The origin of the diversity of leaf venation pattern

Universal Hyperuniform Organization in Looped Leaf Vein Networks

The leaf vein network is a hierarchical vascular system that transports water and nutrients to the leaf cells. The thick primary veins form a branched network, while the secondary veins can develop closed loops forming a well-defined cellular structure. Through extensive analysis of a variety of distinct leaf species, we discover that the apparently disordered cellular structures of the secondary vein networks exhibit a universal hyperuniform organization and possess a hidden order on large scales. Disorder hyperuniform systems lack conventional long-range order, yet they completely suppress normalized infinite-wavelength density fluctuations like crystals. Specifically, we find that the distributions of the geometric centers associated with the vein network loops possess a vanishing static structure factor in the limit that the wave number k goes to 0, i.e., S(k)∼k^{α}, where α≈0.64±0.021, providing an example of class III hyperuniformity in biology. This hyperuniform organization leads to superior efficiency of diffusive transport, as evidenced by the much faster convergence of the time-dependent spreadability S(t) to its longtime asymptotic limit, compared to that of other uncorrelated or correlated disordered but nonhyperuniform organizations. Our results also have implications for the discovery and design of novel disordered network materials with optimal transport properties.

Leaf Vein Patterning

Leaves form veins whose patterns vary from a single vein running the length of the leaf to networks of staggering complexity where huge numbers of veins connect to other veins at both ends. For the longest time, vein formation was thought to be controlled only by the polar, cell-to-cell transport of the plant hormone auxin; recent evidence suggests that is not so. Instead, it turns out that vein patterning features are best accounted for by a combination of polar auxin transport, facilitated auxin diffusion through plasmodesma intercellular channels, and auxin signal transduction-though the latter's precise contribution remains unclear. Equally unclear remain the sites of auxin production during leaf development, on which that vein patterning mechanism ought to depend. Finally, whether that vein patterning mechanism can account for the variety of vein arrangements found in nature remains unknown. Addressing those questions will be the exciting challenge of future research.

Spatially resolved gene regulatory networks in Asian rice (Oryza sativa cv. Nipponbare) leaves

Transcriptome profiles in plants are heterogenous at every level of morphological organization. Even within organs, cells of the same type can have different patterns of gene expression depending on where they are positioned within tissues. This heterogeneity is associated with non-uniform distribution of biological processes within organs. The regulatory mechanisms that establish and sustain the spatial heterogeneity are unknown. Here, we identify regulatory modules that support functional specialization of different parts of Oryza sativa cv. Nipponbare leaves by leveraging transcriptome data, transcription factor binding motifs and global gene regulatory network prediction algorithms. We generated a global gene regulatory network in which we identified six regulatory modules that were active in different parts of the leaf. The regulatory modules were enriched for genes involved in spatially relevant biological processes, such as cell wall deposition, environmental sensing and photosynthesis. Strikingly, more than 86.9% of genes in the network were regulated by members of only five transcription factor families. We also generated targeted regulatory networks for the large MYB and bZIP/bHLH families to identify interactions that were masked in the global prediction. This analysis will provide a baseline for future single cell and array-based spatial transcriptome studies and for studying responses to environmental stress and demonstrates the extent to which seven coarse spatial transcriptome analysis can provide insight into the regulatory mechanisms supporting functional specialization within leaves.

