN1b are polarized to different degrees with the auxin flux. Our results suggest that examination and modeling of PIN dynamics in plants outside of Brassicaceae will offer insights into auxin-driven patterning obscured by the loss of the SoPIN1 clade in Brassicaceae.

Computational models and functional studies using the plant Arabidopsis thaliana have led to competing models for how the PIN-FORMED1 (PIN1) auxin transporter polarizes in the cell to create both the maxima required for organ initiation and the narrow streams required for vein patterning. Here we identify a previously uncharacterized PIN protein most closely related to PIN1 that is present in all flowering plants but lost in the Brassicaceae, including Arabidopsis. We localized this protein, here termed Sister-of-PIN1 (SoPIN1), along with duplicate members of PIN1 (PIN1a and PIN1b), in two grass species. Our localization data provide striking evidence for a spatial and temporal split between SoPIN1 and the two PIN1s during organ initiation in grasses. Based on our localization results we created a computational model showing that the observed patterns of expression and polarization of the grass PINs can emerge assuming SoPIN1 polarizes up the gradient of auxin concentration while the PIN1 members polarize with the auxin flux. This model reveals a minimal framework of necessary functions involved in auxin-transport-mediated patterning in the shoot and demonstrates that work outside of Arabidopsis is essential to understanding how auxin-transport mediates patterning in most flowering plants.

Molecular control of cell specification and cell differentiation during procambial development

Land plants develop vascular tissues that enable the long-distance transport of water and nutrients in xylem and phloem, provide mechanical support for their vertical growth, and produce cells in radial growth. Vascular tissues are produced in many parts of the plant and during different developmental stages. Early vascular development is focused in procambial meristems, and in some species it continues during the secondary phase of plant development in cambial meristems. In this review, we highlight recent progress in understanding procambial development. This involves the analysis of stem cell-like properties of procambial tissues, specification of xylem and phloem, and differentiation of the conductive tissues. Several major plant hormones, small-RNA species, and transcriptional networks play a role in vascular development. We describe current approaches to integrating these networks as well as their potential role in explaining the diversity and evolution of plant vascular systems.

Interaction between meristem tissue layers controls phyllotaxis

Phyllotaxis and vein formation are among the most conspicuous patterning processes in plants. The expression and polarization of the auxin efflux carrier PIN1 is the earliest marker for both processes, with mathematical models indicating that PIN1 can respond to auxin gradients and/or auxin flux. Here, we use cell-layer-specific PIN1 knockouts and partial complementation of auxin transport mutants to examine the interaction between phyllotactic patterning, which occurs primarily in the L1 surface layer of the meristem, and midvein specification in the inner tissues. We show that PIN1 expression in the L1 is sufficient for correct organ positioning, as long as the L1-specific influx carriers are present. Thus, differentiation of inner tissues can proceed without PIN1 or any of the known polar transporters. On theoretical grounds, we suggest that canalization of auxin flux between an auxin source and an auxin sink may involve facilitated diffusion rather than polar transport.

Juicy stories on female reproductive tissue development: coordinating the hormone flows

In the past 20-30 years, developmental biologists have made tremendous progress in identifying genes required for the specification of individual cell types of an organ and in describing how they interact in genetic networks. In comparison, very little is known about the mechanisms that regulate tissue polarity and overall organ patterning. Gynoecia and fruits from members of the Brassicaceae family of flowering plants provide excellent model systems to study organ patterning and tissue specification because they become partitioned into distinct domains whose formation is determined by polarity establishment both at a cellular and whole tissue level. Interactions among key regulators of Arabidopsis gynoecium and fruit development have revealed a network of upstream transcription factor activities required for such tissue differentiation. Regulation of the plant hormone auxin is emerging as both an immediate downstream output and input of these activities, and here we aim to provide an overview of the current knowledge regarding the link between auxin and female reproductive development in plants. In this review, we will also demonstrate how available data can be exploited in a mathematical modeling approach to reveal and understand the feedback regulatory circuits that underpin the polarity establishment, necessary to guide auxin flows.

