A Growth-Based Framework for Leaf Shape Development and Diversity.

How do genes modify cellular growth to create morphological diversity? We study this problem in two related plants with differently shaped leaves: Arabidopsis thaliana (simple leaf shape) and Cardamine hirsuta (complex shape with leaflets). We use live imaging, modeling, and genetics to deconstruct these organ-level differences into their cell-level constituents: growth amount, direction, and differentiation. We show that leaf shape depends on the interplay of two growth modes: a conserved organ-wide growth mode that reflects differentiation; and a local, directional mode that involves the patterning of growth foci along the leaf edge. Shape diversity results from the distinct effects of two homeobox genes on these growth modes: SHOOTMERISTEMLESS broadens organ-wide growth relative to edge-patterning, enabling leaflet emergence, while REDUCED COMPLEXITY inhibits growth locally around emerging leaflets, accentuating shape differences created by patterning. We demonstrate the predictivity of our findings by reconstructing key features of C. hirsuta leaf morphology in A. thaliana. VIDEO ABSTRACT.

A mechanical transition from tension to buckling underlies the jigsaw puzzle shape morphogenesis of histoblasts in the Drosophila epidermis.

The polygonal shape of cells in proliferating epithelia is a result of the tensile forces of the cytoskeletal cortex and packing geometry set by the cell cycle. In the larval Drosophila epidermis, two cell populations, histoblasts and larval epithelial cells, compete for space as they grow on a limited body surface. They do so in the absence of cell divisions. We report a striking morphological transition of histoblasts during larval development, where they change from a tensed network configuration with straight cell outlines at the level of adherens junctions to a highly folded morphology. The apical surface of histoblasts shrinks while their growing adherens junctions fold, forming deep lobules. Volume increase of growing histoblasts is accommodated basally, compensating for the shrinking apical area. The folded geometry of apical junctions resembles elastic buckling, and we show that the imbalance between the shrinkage of the apical domain of histoblasts and the continuous growth of junctions triggers buckling. Our model is supported by laser dissections and optical tweezer experiments together with computer simulations. Our analysis pinpoints the ability of histoblasts to store mechanical energy to a much greater extent than most other epithelial cell types investigated so far, while retaining the ability to dissipate stress on the hours time scale. Finally, we propose a possible mechanism for size regulation of histoblast apical size through the lateral pressure of the epidermis, driven by the growth of cells on a limited surface. Buckling effectively compacts histoblasts at their apical plane and may serve to avoid physical harm to these adult epidermis precursors during larval life. Our work indicates that in growing nondividing cells, compressive forces, instead of tension, may drive cell morphology.

A CUC1/auxin genetic module links cell polarity to patterned tissue growth and leaf shape diversity in crucifer plants.

How tissue-level information encoded by fields of regulatory gene activity is translated into the patterns of cell polarity and growth that generate the diverse shapes of different species remains poorly understood. Here, we investigate this problem in the case of leaf shape differences between Arabidopsis thaliana, which has simple leaves, and its relative Cardamine hirsuta that has complex leaves divided into leaflets. We show that patterned expression of the transcription factor CUP-SHAPED COTYLEDON1 in C. hirsuta (ChCUC1) is a key determinant of leaf shape differences between the two species. Through inducible genetic perturbations, time-lapse imaging of growth, and computational modeling, we find that ChCUC1 provides instructive input into auxin-based leaf margin patterning. This input arises via transcriptional regulation of multiple auxin homeostasis components, including direct activation of WAG kinases that are known to regulate the polarity of PIN-FORMED auxin transporters. Thus, we have uncovered a mechanism that bridges biological scales by linking spatially distributed and species-specific transcription factor expression to cell-level polarity and growth, to shape diverse leaf forms.

LMI1 homeodomain protein regulates organ proportions by spatial modulation of endoreduplication.