Axes and polarities in leaf vein formation

For multicellular organisms to develop, cells must grow, divide, and differentiate along preferential or exclusive orientations or directions. Moreover, those orientations, or axes, and directions, or polarities, must be coordinated between cells within and between tissues. Therefore, how axes and polarities are coordinated between cells is a key question in biology. In animals, such coordination mainly depends on cell migration and direct interaction between proteins protruding from the plasma membrane. Both cell movements and direct cell-cell interactions are prevented in plants by cell walls that surround plant cells and keep them apart and in place. Therefore, plants have evolved unique mechanisms to coordinate their cell axes and polarities. Here I will discuss evidence suggesting that understanding how leaf veins form may uncover those unique mechanisms. Indeed, unlike previously thought, the cell-to-cell polar transport of the plant hormone auxin along developing veins cannot account for many features of vein patterning. Instead, those features can be accounted for by models of vein patterning that combine polar auxin transport with auxin diffusion through plasmodesmata along the axis of developing veins. Though it remains unclear whether such a combination of polar transport and axial diffusion of auxin can account for the formation of the variety of vein patterns found in plant leaves, evidence suggests that such a combined mechanism may control plant developmental processes beyond vein patterning.

Developmental regulation of leaf venation patterns: monocot versus eudicots and the role of auxin

Organisation and patterning of the vascular network in land plants varies in different taxonomic, developmental and environmental contexts. In leaves, the degree of vascular strand connectivity influences both light and CO₂ harvesting capabilities as well as hydraulic capacity. As such, developmental mechanisms that regulate leaf venation patterning have a direct impact on physiological performance. Development of the leaf venation network requires the specification of procambial cells within the ground meristem of the primordium and subsequent proliferation and differentiation of the procambial lineage to form vascular strands. An understanding of how diverse venation patterns are manifest therefore requires mechanistic insight into how procambium is dynamically specified in a growing leaf. A role for auxin in this process was identified many years ago, but questions remain. In this review we first provide an overview of the diverse venation patterns that exist in land plants, providing an evolutionary perspective. We then focus on the developmental regulation of leaf venation patterns in angiosperms, comparing patterning in eudicots and monocots, and the role of auxin in each case. Although common themes emerge, we conclude that the developmental mechanisms elucidated in eudicots are unlikely to fully explain how parallel venation patterns in monocot leaves are elaborated.

Discovery of spatial pattern of prickles on stem of Rosa hybrida 'Red Queen' and mathematical model of the pattern

The developmental patterns of many organisms are orchestrated by the diffusion of factors. Here, we report a novel pattern on plant stems that appears to be controlled by inhibitor diffusion. Prickles on rose stems appear to be randomly distributed, but we deciphered spatial patterns of prickles on Rosa hybrida cv. ‘Red Queen’ stem. The prickles primarily emerged at 90 to 135 degrees from the spiral phyllotaxis that connected leaf primordia. We proposed a simple mathematical model that explained the emergence of the spatial patterns and reproduced the prickle density distribution on rose stems. We confirmed the model can reproduce the observed prickle patterning on stems of other plant species using other model parameters. These results indicated that the spatial patterns of prickles on stems of different plant species are organized by similar systems. Rose cultivation by humans has a long history. However, prickle development is still unclear and this is the first report of prickle spatial pattern with a mathematical model. Comprehensive analysis of the spatial pattern, genome, and metabolomics of other plant species may lead to novel insights for prickle development.

Of Cells, Strands, and Networks: Auxin and the Patterned Formation of the Vascular System

Throughout plant development, vascular cells continually form from within a population of seemingly equivalent cells. Vascular cells connect end to end to form continuous strands, and vascular strands connect at both or either end to form networks of exquisite complexity and mesmerizing beauty. Here we argue that experimental evidence gained over the past few decades implicates the plant hormone auxin-its production, transport, perception, and response-in all the steps that lead to the patterned formation of the plant vascular system, from the formation of vascular cells to their connection into vascular networks. We emphasize the organizing principles of the cell- and tissue-patterning process, rather than its molecular subtleties. In the picture that emerges, cells compete for an auxin-dependent, cell-polarizing signal; positive feedback between cell polarization and cell-to-cell movement of the polarizing signal leads to gradual selection of cell files; and selected cell files differentiate into vascular strands that drain the polarizing signal from the neighboring cells. Although the logic of the patterning process has become increasingly clear, the molecular details remain blurry; the future challenge will be to bring them into razor-sharp focus.

