The mechanics behind plant development

Curvature-driven spatial patterns in growing 3D domains: A mechanochemical model for phyllotaxis

Here we discuss the formation of phyllotactic patterns in the shoot apical meristem (SAM) of plants, where the spatial distribution of the phytohormone auxin determines phyllotaxis in a domain that is growing and changing in time. We assume that the concentration of auxin modifies the mechanical properties of the domain and that the mechanical stress field in the SAM orients the flux of auxin. To study this problem we propose a mechanism for pattern formation in growing domains with variable curvature. The dynamics of chemicals is modeled by a reaction-diffusion system that produces a three dimensional pattern of chemical concentrations that changes the stress field in the domain while growing. The growth process is modeled by a phase-field order parameter which determines the location of the boundaries of the domain. This field is coupled to the chemical concentration through a curvature term that affects the local mechanical stress in the domain. The local stress changes in turn modify the chemical patterns. Our model constitutes a useful and novel approach in theoretical biology, as many developmental processes in organisms seem to be affected by the changes of curvature, size, mechanical stress and other physical aspects. Several patterns seen in many plants are reproduced under certain conditions by our model.

The Physiological Mechanisms Behind the Earlywood-To-Latewood Transition: A Process-Based Modeling Approach

In extratropical ecosystems, the growth of trees is cyclic, producing tree rings composed of large-lumen and thin-walled cells (earlywood) alternating with narrow-lumen and thick-walled cells (latewood). So far, the physiology behind wood formation processes and the associated kinetics has rarely been considered to explain this pattern. We developed a process-based mechanistic model that simulates the development of conifer tracheids, explicitly considering the processes of cell enlargement and the deposition and lignification of cell walls. The model assumes that (1) wall deposition gradually slows down cell enlargement and (2) the deposition of cellulose and lignin is regulated by the availability of soluble sugars. The model reliably reproduces the anatomical traits and kinetics of the tracheids of four conifer species. At the beginning of the growing season, low sugar availability in the cambium results in slow wall deposition that allows for a longer enlargement time; thus, large cells with thin walls (i.e., earlywood) are produced. In late summer and early autumn, high sugar availability produces narrower cells having thick cell walls (i.e., latewood). This modeling framework provides a mechanistic link between plant ecophysiology and wood phenology and significantly contributes to understanding the role of sugar availability during xylogenesis.

Spatial regularity control of phyllotaxis pattern generated by the mutual interaction between auxin and PIN1

Phyllotaxis, the arrangement of leaves on a plant stem, is well known because of its beautiful geometric configuration, which is derived from the constant spacing between leaf primordia. This phyllotaxis is established by mutual interaction between a diffusible plant hormone auxin and its efflux carrier PIN1, which cooperatively generate a regular pattern of auxin maxima, small regions with high auxin concentrations, leading to leaf primordia. However, the molecular mechanism of the regular pattern of auxin maxima is still largely unknown. To better understand how the phyllotaxis pattern is controlled, we investigated mathematical models based on the auxin-PIN1 interaction through linear stability analysis and numerical simulations, focusing on the spatial regularity control of auxin maxima. As in previous reports, we first confirmed that this spatial regularity can be reproduced by a highly simplified and abstract model. However, this model lacks the extracellular region and is not appropriate for considering the molecular mechanism. Thus, we investigated how auxin maxima patterns are affected under more realistic conditions. We found that the spatial regularity is eliminated by introducing the extracellular region, even in the presence of direct diffusion between cells or between extracellular spaces, and this strongly suggests the existence of an unknown molecular mechanism. To unravel this mechanism, we assumed a diffusible molecule to verify various feedback interactions with auxin-PIN1 dynamics. We revealed that regular patterns can be restored by a diffusible molecule that mediates the signaling from auxin to PIN1 polarization. Furthermore, as in the one-dimensional case, similar results are observed in the two-dimensional space. These results provide a great insight into the theoretical and molecular basis for understanding the phyllotaxis pattern. Our theoretical analysis strongly predicts a diffusible molecule that is pivotal for the phyllotaxis pattern but is yet to be determined experimentally.

