Reviewing models of auxin canalization in the context of leaf vein pattern formation in Arabidopsis

Brassinosteroid signaling and auxin transport are required to establish the periodic pattern of Arabidopsis shoot vascular bundles

The plant vascular system provides transport and support capabilities that are essential for plant growth and development, yet the mechanisms directing the arrangement of vascular bundles within the shoot inflorescence stem remain unknown. We used computational and experimental biology to evaluate the role of auxin and brassinosteroid hormones in vascular patterning in Arabidopsis. We show that periodic auxin maxima controlled by polar transport and not overall auxin levels underlie vascular bundle spacing, whereas brassinosteroids modulate bundle number by promoting early procambial divisions. Overall, this study demonstrates that auxin polar transport coupled to brassinosteroid signaling is required to determine the radial pattern of vascular bundles in shoots.

Auxin-regulated cell polarity: an inside job?

Auxin is now known to be a key regulator of polar events in plant cells. The mechanism by which auxin conveys a polar signal to the cell is unknown, but one well-known hypothesis is that the auxin flux across the plasma membrane regulates vesicle trafficking. This hypothesis remains controversial because of its reliance on an as-yet-undiscovered membrane flux sensor. In this article I suggest instead that the polar signal is the auxin gradient within the cell cytoplasm. A computer model of vascular development is presented that demonstrates the plausibility of this scenario. The auxin-binding protein ABP1 might be the receptor for the auxin gradient.

Plant intelligence: why, why not or where?

The concept of plant intelligence, as proposed by Anthony Trewavas, has raised considerable discussion. However, plant intelligence remains loosely defined; often it is either perceived as practically synonymous to Darwinian fitness, or reduced to a mere decorative metaphor. A more strict view can be taken, emphasizing necessary prerequisites such as memory and learning, which requires clarifying the definition of memory itself. To qualify as memories, traces of past events have to be not only stored, but also actively accessed. We propose a criterion for eliminating false candidates of possible plant intelligence phenomena in this stricter sense: an "intelligent" behavior must involve a component that can be approximated by a plausible algorithmic model involving recourse to stored information about past states of the individual or its environment. Re-evaluation of previously presented examples of plant intelligence shows that only some of them pass our test.

Integration of transport-based models for phyllotaxis and midvein formation

The plant hormone auxin mediates developmental patterning by a mechanism that is based on active transport. In the shoot apical meristem, auxin gradients are thought to be set up through a feedback loop between auxin and the activity and polar localization of its transporter, the PIN1 protein. Two distinct molecular mechanisms for the subcellular polarization of PIN1 have been proposed. For leaf positioning (phyllotaxis), an "up-the-gradient" PIN1 polarization mechanism has been proposed, whereas the formation of vascular strands is thought to proceed by "with-the-flux" PIN1 polarization. These patterning mechanisms intersect during the initiation of the midvein, which raises the question of how two different PIN1 polarization mechanisms may work together. Our detailed analysis of PIN1 polarization during midvein initiation suggests that both mechanisms for PIN1 polarization operate simultaneously. Computer simulations of the resulting dual polarization model are able to reproduce the dynamics of observed PIN1 localization. In addition, the appearance of high auxin concentration in our simulations throughout the initiation of the midvein is consistent with experimental observation and offers an explanation for a long-standing criticism of the canalization hypothesis; namely, how both high flux and high concentration can occur simultaneously in emerging veins.

The role of auxin transport in plant patterning mechanisms

In plants, many patterning processes involve the phytohormone auxin, and controlling how it moves around plays a critical role in pattern formation.

Flux-based transport enhancement as a plausible unifying mechanism for auxin transport in meristem development

Plants continuously generate new organs through the activity of populations of stem cells called meristems. The shoot apical meristem initiates leaves, flowers, and lateral meristems in highly ordered, spiralled, or whorled patterns via a process called phyllotaxis. It is commonly accepted that the active transport of the plant hormone auxin plays a major role in this process. Current hypotheses propose that cellular hormone transporters of the PIN family would create local auxin maxima at precise positions, which in turn would lead to organ initiation. To explain how auxin transporters could create hormone fluxes to distinct regions within the plant, different concepts have been proposed. A major hypothesis, canalization, proposes that the auxin transporters act by amplifying and stabilizing existing fluxes, which could be initiated, for example, by local diffusion. This convincingly explains the organised auxin fluxes during vein formation, but for the shoot apical meristem a second hypothesis was proposed, where the hormone would be systematically transported towards the areas with the highest concentrations. This implies the coexistence of two radically different mechanisms for PIN allocation in the membrane, one based on flux sensing and the other on local concentration sensing. Because these patterning processes require the interaction of hundreds of cells, it is impossible to estimate on a purely intuitive basis if a particular scenario is plausible or not. Therefore, computational modelling provides a powerful means to test this type of complex hypothesis. Here, using a dedicated computer simulation tool, we show that a flux-based polarization hypothesis is able to explain auxin transport at the shoot meristem as well, thus providing a unifying concept for the control of auxin distribution in the plant. Further experiments are now required to distinguish between flux-based polarization and other hypotheses.