Developmental and biophysical determinants of grass leaf size worldwide

One of the most notable ecological trends-described more than 2,300  years ago by Theophrastus-is the association of small leaves with dry and cold climates, which has recently been recognized for eudicotyledonous plants at a global scale^1-3. For eudicotyledons, this pattern has been attributed to the fact that small leaves have a thinner boundary layer that helps to avoid extreme leaf temperatures⁴ and their leaf development results in vein traits that improve water transport under cold or dry climates^5,6. However, the global distribution of leaf size and its adaptive basis have not been tested in the grasses, which represent a diverse lineage that is distinct in leaf morphology and that contributes 33% of terrestrial primary productivity (including the bulk of crop production)⁷. Here we demonstrate that grasses have shorter and narrower leaves under colder and drier climates worldwide. We show that small grass leaves have thermal advantages and vein development that contrast with those of eudicotyledons, but that also explain the abundance of small leaves in cold and dry climates. The worldwide distribution of leaf size in grasses exemplifies how biophysical and developmental processes result in convergence across major lineages in adaptation to climate globally, and highlights the importance of leaf size and venation architecture for grass performance in past, present and future ecosystems.

Leaf vascular architecture in temperate dicotyledons: correlations and link to functional traits

Using 227 dicotyledonous species in temperate region, we found the relationships among densities of different-order veins, creating diversity of leaf vascular architectures. Dicotyledonous angiosperms commonly possess a hierarchical leaf vascular system, wherein veins of different orders have different functions. Minor vein spacing determines leaf hydraulic efficiency, whereas the major veins provide mechanical support. However, there is limited information on the coordination between these vein orders across species, limiting our understanding of how diversity in vein architecture is arrayed. We aimed to examine the (1) relationships between vein densities at two spatial scales (lower- vs. higher-order veins and among minor veins) and (2) relationships of vein densities with plant functional traits. We studied ten traits related to vein densities and three functional traits (leaf dry mass per area [LMA], leaf longevity [LL], and adult plant height [H_adult]) for 227 phylogenetically diverse plant species that occur in temperate regions and examined the vein-vein and vein-functional traits relationships across species. The densities of lower- and higher-order veins were positively correlated across species. The minor vein density was positively correlated with the densities of both areoles and free-ending veins, and vascular networks with higher minor vein density tended to have a lower ratio of free-ending veins to areoles across species. Neither densities of lower- nor higher-order veins were related to LMA and LL. On the other hand, the densities of veins and areoles tended to be positively correlated with H_adult. These results suggest that densities of different-order veins are developmentally coordinated across dicotyledonous angiosperms and form the independent axis in resource use strategies based on the leaf economics spectrum.

On the mechanisms of development in monocot and eudicot leaves

Contents Summary 706 I. Introduction 707 II. Leaf zones in monocot and eudicot leaves 707 III. Monocot and eudicot leaf initiation: differences in degree and timing, but not kind 710 IV. Reticulate and parallel venation: extending the model? 711 V. Flat laminar growth: patterning and coordination of adaxial-abaxial and mediolateral axes 713 VI. Stipules and ligules: ontogeny of primordial elaborations 715 VII. Leaf architecture 716 VIII. Stomatal development: shared and diverged mechanisms for making epidermal pores 717 IX. Conclusion 719 Acknowledgements 720 References 720 SUMMARY: Comparisons of concepts in monocot and eudicot leaf development are presented, with attention to the morphologies and mechanisms separating these angiosperm lineages. Monocot and eudicot leaves are distinguished by the differential elaborations of upper and lower leaf zones, the formation of sheathing/nonsheathing leaf bases and vasculature patterning. We propose that monocot and eudicot leaves undergo expansion of mediolateral domains at different times in ontogeny, directly impacting features such as venation and leaf bases. Furthermore, lineage-specific mechanisms in compound leaf development are discussed. Although models for the homologies of enigmatic tissues, such as ligules and stipules, are proposed, tests of these hypotheses are rare. Likewise, comparisons of stomatal development are limited to Arabidopsis and a few grasses. Future studies may investigate correlations in the ontogenies of parallel venation and linear stomatal files in monocots, and the reticulate patterning of veins and dispersed stoma in eudicots. Although many fundamental mechanisms of leaf development are shared in eudicots and monocots, variations in the timing, degree and duration of these ontogenetic events may contribute to key differences in morphology. We anticipate that the incorporation of an ever-expanding number of sequenced genomes will enrich our understanding of the developmental mechanisms generating eudicot and monocot leaves.

