Physical models of plant development

A continuum mechanics model of the plant cell wall reveals interplay between enzyme action and cell wall structure

Plant cell growth is regulated through manipulation of the cell wall network, which consists of oriented cellulose microfibrils embedded within a ground matrix incorporating pectin and hemicellulose components. There remain many unknowns as to how this manipulation occurs. Experiments have shown that cellulose reorients in cell walls as the cell expands, while recent data suggest that growth is controlled by distinct collections of hemicellulose called biomechanical hotspots, which join the cellulose molecule together. The enzymes expansin and Cel12A have both been shown to induce growth of the cell wall; however, while Cel12A's wall-loosening action leads to a reduction in the cell wall strength, expansin's has been shown to increase the strength of the cell wall. In contrast, members of the XTH enzyme family hydrolyse hemicellulose but do not appear to cause wall creep. This experimentally observed behaviour still awaits a full explanation. We derive and analyse a mathematical model for the effective mechanical properties of the evolving cell wall network, incorporating cellulose microfibrils, which reorient with cell growth and are linked via biomechanical hotspots made up of regions of crosslinking hemicellulose. Assuming a visco-elastic response for the cell wall and using a continuum approach, we calculate the total stress resultant of the cell wall for a given overall growth rate. By changing appropriate parameters affecting breakage rate and viscous properties, we provide evidence for the biomechanical hotspot hypothesis and develop mechanistic understanding of the growth-inducing enzymes.

Anisotropic cell growth at the leaf base promotes age-related changes in leaf shape in Arabidopsis thaliana

Plants undergo extended morphogenesis. The shoot apical meristem (SAM) allows for reiterative development and the formation of new structures throughout the life of the plant. Intriguingly, the SAM produces morphologically different leaves in an age-dependent manner, a phenomenon known as heteroblasty. In Arabidopsis thaliana, the SAM produces small orbicular leaves in the juvenile phase, but gives rise to large elliptical leaves in the adult phase. Previous studies have established that a developmental decline of microRNA156 (miR156) is necessary and sufficient to trigger this leaf shape switch, although the underlying mechanism is poorly understood. Here we show that the gradual increase in miR156-targeted SQUAMOSA PROMOTER BINDING PROTEIN-LIKE transcription factors with age promotes cell growth anisotropy in the abaxial epidermis at the base of the leaf blade, evident by the formation of elongated giant cells. Time-lapse imaging and developmental genetics further revealed that the establishment of adult leaf shape is tightly associated with the longitudinal cell expansion of giant cells, accompanied by a prolonged cell proliferation phase in their vicinity. Our results thus provide a plausible cellular mechanism for heteroblasty in Arabidopsis, and contribute to our understanding of anisotropic growth in plants.

Revisiting the relationship between turgor pressure and plant cell growth

Growth is central to plant morphogenesis. Plant cells are encased in rigid cell walls, and they must overcome physical confinement to grow to specific sizes and shapes. Cell wall tension and turgor pressure are the main mechanical components impacting plant cell growth. Cell wall mechanics has been the focus of most plant biomechanical studies, and turgor pressure was often considered as a constant and largely passive component. Nevertheless, it is increasingly accepted that turgor pressure plays a significant role in plant growth. Numerous theoretical and experimental studies suggest that turgor pressure can be both spatially inhomogeneous and actively modulated during morphogenesis. Here, we revisit the pressure-growth relationship by reviewing recent advances in investigating the interactions between cellular/tissular pressure and growth.

Morphogenesis at the shoot meristem

Shoot apical meristems are populations of stem cells which initiate the aerial parts of higher plants. Work during the last decades has revealed a complex network of molecular regulators, which control both meristem maintenance and the production of different types of organs. The behavior of this network in time and space is defined by the local interactions between regulators and also involves hormonal regulation. In particular, auxin and cytokinin are intimately implicated in the coordination of gene expression patterns. To control growth patterns at the shoot meristem the individual components of the network influence directions and rates of cell growth. This requires interference with the mechanical properties of the cells. How this complex multiscale process, characterized by multiple feedbacks, is controlled remains largely an open question. Fortunately, genetics, live imaging, computational modelling and a number of other recently developed tools offer interesting albeit challenging perspectives.