Shoot apical meristem and plant body organization: a cross-species comparative study

BACKGROUND AND AIMS

The shoot apical meristem (SAM) is the key organizing element in the plant body and is responsible for the core of plant body organization and shape. Surprisingly, there are almost no comparative data that would show links between parameters of the SAM and whole-plant traits as drivers of the plant's response to the environment.

METHODS

Interspecific differences in SAM anatomy were examined in 104 perennial herbaceous angiosperms.

KEY RESULTS

There were differences in SAM parameters among individual species, their phylogenetic patterns, and how their variation is linked to variation in plant above-ground organs and hence species' environmental niches. SAM parameters were correlated with the size-related traits of leaf area, seed mass and stem diameter. Of the two key SAM parameters (cell size and number), variation in all organ traits was linked more strongly to cell number, with cell size being important only for seed mass. Some of these correlations were due to shared phylogenetic history (e.g. SAM diameter versus stem diameter), whereas others were due to parallel evolution (e.g. SAM cell size and seed mass).

CONCLUSION

These findings show that SAM parameters provide a functional link among sizes and numbers of plant organs, constituting species' environmental responses.

Nanosensor Technology Applied to Living Plant Systems

An understanding of plant biology is essential to solving many long-standing global challenges, including sustainable and secure food production and the generation of renewable fuel sources. Nanosensor platforms, sensors with a characteristic dimension that is nanometer in scale, have emerged as important tools for monitoring plant signaling pathways and metabolism that are nondestructive, minimally invasive, and capable of real-time analysis. This review outlines the recent advances in nanotechnology that enable these platforms, including the measurement of chemical fluxes even at the single-molecule level. Applications of nanosensors to plant biology are discussed in the context of nutrient management, disease assessment, food production, detection of DNA proteins, and the regulation of plant hormones. Current trends and future needs are discussed with respect to the emerging trends of precision agriculture, urban farming, and plant nanobionics.

Nanoscale movements of cellulose microfibrils in primary cell walls

The growing plant cell wall is commonly considered to be a fibre-reinforced structure whose strength, extensibility and anisotropy depend on the orientation of crystalline cellulose microfibrils, their bonding to the polysaccharide matrix and matrix viscoelasticity1-4. Structural reinforcement of the wall by stiff cellulose microfibrils is central to contemporary models of plant growth, mechanics and meristem dynamics4-12. Although passive microfibril reorientation during wall extension has been inferred from theory and from bulk measurements13-15, nanometre-scale movements of individual microfibrils have not been directly observed. Here we combined nanometre-scale imaging of wet cell walls by atomic force microscopy (AFM) with a stretching device and endoglucanase treatment that induces wall stress relaxation and creep, mimicking wall behaviours during cell growth. Microfibril movements during forced mechanical extensions differ from those during creep of the enzymatically loosened wall. In addition to passive angular reorientation, we observed a diverse repertoire of microfibril movements that reveal the spatial scale of molecular connections between microfibrils. Our results show that wall loosening alters microfibril connectivity, enabling microfibril dynamics not seen during mechanical stretch. These insights into microfibril movements and connectivities need to be incorporated into refined models of plant cell wall structure, growth and morphogenesis.