The arrangement of lateral veins along the midvein of leaves is not related to leaf phyllotaxis

Positions of leaves along a stem usually adhere to a genetically determined, species-specific pattern known as a leaf phyllotaxis. We investigated whether the arrangement of lateral secondary veins along primary midveins adhered to a species-specific pattern that resembled an alternate or opposite phyllotaxis. We analyzed the venation of temperate dicotyledonous species from different taxonomic groups and chose 18 woody and 12 herbaceous species that have reticulated leaf venation. The arrangement of the lateral veins was neither alternate nor opposite for any of the species. Lateral vein arrangements were instead mixtures of symmetric and asymmetric patterns. Our results show that lateral vein arrangements are related neither to stem-level leaf phyllotaxis (alternate vs. opposite) nor to life form (woody vs. herbaceous). Our results are therefore generally consistent with the canalization hypothesis that the locations of lateral veins are not completely specified genetically prior to leaf formation.

Coordination of cell polarity and the patterning of leaf vein networks

During development, the behavior of cells in tissues is coordinated along specific orientations or directions by coordinating the polar localization of components in those cells. The coordination of such cell polarity is perhaps nowhere more spectacular than in developing leaves, where the polarity of hundreds of cells is coordinated in the leaf epidermis and inner tissue to pattern vein networks. Available evidence suggests that the spectacular coordination of cell polarity that patterns vein networks is controlled by auxin transport and levels, and by genes that have been implicated in the polar localization of auxin transporters.

The bias of a two-dimensional view: comparing two-dimensional and three-dimensional mesophyll surface area estimates using noninvasive imaging

The mesophyll surface area exposed to intercellular air space per leaf area (S_m ) is closely associated with CO₂ diffusion and photosynthetic rates. S_m is typically estimated from two-dimensional (2D) leaf sections and corrected for the three-dimensional (3D) geometry of mesophyll cells, leading to potential differences between the estimated and actual cell surface area. Here, we examined how 2D methods used for estimating S_m compare with 3D values obtained from high-resolution X-ray microcomputed tomography (microCT) for 23 plant species, with broad phylogenetic and anatomical coverage. Relative to 3D, uncorrected 2D S_m estimates were, on average, 15-30% lower. Two of the four 2D S_m methods typically fell within 10% of 3D values. For most species, only a few 2D slices were needed to accurately estimate S_m within 10% of the whole leaf sample median. However, leaves with reticulate vein networks required more sections because of a more heterogeneous vein coverage across slices. These results provide the first comparison of the accuracy of 2D methods in estimating the complex 3D geometry of internal leaf surfaces. Because microCT is not readily available, we provide guidance for using standard light microscopy techniques, as well as recommending standardization of reporting S_m values.

Computational Modeling of Auxin: A Foundation for Plant Engineering

Since the development of agriculture, humans have relied on the cultivation of plants to satisfy our increasing demand for food, natural products, and other raw materials. As we understand more about plant development, we can better manipulate plants to fulfill our particular needs. Auxins are a class of simple metabolites that coordinate many developmental activities like growth and the appearance of functional structures in plants. Computational modeling of auxin has proven to be an excellent tool in elucidating many mechanisms that underlie these developmental events. Due to the complexity of these mechanisms, current modeling efforts are concerned only with single phenomena focused on narrow spatial and developmental contexts; but a general model of plant development could be assembled by integrating the insights from all of them. In this perspective, we summarize the current collection of auxin-driven computational models, focusing on how they could come together into a single model for plant development. A model of this nature would allow researchers to test hypotheses in silico and yield accurate predictions about the behavior of a plant under a given set of physical and biochemical constraints. It would also provide a solid foundation toward the establishment of plant engineering, a proposed discipline intended to enable the design and production of plants that exhibit an arbitrarily defined set of features.