How the interplay between cell- and tissue-level processes produces correctly proportioned organs is a key problem in biology. In plants, the relative size of leaves compared with their lateral appendages, called stipules, varies tremendously throughout development and evolution, yet relevant mechanisms remain unknown. Here we use genetics, live imaging, and modeling to show that in Arabidopsis leaves, the LATE MERISTEM IDENTITY1 (LMI1) homeodomain protein regulates stipule proportions via an endoreduplication-dependent trade-off that limits tissue size despite increasing cell growth. LM1 acts through directly activating the conserved mitosis blocker WEE1, which is sufficient to bypass the LMI1 requirement for leaf proportionality.

A common developmental program can produce diverse leaf shapes.

Eudicot leaves have astoundingly diverse shapes. The central problem addressed in this paper is the developmental origin of this diversity. To investigate this problem, we propose a computational model of leaf development that generalizes the largely conserved molecular program for the reference plants Arabidopsis thaliana, Cardamine hirsuta and Solanum lycopersicum. The model characterizes leaf development as a product of three interwoven processes: the patterning of serrations, lobes and/or leaflets on the leaf margin; the patterning of the vascular system; and the growth of the leaf blade spanning the main veins. The veins play a significant morphogenetic role as a local determinant of growth directions. We show that small variations of this model can produce diverse leaf shapes, from simple to lobed to compound. It is thus plausible that diverse shapes of eudicot leaves result from small variations of a common developmental program.

Auxin-driven patterning with unidirectional fluxes.

The plant hormone auxin plays an essential role in the patterning of plant structures. Biological hypotheses supported by computational models suggest that auxin may fulfil this role by regulating its own transport, but the plausibility of previously proposed models has been questioned. We applied the notion of unidirectional fluxes and the formalism of Petri nets to show that the key modes of auxin-driven patterning-the formation of convergence points and the formation of canals-can be implemented by biochemically plausible networks, with the fluxes measured by dedicated tally molecules or by efflux and influx carriers themselves. Common elements of these networks include a positive feedback of auxin efflux on the allocation of membrane-bound auxin efflux carriers (PIN proteins), and a modulation of this allocation by auxin in the extracellular space. Auxin concentration in the extracellular space is the only information exchanged by the cells. Canalization patterns are produced when auxin efflux and influx act antagonistically: an increase in auxin influx or concentration in the extracellular space decreases the abundance of efflux carriers in the adjacent segment of the membrane. In contrast, convergence points emerge in networks in which auxin efflux and influx act synergistically. A change in a single reaction rate may result in a dynamic switch between these modes, suggesting plausible molecular implementations of coordinated patterning of organ initials and vascular strands predicted by the dual polarization theory.

A division in PIN-mediated auxin patterning during organ initiation in grasses.

The hormone auxin plays a crucial role in plant morphogenesis. In the shoot apical meristem, the PIN-FORMED1 (PIN1) efflux carrier concentrates auxin into local maxima in the epidermis, which position incipient leaf or floral primordia. From these maxima, PIN1 transports auxin into internal tissues along emergent paths that pattern leaf and stem vasculature. In Arabidopsis thaliana, these functions are attributed to a single PIN1 protein. Using phylogenetic and gene synteny analysis we identified an angiosperm PIN clade sister to PIN1, here termed Sister-of-PIN1 (SoPIN1), which is present in all sampled angiosperms except for Brassicaceae, including Arabidopsis. Additionally, we identified a conserved duplication of PIN1 in the grasses: PIN1a and PIN1b. In Brachypodium distachyon, SoPIN1 is highly expressed in the epidermis and is consistently polarized toward regions of high expression of the DR5 auxin-signaling reporter, which suggests that SoPIN1 functions in the localization of new primordia. In contrast, PIN1a and PIN1b are highly expressed in internal tissues, suggesting a role in vascular patterning. PIN1b is expressed in broad regions spanning the space between new primordia and previously formed vasculature, suggesting a role in connecting new organs to auxin sinks in the older tissues. Within these regions, PIN1a forms narrow canals that likely pattern future veins. Using a computer model, we reproduced the observed spatio-temporal expression and localization patterns of these proteins by assuming that SoPIN1 is polarized up the auxin gradient, and PIN1a and PIN1b are polarized to different degrees with the auxin flux. Our results suggest that examination and modeling of PIN dynamics in plants outside of Brassicaceae will offer insights into auxin-driven patterning obscured by the loss of the SoPIN1 clade in Brassicaceae.

