A theoretical model for ROP localisation by auxin in Arabidopsis root hair cells

Rho of Plants patterning: linking mathematical models and molecular diversity

ROPs (Rho of Plants) are plant specific small GTPases involved in many membrane patterning processes and play important roles in the establishment and communication of cell polarity. These small GTPases can produce a wide variety of patterns, ranging from a single cluster in tip-growing root hairs and pollen tubes to an oriented stripe pattern controlling protoxylem cell wall deposition. For an understanding of what controls these various patterns, models are indispensable. Consequently, many modelling studies on small GTPase patterning exist, often focusing on yeast or animal cells. Multiple patterns occurring in plants, however, require the stable co-existence of multiple active ROP clusters, which does not occur with the most common yeast/animal models. The possibility of such patterns critically depends on the precise model formulation. Additionally, different small GTPases are usually treated interchangeably in models, even though plants possess two types of ROPs with distinct molecular properties, one of which is unique to plants. Furthermore, the shape and even the type of ROP patterns may be affected by the cortical cytoskeleton, and cortex composition and anisotropy differ dramatically between plants and animals. Here, we review insights into ROP patterning from modelling efforts across kingdoms, as well as some outstanding questions arising from these models and recent experimental findings.

Phosphorylation of RhoGDI1, a Rho GDP dissociation inhibitor, regulates root hair development in Arabidopsis under salt stress

To ensure optimal growth, plants actively regulate their growth and development based on environmental changes. Among these, salt stress significantly influences growth and yield. In this study, we demonstrate that the growth of root hairs of salt-stressed Arabidopsis thaliana seedlings is regulated by the SALT OVERLY SENSITIVE 2 (SOS2)-GUANOSINE NUCLEOTIDE DIPHOSPHATE DISSOCIATION INHIBITOR 1 (RhoGDI1)-Rho GTPASE OF PLANTS 2 (ROP2) module. We show here that the kinase SOS2 is activated by salt stress and subsequently phosphorylates RhoGDI1, a root hair regulator, thereby decreasing its stability. This change in RhoGDI1 abundance resulted in a fine-tuning of polar localization of ROP2 and root hair initiation followed by polar growth, demonstrating how SOS2-regulated root hair development is critical for plant growth under salt stress. Our results reveal how a tissue-specific response to salt stress balances the relationship of salt resistance and basic growth.

Spatial models of pattern formation during phagocytosis

Phagocytosis, the biological process in which cells ingest large particles such as bacteria, is a key component of the innate immune response. Fcγ receptor (FcγR)-mediated phagocytosis is initiated when these receptors are activated after binding immunoglobulin G (IgG). Receptor activation initiates a signaling cascade that leads to the formation of the phagocytic cup and culminates with ingestion of the foreign particle. In the experimental system termed "frustrated phagocytosis", cells attempt to internalize micropatterned disks of IgG. Cells that engage in frustrated phagocytosis form "rosettes" of actin-enriched structures called podosomes around the IgG disk. The mechanism that generates the rosette pattern is unknown. We present data that supports the involvement of Cdc42, a member of the Rho family of GTPases, in pattern formation. Cdc42 acts downstream of receptor activation, upstream of actin polymerization, and is known to play a role in polarity establishment. Reaction-diffusion models for GTPase spatiotemporal dynamics exist. We demonstrate how the addition of negative feedback and minor changes to these models can generate the experimentally observed rosette pattern of podosomes. We show that this pattern formation can occur through two general mechanisms. In the first mechanism, an intermediate species forms a ring of high activity around the IgG disk, which then promotes rosette organization. The second mechanism does not require initial ring formation but relies on spatial gradients of intermediate chemical species that are selectively activated over the IgG patch. Finally, we analyze the models to suggest experiments to test their validity.

