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.     

Modeling of Branching Patterns in Plants

A major determinant of plant architecture is the arrangement of branches around the stem, known as phyllotaxis. However, the specific form of branching conditions is not known. Here we discuss this question and suggest a branching model which seems to be in agreement with biological observations. Recently, a number of models connected with the genetic network or molecular biology regulation of the processes of pattern formation appeared. Most of these models consider the plant hormone, auxin, transport and distribution in the apical meristem as the main factors for pattern formation and phyllotaxis. However, all these models do not take into consideration the whole plant morphogenesis, concentrating on the events in the shoot or root apex. On the other hand, other approaches for modeling phyllotaxis, where the whole plant is considered, usually are mostly phenomenological, and due to it, do not describe the details of plant growth and branching mechanism. In this work, we develop a mathematical model and study pattern formation of the whole, though simplified, plant organism where the main physiological factors of plant growth and development are taken into consideration. We model a growing plant as a system of intervals, which we will consider as branches. We assume that the number and location of the branches are not given a priori, but appear and grow according to certain rules, elucidated by the application of mathematical modeling. Four variables are included in our model: concentrations of the plant hormones auxin and cytokinin, proliferation and growth factor, and nutrients—we observe a wide variety of plant forms and study more specifically the involvement of each variable in the branching process. Analysis of the numerical simulations shows that the process of pattern formation in plants depends on the interaction of all these variables. While concentrations of auxin and cytokinin determine the appearance of a new bud, its growth is determined by the concentrations of nutrients and proliferation factors. Possible mechanisms of apical domination in the frame of our model are discussed.     

Self-Organization of Plant Vascular Systems: Claims and Counter-Claims about the Flux-Based Auxin Transport Model

The plant hormone auxin plays a central role in growth and morphogenesis. In shoot apical meristems, auxin flux is polarized through its interplay with PIN proteins. Concentration-based mathematical models of the flux can explain some aspects of phyllotaxis for the L1 surface layer, where auxin accumulation points act as sinks and develop into primordia. The picture differs in the interior of the meristem, where the primordia act as auxin sources, leading to the initiation of the vascular system. Self-organization of the auxin flux involves large numbers of molecules and is difficult to treat by intuitive reasoning alone; mathematical models are therefore vital to understand these phenomena. We consider a leading computational model based on the so-called flux hypothesis. This model has been criticized and extended in various ways. One of the basic counter-arguments is that simulations yield auxin concentrations inside canals that are lower than those seen experimentally. Contrary to what is claimed in the literature, we show that the model can lead to higher concentrations within canals for significant parameter regimes. We then study the model in the usual case where the response function Φ defining the model is quadratic and unbounded, and show that the steady state vascular patterns are formed of loopless directed trees. Moreover, we show that PIN concentrations can diverge in finite time, thus explaining why previous simulation studies introduced cut-offs which force the system to have bounded PIN concentrations. Hence, contrary to previous claims, extreme PIN concentrations are not due to numerical problems but are intrinsic to the model. On the other hand, we show that PIN concentrations remain bounded for bounded Φ, and simulations show that in this case, loops can emerge at steady state.     

Canalization without flux sensors: a traveling-wave hypothesis

In 1969, Tsvi Sachs published his seminal hypothesis of vascular development in plants: the canalization hypothesis. A positive feedback loop between the flux of the phytohormone auxin and the cells' auxin transport capacity would canalize auxin progressively into discrete channels, which would then differentiate into vascular tissues. Recent experimental studies confirm the central role of polar auxin flux in plant vasculogenesis, but it is unclear if and by which mechanism plant cells could respond to auxin flux. In this Opinion article, we review auxin perception mechanisms and argue that these respond more likely to auxin concentrations than to auxin flux. We propose an alternative mechanism for polar auxin channeling, which is more consistent with recent molecular observations.     