Topological Phenotypes Constitute a New Dimension in the Phenotypic Space of Leaf Venation Networks

The leaves of angiosperms contain highly complex venation networks consisting of recursively nested, hierarchically organized loops. We describe a new phenotypic trait of reticulate vascular networks based on the topology of the nested loops. This phenotypic trait encodes information orthogonal to widely used geometric phenotypic traits, and thus constitutes a new dimension in the leaf venation phenotypic space. We apply our metric to a database of 186 leaves and leaflets representing 137 species, predominantly from the Burseraceae family, revealing diverse topological network traits even within this single family. We show that topological information significantly improves identification of leaves from fragments by calculating a “leaf venation fingerprint” from topology and geometry. Further, we present a phenomenological model suggesting that the topological traits can be explained by noise effects unique to specimen during development of each leaf which leave their imprint on the final network. This work opens the path to new quantitative identification techniques for leaves which go beyond simple geometric traits such as vein density and is directly applicable to other planar or sub-planar networks such as blood vessels in the brain.

Planar reticular networks are ubiquitous in nature and engineering, formed for instance by the arterial vasculature in the mammalian neocortex, urban street grids or the vascular network of plant leaves. We use a topological metric to characterize the way loops are nested in such networks and analyze a large database of 186 leaves and leaflets, revealing for the first time that the nesting of the networks’ cycles constitutes a distinct phenotypic trait orthogonal to previously used geometric features. Furthermore, we demonstrate that the information contained in the leaf topology can significantly improve specimen identification from fragments, and provide an empirical growth model that can explain much of the observed data. Our work can improve understanding of the functional significance of the various leaf vein architectures and their correlation with the environment. It can pave the way for similar analyses in diverse areas of research involving reticulate networks.

Mathematical study for the mechanism of vascular and spot patterns by auxin and pin dynamics in plant development

Inhomogeneous distribution of auxin is essential in various differentiation processes of plant development. Auxin transfer between cells by efflux carrier protein called PINFORMED (PIN) has been considered to be responsible for inhomogeneous distribution of auxin. Two major types of auxin distribution patterns are "spot" patterns and "passage" patterns, which are responsible for determining the position of the primordia of a leaf or flower in shoot apical meristem and formation of leaf veins, respectively. In this study, we studied the pattern formation of auxin distribution mediated by polarization of PIN using mathematical methods. We developed several different models which show possible interaction mechanisms between auxin and PIN on 2-dimentional hexagonal cellular lattice, (1) Basic auxin flux model, (2) auxin-dependent PIN degradation model and (3) auxin self-feedback model. We analyzed these models by numerical calculation and mathematical analysis. From intensive numerical calculations under different conditions, we found that some models show three different types of pattern formations in dynamics, (a) homogeneous, (b) passage and (c) spot pattern depending on parameter condition. We analyzed these models mathematically using approximation of 1-dimensional periodic space. We determined the conditions that passage and spot patterns are generated in each model, respectively. After these analyses, we propose possible mechanisms by which plants switch passage and spot patterns in different organs by small modification.