Mechano-chemical aspects of organ formation in Arabidopsis thaliana: the relationship between auxin and pectin

How instructive signals are translated into robust and predictable changes in growth is a central question in developmental biology. Recently, much interest has centered on the feedback between chemical instructions and mechanical changes for pattern formation in development. In plants, the patterned arrangement of aerial organs, or phyllotaxis, is instructed by the phytohormone auxin; however, it still remains to be seen how auxin is linked, at the apex, to the biochemical and mechanical changes of the cell wall required for organ outgrowth. Here, using Atomic Force Microscopy, we demonstrate that auxin reduces tissue rigidity prior to organ outgrowth in the shoot apex of Arabidopsis thaliana, and that the de-methyl-esterification of pectin is necessary for this reduction. We further show that development of functional organs produced by pectin-mediated ectopic wall softening requires auxin signaling. Lastly, we demonstrate that coordinated localization of the auxin transport protein, PIN1, is disrupted in a naked-apex produced by increasing cell wall rigidity. Our data indicates that a feedback loop between the instructive chemical auxin and cell wall mechanics may play a crucial role in phyllotactic patterning.

Patterning of leaf vein networks by convergent auxin transport pathways

The formation of leaf vein patterns has fascinated biologists for centuries. Transport of the plant signal auxin has long been implicated in vein patterning, but molecular details have remained unclear. Varied evidence suggests a central role for the plasma-membrane (PM)-localized PIN-FORMED1 (PIN1) intercellular auxin transporter of Arabidopsis thaliana in auxin-transport-dependent vein patterning. However, in contrast to the severe vein-pattern defects induced by auxin transport inhibitors, pin1 mutant leaves have only mild vein-pattern defects. These defects have been interpreted as evidence of redundancy between PIN1 and the other four PM-localized PIN proteins in vein patterning, redundancy that underlies many developmental processes. By contrast, we show here that vein patterning in the Arabidopsis leaf is controlled by two distinct and convergent auxin-transport pathways: intercellular auxin transport mediated by PM-localized PIN1 and intracellular auxin transport mediated by the evolutionarily older, endoplasmic-reticulum-localized PIN6, PIN8, and PIN5. PIN6 and PIN8 are expressed, as PIN1 and PIN5, at sites of vein formation. pin6 synthetically enhances pin1 vein-pattern defects, and pin8 quantitatively enhances pin1pin6 vein-pattern defects. Function of PIN6 is necessary, redundantly with that of PIN8, and sufficient to control auxin response levels, PIN1 expression, and vein network formation; and the vein pattern defects induced by ectopic PIN6 expression are mimicked by ectopic PIN8 expression. Finally, vein patterning functions of PIN6 and PIN8 are antagonized by PIN5 function. Our data define a new level of control of vein patterning, one with repercussions on other patterning processes in the plant, and suggest a mechanism to select cell files specialized for vascular function that predates evolution of PM-localized PIN proteins.

Pin1-independent leaf initiation in Arabidopsis

Phyllotaxis, the regular arrangement of leaves and flowers around the stem, is a key feature of plant architecture. Current models propose that the spatiotemporal regulation of organ initiation is controlled by a positive feedback loop between the plant hormone auxin and its efflux carrier PIN-FORMED1 (PIN1). Consequently, pin1 mutants give rise to naked inflorescence stalks with few or no flowers, indicating that PIN1 plays a crucial role in organ initiation. However, pin1 mutants do produce leaves. In order to understand the regulatory mechanisms controlling leaf initiation in Arabidopsis (Arabidopsis thaliana) rosettes, we have characterized the vegetative pin1 phenotype in detail. We show that although the timing of leaf initiation in vegetative pin1 mutants is variable and divergence angles clearly deviate from the canonical 137° value, leaves are not positioned at random during early developmental stages. Our data further indicate that other PIN proteins are unlikely to explain the persistence of leaf initiation and positioning during pin1 vegetative development. Thus, phyllotaxis appears to be more complex than suggested by current mechanistic models.

Auxin transport at cellular level: new insights supported by mathematical modelling

The molecular basis of cellular auxin transport is still not fully understood. Although a number of carriers have been identified and proved to be involved in auxin transport, their regulation and possible activity of as yet unknown transporters remain unclear. Nevertheless, using single-cell-based systems it is possible to track the course of auxin accumulation inside cells and to specify and quantify some auxin transport parameters. The synthetic auxins 2,4-dichlorophenoxyacetic acid (2,4-D) and naphthalene-1-acetic acid (NAA) are generally considered to be suitable tools for auxin transport studies because they are transported specifically via either auxin influx or efflux carriers, respectively. Our results indicate that NAA can be metabolized rapidly in tobacco BY-2 cells. The predominant metabolite has been identified as NAA glucosyl ester and it is shown that all NAA metabolites were retained inside the cells. This implies that the transport efficiency of auxin efflux transporters is higher than previously assumed. By contrast, the metabolism of 2,4-D remained fairly weak. Moreover, using data on the accumulation of 2,4-D measured in the presence of auxin transport inhibitors, it is shown that 2,4-D is also transported by efflux carriers. These results suggest that 2,4-D is a promising tool for determining both auxin influx and efflux activities. Based on the accumulation data, a mathematical model of 2,4-D transport at a single-cell level is proposed. Optimization of the model provides estimates of crucial transport parameters and, together with its validation by successfully predicting the course of 2,4-D accumulation, it confirms the consistency of the present concept of cellular auxin transport.