A dive into the cell wall with Arabidopsis

One of the many legacies of the work of Michel Caboche is our understanding of plant cell wall synthesis and metabolism thanks to the use of Arabidopsis mutants. Here I describe how he was instrumental in initiating the genetic study of plant cell walls. I also show, with a few examples for cellulose and pectins, how this approach has led to important new insights in cell wall synthesis and how the metabolism of pectins contributes to plant growth and morphogenesis. I also illustrate the limitations of the use of mutants to explain processes at the scale of cells, organs or whole plants in terms of the physico-chemical properties of cell wall polymers. Finally, I sketch how new approaches can cope with these limitations.

Mathematical models of neuronal growth

The establishment of a functioning neuronal network is a crucial step in neural development. During this process, neurons extend neurites—axons and dendrites—to meet other neurons and interconnect. Therefore, these neurites need to migrate, grow, branch and find the correct path to their target by processing sensory cues from their environment. These processes rely on many coupled biophysical effects including elasticity, viscosity, growth, active forces, chemical signaling, adhesion and cellular transport. Mathematical models offer a direct way to test hypotheses and understand the underlying mechanisms responsible for neuron development. Here, we critically review the main models of neurite growth and morphogenesis from a mathematical viewpoint. We present different models for growth, guidance and morphogenesis, with a particular emphasis on mechanics and mechanisms, and on simple mathematical models that can be partially treated analytically.

Future Challenges in Plant Systems Biology

Plant systems biology is currently facing several important challenges, whose nature depend on the considered frame of reference and associated scale. This review covers some of the issues associated respectively with the molecular, tissue, and whole-plant scales, as well as discusses the potential for latest advances in synthetic biology and machine-learning methods to be of use in the future of plant systems biology.

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 crosstalk between auxin and brassinosteroid regulates leaf shape by modulating growth anisotropy

Leaf shape is highly variable within and among plant species, ranging from slender to oval shaped. This is largely determined by the proximodistal axis of growth. However, little is known about how proximal-distal growth is controlled to determine leaf shape. Here, we show that Arabidopsis leaf and sepal proximodistal growth is tuned by two phytohormones. Two class A AUXIN RESPONSE FACTORs (ARFs), ARF6 and ARF8, activate the transcription of DWARF4, which encodes a key brassinosteroid (BR) biosynthetic enzyme. At the cellular level, the phytohormones promote more directional cell expansion along the proximodistal axis, as well as final cell sizes. BRs promote the demethyl-esterification of cell wall pectins, leading to isotropic in-plane cell wall loosening. Notably, numerical simulation showed that isotropic cell wall loosening could lead to directional cell and organ growth along the proximodistal axis. Taken together, we show that auxin acts through biosynthesis of BRs to determine cell wall mechanics and directional cell growth to generate leaves of variable roundness.

Lockhart with a twist: Modelling cellulose microfibril deposition and reorientation reveals twisting plant cell growth mechanisms

Plant morphology emerges from cellular growth and structure. The turgor-driven diffuse growth of a cell can be highly anisotropic: significant longitudinally and negligible radially. Such anisotropy is ensured by cellulose microfibrils (CMF) reinforcing the cell wall in the hoop direction. To maintain the cell's integrity during growth, new wall material including CMF must be continually deposited. We develop a mathematical model representing the cell as a cylindrical pressure vessel and the cell wall as a fibre-reinforced viscous sheet, explicitly including the mechano-sensitive angle of CMF deposition. The model incorporates interactions between turgor, external forces, CMF reorientation during wall extension, and matrix stiffening. Using the model, we reinterpret some recent experimental findings, and reexamine the popular hypothesis of CMF/microtubule alignment. We explore how the handedness of twisting cell growth depends on external torque and intrinsic wall properties, and find that cells twist left-handedly 'by default' in some suitable sense. Overall, this study provides a unified mechanical framework for understanding left- and right-handed twist-growth as seen in many plants.