Unified framework for localized patterns in reaction-diffusion systems; the Gray-Scott and Gierer-Meinhardt cases

A recent study of canonical activator-inhibitor Schnakenberg-like models posed on an infinite line is extended to include models, such as Gray-Scott, with bistability of homogeneous equilibria. A homotopy is studied that takes a Schnakenberg-like glycolysis model to the Gray-Scott model. Numerical continuation is used to understand the complete sequence of transitions to two-parameter bifurcation diagrams within the localized pattern parameter regime as the homotopy parameter varies. Several distinct codimension-two bifurcations are discovered including cusp and quadruple zero points for homogeneous steady states, a degenerate heteroclinic connection and a change in connectedness of the homoclinic snaking structure. The analysis is repeated for the Gierer-Meinhardt system, which lies outside the canonical framework. Similar transitions are found under homotopy between bifurcation diagrams for the case where there is a constant feed in the active field, to it being in the inactive field. Wider implications of the results are discussed for other pattern-formation systems arising as models of natural phenomena. This article is part of the theme issue 'Recent progress and open frontiers in Turing's theory of morphogenesis'.

Describing the movement of molecules in reduced-dimension models

When addressing spatial biological questions using mathematical models, symmetries within the system are often exploited to simplify the problem by reducing its physical dimension. In a reduced-dimension model molecular movement is restricted to the reduced dimension, changing the nature of molecular movement. This change in molecular movement can lead to quantitatively and even qualitatively different results in the full and reduced systems. Within this manuscript we discuss the condition under which restricted molecular movement in reduced-dimension models accurately approximates molecular movement in the full system. For those systems which do not satisfy the condition, we present a general method for approximating unrestricted molecular movement in reduced-dimension models. We will derive a mathematically robust, finite difference method for solving the 2D diffusion equation within a 1D reduced-dimension model. The methods described here can be used to improve the accuracy of many reduced-dimension models while retaining benefits of system simplification.

The nonlinear initiation of side-branching by activator-inhibitor-substrate (Turing) morphogenesis

An understanding of the underlying mechanism of side-branching is paramount in controlling and/or therapeutically treating mammalian organs, such as lungs, kidneys, and glands. Motivated by an activator-inhibitor-substrate approach that is conjectured to dominate the initiation of side-branching in a pulmonary vascular pattern, I demonstrate a distinct transverse front instability in which new fingers grow out of an oscillatory breakup dynamics at the front line without any typical length scale. These two features are attributed to unstable peak solutions in 1D that subcritically emanate from Turing bifurcation and that exhibit repulsive interactions. The results are based on a bifurcation analysis and numerical simulations and provide a potential strategy toward also developing a framework of side-branching for other biological systems, such as plant roots and cellular protrusions.

The value of asymmetry: how polarity proteins determine plant growth and morphology

Cell polarity is indispensable for forming complex multicellular organisms. Proteins that polarize at specific plasma membrane domains can either serve as scaffolds for effectors or coordinate intercellular communication and transport. Here, I give an overview of polarity protein complexes and their fundamental importance for plant development, and summarize novel mechanistic insights into their molecular networks. Examples are presented for proteins that polarize at specific plasma membrane domains to orient cell division planes, alter cell fate progression, control transport, direct cell growth, read global polarity axes, or integrate external stimuli into plant growth. The recent advances in characterizing protein polarity during plant development enable a better understanding of coordinated plant growth and open up intriguing paths that could provide a means to modulate plant morphology and adaptability in the future.

Robust banded protoxylem pattern formation through microtubule-based directional ROP diffusion restriction

In plant vascular tissue development, different cell wall patterns are formed, offering different mechanical properties optimised for different growth stages. Critical in these patterning processes are Rho of Plants (ROP) proteins, a class of evolutionarily conserved small GTPase proteins responsible for local membrane domain formation in many organisms. While te spotted metaxylem pattern can easily be understood as a result of a Turing-style reaction-diffusion mechanism, it remains an open question how the consistent orientation of evenly spaced bands and spirals as found in protoxylem is achieved. We hypothesise that this orientation results from an interaction between ROPs and an array of transversely oriented cortical microtubules that acts as a directional diffusion barrier. Here, we explore this hypothesis using partial differential equation models with anisotropic ROP diffusion and show that a horizontal microtubule array acting as a vertical diffusion barrier to active ROP can yield a horizontally banded ROP pattern. We then study the underlying mechanism in more detail, finding that it can only orient curved pattern features but not straight lines. This implies that, once formed, banded and spiral patterns cannot be reoriented by this mechanism. Finally, we observe that ROPs and microtubules together only form ultimately static patterns if the interaction is implemented with sufficient biological realism.