Posttranslational modification and trafficking of PIN auxin efflux carriers

Cell-to-cell communication is absolutely essential for multicellular organisms. Both animals and plants use chemicals called hormones for intercellular signaling. However, multicellularity of plants and animals has evolved independently, which led to establishment of distinct strategies in order to cope with variations in an ever-changing environment. The phytohormone auxin is crucial to plant development and patterning. PIN auxin efflux carrier-driven polar auxin transport regulates plant development as it controls asymmetric auxin distribution (auxin gradients), which in turn modulates a wide range of developmental processes. Internal and external cues trigger a number of posttranslational PIN auxin carrier modifications that were demonstrated to decisively influence variations in adaptive growth responses. In this review, we highlight recent advances in the analysis of posttranslational modification of PIN auxin efflux carriers, such as phosphorylation and ubiquitylation, and discuss their eminent role in directional vesicle trafficking, PIN protein de-/stabilization and auxin transport activity. We conclude with updated models, in which we attempt to integrate the mechanistic relevance of posttranslational modifications of PIN auxin carriers for the dynamic nature of plant development.

Computational models of plant development and form

The use of computational techniques increasingly permeates developmental biology, from the acquisition, processing and analysis of experimental data to the construction of models of organisms. Specifically, models help to untangle the non-intuitive relations between local morphogenetic processes and global patterns and forms. We survey the modeling techniques and selected models that are designed to elucidate plant development in mechanistic terms, with an emphasis on: the history of mathematical and computational approaches to developmental plant biology; the key objectives and methodological aspects of model construction; the diverse mathematical and computational methods related to plant modeling; and the essence of two classes of models, which approach plant morphogenesis from the geometric and molecular perspectives. In the geometric domain, we review models of cell division patterns, phyllotaxis, the form and vascular patterns of leaves, and branching patterns. In the molecular-level domain, we focus on the currently most extensively developed theme: the role of auxin in plant morphogenesis. The review is addressed to both biologists and computational modelers.

A new development: evolving concepts in leaf ontogeny

Elucidation of gene regulatory networks (GRNs) underlying aspects of leaf development in multiple model species has uncovered surprisingly plastic regulatory architecture. The meticulously mapped network interactions in one model species cannot now be assumed to map directly onto a different species. Despite these overall differences, however, many modules do appear to be almost universal. Extrapolating findings across different model systems will demand great care but promises to reveal a rich tapestry of themes in GRN architecture and regulation. The purpose of this review is to approach the field of leaf development from the perspectives of the evolution of developmental systems that orchestrate leaf development.

Modeling antiviral resistance in plants

The goal of this chapter is to describe in simple terms how the use of ordinary differential equation (ODE) modeling, in conjunction with experimentation, can be utilized to improve our understanding of the dynamics of gene silencing and virus resistance in plants.

Multiscale modelling of auxin transport in the plant-root elongation zone

In the root elongation zone of a plant, the hormone auxin moves in a polar manner due to active transport facilitated by spatially distributed influx and efflux carriers present on the cell membranes. To understand how the cell-scale active transport and passive diffusion combine to produce the effective tissue-scale flux, we apply asymptotic methods to a cell-based model of auxin transport to derive systematically a continuum description from the spatially discrete one. Using biologically relevant parameter values, we show how the carriers drive the dominant tissue-scale auxin flux and we predict how the overall auxin dynamics are affected by perturbations to these carriers, for example, in knockout mutants. The analysis shows how the dominant behaviour depends on the cells' lengths, and enables us to assess the relative importance of the diffusive auxin flux through the cell wall. Other distinguished limits are also identified and their potential roles discussed. As well as providing insight into auxin transport, the study illustrates the use of multiscale (cell to tissue) methods in deriving simplified models that retain the essential biology and provide understanding of the underlying dynamics.