Plant multiscale networks: charting plant connectivity by multi-level analysis and imaging techniques

In multicellular and even single-celled organisms, individual components are interconnected at multiscale levels to produce enormously complex biological networks that help these systems maintain homeostasis for development and environmental adaptation. Systems biology studies initially adopted network analysis to explore how relationships between individual components give rise to complex biological processes. Network analysis has been applied to dissect the complex connectivity of mammalian brains across different scales in time and space in The Human Brain Project. In plant science, network analysis has similarly been applied to study the connectivity of plant components at the molecular, subcellular, cellular, organic, and organism levels. Analysis of these multiscale networks contributes to our understanding of how genotype determines phenotype. In this review, we summarized the theoretical framework of plant multiscale networks and introduced studies investigating plant networks by various experimental and computational modalities. We next discussed the currently available analytic methodologies and multi-level imaging techniques used to map multiscale networks in plants. Finally, we highlighted some of the technical challenges and key questions remaining to be addressed in this emerging field.

How Mechanical Forces Shape Plant Organs

Plants produce organs of various shapes and sizes. While much has been learned about genetic regulation of organogenesis, the integration of mechanics in the process is also gaining attention. Here, we consider the role of forces as instructive signals in organ morphogenesis. Turgor pressure is the primary cause of mechanical signals in developing organs. Because plant cells are glued to each other, mechanical signals act, in essence, at multiple scales, through cell wall contiguity and water flux. In turn, cells use such signals to resist mechanical stress, for instance, by reinforcing their cell walls. We show that the three elemental shapes behind plant organs - spheres, cylinders and lamina - can be actively maintained by such a mechanical feedback. Combinations of this 3-letter alphabet can generate more complex shapes. Furthermore, mechanical conflicts emerge at the boundary between domains exhibiting different growth rates or directions. These secondary mechanical signals contribute to three other organ shape features - folds, shape reproducibility and growth arrest. The further integration of mechanical signals with the molecular network offers many fruitful prospects for the scientific community, including the role of proprioception in organ shape robustness or the definition of cell and organ identities as a result of an interplay between biochemical and mechanical signals.

Expression Levels of Genes Encoding Proteins Involved in the Cell Wall-Plasma Membrane-Cytoskeleton Continuum Are Associated With the Maturation-Related Adventitious Rooting Competence of Pine Stem Cuttings

Stem cutting recalcitrance to adventitious root formation is a major limitation for the clonal propagation or micropropagation of elite genotypes of many forest tree species, especially at the adult stage of development. The interaction between the cell wall-plasma membrane and cytoskeleton may be involved in the maturation-related decline of adventitious root formation. Here, pine homologs of several genes encoding proteins involved in the cell wall-plasma membrane-cytoskeleton continuum were identified, and the expression levels of 70 selected genes belonging to the aforementioned group and four genes encoding auxin carrier proteins were analyzed during adventitious root formation in rooting-competent and non-competent cuttings of Pinus radiata. Variations in the expression levels of specific genes encoding cell wall components and cytoskeleton-related proteins were detected in rooting-competent and non-competent cuttings in response to wounding and auxin treatments. However, the major correlation of gene expression with competence for adventitious root formation was detected in a family of genes encoding proteins involved in sensing the cell wall and membrane disturbances, such as specific receptor-like kinases (RLKs) belonging to the lectin-type RLKs, wall-associated kinases, Catharanthus roseus RLK1-like kinases and leucine-rich repeat RLKs, as well as downstream regulators of the small guanosine triphosphate (GTP)-binding protein family. The expression of these genes was more affected by organ and age than by auxin and time of induction.