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.

Distinct RopGEFs Successively Drive Polarization and Outgrowth of Root Hairs

Root hairs are tubular protrusions of the root epidermis that significantly enlarge the exploitable soil volume in the rhizosphere. Trichoblasts, the cell type responsible for root hair formation, switch from cell elongation to tip growth through polarization of the growth machinery to a predefined root hair initiation domain (RHID) at the plasma membrane. The emergence of this polar domain resembles the establishment of cell polarity in other eukaryotic systems [1-3]. Rho-type GTPases of plants (ROPs) are among the first molecular determinants of the RHID [4, 5], and later play a central role in polar growth [6]. Numerous studies have elucidated mechanisms that position the RHID in the cell [7-9] or regulate ROP activity [10-18]. The molecular players that target ROPs to the RHID and initiate outgrowth, however, have not been identified. We dissected the timing of the growth machinery assembly in polarizing hair cells and found that positioning of molecular players and outgrowth are temporally separate processes that are each controlled by specific ROP guanine nucleotide exchange factors (GEFs). A functional analysis of trichoblast-specific GEFs revealed GEF3 to be required for normal ROP polarization and thus efficient root hair emergence, whereas GEF4 predominantly regulates subsequent tip growth. Ectopic expression of GEF3 induced the formation of spatially confined, ROP-recruiting domains in other cell types, demonstrating the role of GEF3 to serve as a membrane landmark during cell polarization.

Theoretical models for branch formation in plants

Various branch architectures are observed in living organisms including plants. Branch formation has traditionally been an area of interest in the field of developmental biology, and theoretical approaches are now commonly used to understand the complex mechanisms involved. In this review article, we provide an overview of theoretical approaches including mathematical models and computer simulations for studying plant branch formation. These approaches cover a wide range of topics. In particular, we focus on the importance of positional information in branch formation, which has been especially revealed by theoretical research in plants including computations of developmental processes.

Small GTPase patterning: How to stabilise cluster coexistence

Many biological processes have to occur at specific locations on the cell membrane. These locations are often specified by the localised activity of small GTPase proteins. Some processes require the formation of a single cluster of active GTPase, also called unipolar polarisation (here “polarisation”), whereas others need multiple coexisting clusters. Moreover, sometimes the pattern of GTPase clusters is dynamically regulated after its formation. This raises the question how the same interacting protein components can produce such a rich variety of naturally occurring patterns. Most currently used models for GTPase-based patterning inherently yield polarisation. Such models may at best yield transient coexistence of at most a few clusters, and hence fail to explain several important biological phenomena. These existing models are all based on mass conservation of total GTPase and some form of direct or indirect positive feedback. Here, we show that either of two biologically plausible modifications can yield stable coexistence: including explicit GTPase turnover, i.e., breaking mass conservation, or negative feedback by activation of an inhibitor like a GAP. Since we start from two different polarising models our findings seem independent of the precise self-activation mechanism. By studying the net GTPase flows among clusters, we provide insight into how these mechanisms operate. Our coexistence models also allow for dynamical regulation of the final pattern, which we illustrate with examples of pollen tube growth and the branching of fungal hyphae. Together, these results provide a better understanding of how cells can tune a single system to generate a wide variety of biologically relevant patterns.