Transcriptional activation of Arabidopsis axis patterning genes WOX8/9 links zygote polarity to embryo development

In most flowering plants, the apical-basal body axis is established by an asymmetric division of the polarized zygote. In Arabidopsis, early embryo patterning is regulated by WOX homeobox genes, which are coexpressed in the zygote but become restricted to apical (WOX2) and basal (WOX8/9) cells. How the asymmetry of zygote division is regulated and connected to the daughter cell fates is largely unknown. Here, we show that expression of WOX8 is independent of the axis patterning signal auxin, but, together with the redundant gene WOX9, is activated in the zygote, its basal daughter cell, and the hypophysis by the zinc-finger transcription factor WRKY2. In wrky2 mutants, egg cells polarize normally but zygotes fail to reestablish polar organelle positioning from a transient symmetric state, resulting in equal cell division and distorted embryo development. Both defects are rescued by overexpressing WOX8, indicating that WRKY2-dependent WOX8 transcription links zygote polarization with embryo patterning.

Quantitative predictions on auxin-induced polar distribution of PIN proteins during vein formation in leaves

The dynamic patterning of the plant hormone auxin and its efflux facilitator the PIN protein are the key regulators for the spatial and temporal organization of plant development. In particular auxin induces the polar localization of its own efflux facilitator. Due to this positive feedback, auxin flow is directed and patterns of auxin and PIN arise. During the earliest stage of vein initiation in leaves auxin accumulates in a single cell in a rim of epidermal cells from which it flows into the ground meristem tissue of the leaf blade. There the localized auxin supply yields the successive polarization of PIN distribution along a strand of cells. We model the auxin and PIN dynamics within cells with a minimal canalization model. Solving the model analytically we uncover an excitable polarization front that triggers a polar distribution of PIN proteins in cells. As polarization fronts may extend to opposing directions from their initiation site, we suggest a possible resolution to the puzzling occurrence of bipolar cells, thus we offer an explanation for the development of closed, looped veins. Employing non-linear analysis, we identify the role of the contributing microscopic processes during polarization. Furthermore, we deduce quantitative predictions on polarization fronts establishing a route to determine the up to now largely unknown kinetic rates of auxin and PIN dynamics.

Variability in the control of cell division underlies sepal epidermal patterning in Arabidopsis thaliana

How growth and proliferation are precisely controlled in organs during development and how the regulation of cell division contributes to the formation of complex cell type patterns are important questions in developmental biology. Such a pattern of diverse cell sizes is characteristic of the sepals, the outermost floral organs, of the plant Arabidopsis thaliana. To determine how the cell size pattern is formed in the sepal epidermis, we iterate between generating predictions from a computational model and testing these predictions through time-lapse imaging. We show that the cell size diversity is due to the variability in decisions of individual cells about when to divide and when to stop dividing and enter the specialized endoreduplication cell cycle. We further show that altering the activity of cell cycle inhibitors biases the timing and changes the cell size pattern as our model predicts. Models and observations together demonstrate that variability in the time of cell division is a major determinant in the formation of a characteristic pattern.

Plant development: a TALE story

Plant development depends on the activity of a group of dividing cells called the meristem. Extensive genetic analyses have identified the major regulators of the shoot apical meristem (SAM), which control the development of all aerial organs. Among them, the three-amino-acid-loop-extension (TALE) class of homeoproteins has been shown to control meristem formation and/or maintenance, organ morphogenesis, organ position, and several aspects of the reproductive phase. This family contains the KNOTTED-like homeodomain (KNOX) and BEL1-like Homeodomain (BELL) members, which function as heterodimers. In this review, we have reported the functions of the TALE members throughout the Arabidopsis life cycle. Genetic analyses revealed a complex network, as TALE members exhibit both overlapping and antagonistic activities. The characterization of a new KNOX member (KNATM), which lacks a homeodomain and interacts with other members to modulate their activities, adds another layer of complexity to this network. While the mode of action of these transcription factors is still largely unknown, they have been implicated in the regulation of several hormonal pathways, providing a link between gene regulatory networks and signaling in the SAM.

Computational morphodynamics: a modeling framework to understand plant growth

Computational morphodynamics utilizes computer modeling to understand the development of living organisms over space and time. Results from biological experiments are used to construct accurate and predictive models of growth. These models are then used to make novel predictions that provide further insight into the processes involved, which can be tested experimentally to either confirm or rule out the validity of the computational models. This review highlights two fundamental challenges: (a) to understand the feedback between mechanics of growth and chemical or molecular signaling, and (b) to design models that span and integrate single cell behavior with tissue development. We review different approaches to model plant growth and discuss a variety of model types that can be implemented to demonstrate how the interplay between computational modeling and experimentation can be used to explore the morphodynamics of plant development.