Alignment between PIN1 polarity and microtubule orientation in the shoot apical meristem reveals a tight coupling between morphogenesis and auxin transport

Morphogenesis during multicellular development is regulated by intercellular signaling molecules as well as by the mechanical properties of individual cells. In particular, normal patterns of organogenesis in plants require coordination between growth direction and growth magnitude. How this is achieved remains unclear. Here we show that in Arabidopsis thaliana, auxin patterning and cellular growth are linked through a correlated pattern of auxin efflux carrier localization and cortical microtubule orientation. Our experiments reveal that both PIN1 localization and microtubule array orientation are likely to respond to a shared upstream regulator that appears to be biomechanical in nature. Lastly, through mathematical modeling we show that such a biophysical coupling could mediate the feedback loop between auxin and its transport that underlies plant phyllotaxis.     

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.     

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.     

Phyllotaxis--a new chapter in an old tale about beauty and magic numbers

Phyllotaxis, the regular arrangement of leaves and flowers around the stem, is one of the most fascinating patterning phenomena in biology. Numerous theoretical models, that are based on biochemical, biophysical and other principles, have been proposed to explain the development of the patterns. Recently, auxin has been identified as the inducer of organ formation. An emerging model for phyllotaxis states that polar auxin transport in the plant apex generates local peaks in auxin concentration that determine the site of organ formation and thereby the different phyllotactic patterns found in nature. The PIN proteins play a primary role in auxin transport. These proteins are localized in a polar fashion, reflecting the directionality of polar auxin transport. Recent evidence shows that most aspects of phyllotaxis can be explained by the expression pattern and the dynamic subcellular localization of PIN1.     

Noise and robustness in phyllotaxis

A striking feature of vascular plants is the regular arrangement of lateral organs on the stem, known as phyllotaxis. The most common phyllotactic patterns can be described using spirals, numbers from the Fibonacci sequence and the golden angle. This rich mathematical structure, along with the experimental reproduction of phyllotactic spirals in physical systems, has led to a view of phyllotaxis focusing on regularity. However all organisms are affected by natural stochastic variability, raising questions about the effect of this variability on phyllotaxis and the achievement of such regular patterns. Here we address these questions theoretically using a dynamical system of interacting sources of inhibitory field. Previous work has shown that phyllotaxis can emerge deterministically from the self-organization of such sources and that inhibition is primarily mediated by the depletion of the plant hormone auxin through polarized transport. We incorporated stochasticity in the model and found three main classes of defects in spiral phyllotaxis--the reversal of the handedness of spirals, the concomitant initiation of organs and the occurrence of distichous angles--and we investigated whether a secondary inhibitory field filters out defects. Our results are consistent with available experimental data and yield a prediction of the main source of stochasticity during organogenesis. Our model can be related to cellular parameters and thus provides a framework for the analysis of phyllotactic mutants at both cellular and tissular levels. We propose that secondary fields associated with organogenesis, such as other biochemical signals or mechanical forces, are important for the robustness of phyllotaxis. More generally, our work sheds light on how a target pattern can be achieved within a noisy background.     

Computer models of auxin transport: a review and commentary

With the recent proliferation of computer models of auxin transport, it is important that plant biologists understand something about these techniques and how to evaluate them. The paper begins with a brief introduction to the parts of a computer model, followed by a discussion of the limitations of the most common auxin modelling technique. Lastly, several recent models of organ initiation in the shoot apical meristem (i.e. phyllotaxis) are reviewed. The cell and molecular biology of phyllotaxis is now understood well enough that computer models can go beyond a simple 'proof of principle' and start to provide insights into gene function.     

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.     

Auxin: A major regulator of organogenesis

Plant development is characterized by the continuous initiation of tissues and organs. The meristems, which are small stem cell populations, are involved in this process. The shoot apical meristem produces lateral organs at its flanks and generates the growing stem. These lateral organs are arranged in a stereotyped pattern called phyllotaxis. Organ initiation in the peripheral zone of the meristem involves accumulation of the plant hormone auxin. Auxin is transported in a polar way by influx and efflux carriers located at cell membranes. Polar localization of the PIN1 efflux carrier in meristematic cells generates auxin concentration gradients and PIN1 localization depends, in turn, on auxin gradients: this feedback loop generates a dynamic auxin distribution which controls phyllotaxis. Furthermore, PIN-dependent local auxin gradients represent a common module for organ initiation, in the shoot and in the root.     

Auxin regulates the initiation and radial position of plant lateral organs

Leaves originate from the shoot apical meristem, a small mound of undifferentiated tissue at the tip of the stem. Leaf formation begins with the selection of a group of founder cells in the so-called peripheral zone at the flank of the meristem, followed by the initiation of local growth and finally morphogenesis of the resulting bulge into a differentiated leaf. Whereas the mechanisms controlling the switch between meristem propagation and leaf initiation are being identified by genetic and molecular analyses, the radial positioning of leaves, known as phyllotaxis, remains poorly understood. Hormones, especially auxin and gibberellin, are known to influence phyllotaxis, but their specific role in the determination of organ position is not clear. We show that inhibition of polar auxin transport blocks leaf formation at the vegetative tomato meristem, resulting in pinlike naked stems with an intact meristem at the tip. Microapplication of the natural auxin indole-3-acetic acid (IAA) to the apex of such pins restores leaf formation. Similarly, exogenous IAA induces flower formation on Arabidopsis pin-formed1-1 inflorescence apices, which are blocked in flower formation because of a mutation in a putative auxin transport protein. Our results show that auxin is required for and sufficient to induce organogenesis both in the vegetative tomato meristem and in the Arabidopsis inflorescence meristem. In this study, organogenesis always strictly coincided with the site of IAA application in the radial dimension, whereas in the apical-basal dimension, organ formation always occurred at a fixed distance from the summit of the meristem. We propose that auxin determines the radial position and the size of lateral organs but not the apical-basal position or the identity of the induced structures.     