Two tonoplast MATE proteins function as turgor-regulating chloride channels in Arabidopsis

The central vacuole in a plant cell occupies the majority of the cellular volume and plays a key role in turgor regulation. The vacuolar membrane (tonoplast) contains a large number of transporters that mediate fluxes of solutes and water, thereby adjusting cell turgor in response to developmental and environmental signals. We report that two tonoplast Detoxification efflux carrier (DTX)/Multidrug and Toxic Compound Extrusion (MATE) transporters, DTX33 and DTX35, function as chloride channels essential for turgor regulation in Arabidopsis Ectopic expression of each transporter in Nicotiana benthamiana mesophyll cells elicited a large voltage-dependent inward chloride current across the tonoplast, showing that DTX33 and DTX35 each constitute a functional channel. Both channels are highly expressed in Arabidopsis tissues, including root hairs and guard cells that experience rapid turgor changes during root-hair elongation and stomatal movements. Disruption of these two genes, either in single or double mutants, resulted in shorter root hairs and smaller stomatal aperture, with double mutants showing more severe defects, suggesting that these two channels function additively to facilitate anion influx into the vacuole during cell expansion. In addition, dtx35 single mutant showed lower fertility as a result of a defect in pollen-tube growth. Indeed, patch-clamp recording of isolated vacuoles indicated that the inward chloride channel activity across the tonoplast was impaired in the double mutant. Because MATE proteins are widely known transporters of organic compounds, finding MATE members as chloride channels expands the functional definition of this large family of transporters.

Highly sensitive optical interferometric technique reveals stress-dependent instantaneous nanometric growth fluctuations of Chinese chive leaf under heavy metal stress

Plant growth apart from being a complex and highly dynamic is dependent on its immediate environment. Leaf expansion measurements using Statistical Interferometry Technique, a sensitive interferometric technique at nanometric accuracy and at sub-second levels revealed the presence of characteristic nanometric intrinsic fluctuations [Plant Biotechnology 31, 195 (2014)]. In this paper, we demonstrate that the nanometric intrinsic fluctuations are sensitive enough that they change under exposure of heavy metals, essential micronutrient zinc and non-essential element cadmium, at relatively low concentrations in the leaves of Chinese chive (Allium tuberosum). The nanometric intrinsic fluctuations of leaves were observed for 4h under three cadmium concentrations or two zinc concentrations. Results showed significant reduction of nanometric intrinsic fluctuations for all cadmium concentrations, and in contrast significant increase of nanometric intrinsic fluctuations for all zinc concentrations. There was significant reduction of nanometric intrinsic fluctuations for cadmium exposure of concentrations of 0.001mM for even an hour, and significant increment of nanometric intrinsic fluctuations under 0.75mM zinc from 1hr exposure. For comparison, antioxidative enzymes and metal uptake were also measured under 4hr exposure of cadmium or zinc. However, no significant changes could be seen in antioxidative enzymes within 4h under the smaller concentration of 0.001mM cadmium as seen for nanometric intrinsic fluctuations. The results imply that nanometric intrinsic fluctuations can be not only used as a measure for heavy metal stress but also it can be more sensitive to detect the toxic as well as positive effects of smaller amounts of heavy metal on plants at an early stage.

Activation tagging of Arabidopsis POLYGALACTURONASE INVOLVED IN EXPANSION2 promotes hypocotyl elongation, leaf expansion, stem lignification, mechanical stiffening, and lodging

Pectin is the most abundant component of primary cell walls in eudicot plants. The modification and degradation of pectin affects multiple processes during plant development, including cell expansion, organ initiation, and cell separation. However, the extent to which pectin degradation by polygalacturonases affects stem development and secondary wall formation remains unclear. Using an activation tag screen, we identified a transgenic Arabidopsis thaliana line with longer etiolated hypocotyls, which overexpresses a gene encoding a polygalacturonase. We designated this gene as POLYGALACTURONASE INVOLVED IN EXPANSION2 (PGX2), and the corresponding activation tagged line as PGX2^AT . PGX2 is widely expressed in young seedlings and in roots, stems, leaves, flowers, and siliques of adult plants. PGX2-GFP localizes to the cell wall, and PGX2^AT plants show higher total polygalacturonase activity and smaller pectin molecular masses than wild-type controls, supporting a function for this protein in apoplastic pectin degradation. A heterologously expressed, truncated version of PGX2 also displays polygalacturonase activity in vitro. Like previously identified PGX1^AT plants, PGX2^AT plants have longer hypocotyls and larger rosette leaves, but they also uniquely display early flowering, earlier stem lignification, and lodging stems with enhanced mechanical stiffness that is possibly due to decreased stem thickness. Together, these results indicate that PGX2 both functions in cell expansion and influences secondary wall formation, providing a possible link between these two developmental processes.