Auxin Signaling

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

The Microtubule-Associated Protein MAP18 Affects ROP2 GTPase Activity during Root Hair Growth

Establishment and maintenance of the polar site are important for root hair tip growth. We previously reported that Arabidopsis (Arabidopsis thaliana) MICROTUBULE-ASSOCIATED PROTEIN18 (MAP18) functions in controlling the direction of pollen tube growth and root hair elongation. Additionally, the Rop GTPase ROP2 was reported as a positive regulator of both root hair initiation and tip growth in Arabidopsis. Both loss of function of ROP2 and knockdown of MAP18 lead to a decrease in root hair length, whereas overexpression of either MAP18 or ROP2 causes multiple tips or a branching hair phenotype. However, it is unclear whether MAP18 and ROP2 coordinately regulate root hair growth. In this study, we demonstrate that MAP18 and ROP2 interact genetically and functionally. MAP18 interacts physically with ROP2 in vitro and in vivo and preferentially binds to the inactive form of the ROP2 protein. MAP18 promotes ROP2 activity during root hair tip growth. Further investigation revealed that MAP18 competes with RhoGTPase GDP DISSOCIATION INHIBITOR1/SUPERCENTIPEDE1 for binding to ROP2, in turn affecting the localization of active ROP2 in the plasma membrane of the root hair tip. These results reveal a novel function of MAP18 in the regulation of ROP2 activation during root hair growth.

Growth regulation in tip-growing cells that develop on the epidermis

Plants develop tip-growing extensions-root hairs and rhizoids-that initiate as swellings on the outer surface of individual epidermal cells. A conserved genetic mechanism controls the earliest stages in the initiation of these swellings. The same mechanism controls the formation of multicellular structures that develop from swellings on epidermal cells in early diverging land plants. Details of the molecular events that regulate the positioning of the swellings involve sterols and phosphatidylinositol phosphates. The final length of root hairs is determined by the intensity of a pulse of transcription factor synthesis. Genes encoding similar transcription factors control root hair development in cereals and are potential targets for crop improvement.

Dynamic regulation of auxin oxidase and conjugating enzymes AtDAO1 and GH3 modulates auxin homeostasis

The hormone auxin is a key regulator of plant growth and development, and great progress has been made understanding auxin transport and signaling. Here, we show that auxin metabolism and homeostasis are also regulated in a complex manner. The principal auxin degradation pathways in Arabidopsis include oxidation by Arabidopsis thaliana gene DIOXYGENASE FOR AUXIN OXIDATION 1/2 (AtDAO1/2) and conjugation by Gretchen Hagen3s (GH3s). Metabolic profiling of dao1-1 root tissues revealed a 50% decrease in the oxidation product 2-oxoindole-3-acetic acid (oxIAA) and increases in the conjugated forms indole-3-acetic acid aspartic acid (IAA-Asp) and indole-3-acetic acid glutamic acid (IAA-Glu) of 438- and 240-fold, respectively, whereas auxin remains close to the WT. By fitting parameter values to a mathematical model of these metabolic pathways, we show that, in addition to reduced oxidation, both auxin biosynthesis and conjugation are increased in dao1-1 Transcripts of AtDAO1 and GH3 genes increase in response to auxin over different timescales and concentration ranges. Including this regulation of AtDAO1 and GH3 in an extended model reveals that auxin oxidation is more important for auxin homoeostasis at lower hormone concentrations, whereas auxin conjugation is most significant at high auxin levels. Finally, embedding our homeostasis model in a multicellular simulation to assess the spatial effect of the dao1-1 mutant shows that auxin increases in outer root tissues in agreement with the dao1-1 mutant root hair phenotype. We conclude that auxin homeostasis is dependent on AtDAO1, acting in concert with GH3, to maintain auxin at optimal levels for plant growth and development.