Regulating the regulator: the control of auxin transport

With the discovery of the phytohormone auxin in the late 1920s, it became possible to link the regulation of complex plant growth responses to a single biologically active compound. Among all the plant growth regulators characterised so far, only auxin appears to be actively transported throughout the plant to create complex variations in concentration patterns and flow directions over time. This stimulated interest in the specific mechanisms underlying auxin transport as key factors in plant growth responses. Research in the last decade revealed several genes involved in the controlled transport of auxin and greatly improved our understanding of the basic principles of auxin-mediated responses. We are at this point, however, only starting to understand the complex interplay and control of factors that ultimately underlie the observed spatiotemporal variations in auxin transport and thus mediate plant growth and environmental responses. This review highlights important findings that provide us with a framework of molecular players and potential regulatory mechanisms that should contribute to the formulation of a comprehensive dynamic model of spatiotemporal auxin distribution.     

Simulation of organ patterning on the floral meristem using a polar auxin transport model

An intriguing phenomenon in plant development is the timing and positioning of lateral organ initiation, which is a fundamental aspect of plant architecture. Although important progress has been made in elucidating the role of auxin transport in the vegetative shoot to explain the phyllotaxis of leaf formation in a spiral fashion, a model study of the role of auxin transport in whorled organ patterning in the expanding floral meristem is not available yet. We present an initial simulation approach to study the mechanisms that are expected to play an important role. Starting point is a confocal imaging study of Arabidopsis floral meristems at consecutive time points during flower development. These images reveal auxin accumulation patterns at the positions of the organs, which strongly suggests that the role of auxin in the floral meristem is similar to the role it plays in the shoot apical meristem. This is the basis for a simulation study of auxin transport through a growing floral meristem, which may answer the question whether auxin transport can in itself be responsible for the typical whorled floral pattern. We combined a cellular growth model for the meristem with a polar auxin transport model. The model predicts that sepals are initiated by auxin maxima arising early during meristem outgrowth. These form a pre-pattern relative to which a series of smaller auxin maxima are positioned, which partially overlap with the anlagen of petals, stamens, and carpels. We adjusted the model parameters corresponding to properties of floral mutants and found that the model predictions agree with the observed mutant patterns. The predicted timing of the primordia outgrowth and the timing and positioning of the sepal primordia show remarkable similarities with a developing flower in nature.     

Plant signalling: the inexorable rise of auxin

The flow of signalling molecules across a field of cells to generate a pattern that is then transduced into a differential response in those cells is a fundamental concept in developmental biology. Recent studies have identified a system that regulates the flux of the growth factor auxin through plant tissues via the subcellular asymmetric localization of specific transporters. The recurrent use of this auxin transport system in different developmental and physiological contexts reveals a fundamental mechanism underpinning organogenesis, stem cell positioning and the growth response of the plant to the environment. Here, I will discuss key advances in the identification of auxin transporters and their integration with auxin signal transduction pathways.     

Self-organization of the vascular system in plant leaves: inter-dependent dynamics of auxin flux and carrier proteins

The vegetative hormone Auxin is involved in vascular tissues formation throughout the plant. Trans-membrane carrier proteins transporting auxin from cell to cell and distributed asymmetrically around each cell give to auxin a polarized movement in tissues, creating streams of auxin that presume future vascular bundles. According to the canalization hypothesis, auxin transport ability of cells is thought to increase with auxin flux, resulting in the self-enhancement of this flux along auxin paths. In this study we evaluate a series of models based on canalization hypothesis using carrier proteins, under different assumptions concerning auxin flux formation and carrier protein dynamics. Simulations are run on a hexagonal lattice with uniform auxin production. A single cell located in the margin of the lattice indicates the petiole, and acts as an auxin sink. The main results are: (1) We obtain branching auxin distribution patterns. (2) The type of self-enhancement described by the functional form of the carrier proteins regulation responding to the auxin flux intensity in different parts of a cell, has a strong effect on the possibility of generating the branching patterns. For response functions with acceleration in the increase of carrier protein numbers compared to the auxin flux, branching patterns are likely to be generated. For linear or decelerating response functions, no branching patterns are formed. (3) When branching patterns are formed, auxin distribution greatly differs between the case in which the number of carrier proteins in different parts of a cell are regulated independently, and the case in which different parts of a cell compete for a limited number of carrier proteins. In the former case, the auxin level is lower in veins than in the surrounding tissue, while in the latter, the auxin is present in greater abundance in veins. These results suggest that canalization is a good candidate for describing plant vein pattern formation.     