Exogenous Cellulase Switches Cell Interdigitation to Cell Elongation in an RIC1-dependent Manner in Arabidopsis thaliana Cotyledon Pavement Cells

Pavement cells in cotyledons and true leaves exhibit a jigsaw puzzle-like morphology in most dicotyledonous plants. Among the molecular mechanisms mediating cell morphogenesis, two antagonistic Rho-like GTPases regulate local cell outgrowth via cytoskeletal rearrangements. Analyses of several cell wall-related mutants suggest the importance of cell wall mechanics in the formation of interdigitated patterns. However, how these factors are integrated is unknown. In this study, we observed that the application of exogenous cellulase to hydroponically grown Arabidopsis thaliana cotyledons switched the interdigitation of pavement cells to the production of smoothly elongated cells. The cellulase-induced inhibition of cell interdigitation was not observed in a RIC1 knockout mutant. This gene encodes a Rho-like GTPase-interacting protein important for localized cell growth suppression via microtubule bundling on concave cell interfaces. Additionally, to characterize pavement cell morphologies, we developed a mathematical model that considers the balance between cell and cell wall growth, restricted global cell growth orientation, and regulation of local cell outgrowth mediated by a Rho-like GTPase-cytoskeleton system. Our computational simulations fully support our experimental observations, and suggest that interdigitated patterns form because of mechanical buckling in the absence of Rho-like GTPase-dependent regulation of local cell outgrowth. Our model clarifies the cell wall mechanics influencing pavement cell morphogenesis.

Mechanical Behavior of Cells within a Cell-Based Model of Wheat Leaf Growth

Understanding the principles and mechanisms of cell growth coordination in plant tissue remains an outstanding challenge for modern developmental biology. Cell-based modeling is a widely used technique for studying the geometric and topological features of plant tissue morphology during growth. We developed a quasi-one-dimensional model of unidirectional growth of a tissue layer in a linear leaf blade that takes cell autonomous growth mode into account. The model allows for fitting of the visible cell length using the experimental cell length distribution along the longitudinal axis of a wheat leaf epidermis. Additionally, it describes changes in turgor and osmotic pressures for each cell in the growing tissue. Our numerical experiments show that the pressures in the cell change over the cell cycle, and in symplastically growing tissue, they vary from cell to cell and strongly depend on the leaf growing zone to which the cells belong. Therefore, we believe that the mechanical signals generated by pressures are important to consider in simulations of tissue growth as possible targets for molecular genetic regulators of individual cell growth.

Mapping the subcellular mechanical properties of live cells in tissues with fluorescence emission-Brillouin imaging

Extracellular matrices (ECMs) are central to the advent of multicellular life, and their mechanical properties are modulated by and impinge on intracellular signaling pathways that regulate vital cellular functions. High spatial-resolution mapping of mechanical properties in live cells is, however, extremely challenging. Thus, our understanding of how signaling pathways process physiological signals to generate appropriate mechanical responses is limited. We introduce fluorescence emission-Brillouin scattering imaging (FBi), a method for the parallel and all-optical measurements of mechanical properties and fluorescence at the submicrometer scale in living organisms. Using FBi, we showed that changes in cellular hydrostatic pressure and cytoplasm viscoelasticity modulate the mechanical signatures of plant ECMs. We further established that the measured "stiffness" of plant ECMs is symmetrically patterned in hypocotyl cells undergoing directional growth. Finally, application of this method to Arabidopsis thaliana with photoreceptor mutants revealed that red and far-red light signals are essential modulators of ECM viscoelasticity. By mapping the viscoelastic signatures of a complex ECM, we provide proof of principle for the organism-wide applicability of FBi for measuring the mechanical outputs of intracellular signaling pathways. As such, our work has implications for investigations of mechanosignaling pathways and developmental biology.