Vein patterning screens and the defectively organized tributaries mutants in Arabidopsis thaliana

Leaf veins form a closed network that transports essential photosynthates, water and signaling molecules to the developing plant. The formation of the patterns of these networks during leaf ontogeny is an active subject of modeling and computer simulation. To investigate the vein patterning process, we performed screens for defects in juvenile leaf vein patterning in Arabidopsis thaliana lines subjected to mutagenesis via diepoxybutane, activation tagging or the Dissociation/Activator transposon. We identified over 40 vein pattern defective lines, providing a phenotypic resource for the testing of vein patterning models. In addition, we report the chromosomal linkage for 13 of these, eight of which were successfully cloned. We further describe the phenotypes of five of these mutants, which we call the defectively organized tributaries (dot) mutants, and their corresponding molecular identities. The diversity of the individual genes affected in this collection of pattern mutants suggests that vein pattern is highly sensitive to perturbations in many cellular processes. Despite this diversity of causes, the resulting pattern defects fall into a limited number of classes, including parallel, spurred, misaligned, open, midvein gap and irregularly spaced. These classes may represent sensitivities to cellular processes associated with the DOT genes. The ontogeny of common defective patterns should be accommodated into any robust model for the ontogeny and evolution of pattern.

Conditional repression of AUXIN BINDING PROTEIN1 reveals that it coordinates cell division and cell expansion during postembryonic shoot development in Arabidopsis and tobacco

AUXIN BINDING PROTEIN1 (ABP1) has long been characterized as a potentially important mediator of auxin action in plants. Analysis of the functional requirement for ABP1 during development was hampered because of embryo lethality of the null mutant in Arabidopsis thaliana. Here, we used conditional repression of ABP1 to investigate its function during vegetative shoot development. Using an inducible cellular immunization approach and an inducible antisense construct, we showed that decreased ABP1 activity leads to a severe retardation of leaf growth involving an alteration in cell division frequency, an altered pattern of endocycle induction, a decrease in cell expansion, and a change in expression of early auxin responsive genes. In addition, local repression of ABP1 activity in the shoot apical meristem revealed an additional role for ABP1 in cell plate formation and cell shape. Moreover, cells at the site of presumptive leaf initiation were more sensitive to ABP1 repression than other regions of the meristem. This spatial context-dependent response of the meristem to ABP1 inactivation and the other data presented here are consistent with a model in which ABP1 acts as a coordinator of cell division and expansion, with local auxin levels influencing ABP1 effectiveness.

A system for modelling cell-cell interactions during plant morphogenesis

BACKGROUND AND AIMS

During the development of multicellular organisms, cells are capable of interacting with each other through a range of biological and physical mechanisms. A description of these networks of cell-cell interactions is essential for an understanding of how cellular activity is co-ordinated in regionalized functional entities such as tissues or organs. The difficulty of experimenting on living tissues has been a major limitation to describing such systems, and computer modelling appears particularly helpful to characterize the behaviour of multicellular systems. The experimental difficulties inherent to the multitude of parallel interactions that underlie cellular morphogenesis have led to the need for computer models.

METHODS

A new generic model of plant cellular morphogenesis is described that expresses interactions amongst cellular entities explicitly: the plant is described as a multi-scale structure, and interactions between distinct entities is established through a topological neighbourhood. Tissues are represented as 2D biphasic systems where the cell wall responds to turgor pressure through a viscous yielding of the cell wall.

KEY RESULTS

This principle was used in the development of the CellModeller software, a generic tool dedicated to the analysis and modelling of plant morphogenesis. The system was applied to three contrasting study cases illustrating genetic, hormonal and mechanical factors involved in plant morphogenesis.

CONCLUSIONS

Plant morphogenesis is fundamentally a cellular process and the CellModeller software, through its underlying generic model, provides an advanced research tool to analyse coupled physical and biological morphogenetic mechanisms.