Modelling biomechanics of bark patterning in grasstrees.

BACKGROUND AND AIMS: Bark patterns are a visually important characteristic of trees, typically attributed to fractures occurring during secondary growth of the trunk and branches. An understanding of bark pattern formation has been hampered by insufficient information regarding the biomechanical properties of bark and the corresponding difficulties in faithfully modelling bark fractures using continuum mechanics. This study focuses on the genus Xanthorrhoea (grasstrees), which have an unusual bark-like structure composed of distinct leaf bases connected by sticky resin. Due to its discrete character, this structure is well suited for computational studies. METHODS: A dynamic computational model of grasstree development was created. The model captures both the phyllotactic pattern of leaf bases during primary growth and the changes in the trunk's width during secondary growth. A biomechanical representation based on a system of masses connected by springs is used for the surface of the trunk, permitting the emergence of fractures during secondary growth to be simulated. The resulting fracture patterns were analysed statistically and compared with images of real trees. KEY RESULTS: The model reproduces key features of grasstree bark patterns, including their variability, spanning elongated and reticulate forms. The patterns produced by the model have the same statistical character as those seen in real trees. CONCLUSIONS: The model was able to support the general hypothesis that the patterns observed in the grasstree bark-like layer may be explained in terms of mechanical fractures driven by secondary growth. Although the generality of the results is limited by the unusual structure of grasstree bark, it supports the hypothesis that bark pattern formation is primarily a biomechanical phenomenon.

Model for the regulation of Arabidopsis thaliana leaf margin development.

Biological shapes are often produced by the iterative generation of repeated units. The mechanistic basis of such iteration is an area of intense investigation. Leaf development in the model plant Arabidopsis is one such example where the repeated generation of leaf margin protrusions, termed serrations, is a key feature of final shape. However, the regulatory logic underlying this process is unclear. Here, we use a combination of developmental genetics and computational modeling to show that serration development is the morphological read-out of a spatially distributed regulatory mechanism, which creates interspersed activity peaks of the growth-promoting hormone auxin and the cup-shaped cotyledon2 (CUC2) transcription factor. This mechanism operates at the growing leaf margin via a regulatory module consisting of two feedback loops working in concert. The first loop relates the transport of auxin to its own distribution, via polar membrane localization of the pinformed1 (PIN1) efflux transporter. This loop captures the potential of auxin to generate self-organizing patterns in diverse developmental contexts. In the second loop, CUC2 promotes the generation of PIN1-dependent auxin activity maxima while auxin represses CUC2 expression. This CUC2-dependent loop regulates activity of the conserved auxin efflux module in leaf margins to generate stable serration patterns. Conceptualizing leaf margin development via this mechanism also helps to explain how other developmental regulators influence leaf shape.

Cell-cycle-linked growth reprogramming encodes developmental time into leaf morphogenesis.

How is time encoded into organ growth and morphogenesis? We address this question by investigating heteroblasty, where leaf development and form are modified with progressing plant age. By combining morphometric analyses, fate-mapping through live-imaging, computational analyses, and genetics, we identify age-dependent changes in cell-cycle-associated growth and histogenesis that underpin leaf heteroblasty. We show that in juvenile leaves, cell proliferation competence is rapidly released in a "proliferation burst" coupled with fast growth, whereas in adult leaves, proliferative growth is sustained for longer and at a slower rate. These effects are mediated by the SPL9 transcription factor in response to inputs from both shoot age and individual leaf maturation along the proximodistal axis. SPL9 acts by activating CyclinD3 family genes, which are sufficient to bypass the requirement for SPL9 in the control of leaf shape and in heteroblastic reprogramming of cellular growth. In conclusion, we have identified a mechanism that bridges across cell, tissue, and whole-organism scales by linking cell-cycle-associated growth control to age-dependent changes in organ geometry.