Plant Organ Growth: Stopping Under Stress

Plant organs reproducibly reach a set size and shape, and a key question is what prevents overgrowth. A new study uses imaging and computer modelling of the Arabidopsis sepal to show that mechanics determines growth arrest and thus final organ shape.

RhVI1 is a membrane-anchored vacuolar invertase highly expressed in Rosa hybrida L. petals

Invertases are a widespread group of enzymes that catalyse the conversion of sucrose into fructose and glucose. Plants invertases and their substrates are essential factors that play an active role in primary metabolism and in cellular differentiation and by these activities they sustain development and growth. Being naturally present in multiple isoforms, invertases are known to be highly differentiated and tissue specific in such a way that every isoform is characteristic of a specific part of the plant. In this work, we report the identification of the invertase RhVI1 that was found to be highly expressed in rose petals. A characterization of this protein revealed that RhVI1 is a glycosylated membrane-anchored protein associated with the cytosolic side of the vacuolar membrane which occurs in vivo in a monomeric form. Purification yields have shown that the levels of expression decreased during the passage of petals from buds to mature and pre-senescent flowers. Moreover, the activity assay indicates RhVI1 to be an acidic vacuolar invertase. The physiological implications of these findings are discussed, suggesting a possible role of this protein during anthesis.

Mechanical Stress Induces Remodeling of Vascular Networks in Growing Leaves

Differentiation into well-defined patterns and tissue growth are recognized as key processes in organismal development. However, it is unclear whether patterns are passively, homogeneously dilated by growth or whether they remodel during tissue expansion. Leaf vascular networks are well-fitted to investigate this issue, since leaves are approximately two-dimensional and grow manyfold in size. Here we study experimentally and computationally how vein patterns affect growth. We first model the growing vasculature as a network of viscoelastic rods and consider its response to external mechanical stress. We use the so-called texture tensor to quantify the local network geometry and reveal that growth is heterogeneous, resembling non-affine deformations in composite materials. We then apply mechanical forces to growing leaves after veins have differentiated, which respond by anisotropic growth and reorientation of the network in the direction of external stress. External mechanical stress appears to make growth more homogeneous, in contrast with the model with viscoelastic rods. However, we reconcile the model with experimental data by incorporating randomness in rod thickness and a threshold in the rod growth law, making the rods viscoelastoplastic. Altogether, we show that the higher stiffness of veins leads to their reorientation along external forces, along with a reduction in growth heterogeneity. This process may lead to the reinforcement of leaves against mechanical stress. More generally, our work contributes to a framework whereby growth and patterns are coordinated through the differences in mechanical properties between cell types.

PtrWRKY19, a novel WRKY transcription factor, contributes to the regulation of pith secondary wall formation in Populus trichocarpa

WRKY proteins are one of the largest transcription factor families in higher plants and play diverse roles in various biological processes. Previous studies have shown that some WRKY members act as negative regulators of secondary cell wall formation in pith parenchyma cells. However, the regulatory mechanism of pith secondary wall formation in tree species remains largely unknown. In this study, PtrWRKY19 encoding a homolog of Arabidopsis WRKY12 was isolated from Populus trichocarpa. PtrWRKY19 was expressed in all tissues tested, with highest expression in stems, especially in pith. PtrWRKY19 was located in the nucleus and functioned as a transcriptional repressor. Ectopic expression of PtrWRKY19 in an atwrky12 mutant successfully rescued the phenotype in pith cell walls caused by the defect of AtWRKY12, suggesting that PtrWRKY19 had conserved functions for homologous AtWRKY12. Overexpression of PtrWRKY19 in poplar plants led to a significant increase in the number of pith parenchyma cells. qRT-PCR analysis showed that lignin biosynthesis-related genes were repressed in transgenic plants. In transcient reporter assays, PtrWRKY19 was identified to repress transcription from the PtoC4H2 promoter containing the conserved W-box elements. These results indicated that PtrWRKY19 may function as a negative regulator of pith secondary wall formation in poplar.