Modeling Auxin Transport and Plant Development

The plant hormone auxin plays a critical role in plant development. Central to its function is its distribution in plant tissues, which is, in turn, largely shaped by intercellular polar transport processes. Auxin transport relies on diffusive uptake as well as carrier-mediated transport via influx and efflux carriers. Mathematical models have been used to both refine our theoretical understanding of these processes and to test new hypotheses regarding the localization of efflux carriers to understand auxin patterning at the tissue level. Here we review models for auxin transport and how they have been applied to patterning processes, including the elaboration of plant vasculature and primordium positioning. Second, we investigate the possible role of auxin influx carriers such as AUX1 in patterning auxin in the shoot meristem. We find that AUX1 and its relatives are likely to play a crucial role in maintaining high auxin levels in the meristem epidermis. We also show that auxin influx carriers may play an important role in stabilizing auxin distribution patterns generated by auxin-gradient type models for phyllotaxis.     

Flavonoids act as negative regulators of auxin transport in vivo in arabidopsis

Polar transport of the plant hormone auxin controls many aspects of plant growth and development. A number of synthetic compounds have been shown to block the process of auxin transport by inhibition of the auxin efflux carrier complex. These synthetic auxin transport inhibitors may act by mimicking endogenous molecules. Flavonoids, a class of secondary plant metabolic compounds, have been suggested to be auxin transport inhibitors based on their in vitro activity. The hypothesis that flavonoids regulate auxin transport in vivo was tested in Arabidopsis by comparing wild-type (WT) and transparent testa (tt4) plants with a mutation in the gene encoding the first enzyme in flavonoid biosynthesis, chalcone synthase. In a comparison between tt4 and WT plants, phenotypic differences were observed, including three times as many secondary inflorescence stems, reduced plant height, decreased stem diameter, and increased secondary root development. Growth of WT Arabidopsis plants on naringenin, a biosynthetic precursor to those flavonoids with auxin transport inhibitor activity in vitro, leads to a reduction in root growth and gravitropism, similar to the effects of synthetic auxin transport inhibitors. Analyses of auxin transport in the inflorescence and hypocotyl of independent tt4 alleles indicate that auxin transport is elevated in plants with a tt4 mutation. In hypocotyls of tt4, this elevated transport is reversed when flavonoids are synthesized by growth of plants on the flavonoid precursor, naringenin. These results are consistent with a role for flavonoids as endogenous regulators of auxin transport.     

Auxin dynamics after decapitation are not correlated with the initial growth of axillary buds

One of the first and most enduring roles identified for the plant hormone auxin is the mediation of apical dominance. Many reports have claimed that reduced stem indole-3-acetic acid (IAA) levels and/or reduced basipetal IAA transport directly or indirectly initiate bud growth in decapitated plants. We have tested whether auxin inhibits the initial stage of bud release, or subsequent stages, in garden pea (Pisum sativum) by providing a rigorous examination of the dynamics of auxin level, auxin transport, and axillary bud growth. We demonstrate that after decapitation, initial bud growth occurs prior to changes in IAA level or transport in surrounding stem tissue and is not prevented by an acropetal supply of exogenous auxin. We also show that auxin transport inhibitors cause a similar auxin depletion as decapitation, but do not stimulate bud growth within our experimental time-frame. These results indicate that decapitation may trigger initial bud growth via an auxin-independent mechanism. We propose that auxin operates after this initial stage, mediating apical dominance via autoregulation of buds that are already in transition toward sustained growth.     

Modelling of auxin transport affected by gravity and differential radial growth

When a tree stem deviates from verticality, as a result of different environmental factors, patterns of differential radial growth appear. Higher rates of wood production have been observed on the lower side of the tree and lower rates in the opposite side. Biological studies on plant hormones have shown that the concentration of auxin induces radial growth. They also have demonstrated the redistribution of auxin transport in response to gravity. Auxin is then designated as a mediator for differential growth. This paper presents a model for three-dimensional (3-D) auxin transport in conifer trees, which includes gravity dependence. We obtain realistic heterogeneous patterns of auxin distribution over the tree. Then, we propose a law of growth based on auxin concentration to simulate successive differential radial growths. The predicted growths are compared with experimental results of reconstruction of 3-D annual growth of Radiata pine.     