Epidermal restriction confers robustness to organ shapes

The shape of comparable tissues and organs is consistent among individuals of a given species, but how this consistency or robustness is achieved remains an open question. The interaction between morphogenetic factors determines organ formation and subsequent shaping, which is ultimately a mechanical process. Using a computational approach, we show that the epidermal layer is essential for the robustness of organ geometry control. Specifically, proper epidermal restriction allows organ asymmetry maintenance, and the tensile epidermal layer is sufficient to suppress local variability in growth, leading to shape robustness. The model explains the enhanced organ shape variations in epidermal mutant plants. In addition, differences in the patterns of epidermal restriction may underlie the initial establishment of organ asymmetry. Our results show that epidermal restriction can answer the longstanding question of how cellular growth noise is averaged to produce precise organ shapes, and the findings also shed light on organ asymmetry establishment.

Microtubule-Mediated Wall Anisotropy Contributes to Leaf Blade Flattening

Plant organs can adopt a wide range of shapes, resulting from highly directional cell growth and divisions. We focus here on leaves and leaf-like organs in Arabidopsis and tomato, characterized by the formation of thin, flat laminae. Combining experimental approaches with 3D mechanical modeling, we provide evidence that leaf shape depends on cortical microtubule mediated cellulose deposition along the main predicted stress orientations, in particular, along the adaxial-abaxial axis in internal cell walls. This behavior can be explained by a mechanical feedback and has the potential to sustain and even amplify a preexisting degree of flatness, which in turn depends on genes involved in the control of organ polarity and leaf margin formation.

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Microtubules and cellulose microfibrils align along the ad-abaxial direction

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Microtubule-mediated cell growth anisotropy contributes to leaf flattening

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Mechanical feedback accounts for microtubule alignments in the ad-abaxial direction

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Final organ shape depends on the degree of initial asymmetry of primordia

Mechanical feedback-loop regulation of morphogenesis in plants

Morphogenesis is a highly controlled biological process that is crucial for organisms to develop cells and organs of a particular shape. Plants have the remarkable ability to adapt to changing environmental conditions, despite being sessile organisms with their cells affixed to each other by their cell wall. It is therefore evident that morphogenesis in plants requires the existence of robust sensing machineries at different scales. In this Review, I provide an overview on how mechanical forces are generated, sensed and transduced in plant cells. I then focus on how such forces regulate growth and form of plant cells and tissues.

Cellular Heterogeneity in Pressure and Growth Emerges from Tissue Topology and Geometry

Cell-to-cell heterogeneity prevails in many systems, as exemplified by cell growth, although the origin and function of such heterogeneity are often unclear. In plants, growth is physically controlled by cell wall mechanics and cell hydrostatic pressure, alias turgor pressure. Whereas cell wall heterogeneity has received extensive attention, the spatial variation of turgor pressure is often overlooked. Here, combining atomic force microscopy and a physical model of pressurized cells, we show that turgor pressure is heterogeneous in the Arabidopsis shoot apical meristem, a population of stem cells that generates all plant aerial organs. In contrast with cell wall mechanical properties that appear to vary stochastically between neighboring cells, turgor pressure anticorrelates with cell size and cell neighbor number (local topology), in agreement with the prediction by our model of tissue expansion, which couples cell wall mechanics and tissue hydraulics. Additionally, our model predicts two types of correlations between pressure and cellular growth rate, where high pressure may lead to faster- or slower-than-average growth, depending on cell wall extensibility, yield threshold, osmotic pressure, and hydraulic conductivity. The meristem exhibits one of these two regimes, depending on conditions, suggesting that, in this tissue, water conductivity may contribute to growth control. Our results unravel cell pressure as a source of patterned heterogeneity and illustrate links between local topology, cell mechanical state, and cell growth, with potential roles in tissue homeostasis.

Discrete mechanical growth model for plant tissue

We present a discrete mechanical model to study plant development. The method is built up of mass points, springs and hinges mimicking the plant cell wall’s microstructure. To model plastic growth the resting lengths of springs are adjusted; when springs exceed a threshold length, new mass points, springs and hinges, are added. We formulate a stiffness tensor for the springs and hinges as a function of the fourth rank tensor of elasticity and the geometry of the mesh. This allows us to approximate the material law as a generalized orthotropic Hooke’s law, and control material properties during growth. The material properties of the model are illustrated in numerical simulations for finite strain and plastic growth. To solve the equations of motion of mass points we assume elastostatics and use Verlet integration. The method is demonstrated in simulations when anisotropic growth causes emergent residual strain fields in cell walls and a bending of tissue. The method can be used in multilevel models to study plant development, for example by coupling it to models for cytoskeletal, hormonal and gene regulatory processes.