Auxin transport-dependent, stage-specific dynamics of leaf vein formation

For centuries, the formation of vein patterns in the leaf has intrigued biologists, mathematicians and philosophers. In leaf development, files of vein-forming procambial cells emerge from seemingly homogeneous subepidermal tissue through the selection of anatomically inconspicuous preprocambial cells. Although the molecular details underlying the orderly differentiation of veins in the leaf remain elusive, gradually restricted transport paths of the plant hormone auxin have long been implicated in defining sites of vein formation. Several recent advances now appear to converge on a more precise definition of the role of auxin flow at different stages of vascular development. The picture that emerges is that of vein formation as a self-organizing, reiterative, auxin transport-dependent process.

The role of elastic stresses on leaf venation morphogenesis

We explore the possible role of elastic mismatch between epidermis and mesophyll as a driving force for the development of leaf venation. The current prevalent ‘canalization’ hypothesis for the formation of veins claims that the transport of the hormone auxin out of the leaves triggers cell differentiation to form veins. Although there is evidence that auxin plays a fundamental role in vein formation, the simple canalization mechanism may not be enough to explain some features observed in the vascular system of leaves, in particular, the abundance of vein loops. We present a model based on the existence of mechanical instabilities that leads very naturally to hierarchical patterns with a large number of closed loops. When applied to the structure of high-order veins, the numerical results show the same qualitative features as actual venation patterns and, furthermore, have the same statistical properties. We argue that the agreement between actual and simulated patterns provides strong evidence for the role of mechanical effects on venation development.

Leaf venation patterns of most angiosperm plants are hierarchical structures that develop during leaf growth. A remarkable characteristic of these structures is the abundance of closed loops: the venation array divides the leaf surface into disconnected polygonal sectors. The initial vein generations are repetitive within the same species, while high-order vein generations are much more diverse but still show preserved statistical properties. The accepted view of vein formation is the auxin canalization hypothesis: a high flow of the hormone auxin triggers cell differentiation to form veins. Although the role of auxin in vein formation is well established, some issues are difficult to explain within this model, in particular, the abundance of loops of high-order veins. In this work, we explore the previously proposed idea that elastic stresses may play an important role in the development of venation patterns. This appealing hypothesis naturally explains the existence of hierarchical structures with abundant closed loops. To test whether it can sustain a quantitative comparison with actual venation patterns, we have developed and implemented a numerical model and statistically compare actual and simulated patterns. The overall similarity we found indicates that elastic stresses should be included in a complete description of leaf venation development.

Auxin: the looping star in plant development

The phytohormone auxin is a key factor in plant growth and development. Forward and reverse genetic strategies have identified important molecular components in auxin perception, signaling, and transport. These advances resulted in the identification of some of the underlying regulatory mechanisms as well as the emergence of functional frameworks for auxin action. This review focuses on the feedback loops that form an integrative part of these regulatory mechanisms.

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.

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.

Patterning the axis in plants – auxin in control

Axis formation and patterning are fundamental processes establishing the body organization of multicellular organisms. In plants, patterning is not confined to embryogenesis but continues to produce new structures--lateral organs--along the growing primary body axis and also initiates secondary body axes. The signalling molecule auxin has been identified as a key player in plant axial patterning. The shoot and root sections of the axis seem to produce lateral organs in different ways. However, very recent findings suggest a general mechanism of branching triggered by local accumulation of auxin in a 'zone of competence' at the margin of stem-cell systems. How the general auxin signal is converted into organ-specific developmental programs remains a major challenge for the future.

Arabidopsis nucleolin affects plant development and patterning

Nucleolin is a major nucleolar protein implicated in many aspects of ribosomal biogenesis, including early events such as processing of the large 35S preribosomal RNA. We found that the Arabidopsis (Arabidopsis thaliana) parallel1 (parl1) mutant, originally identified by its aberrant leaf venation, corresponds to the Arabidopsis nucleolin gene. parl1 mutants display parallel leaf venation, aberrant localization of the provascular marker Athb8:beta-glucuronidase, the auxin-sensitive reporter DR5:beta-glucuronidase, and auxin-dependent growth defects. PARL1 is highly similar to the yeast (Saccharomyces cerevisiae) nucleolin NUCLEAR SIGNAL RECOGNITION 1 (NSR1) multifunctional protein; the Arabidopsis PARL1 gene can rescue growth defects of yeast nsr1 null mutants. This suggests that PARL1 protein may have roles similar to those of the yeast nucleolin in nuclear signal recognition, ribosomal processing, and ribosomal subunit accumulation. Based on the range of auxin-related defects in parl1 mutants, we propose that auxin-dependent organ growth and patterning is highly sensitive to the efficiency of nucleolin-dependent ribosomal processing.