Effect of simulated microgravity on auxin polar transport in inflorescence axis of Arabidopsis thaliana.

The morphology, growth and development of higher plants are strongly influenced by environmental stimuli on the earth, which affect the changes in the dynamics of plant hormones in plants. Qualitative and quantitative changes in plant hormones are the most important internal factor to regulate plant growth and development. Among them, auxin (IAA) is of most significant. There are numerous reports concerning the physiological roles of auxin in plant growth and development (Matthysse and Scott 1984). One of the characteristics of auxin is to have the ability of polar transport along the vector of gravity on the earth (Schneider and Wightman 1978), suggesting that the activity of auxin polar transport is also important for the growth and development of plants. It has recently been reported that the normal activity of auxin polar transport in inflorescence axis of Arabidopsis thaliana was required for flower formation (Okada et al. 1991, Ueda et al. 1992). Considering the above evidence together with the fact that gravity affects the morphology, growth and development of higher plants, gravity might affect the qualitative and quantitative changes in plant hormones including the activity of auxin polar transport. In this paper, we report the effect of microgravity condition simulated by a three-dimensional (3-D) or a horizontal clinostat on the activity of auxin polar transport in inflorescence axis of Arabidopsis thaliana.     

The POLARIS peptide of Arabidopsis regulates auxin transport and root growth via effects on ethylene signaling

The rate and plane of cell division and anisotropic cell growth are critical for plant development and are regulated by diverse mechanisms involving several hormone signaling pathways. Little is known about peptide signaling in plant growth; however, Arabidopsis thaliana POLARIS (PLS), encoding a 36-amino acid peptide, is required for correct root growth and vascular development. Mutational analysis implicates a role for the peptide in hormone responses, but the basis of PLS action is obscure. Using the Arabidopsis root as a model to study PLS action in plant development, we discovered a link between PLS, ethylene signaling, auxin homeostasis, and microtubule cytoskeleton dynamics. Mutation of PLS results in an enhanced ethylene-response phenotype, defective auxin transport and homeostasis, and altered microtubule sensitivity to inhibitors. These defects, along with the short-root phenotype, are suppressed by genetic and pharmacological inhibition of ethylene action. PLS expression is repressed by ethylene and induced by auxin. Our results suggest a mechanism whereby PLS negatively regulates ethylene responses to modulate cell division and expansion via downstream effects on microtubule cytoskeleton dynamics and auxin signaling, thereby influencing root growth and lateral root development. This mechanism involves a regulatory loop of auxin-ethylene interactions.     

Interaction of PIN and PGP transport mechanisms in auxin distribution-dependent development

The signalling molecule auxin controls plant morphogenesis via its activity gradients, which are produced by intercellular auxin transport. Cellular auxin efflux is the rate-limiting step in this process and depends on PIN and phosphoglycoprotein (PGP) auxin transporters. Mutual roles for these proteins in auxin transport are unclear, as is the significance of their interactions for plant development. Here, we have analysed the importance of the functional interaction between PIN- and PGP-dependent auxin transport in development. We show by analysis of inducible overexpression lines that PINs and PGPs define distinct auxin transport mechanisms: both mediate auxin efflux but they play diverse developmental roles. Components of both systems are expressed during embryogenesis, organogenesis and tropisms, and they interact genetically in both synergistic and antagonistic fashions. A concerted action of PIN- and PGP-dependent efflux systems is required for asymmetric auxin distribution during these processes. We propose a model in which PGP-mediated efflux controls auxin levels in auxin channel-forming cells and, thus, auxin availability for PIN-dependent vectorial auxin movement.     