Methods to quantify primary plant cell wall mechanics

The primary plant cell wall is a dynamically regulated composite material of multiple biopolymers that forms a scaffold enclosing the plant cells. The mechanochemical make-up of this polymer network regulates growth, morphogenesis, and stability at the cell and tissue scales. To understand the dynamics of cell wall mechanics, and how it correlates with cellular activities, several experimental frameworks have been deployed in recent years to quantify the mechanical properties of plant cells and tissues. Here we critically review the application of biomechanical tool sets pertinent to plant cell mechanics and outline some of their findings, relevance, and limitations. We also discuss methods that are less explored but hold great potential for the field, including multiscale in silico mechanical modeling that will enable a unified understanding of the mechanical behavior across the scales. Our overview reveals significant differences between the results of different mechanical testing techniques on plant material. Specifically, indentation techniques seem to consistently report lower values compared with tensile tests. Such differences may in part be due to inherent differences among the technical approaches and consequently the wall properties that they measure, and partly due to differences between experimental conditions.

Mathematical principles and models of plant growth mechanics: from cell wall dynamics to tissue morphogenesis

Plant growth research produces a catalogue of complex open questions. We argue that plant growth is a highly mechanical process, and that mathematics gives an underlying framework with which to probe its fundamental unrevealed mechanisms. This review serves to illustrate the biological insights afforded by mathematical modelling and demonstrate the breadth of mathematically rich problems available within plant sciences, thereby promoting a mutual appreciation across the disciplines. On the one hand, we explain the general mathematical principles behind mechanical growth models; on the other, we describe how modelling addresses specific problems in microscale cell wall mechanics, tip growth, morphogenesis, and stress feedback. We conclude by identifying possible future directions for both biologists and mathematicians, including as yet unanswered questions within various topics, stressing that interdisciplinary collaboration is vital for tackling the challenge of understanding plant growth mechanics.

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.

Cell-Based Model of the Generation and Maintenance of the Shape and Structure of the Multilayered Shoot Apical Meristem of Arabidopsis thaliana

One of the central problems in animal and plant developmental biology is deciphering how chemical and mechanical signals interact within a tissue to produce organs of defined size, shape, and function. Cell walls in plants impose a unique constraint on cell expansion since cells are under turgor pressure and do not move relative to one another. Cell wall extensibility and constantly changing distribution of stress on the wall are mechanical properties that vary between individual cells and contribute to rates of expansion and orientation of cell division. How exactly cell wall mechanical properties influence cell behavior is still largely unknown. To address this problem, a novel, subcellular element computational model of growth of stem cells within the multilayered shoot apical meristem (SAM) of Arabidopsis thaliana is developed and calibrated using experimental data. Novel features of the model include separate, detailed descriptions of cell wall extensibility and mechanical stiffness, deformation of the middle lamella, and increase in cytoplasmic pressure generating internal turgor pressure. The model is used to test novel hypothesized mechanisms of formation of the shape and structure of the growing, multilayered SAM based on WUS concentration of individual cells controlling cell growth rates and layer-dependent anisotropic mechanical properties of subcellular components of individual cells determining anisotropic cell expansion directions. Model simulations also provide a detailed prediction of distribution of stresses in the growing tissue which can be tested in future experiments.