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.     

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.     

Phyllotaxis

Phyllotaxis, the regular arrangement of leaves or flowers around a plant stem, is an example of developmental pattern formation and organogenesis. Phyllotaxis is characterized by the divergence angles between the organs, the most common angle being 137.5 degrees , the golden angle. The quantitative aspects of phyllotaxis have stimulated research at the interface between molecular biology, physics and mathematics. This review documents the rich history of different approaches and conflicting hypotheses, and then focuses on recent molecular work that establishes a novel patterning mechanism based on active transport of the plant hormone auxin. Finally, it shows how computer simulations can help to formulate quantitative models that in turn can be tested by experiment. The accumulation of ever increasing amounts of experimental data makes quantitative modeling of interest for many developmental systems.     

Auxin and phyllotaxis

Our understanding of phyllotaxis is still largely based on surgical and pharmacological experiments carried out before 1970. Recent experiments implicate the plant hormone auxin in the regulation of phyllotaxis. A recent paper shows how the polar auxin transport mutant, pin1-1, which fails to make flowers, affects the expression of well known meristem genes. This work opens the door for the genetic analysis of phyllotaxis.     

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.     

Root System Architecture from Coupling Cell Shape to Auxin Transport

Lateral organ position along roots and shoots largely determines plant architecture, and depends on auxin distribution patterns. Determination of the underlying patterning mechanisms has hitherto been complicated because they operate during growth and division. Here, we show by experiments and computational modeling that curvature of the Arabidopsis root influences cell sizes, which, together with tissue properties that determine auxin transport, induces higher auxin levels in the pericycle cells on the outside of the curve. The abundance and position of the auxin transporters restricts this response to the zone competent for lateral root formation. The auxin import facilitator, AUX1, is up-regulated by auxin, resulting in additional local auxin import, thus creating a new auxin maximum that triggers organ formation. Longitudinal spacing of lateral roots is modulated by PIN proteins that promote auxin efflux, and pin2,3,7 triple mutants show impaired lateral inhibition. Thus, lateral root patterning combines a trigger, such as cell size difference due to bending, with a self-organizing system that mediates alterations in auxin transport.     

Morphogenesis in cell colonies grown from Convolvulus cell suspensions plated on synthetic media

Filtered cell suspensions of cultured callus tissue derived from the roots of Convolvulus arvensis L. were plated out on synthetic agar nutrient media in petri plates. Cell colonies which formed from the single cells or small cell groups in the suspension showed a considerable range of developmental patterns depending upon the physical and chemical environment to which they were exposed. Variation of the auxin and kinin concentrations and the nature and concentration of the source of reduced N compounds had the most profound effects on colony development. High auxin favored cell enlargement, high kinin favored the development of compact colonies composed of many small cells. Both auxin and kinin were required for cell colony formation. Cell differentiation responses which were observed but not subject to experimental control included formation of starch- and crystal-storing cells, differentiation of tracheary elements, formation of cellular filaments, and development of chlorophyllous tissue. Organ initiation was studied in cell colonies developed directly from plated cell suspensions and in cell colonies subcultured on various nutrient media. Bud initiation was produced repeatedly on media containing NAA at 10^-8 to 10^-6 m combined with kinetin at 10^-6 m . Root initiation was induced infrequently and unpredictably. Once roots had been formed from cell colonies derived from cell suspensions, the roots could be subcultured and induced to form buds; these in turn grew into whole plants. Subculture of young cell colonies to media containing different combinations of growth substances made possible a study of the effects of auxin and kinin on organization of primordia by the cell colonies. By following marked single cells plated on synthetic media, it was possible to produce single-cell clones which under proper nutrient conditions were induced to form buds. The value of the combined techniques of cell suspension culture and cell plating for the study of the physical and chemical factors influencing cell differentiation and organized development are pointed out.     

Abscisic acid is required for somatic embryo initiation through mediating spatial auxin response in Arabidopsis

Abscisic acid (ABA) regulates many aspects of plant development, including somatic embryo (SE) initiation. However, mechanisms of ABA functions on SE initiation have remained to be investigated. In this study, we examined the endogenous ABA contents of calli in Arabidopsis during the SE inductive process. We further found that the capacity for SE initiation was strongly impaired by treatment of fluridone, a potent inhibitor of ABA biosynthesis, as well as by mutation of ABA biosynthetic gene ABA2, suggesting that ABA is required for SE initiation. Furthermore, treatment of fluridone inhibited local auxin biosynthesis and auxin polar transport in the embryonic calli, resulting in the disturbance of auxin response pattern and the decreased regeneration frequency of SEs. However, application of exogenous ABA in the medium almost recovered patterns of auxin response and SE initiation. Thus, the results suggest that ABA functions on SE initiation through mediating both auxin biosynthesis and polar transport for establishment of auxin response pattern in callus. Our study provides new information for understanding mechanisms of SE initiation.