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.

From genes to shape in leaf development and evolution.

Plant leaves display tremendous variation in shape. Here, we discuss how information obtained from genetics, live imaging and computational modeling has helped conceptualize the ways in which gene activity is translated into different leaf shapes. In this framework, the action of genes on leaf form can be captured as the sum of their effects on the amount, duration, and direction of cellular growth, which together produce leaf geometry. We use three different examples to illustrate this point. First, the emergence of complex versus simple leaves in eudicots, which arises from differences in organ-wide growth duration as well as local growth repression at the leaf margin. Second, the development of strap-shaped grass leaves with a broad sheathing base versus the typical eudicot leaves with a narrow petiole, where these features of grass leaves emerged through lateral expansion of the zone of leaf progenitor cells, coupled with later remodeling of growth of early domains of the leaf blade. Third, the formation of insect traps on carnivorous plants that arose through constrained directional growth that produced a 3D deformation. In all the above examples, changes in gene expression of different classes of homeobox genes have contributed to the altered growth patterns underlying these different aspects of leaf shape diversity.

The cellular basis for synergy between RCO and KNOX1 homeobox genes in leaf shape diversity.

Leaves of seed plants provide an attractive system to study the development and evolution of form. Leaves show varying degrees of margin complexity ranging from simple, as in Arabidopsis thaliana, to fully dissected into leaflets in the closely related species Cardamine hirsuta. Leaflet formation requires actions of Class I KNOTTED1-LIKE HOMEOBOX (KNOX1) and REDUCED COMPLEXITY (RCO) homeobox genes, which are expressed in the leaves of C. hirsuta but not A. thaliana. Evolutionary studies indicate that diversification of KNOX1 and RCO genes was repeatedly associated with increased leaf complexity. However, whether this gene combination represents a developmentally favored avenue for leaflet formation remains unknown, and the cell-level events through which the combined action of these genes drives leaflet formation are also poorly understood. Here we show, through a genetic screen, that when a C. hirsuta RCO transgene is expressed in A. thaliana, then ectopic KNOX1 expression in leaves represents a preferred developmental path for leaflet formation. Using time-lapse growth analysis, we demonstrate that KNOX1 expression in the basal domain of leaves leads to prolonged and anisotropic cell growth. This KNOX1 action, in synergy with local growth repression by RCO, is instrumental in generating rachises and petiolules, the linear geometrical elements, that bear leaflets in complex leaves. Our results show how the combination of cell-level growth analyses and genetics can help us understand how evolutionary modifications in expression of developmentally important genes are translated into diverse leaf shapes.

Cytokinin promotes growth cessation in the Arabidopsis root.

The Arabidopsis root offers good opportunities to investigate how regulated cellular growth shapes different tissues and organs, a key question in developmental biology. Along the root's longitudinal axis, cells sequentially occupy different developmental states. Proliferative meristematic cells give rise to differentiating cells, which rapidly elongate in the elongation zone, then mature and stop growing in the differentiation zone. The phytohormone cytokinin contributes to this zonation by positioning the boundary between the meristem and the elongation zone, called the transition zone. However, the cellular growth profile underlying root zonation is not well understood, and the cellular mechanisms that mediate growth cessation remain unclear. By using time-lapse imaging, genetics, and computational analysis, we analyze the effect of cytokinin on root zonation and cellular growth. We found that cytokinin promotes growth cessation in the distal (shootward) elongation zone in conjunction with accelerating the transition from elongation to differentiation. We estimated cell-wall stiffness by using osmotic treatment experiments and found that cytokinin-mediated growth cessation is associated with cell-wall stiffening and requires the action of an auxin influx carrier, AUX1. Our measurement of growth and cell-wall mechanical properties at a cellular resolution reveal mechanisms via which cytokinin influences cell behavior to shape tissue patterns.