Regulation of plant cell wall stiffness by mechanical stress: a mesoscale physical model

A crucial question in developmental biology is how cell growth is coordinated in living tissue to generate complex and reproducible shapes. We address this issue here in plants, where stiff extracellular walls prevent cell migration and morphogenesis mostly results from growth driven by turgor pressure. How cells grow in response to pressure partly depends on the mechanical properties of their walls, which are generally heterogeneous, anisotropic and dynamic. The active control of these properties is therefore a cornerstone of plant morphogenesis. Here, we focus on wall stiffness, which is under the control of both molecular and mechanical signaling. Indeed, in plant tissues, the balance between turgor and cell wall elasticity generates a tissue-wide stress field. Within cells, mechano-sensitive structures, such as cortical microtubules, adapt their behavior accordingly and locally influence cell wall remodeling dynamics. To fully apprehend the properties of this feedback loop, modeling approaches are indispensable. To that end, several modeling tools in the form of virtual tissues have been developed. However, these models often relate mechanical stress and cell wall stiffness in relatively abstract manners, where the molecular specificities of the various actors are not fully captured. In this paper, we propose to refine this approach by including parsimonious biochemical and biomechanical properties of the main molecular actors involved. Through a coarse-grained approach and through finite element simulations, we study the role of stress-sensing microtubules on organ-scale mechanics.

Similar bowtie structures and distinct largest strong components are identified in the transcriptional regulatory networks of Arabidopsis thaliana during photomorphogenesis and heat shock

Photomorphogenesis and heat shock are critical biological processes of plants. A recent research constructed the transcriptional regulatory networks (TRNs) of Arabidopsis thaliana during these processes using DNase-seq. In this study, by strong decomposition, we revealed that each of these TRNs can be represented as a similar bowtie structure with only one non-trivial and distinct strong component. We further identified distinct patterns of variation of a few light-related genes in these bowtie structures during photomorphogenesis. These results suggest that bowtie structure may be a common property of TRNs of plants, and distinct variation patterns of genes in bowtie structures of TRNs during biological processes may reflect distinct functions. Overall, our study provides an insight into the molecular mechanisms underlying photomorphogenesis and heat shock, and emphasizes the necessity to investigate the strong connectivity structures while studying TRNs.

Flower development: from morphodynamics to morphomechanics

The shoot apical meristem (SAM) is a small population of stem cells that continuously generates organs and tissues. We will discuss here flower formation at the SAM, which involves a complex network of regulatory genes and signalling molecules. A major downstream target of this network is the extracellular matrix or cell wall, which is a local determinant for both growth rates and growth directions. We will discuss here a number of recent studies aimed at analysing the link between cell wall structure and molecular regulation. This has involved multidisciplinary approaches including quantitative imaging, molecular genetics, computational biology and biophysics. A scenario emerges where molecular networks impact on both cell wall anisotropy and synthesis, thus causing the rapid outgrowth of organs at specific locations. More specifically, this involves two interdependent processes: the activation of wall remodelling enzymes and changes in microtubule dynamics.This article is part of the themed issue 'Systems morphodynamics: understanding the development of tissue hardware'.

Mechanical regulation of organ asymmetry in leaves

How appendages, such as plant leaves or animal limbs, develop asymmetric shapes remains a fundamental question in biology. Although ongoing research has revealed the genetic regulation of organ pattern formation, how gene activity ultimately directs organ shape remains unclear. Here, we show that leaf dorsoventral (adaxial-abaxial) polarity signals lead to mechanical heterogeneity of the cell wall, related to the methyl-esterification of cell-wall pectins in tomato and Arabidopsis. Numerical simulations predicate that mechanical heterogeneity is sufficient to produce the asymmetry seen in planar leaves. Experimental tests that alter pectin methyl-esterification, and therefore cell wall mechanical properties, support this model and lead to polar changes in gene expression, suggesting the existence of a feedback mechanism for mechanical signals in morphogenesis. Thus, mechanical heterogeneity within tissue may underlie organ shape asymmetry.