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.

Towards the systems biology of auxin-transport-mediated patterning

Polar auxin transport intimately connects plant cell polarity and multicellular patterning. Through the transport of the small molecule indole-3-acetic acid, plant cells integrate their polarities and communicate the degree of their polarization. In this way, they generate an apical-basal axis that serves as a positional reference anchoring subsequent patterning events. Research in recent years has brought the molecular mechanisms underlying auxin perception and auxin transport to light. This knowledge has been used to derive spectacular molecular visualization tools and animated computer simulations, which are now allied in a joint systems biology effort towards a mathematical description of auxin-transport-mediated patterning processes.

From genes to patterns: Auxin distribution and auxin-dependent gene regulation in plant pattern formation

It has long been recognized that the plant hormone auxin plays integral roles in a variety of plant processes. More recently, it has become clear that these processes include some of the most basic pattern formation mechanisms needed to establish a functional plant body. Considerable insight into how this regulation plays out at the molecular level has been attained in recent years. Of special note are the complementary actions of the auxin efflux carrier proteins responsible for the formation of instructive auxin concentration gradients and the transcription factor complexes required for the appropriate interpretation of such instructions. The numerous players involved and the complexity of their regulation provide insight into how a single plant hormone can operate in such a multifunctional fashion. Many new features of auxin action can now be quantified and visualized, and three-dimensional models of auxin patterning can be tested and mathematically modeled. With these new advances, the developmental biology of auxin-mediated patterning has turned into a subject of plant systems biology research.

Dynamics of MONOPTEROS and PIN-FORMED1 expression during leaf vein pattern formation in Arabidopsis thaliana

Genetic evidence links the Arabidopsis MONOPTEROS (MP) and PIN-FORMED1 (PIN1) genes to the patterning of leaf veins. To elucidate their potential functions and interactions in this process, we have assessed the dynamics of MP and PIN1 expression during vascular patterning in Arabidopsis leaf primordia. Both genes undergo a dynamic process of gradual refinement of expression into files one to two cells wide before overt vascular differentiation. The subcellular distribution of PIN1 is also gradually refined from a non-polar distribution in isodiametric cells to strongly polarized in elongated procambial cells and provides an indication of overall directions of auxin flow. We found evidence that MP expression can be activated by auxin exposure and that PIN1 as well as DR5::GUS expression is defective in mp mutant leaves. Taken together the results suggest a feedback regulatory loop that involves auxin, MP and PIN1 and provide novel experimental support for the canalization-of-auxin-flow hypothesis.

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.

Tracheid analysis and modeling of the minor veins of the coleus and smilax leaves

Tracheid analysis was carried out on the veinlets and minor veins of the coleus (Solenostemon scutellarioides [L.] Codd) leaf. Third- to fifth-order, or minor, veins average 3.4 tracheids in tandem and they bipartition islets when these enclosed islets reach a critical size; both these features of vein length and islet size contribute to a self-similar process of vein pattern generation. An areole was calculated to be initially comprised of about ten cells making the patterning event for vein formation requiring only a few cells. An algorithmic model developed here for minor vein formation includes five production rules, and this computer model explains the 3-4 tracheids per minor vein, presence of isolated tracheids, the structure of veinlets, and the elaborate branching patterns of veinlets in coleus and other plants.

Dynamic integration of auxin transport and signalling

Recent years have seen rapid progress in our understanding of the mechanism of action of the plant hormone auxin. A major emerging theme is the central importance of the interplay between auxin signalling and the active transport of auxin through the plant to create dynamic patterns of auxin accumulation. Even in tissues where auxin distribution patterns appear stable, they are the product of standing waves, with auxin flowing through the tissue, maintaining local pockets of high and low concentration. The auxin distribution patterns result in changes in gene expression to trigger diverse, context-dependent growth and differentiation responses. Multi-level feedback loops between the signal transduction network and the auxin transport network provide self-stabilising patterns that remain sensitive to the external environment and to the developmental progression of the plant. The full biological implications of the behaviour of this system are only just beginning to be understood through a combination of experimental manipulation and mathematical modelling.