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.

Plant cell wall extensibility: connecting plant cell growth with cell wall structure, mechanics, and the action of wall-modifying enzymes

The advent of user-friendly instruments for measuring force/deflection curves of plant surfaces at high spatial resolution has resulted in a recent outpouring of reports of the 'Young's modulus' of plant cell walls. The stimulus for these mechanical measurements comes from biomechanical models of morphogenesis of meristems and other tissues, as well as single cells, in which cell wall stress feeds back to regulate microtubule organization, auxin transport, cellulose deposition, and future growth directionality. In this article I review the differences between elastic modulus and wall extensibility in the context of cell growth. Some of the inherent complexities, assumptions, and potential pitfalls in the interpretation of indentation force/deflection curves are discussed. Reported values of elastic moduli from surface indentation measurements appear to be 10- to >1000-fold smaller than realistic tensile elastic moduli in the plane of plant cell walls. Potential reasons for this disparity are discussed, but further work is needed to make sense of the huge range in reported values. The significance of wall stress relaxation for growth is reviewed and connected to recent advances and remaining enigmas in our concepts of how cellulose, hemicellulose, and pectins are assembled to make an extensible cell wall. A comparison of the loosening action of α-expansin and Cel12A endoglucanase is used to illustrate two different ways in which cell walls may be made more extensible and the divergent effects on wall mechanics.

Mechanism of dynamic reorientation of cortical microtubules due to mechanical stress

Directional growth caused by gravitropism and corresponding bending of plant cells has been explored since 19th century, however, many aspects of mechanisms underlying the perception of gravity at the molecular level are still not well known. Perception of gravity in root and shoot gravitropisms is usually attributed to gravisensitive cells, called statocytes, which exploit sedimentation of macroscopic and heavy organelles, amyloplasts, to sense the direction of gravity. Gravity stimulus is then transduced into distal elongation zone, which is several mm far from statocytes, where it causes stretching. It is suggested that gravity stimulus is conveyed by gradients in auxin flux. We propose a theoretical model that may explain how concentration gradients and/or stretching may indirectly affect the global orientation of cortical microtubules, attached to the cell membrane and induce their dynamic reorientation perpendicular to the gradients. In turn, oriented microtubule arrays direct the growth and orientation of cellulose microfibrils, forming part of the cell external skeleton and determine the shape of the cell. Reorientation of microtubules is also observed in reaction to light in phototropism and mechanical bending, thus suggesting universality of the proposed mechanism.

NAC-MYB-based transcriptional regulation of secondary cell wall biosynthesis in land plants

Plant cells biosynthesize primary cell walls (PCW) in all cells and produce secondary cell walls (SCWs) in specific cell types that conduct water and/or provide mechanical support, such as xylem vessels and fibers. The characteristic mechanical stiffness, chemical recalcitrance, and hydrophobic nature of SCWs result from the organization of SCW-specific biopolymers, i.e., highly ordered cellulose, hemicellulose, and lignin. Synthesis of these SCW-specific biopolymers requires SCW-specific enzymes that are regulated by SCW-specific transcription factors. In this review, we summarize our current knowledge of the transcriptional regulation of SCW formation in plant cells. Advances in research on SCW biosynthesis during the past decade have expanded our understanding of the transcriptional regulation of SCW formation, particularly the functions of the NAC and MYB transcription factors. Focusing on the NAC-MYB-based transcriptional network, we discuss the regulatory systems that evolved in land plants to modify the cell wall to serve as a key component of structures that conduct water and provide mechanical support.