Advances on plant-pathogen interactions from molecular toward systems biology perspectives

In the past 2 decades, progress in molecular analyses of the plant immune system has revealed key elements of a complex response network. Current paradigms depict the interaction of pathogen-secreted molecules with host target molecules leading to the activation of multiple plant response pathways. Further research will be required to fully understand how these responses are integrated in space and time, and exploit this knowledge in agriculture. In this review, we highlight systems biology as a promising approach to reveal properties of molecular plant-pathogen interactions and predict the outcome of such interactions. We first illustrate a few key concepts in plant immunity with a network and systems biology perspective. Next, we present some basic principles of systems biology and show how they allow integrating multiomics data and predict cell phenotypes. We identify challenges for systems biology of plant-pathogen interactions, including the reconstruction of multiscale mechanistic models and the connection of host and pathogen models. Finally, we outline studies on resistance durability through the robustness of immune system networks, the identification of trade-offs between immunity and growth and in silico plant-pathogen co-evolution as exciting perspectives in the field. We conclude that the development of sophisticated models of plant diseases incorporating plant, pathogen and climate properties represent a major challenge for agriculture in the future.

Coordination of plant cell growth and division: collective control or mutual agreement?

Plant tissue growth requires the interdependent cellular processes of cytoplasmic growth, cell wall extension and cell division, but the feedbacks that link these processes are poorly understood. Recent papers have revealed developmentally regulated coupling between plant cell growth and progression through both mitotic cycles and endocycles. Modeling has given insight into the effects of cell geometry and tissue mechanics on the orientation of cell divisions. Developmental inputs by auxin have been highlighted in the control of cell turgor, vacuole function and the microtubule dynamics that underlies oriented growth and division. Overall, recent work emphasizes growth and proliferation as processes that are negotiated within and between cells, rather than imposed on cells across tissues.

Making microscopy count: quantitative light microscopy of dynamic processes in living plants

Cell theory has officially reached 350 years of age as the first use of the word 'cell' in a biological context can be traced to a description of plant material by Robert Hooke in his historic publication 'Micrographia: or some physiological definitions of minute bodies'. The 2015 Royal Microscopical Society Botanical Microscopy meeting was a celebration of the streams of investigation initiated by Hooke to understand at the subcellular scale how plant cell function and form arises. Much of the work presented, and Honorary Fellowships awarded, reflected the advanced application of bioimaging informatics to extract quantitative data from micrographs that reveal dynamic molecular processes driving cell growth and physiology. The field has progressed from collecting many pixels in multiple modes to associating these measurements with objects or features that are meaningful biologically. The additional complexity involves object identification that draws on a different type of expertise from computer science and statistics that is often impenetrable to biologists. There are many useful tools and approaches being developed, but we now need more interdisciplinary exchange to use them effectively. In this review we show how this quiet revolution has provided tools available to any personal computer user. We also discuss the oft-neglected issue of quantifying algorithm robustness and the exciting possibilities offered through the integration of physiological information generated by biosensors with object detection and tracking.

Force-Driven Polymerization and Turgor-Induced Wall Expansion

While many molecular players involved in growth control have been identified in the past decades, it is often unknown how they mechanistically act to induce specific shape changes during development. Plant morphogenesis results from the turgor-induced yielding of the extracellular and load-bearing cell wall. Its mechanochemical equilibrium appears as a fundamental link between molecular growth regulation and the effective shape evolution of the tissue. We focus here on force-driven polymerization of the cell wall as a central process in growth control. We propose that mechanical forces facilitate the insertion of wall components, in particular pectins, a process that can be modulated through genetic regulation. We formalize this idea in a mathematical model, which we subsequently test with published experimental results.

Emerging Trends in Molecular Interactions between Plants and the Broad Host Range Fungal Pathogens Botrytis cinerea and Sclerotinia sclerotiorum