A Model Analysis of Mechanisms for Radial Microtubular Patterns at Root Hair Initiation Sites

Plant cells have two main modes of growth generating anisotropic structures. Diffuse growth where whole cell walls extend in specific directions, guided by anisotropically positioned cellulose fibers, and tip growth, with inhomogeneous addition of new cell wall material at the tip of the structure. Cells are known to regulate these processes via molecular signals and the cytoskeleton. Mechanical stress has been proposed to provide an input to the positioning of the cellulose fibers via cortical microtubules in diffuse growth. In particular, a stress feedback model predicts a circumferential pattern of fibers surrounding apical tissues and growing primordia, guided by the anisotropic curvature in such tissues. In contrast, during the initiation of tip growing root hairs, a star-like radial pattern has recently been observed. Here, we use detailed finite element models to analyze how a change in mechanical properties at the root hair initiation site can lead to star-like stress patterns in order to understand whether a stress-based feedback model can also explain the microtubule patterns seen during root hair initiation. We show that two independent mechanisms, individually or combined, can be sufficient to generate radial patterns. In the first, new material is added locally at the position of the root hair. In the second, increased tension in the initiation area provides a mechanism. Finally, we describe how a molecular model of Rho-of-plant (ROP) GTPases activation driven by auxin can position a patch of activated ROP protein basally along a 2D root epidermal cell plasma membrane, paving the way for models where mechanical and molecular mechanisms cooperate in the initial placement and outgrowth of root hairs.

Cell Fate Determination and the Switch from Diffuse Growth to Planar Polarity in Arabidopsis Root Epidermal Cells

Plant roots fulfill important functions as they serve in water and nutrient uptake, provide anchorage of the plant body in the soil and in some species form the site of symbiotic interactions with soil-living biota. Root hairs, tubular-shaped outgrowths of specific epidermal cells, significantly increase the root's surface area and aid in these processes. In this review we focus on the molecular mechanisms that determine the hair and non-hair cell fate of epidermal cells and that define the site on the epidermal cell where the root hair will be initiated (=planar polarity determination). In the model plant Arabidopsis, trichoblast and atrichoblast cell fate results from intra- and intercellular position-dependent signaling and from complex feedback loops that ultimately regulate GL2 expressing and non-expressing cells. When epidermal cells reach the end of the root expansion zone, root hair promoting transcription factors dictate the establishment of polarity within epidermal cells followed by the selection of the root hair initiation site at the more basal part of the trichoblast. Molecular players in the abovementioned processes as well as the role of phytohormones are discussed, and open areas for future experiments are identified.

Plasma membrane H(+)-ATPase is involved in methyl jasmonate-induced root hair formation in lettuce (Lactuca sativa L.) seedlings

KEY MESSAGE

Our results show that methyl jasmonate induces plasma membrane H (+) -ATPase activity and subsequently influences the apoplastic pH of trichoblasts to maintain a cell wall pH environment appropriate for root hair development. Root hairs, which arise from root epidermal cells, are tubular structures that increase the efficiency of water absorption and nutrient uptake. Plant hormones are critical regulators of root hair development. In this study, we investigated the regulatory role of the plasma membrane (PM) H(+)-ATPase in methyl jasmonate (MeJA)-induced root hair formation. We found that MeJA had a pronounced effect on the promotion of root hair formation in lettuce seedlings, but that this effect was blocked by the PM H(+)-ATPase inhibitor vanadate. Furthermore, MeJA treatment increased PM H(+)-ATPase activity in parallel with H(+) efflux from the root tips of lettuce seedlings and rhizosphere acidification. Our results also showed that MeJA-induced root hair formation was accompanied by hydrogen peroxide accumulation. The apoplastic acidification acted in concert with reactive oxygen species to modulate root hair formation. Our results suggest that the effect of MeJA on root hair formation is mediated by modulation of PM H(+)-ATPase activity.

Protein lipid modifications and the regulation of ROP GTPase function

In eukaryotes, the RHO superfamily of small G-proteins is implicated in the regulation of cell polarity and growth. Rho of Plants (ROPs)/RACs are plant-specific Rho family proteins that have been shown to regulate cell polarity, auxin transport and responses, ABA signalling, and response to pathogens. A hallmark of ROP/RAC function is their localization in specific plasma membrane domains. This short review focuses on the mechanisms responsible for membrane interactions of ROPs/RACs and how they affect ROP/RAC function.