Real-time automated characterization of 3D morphology and mechanics of developing plant cells

In this article, we introduce the real-time cellular force microscope (RT-CFM), a high-throughput microrobotic platform for mechanical stimulation and characterization of single cells. We developed computer vision algorithms that fully automate the positioning of target cells and localization of the sensor tip. The control and acquisition architecture dramatically increases the accuracy, speed, and reliability of force measurements. Pollen tubes provide an ideal model system for the study of plant mechanics at the single-cell level. To quantitatively obtain the physical properties of the plant cell wall, we generated topography and stiffness measurements from 3D scans of living, growing pollen tubes. We report techniques for real-time monitoring and analysis of intracellular calcium fluxes during mechanical intervention. Our platform is compatible with various imaging systems and enables a powerful screening technology to facilitate biomechanical and morphological characterization of developing cells.

A computational framework for 3D mechanical modeling of plant morphogenesis with cellular resolution

The link between genetic regulation and the definition of form and size during morphogenesis remains largely an open question in both plant and animal biology. This is partially due to the complexity of the process, involving extensive molecular networks, multiple feedbacks between different scales of organization and physical forces operating at multiple levels. Here we present a conceptual and modeling framework aimed at generating an integrated understanding of morphogenesis in plants. This framework is based on the biophysical properties of plant cells, which are under high internal turgor pressure, and are prevented from bursting because of the presence of a rigid cell wall. To control cell growth, the underlying molecular networks must interfere locally with the elastic and/or plastic extensibility of this cell wall. We present a model in the form of a three dimensional (3D) virtual tissue, where growth depends on the local modulation of wall mechanical properties and turgor pressure. The model shows how forces generated by turgor-pressure can act both cell autonomously and non-cell autonomously to drive growth in different directions. We use simulations to explore lateral organ formation at the shoot apical meristem. Although different scenarios lead to similar shape changes, they are not equivalent and lead to different, testable predictions regarding the mechanical and geometrical properties of the growing lateral organs. Using flower development as an example, we further show how a limited number of gene activities can explain the complex shape changes that accompany organ outgrowth.

Thermodynamical journey in plant biology

Nonequilibrium irreversible thermodynamics constitute a meaningful point of view suitable to explore life with a rich paradigm. This analytical framework can be used to span the gap from molecular processes to plant function and shows great promise to create a holistic description of life. Since living organisms dissipate energy, exchange entropy and matter with their environment, they can be assimilated to dissipative structures. This concept inherited from nonequilibrium thermodynamics has four properties which defines a scale independent framework suitable to provide a simpler and more comprehensive view of the highly complex plant biology. According to this approach, a biological function is modeled as a cascade of dissipative structures. Each dissipative structure, corresponds to a biological process, which is initiated by the amplification of a fluctuation. Evolution of the process leads to the breakage of the system symmetry and to the export of entropy. Exporting entropy to the surrounding environment corresponds to collecting information about it. Biological actors which break the symmetry of the system and which store information are by consequence, key actors on which experiments and data analysis focus most. This paper aims at illustrating properties of dissipative structure through familiar examples and thus initiating the dialogue between nonequilibrium thermodynamics and plant biology.

Transient silencing of CHALCONE SYNTHASE during fruit ripening modifies tomato epidermal cells and cuticle properties

Tomato (Solanum lycopersicum) fruit ripening is accompanied by an increase in CHALCONE SYNTHASE (CHS) activity and flavonoid biosynthesis. Flavonoids accumulate in the cuticle, giving its characteristic orange color that contributes to the eventual red color of the ripe fruit. Using virus-induced gene silencing in fruits, we have down-regulated the expression of SlCHS during ripening and compared the cuticles derived from silenced and nonsilenced regions. Silenced regions showed a pink color due to the lack of flavonoids incorporated to the cuticle. This change in color was accompanied by several other changes in the cuticle and epidermis. The epidermal cells displayed a decreased tangential cell width; a decrease in the amount of cuticle and its main components, cutin and polysaccharides, was also observed. Flavonoids dramatically altered the cuticle biomechanical properties by stiffening the elastic and viscoelastic phase and by reducing the ability of the cuticle to deform. There seemed to be a negative relation between SlCHS expression and wax accumulation during ripening that could be related to the decreased cuticle permeability to water observed in the regions silencing SlCHS. A reduction in the overall number of ester linkages present in the cutin matrix was also dependent on the presence of flavonoids.