Fungal plant pathogens are major threats to food security worldwide. Sclerotinia sclerotiorum and Botrytis cinerea are closely related Ascomycete plant pathogens causing mold diseases on hundreds of plant species. There is no genetic source of complete plant resistance to these broad host range pathogens known to date. Instead, natural plant populations show a continuum of resistance levels controlled by multiple genes, a phenotype designated as quantitative disease resistance. Little is known about the molecular mechanisms controlling the interaction between plants and S. sclerotiorum and B. cinerea but significant advances were made on this topic in the last years. This minireview highlights a selection of nine themes that emerged in recent research reports on the molecular bases of plant-S. sclerotiorum and plant-B. cinerea interactions. On the fungal side, this includes progress on understanding the role of oxalic acid, on the study of fungal small secreted proteins. Next, we discuss the exchanges of small RNA between organisms and the control of cell death in plant and fungi during pathogenic interactions. Finally on the plant side, we highlight defense priming by mechanical signals, the characterization of plant Receptor-like proteins and the hormone abscisic acid in the response to B. cinerea and S. sclerotiorum, the role of plant general transcription machinery and plant small bioactive peptides. These represent nine trends we selected as remarkable in our understanding of fungal molecules causing disease and plant mechanisms associated with disease resistance to two devastating broad host range fungi.

A Mechanical Model to Interpret Cell-Scale Indentation Experiments on Plant Tissues in Terms of Cell Wall Elasticity and Turgor Pressure

Morphogenesis in plants is directly linked to the mechanical elements of growing tissues, namely cell wall and inner cell pressure. Studies of these structural elements are now often performed using indentation methods such as atomic force microscopy. In these methods, a probe applies a force to the tissue surface at a subcellular scale and its displacement is monitored, yielding force-displacement curves that reflect tissue mechanics. However, the interpretation of these curves is challenging as they may depend not only on the cell probed, but also on neighboring cells, or even on the whole tissue. Here, we build a realistic three-dimensional model of the indentation of a flower bud using SOFA (Simulation Open Framework Architecture), in order to provide a framework for the analysis of force-displacement curves obtained experimentally. We find that the shape of indentation curves mostly depends on the ratio between cell pressure and wall modulus. Hysteresis in force-displacement curves can be accounted for by a viscoelastic behavior of the cell wall. We consider differences in elastic modulus between cell layers and we show that, according to the location of indentation and to the size of the probe, force-displacement curves are sensitive with different weights to the mechanical components of the two most external cell layers. Our results confirm most of the interpretations of previous experiments and provide a guide to future experimental work.

When biochemistry meets mechanics: a systems view of growth control in plants

The emergence of complex shapes during the development of plants is under the control of genetically determined molecular networks. Such regulatory networks, comprising hormones and transcription factors, regulate the collective behavior of cell growth within a tissue. Because all the cells within a tissue are linked together by the cell wall, their collective growth generates a good amount of mechanical stress. In the last few years a compelling amount of evidence has shown that growth-generated mechanical stress can feed back on plant developmental programs by modifying cell growth. This involves primarily responses from the microtubules and interaction with auxin transport and signaling. Here we discuss the most recent advances in the understanding of mechanical feedbacks in plant development.

Mechanically, the Shoot Apical Meristem of Arabidopsis Behaves like a Shell Inflated by a Pressure of About 1 MPa

In plants, the shoot apical meristem contains the stem cells and is responsible for the generation of all aerial organs. Mechanistically, organogenesis is associated with an auxin-dependent local softening of the epidermis. This has been proposed to be sufficient to trigger outgrowth, because the epidermis is thought to be under tension and stiffer than internal tissues in all the aerial part of the plant. However, this has not been directly demonstrated in the shoot apical meristem. Here we tested this hypothesis in Arabidopsis using indentation methods and modeling. We considered two possible scenarios: either the epidermis does not have unique properties and the meristem behaves as a homogeneous linearly-elastic tissue, or the epidermis is under tension and the meristem exhibits the response of a shell under pressure. Large indentation depths measurements with a large tip (~size of the meristem) were consistent with a shell-like behavior. This also allowed us to deduce a value of turgor pressure, estimated at 0.82±0.16 MPa. Indentation with atomic force microscopy provided local measurements of pressure in the epidermis, further confirming the range of values obtained from large deformations. Altogether, our data demonstrate that the Arabidopsis shoot apical meristem behaves like a shell under a MPa range pressure and support a key role for the epidermis in shaping the shoot apex.