Quantifying loopy network architectures

Biology presents many examples of planar distribution and structural networks having dense sets of closed loops. An archetype of this form of network organization is the vasculature of dicotyledonous leaves, which showcases a hierarchically-nested architecture containing closed loops at many different levels. Although a number of approaches have been proposed to measure aspects of the structure of such networks, a robust metric to quantify their hierarchical organization is still lacking. We present an algorithmic framework, the hierarchical loop decomposition, that allows mapping loopy networks to binary trees, preserving in the connectivity of the trees the architecture of the original graph. We apply this framework to investigate computer generated graphs, such as artificial models and optimal distribution networks, as well as natural graphs extracted from digitized images of dicotyledonous leaves and vasculature of rat cerebral neocortex. We calculate various metrics based on the asymmetry, the cumulative size distribution and the Strahler bifurcation ratios of the corresponding trees and discuss the relationship of these quantities to the architectural organization of the original graphs. This algorithmic framework decouples the geometric information (exact location of edges and nodes) from the metric topology (connectivity and edge weight) and it ultimately allows us to perform a quantitative statistical comparison between predictions of theoretical models and naturally occurring loopy graphs.

Quantitative analysis of venation patterns of Arabidopsis leaves by supervised image analysis

The study of transgenic Arabidopsis lines with altered vascular patterns has revealed key players in the venation process, but details of the vascularization process are still unclear, partly because most lines have only been assessed qualitatively. Therefore, quantitative analyses are required to identify subtle perturbations in the pattern and to test dynamic modeling hypotheses using biological measurements. We developed an online framework, designated Leaf Image Analysis Interface (LIMANI), in which venation patterns are automatically segmented and measured on dark-field images. Image segmentation may be manually corrected through use of an interactive interface, allowing supervision and rectification steps in the automated image analysis pipeline and ensuring high-fidelity analysis. This online approach is advantageous for the user in terms of installation, software updates, computer load and data storage. The framework was used to study vascular differentiation during leaf development and to analyze the venation pattern in transgenic lines with contrasting cellular and leaf size traits. The results show the evolution of vascular traits during leaf development, suggest a self-organizing mechanism for leaf venation patterning, and reveal a tight balance between the number of end-points and branching points within the leaf vascular network that does not depend on the leaf developmental stage and cellular content, but on the leaf position on the rosette. These findings indicate that development of LIMANI improves understanding of the interaction between vascular patterning and leaf growth.

Mechanics in Leaf Venation Morphogenesis and their Biomimetic Inspiration to Construct a 2-Dimensional Reinforcement Layout Model

This paper concerns biomimetic exploration of the leaf rib layout problem. Biological venation of organisms is observed to be similar to reinforced plate/shell systems. Similarity analysis makes it clear that dicotyledonous leaves are an ideal research subject. In this paper, global and local regularities are summarized and existing theories on venation morphogenesis are discussed and compared. An energy hypothesis is proposed to cater for interdisciplinary applications. A venation growing model was then used to construct a two-dimensional reinforcement layout model. The biomechanical expressions developed can be an alternative to describe rib-in-plate or fibre-in-composite materials.

The grass leaf developmental gradient as a platform for a systems understanding of the anatomical specialization of C(4) leaves

C(4) photosynthesis relies on spatial and quantitative specializations of common features of leaf anatomy, including venation pattern, bundle sheath cell and chloroplast differentiation, plasmodesmatal abundance, and secondary cell wall enhancement. It has thus far been challenging to dissect the molecular basis for these C(4)-specific alterations in spatial and quantitative patterns of regulation. The target downstream networks of genes and protein interactions that produce these fundamental anatomical features in both C(4) and C(3) species are poorly understood. The developing leaves of monocot grasses provide a base-to-tip gradient of developmental stages that can provide the platform for comprehensive molecular and anatomical data that can yield a better understanding both of the regulators and the targets that produce C(4) patterns, through a variety of gene discovery and systems analysis strategies.