Rapid identification of a natural knockout allele of ARMADILLO REPEAT-CONTAINING KINESIN1 that causes root hair branching by mapping-by-sequencing

In Arabidopsis (Arabidopsis thaliana), branched root hairs are an indicator of defects in root hair tip growth. Among 62 accessions, one accession (Heiligkreuztal2 [HKT2.4]) displayed branched root hairs, suggesting that this accession carries a mutation in a gene of importance for tip growth. We determined 200- to 300-kb mapping intervals using a mapping-by-sequencing approach of F2 pools from crossings of HKT2.4 with three different accessions. The intersection of these mapping intervals was 80 kb in size featuring not more than 36 HKT2.4-specific single nucleotide polymorphisms, only two of which changed the coding potential of genes. Among them, we identified the causative single nucleotide polymorphism changing a splicing site in ARMADILLO REPEAT-CONTAINING KINESIN1. The applied strategies have the potential to complement statistical methods in high-throughput phenotyping studies using different natural accessions to identify causative genes for distinct phenotypes represented by only one or a few accessions.

Coordinating cell polarity: heading in the right direction?

A diverse group of researchers working on both plant and animal systems met at a Company of Biologists workshop to discuss 'Coordinating Cell Polarity'. The meeting included considerable free discussion as well as presentations exploring the ways that groups of cells in these various systems achieve coordinated cell polarity. Here, we discuss commonalities, differences and themes that emerged from these sessions that will serve to inform ongoing studies.

Subcritical Turing bifurcation and the morphogenesis of localized patterns

Subcritical Turing bifurcations of reaction-diffusion systems in large domains lead to spontaneous onset of well-developed localized patterns via the homoclinic snaking mechanism. This phenomenon is shown to occur naturally when balancing source and loss effects are included in a typical reaction-diffusion system, leading to a super- to subcritical transition. Implications are discussed [corrected]for a range of physical problems, arguing that subcriticality leads to naturally robust phase transitions to localized patterns.

Root hairs

Roots hairs are cylindrical extensions of root epidermal cells that are important for acquisition of nutrients, microbe interactions, and plant anchorage. The molecular mechanisms involved in the specification, differentiation, and physiology of root hairs in Arabidopsis are reviewed here. Root hair specification in Arabidopsis is determined by position-dependent signaling and molecular feedback loops causing differential accumulation of a WD-bHLH-Myb transcriptional complex. The initiation of root hairs is dependent on the RHD6 bHLH gene family and auxin to define the site of outgrowth. Root hair elongation relies on polarized cell expansion at the growing tip, which involves multiple integrated processes including cell secretion, endomembrane trafficking, cytoskeletal organization, and cell wall modifications. The study of root hair biology in Arabidopsis has provided a model cell type for insights into many aspects of plant development and cell biology.

Systems analysis of auxin transport in the Arabidopsis root apex

Auxin is a key regulator of plant growth and development. Within the root tip, auxin distribution plays a crucial role specifying developmental zones and coordinating tropic responses. Determining how the organ-scale auxin pattern is regulated at the cellular scale is essential to understanding how these processes are controlled. In this study, we developed an auxin transport model based on actual root cell geometries and carrier subcellular localizations. We tested model predictions using the DII-VENUS auxin sensor in conjunction with state-of-the-art segmentation tools. Our study revealed that auxin efflux carriers alone cannot create the pattern of auxin distribution at the root tip and that AUX1/LAX influx carriers are also required. We observed that AUX1 in lateral root cap (LRC) and elongating epidermal cells greatly enhance auxin's shootward flux, with this flux being predominantly through the LRC, entering the epidermal cells only as they enter the elongation zone. We conclude that the nonpolar AUX1/LAX influx carriers control which tissues have high auxin levels, whereas the polar PIN carriers control the direction of auxin transport within these tissues.