The origin of the diversity of leaf venation pattern

The leaf venation pattern of plants shows remarkable diversity and species-specificity. However, the mechanism underlying the pattern formation and pattern diversity remains unclear. We developed a mathematical model that is based on the positive feedback regulation between plant hormone auxin and its efflux carrier. This system can generate auxin flow pathways by self-organization from an almost homogeneous state. This result explains a well-known experimental phenomenon referred as to "polar auxin transport." The model can produce diverse leaf venation patterns with spatial regularity under similar conditions to those of leaf development, that is, in the presence of leaf expansion and auxin sink. Final venation patterns are strikingly affected by leaf shape and leaf expansion. These results indicate that the positive feedback regulation between auxin and its efflux carrier is a central dynamic in leaf venation pattern formation. The diversity of leaf venation patterns in plant species is probably due to the differences of leaf shape and leaf expansion pattern.

A constant production hypothesis guides leaf venation patterning

We propose a theoretical mechanism that enables the elaboration of veins to supply distant cells during leaf development. In contrast to the more standard view that a signal (e.g., auxin) is produced at isolated sites to stimulate growth, we determine the consequences of the hypothesis that auxin is produced at a constant rate in every cell. High concentration sites for auxin emerge naturally in a reaction-diffusion model, together with global information about leaf shape and existing venation. Because the global information is encoded as auxin concentration and its gradient, those signals provide individual cells with sufficient information to determine their own fate. Unlike other models, a single substance suffices for the reaction-diffusion at early, but not initial, stages of development. Neither complex interactions nor predetermination are necessary. We predict angiosperm areolation patterns in simulation, and our model further implies the Sachs Canalization Hypothesis and resolves a dilemma regarding the role of auxin in cell growth.

Control of leaf vascular patterning by polar auxin transport

The formation of the leaf vascular pattern has fascinated biologists for centuries. In the early leaf primordium, complex networks of procambial cells emerge from homogeneous subepidermal tissue. The molecular nature of the underlying positional information is unknown, but various lines of evidence implicate gradually restricted transport routes of the plant hormone auxin in defining sites of procambium formation. Here we show that a crucial member of the AtPIN family of auxin-efflux-associated proteins, AtPIN1, is expressed prior to pre-procambial and procambial cell fate markers in domains that become restricted toward sites of procambium formation. Subcellular AtPIN1 polarity indicates that auxin is directed to distinct "convergence points" in the epidermis, from where it defines the positions of major veins. Integrated polarities in all emerging veins indicate auxin drainage toward pre-existing veins, but veins display divergent polarities as they become connected at both ends. Auxin application and transport inhibition reveal that convergence point positioning and AtPIN1 expression domain dynamics are self-organizing, auxin-transport-dependent processes. We derive a model for self-regulated, reiterative patterning of all vein orders and postulate at its onset a common epidermal auxin-focusing mechanism for major-vein positioning and phyllotactic patterning.

Modeling plant morphogenesis

Applications of computational techniques to developmental plant biology include the processing of experimental data and the construction of simulation models. Substantial progress has been made in these areas over the past few years. Complex image-processing techniques are used to integrate sequences of two-dimensional images into three-dimensional descriptions of development over time and to extract useful quantitative traits. Large amounts of data are integrated into empirical models of developing plant organs and entire plants. Mechanistic models link molecular-level phenomena with the resulting phenotypes. Several models shed light on the possible properties of active auxin transport and its role in plant morphogenesis.

A plausible model of phyllotaxis

A striking phenomenon unique to the kingdom of plants is the regular arrangement of lateral organs around a central axis, known as phyllotaxis. Recent molecular-genetic experiments indicate that active transport of the plant hormone auxin is the key process regulating phyllotaxis. A conceptual model based on these experiments, introduced by Reinhardt et al. [Reinhardt, D., Pesce, E. R., Stieger, P., Mandel, T., Baltensperger, K., et al. (2003) Nature 426, 255-260], provides an intuitively plausible interpretation of the data, but raises questions of whether the proposed mechanism is, in fact, capable of producing the observed temporal and spatial patterns, is robust, can start de novo, and can account for phyllotactic transitions, such as the frequently observed transition from decussate to spiral phyllotaxis. To answer these questions, we created a computer simulation model based on data described previously or in this paper and reasonable hypotheses. The model reproduces, within the standard error, the divergence angles measured in Arabidopsis seedlings and the effects of selected experimental manipulations. It also reproduces distichous, decussate, and tricussate patterns. The model thus offers a plausible link between molecular mechanisms of morphogenesis and the geometry of phyllotaxis.