How canalization can make loops: a new model of reticulated leaf vascular pattern formation

Formation of the vascular system in plant leaves can be explained by the canalization hypothesis which states that veins are formed in an initially homogeneous field by a self-organizing process between the plant hormone auxin and auxin carrier proteins. Previous models of canalization can generate vein patterns with branching but fail to generate vein patterns with closed loops. However, closed vein loops are commonly observed in plant leaves and are important in making them robust to herbivore attacks and physical damage. Here we propose a new model which generates a vein system with closed loops. We postulate that the "flux bifurcator" level is enhanced in cells with a high auxin flux and that it causes reallocation of auxin carriers toward neighbouring cells also having a high bifurcator level. This causes the auxin flux to bifurcate, allowing vein tips to attach to other veins creating vein loops. We explore several alternative functional forms for the flux bifurcator affecting the reallocation of efflux carriers and examine parameter dependence of the resulting vein pattern.     

Strigolactone Can Promote or Inhibit Shoot Branching by Triggering Rapid Depletion of the Auxin Efflux Protein PIN1 from the Plasma Membrane

Plants continuously extend their root and shoot systems through the action of meristems at their growing tips. By regulating which meristems are active, plants adjust their body plans to suit local environmental conditions. The transport network of the phytohormone auxin has been proposed to mediate this systemic growth coordination, due to its self-organising, environmentally sensitive properties. In particular, a positive feedback mechanism termed auxin transport canalization, which establishes auxin flow from active shoot meristems (auxin sources) to the roots (auxin sinks), has been proposed to mediate competition between shoot meristems and to balance shoot and root growth. Here we provide strong support for this hypothesis by demonstrating that a second hormone, strigolactone, regulates growth redistribution in the shoot by rapidly modulating auxin transport. A computational model in which strigolactone action is represented as an increase in the rate of removal of the auxin export protein, PIN1, from the plasma membrane can reproduce both the auxin transport and shoot branching phenotypes observed in various mutant combinations and strigolactone treatments, including the counterintuitive ability of strigolactones either to promote or inhibit shoot branching, depending on the auxin transport status of the plant. Consistent with this predicted mode of action, strigolactone signalling was found to trigger PIN1 depletion from the plasma membrane of xylem parenchyma cells in the stem. This effect could be detected within 10 minutes of strigolactone treatment and was independent of protein synthesis but dependent on clathrin-mediated membrane trafficking. Together these results support the hypothesis that growth across the plant shoot system is balanced by competition between shoot apices for a common auxin transport path to the root and that strigolactones regulate shoot branching by modulating this competition.     

A molecular basis for auxin action.

The plant hormone auxin is central in the regulation of growth and development, however, the molecular basis for its action has remained enigmatic. In the absence of a molecular model, the wide range of responses elicited by auxin have been difficult to explain. Recent advances using molecular genetic approaches in Arabidopsis have led to the isolation of a number of key genes involved in auxin action. Of particular importance are genes involved in channelling polar auxin transport through the plant. In addition a model for auxin signal transduction, centred on regulated protein degradation, has been developed.     

The auxin influx carrier is essential for correct leaf positioning

Auxin is of vital importance in virtually every aspect of plant growth and development, yet, even after almost a century of intense study, major gaps in our knowledge of its synthesis, distribution, perception, and signal transduction remain. One unique property of auxin is its polar transport, which in many well-documented cases is a critical part of its mode of action. Auxin is actively transported through the action of both influx and efflux carriers. Inhibition of polar transport by the efflux inhibitor N-1-naphthylphthalamic acid (NPA) causes a complete cessation of leaf initiation, a defect that can be reversed by local application of the auxin, indole-3-acetic acid (IAA), to the responsive zone of the shoot apical meristem. In this study, we address the role of the auxin influx carrier in the positioning and outgrowth of leaf primordia at the shoot apical meristem of tomato. By using a combination of transport inhibitors and synthetic auxins, we demonstrate that interference with auxin influx has little effect on organ formation as such, but prevents proper localization of leaf primordia. These results suggest the existence of functional auxin concentration gradients in the shoot apical meristem that are actively set up and maintained by the action of efflux and influx carriers. We propose a model in which efflux carriers control auxin delivery to the shoot apical meristem, whereas influx and efflux carriers regulate auxin distribution within the meristem.