Rho-GTPase-regulated vesicle trafficking in plant cell polarity

ROPs (Rho of plants) belong to a large family of plant-specific Rho-like small GTPases that function as essential molecular switches to control diverse cellular processes including cytoskeleton organization, cell polarization, cytokinesis, cell differentiation and vesicle trafficking. Although the machineries of vesicle trafficking and cell polarity in plants have been individually well addressed, how ROPs co-ordinate those processes is still largely unclear. Recent progress has been made towards an understanding of the co-ordination of ROP signalling and trafficking of PIN (PINFORMED) transporters for the plant hormone auxin in both root and leaf pavement cells. PIN transporters constantly shuttle between the endosomal compartments and the polar plasma membrane domains, therefore the modulation of PIN-dependent auxin transport between cells is a main developmental output of ROP-regulated vesicle trafficking. The present review focuses on these cellular mechanisms, especially the integration of ROP-based vesicle trafficking and plant cell polarity.

Planar polarity, tissue polarity and planar morphogenesis in plants

Plant tissues commonly undergo morphogenesis within a single tissue layer or between associated cells of the same tissue type such as vascular cells. Tissue morphogenesis may rely on an underlying tissue polarity marked by coordinated unidirectional asymmetric localisation of molecules to ends of cells. When observed in the plane of the tissue layer this is referred to as planar polarity and planar morphogenesis. However, planar morphogenesis can also involve multidirectional or differential growth of cells relying on cell-cell communication. Here, we review recent progress towards an understanding of hormonal coordination and molecular mechanisms underlying planar and tissue polarity as well as planar morphogenesis. Furthermore, we discuss the role of physical forces in planar morphogenesis and the contribution of tissue polarity to plant organ shape.

RAC/ROP GTPases and auxin signaling

Auxin functions as a key morphogen in regulating plant growth and development. Studies on auxin-regulated gene expression and on the mechanism of polar auxin transport and its asymmetric distribution within tissues have provided the basis for realizing the molecular mechanisms underlying auxin function. In eukaryotes, members of the Ras and Rho subfamilies of the Ras superfamily of small GTPases function as molecular switches in many signaling cascades that regulate growth and development. Plants do not have Ras proteins, but they contain Rho-like small G proteins called RACs or ROPs that, like fungal and metazoan Rhos, are regulators of cell polarity and may also undertake some Ras functions. Here, we discuss the advances made over the last decade that implicate RAC/ROPs as mediators for auxin-regulated gene expression, rapid cell surface-located auxin signaling, and directional auxin transport. We also describe experimental data indicating that auxin-RAC/ROP crosstalk may form regulatory feedback loops and theoretical modeling that attempts to connect local auxin gradients with RAC/ROP regulation of cell polarity. We hope that by discussing these experimental and modeling studies, this perspective will stimulate efforts to further refine our understanding of auxin signaling via the RAC/ROP molecular switch.

Modelling dynamic plant cells

A major challenge in plant biology is to understand how functions in plant cells emerge from interactions between molecular components. Computational and mathematical modelling can encapsulate the relationships between molecular components and reveal how biological functions emerge. We review recent progress in modelling in metabolism, growth, signalling and circadian rhythms in plant cells. We discuss challenges and opportunities for future directions.

Root hair systems biology

Plant functional genomic studies have largely measured the response of whole plants, organs and tissues, resulting in the dilution of the signal from individual cells. Methods are needed where the full repertoire of functional genomic tools can be applied to a single plant cell. Root hair cells are an attractive model to study the biology of a single, differentiated cell type because of their ease of isolation, polar growth, and role in water and nutrient uptake, as well as being the site of infection by nitrogen-fixing bacteria. This review highlights the recent advances in our understanding of plant root hair biology and examines whether the root hair has potential as a model for plant cell systems biology.

Regulation of shape and patterning in plant development

Plant and animal development depend on both biochemical and biophysical responses. In certain contexts biochemical networks and gradients seem to be sufficient to explain patterning. However the translation of such patterns into shape changes also involves mechanical properties, which, in plants, largely depend on the characteristics of the structural elements, in particular the external matrix or cell wall. More generally, there is a number of emerging links between gene regulatory networks, biochemical gradients, and physical forces, involving multiple feedback loops. It is likely that combining mechanical signals and biochemical gradients could confer more robustness to plant development.