Using positional information to provide context for biological image analysis with MorphoGraphX 2.0.

Positional information is a central concept in developmental biology. In developing organs, positional information can be idealized as a local coordinate system that arises from morphogen gradients controlled by organizers at key locations. This offers a plausible mechanism for the integration of the molecular networks operating in individual cells into the spatially coordinated multicellular responses necessary for the organization of emergent forms. Understanding how positional cues guide morphogenesis requires the quantification of gene expression and growth dynamics in the context of their underlying coordinate systems. Here, we present recent advances in the MorphoGraphX software (Barbier de Reuille et al., 2015⁠) that implement a generalized framework to annotate developing organs with local coordinate systems. These coordinate systems introduce an organ-centric spatial context to microscopy data, allowing gene expression and growth to be quantified and compared in the context of the positional information thought to control them.

Leaf Shape Diversity: From Genetic Modules to Computational Models.

Plant leaves display considerable variation in shape. Here, we introduce key aspects of leaf development, focusing on the morphogenetic basis of leaf shape diversity. We discuss the importance of the genetic control of the amount, duration, and direction of cellular growth for the emergence of leaf form. We highlight how the combined use of live imaging and computational frameworks can help conceptualize how regulated cellular growth is translated into different leaf shapes. In particular, we focus on the morphogenetic differences between simple and complex leaves and how carnivorous plants form three-dimensional insect traps. We discuss how evolution has shaped leaf diversity in the case of complex leaves, by tinkering with organ-wide growth and local growth repression, and in carnivorous plants, by modifying the relative growth of the lower and upper sides of the leaf primordium to create insect-digesting traps.

A WOX/Auxin Biosynthesis Module Controls Growth to Shape Leaf Form.

A key challenge in biology is to understand how the regional control of cell growth gives rise to final organ forms. Plant leaves must coordinate growth along both the proximodistal and mediolateral axes to produce their final shape. However, the cell-level mechanisms controlling this coordination remain largely unclear. Here, we show that, in A. thaliana, WOX5, one of the WUSCHEL-RELATED HOMEOBOX (WOX) family of homeobox genes, acts redundantly with WOX1 and WOX3 (PRESSED FLOWER [PRS]) to control leaf shape. Through genetics and hormone measurements, we find that these WOXs act in part through the regional control of YUCCA (YUC) auxin biosynthetic gene expression along the leaf margin. The requirement for WOX-mediated YUC expression in patterning of leaf shape cannot be bypassed by the epidermal expression of YUC, indicating that the precise domain of auxin biosynthesis is important for leaf form. Using time-lapse growth analysis, we demonstrate that WOX-mediated auxin biosynthesis organizes a proximodistal growth gradient that promotes lateral growth and consequently the characteristic ellipsoid A. thaliana leaf shape. We also provide evidence that WOX proteins shape the proximodistal gradient of differentiation by inhibiting differentiation proximally in the leaf blade and promoting it distally. This regulation allows sustained growth of the blade and enables a leaf to attain its final form. In conclusion, we show that the WOX/auxin regulatory module shapes leaf form by coordinating growth along the proximodistal and mediolateral leaf axes.

Mechanics, geometry and genetics of epidermal cell shape regulation: different pieces of the same puzzle.

Pavement cells in the leaf epidermis of many plant species have intricate shapes that fit together much like the pieces of a jigsaw puzzle. They provide an accessible system to understand the development of complex cell shape. Since a protrusion in one cell must fit into the indentation in its neighbor, puzzle cells are also a good system to study how cell shape is coordinated across a plant tissue. Although molecular mechanisms have been proposed for both the patterning and coordination of puzzle cells, evidence is accumulating that mechanical and/or geometric cues may play a more significant role than previously thought.