Genetic control of leaf-blade morphogenesis by the INSECATUS gene in Pisum sativum

To understand the role of INSECATUS (INS) gene in pea, the leaf blades of wild-type, ins mutant and seven other genotypes, constructed by recombining ins with uni-tac, af, tl and mfp gene mutations, were quantitatively compared. The ins was inherited as a recessive mutant allele and expressed its phenotype in proximal leaflets of full size leaf blades. In ins leaflets, the midvein development was arrested in distal domain and a cleft was formed in lamina above this point. There was change in the identity of ins leaflets such that the intercalary interrupted midvein bore a leaf blade. Such adventitious blades in ins, ins tl and ins tl mfp were like the distal segment of respective main leaf blade. The ins phenotype was not seen in ins af and ins af uni-tac genotypes. There was epistasis of uni-tac over ins. The ins, tl and mfp mutations interacted synergistically to produce highly pronounced ins phenotype in the ins tl mfp triple mutant. The role(s) of INS in leaf-blade organogenesis are: positive regulation of vascular patterning in leaflets, repression of UNI activity in leaflet primordia for ectopic growth and in leaf-blade primordium for indeterminate growth of rachis, delimitation of proximal leaflet domain and together with TL and MFP homeostasis for meristematic activity in leaflet primordia. The variant apically bifid shape of the affected ins leaflets demonstrated that the leaflet shape is dependent on the venation pattern.

Auxin transport-feedback models of patterning in plants

Many patterning events in plants are regulated by the phytohormone auxin. In fact, so many things are under the influence of auxin that it seems difficult to understand how a single hormone can do so much. Auxin moves throughout the plant via a network of specialized membrane-bound import and export proteins, which are often differentially expressed and polarized depending on tissue type. Here, we review simulation models of pattern formation that are based on the control of these transporters by auxin itself. In these transport-feedback models, diversity in patterning comes not from the addition of more morphogens, but rather by varying the mechanism that regulates the transporters.

In silico leaf venation networks: growth and reorganization driven by mechanical forces

Development commonly involves an interplay between signaling, genetic expression and biophysical forces. However, the relative importance of these mechanisms during the different stages of development is unclear. Leaf venation networks provide a fitting context for the examination of these questions. In mature leaves, venation patterns are extremely diverse, yet their local structure satisfies a universal property: at junctions between veins, angles and diameters are related by a vectorial equation analogous to a force balance. Using a cell proliferation model, we reproduce in silico the salient features of venation patterns. Provided that vein cells are given different mechanical properties, tensile forces develop along the veins during growth, causing the network to deform progressively. Our results suggest that the local structure of venation networks results from a reorganization driven by mechanical forces, independently of how veins form. This conclusion is supported by recent observations of vein development in young leaves and by the good quantitative agreement between our simulations and data from mature leaves.

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.

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.

Leaf palmate venation and vascular redundancy confer tolerance of hydraulic disruption

Leaf venation is a showcase of plant diversity, ranging from the grid-like network in grasses, to a wide variety of dendritic systems in other angiosperms. A principal function of the venation is to deliver water; however, a hydraulic significance has never been demonstrated for contrasting major venation architectures, including the most basic dichotomy, "pinnate" and "palmate" systems. We hypothesized that vascular redundancy confers tolerance of vein breakage such as would occur during mechanical or insect damage. We subjected leaves of woody angiosperms of contrasting venation architecture to severing treatments in vivo, and, after wounds healed, made detailed measurements of physiological performance relative to control leaves. When the midrib was severed near the leaf base, the pinnately veined leaves declined strongly in leaf hydraulic conductance, stomatal conductance, and photosynthetic rate, whereas palmately veined leaves were minimally affected. Across all of the species examined, a higher density of primary veins predicted tolerance of midrib damage. This benefit for palmate venation is consistent with its repeated evolution and its biogeographic and habitat distribution. All leaves tested showed complete tolerance of damage to second- and higher-order veins, demonstrating that the parallel flow paths provided by the redundant, reticulate minor vein network protect the leaf from the impact of hydraulic disruption. These findings point to a hydraulic explanation for the diversification of low-order vein architecture and the commonness of reticulate, hierarchical leaf venation. These structures suggest roles for both economic constraints and risk tolerance in shaping leaf morphology during 130 million years of flowering plant evolution.

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.