Flowers under pressure: ins and outs of turgor regulation in development

BACKGROUND

Turgor pressure is an essential feature of plants; however, whereas its physiological importance is unequivocally recognized, its relevance to development is often reduced to a role in cell elongation.

SCOPE

This review surveys the roles of turgor in development, the molecular mechanisms of turgor regulation and the methods used to measure turgor and related quantities, while also covering the basic concepts associated with water potential and water flow in plants. Three key processes in flower development are then considered more specifically: flower opening, anther dehiscence and pollen tube growth.

CONCLUSIONS

Many molecular determinants of turgor and its regulation have been characterized, while a number of methods are now available to quantify water potential, turgor and hydraulic conductivity. Data on flower opening, anther dehiscence and lateral root emergence suggest that turgor needs to be finely tuned during development, both spatially and temporally. It is anticipated that a combination of biological experiments and physical measurements will reinforce the existing data and reveal unexpected roles of turgor in development.

Putting theory to the test: which regulatory mechanisms can drive realistic growth of a root?

In recent years there has been a strong development of computational approaches to mechanistically understand organ growth regulation in plants. In this study, simulation methods were used to explore which regulatory mechanisms can lead to realistic output at the cell and whole organ scale and which other possibilities must be discarded as they result in cellular patterns and kinematic characteristics that are not consistent with experimental observations for the Arabidopsis thaliana primary root. To aid in this analysis, a ‘Uniform Longitudinal Strain Rule’ (ULSR) was formulated as a necessary condition for stable, unidirectional, symplastic growth. Our simulations indicate that symplastic structures are robust to differences in longitudinal strain rates along the growth axis only if these differences are small and short-lived. Whereas simple cell-autonomous regulatory rules based on counters and timers can produce stable growth, it was found that steady developmental zones and smooth transitions in cell lengths are not feasible. By introducing spatial cues into growth regulation, those inadequacies could be avoided and experimental data could be faithfully reproduced. Nevertheless, a root growth model based on previous polar auxin-transport mechanisms violates the proposed ULSR due to the presence of lateral gradients. Models with layer-specific regulation or layer-driven growth offer potential solutions. Alternatively, a model representing the known cross-talk between auxin, as the cell proliferation promoting factor, and cytokinin, as the cell differentiation promoting factor, predicts the effect of hormone-perturbations on meristem size. By down-regulating PIN-mediated transport through the transcription factor SHY2, cytokinin effectively flattens the lateral auxin gradient, at the basal boundary of the division zone, (thereby imposing the ULSR) to signal the exit of proliferation and start of elongation. This model exploration underlines the value of generating virtual root growth kinematics to dissect and understand the mechanisms controlling this biological system.

The growth of a plant root is driven by cell division and cell expansion occurring in spatially distinct developmental zones. Although these zones are in principle stable, depending on the conditions, their size and properties can be modulated. This has been meticulously described by kinematic studies, which have led to the proposal of mechanisms underpinning those observations. At the same time, much knowledge of the identities and interactions of molecules involved in these mechanisms has accumulated, in particular from the model species Arabidopsis thaliana. Here we attempt to resolve the longstanding question whether observed growth patterns can be explained by autonomous decision-making at the level of individual cells or if the aid of some external signal is required. We then ask, building on the accumulated molecular information, which minimal models can provide for stable growth while keeping sufficient flexibility to regulate growth. Therefore, we constructed computational models for different growth mechanisms operating in a virtual two-dimensional Arabidopsis root and compared their behaviour with biological experiments. The simulations provide strong indications that spatial signals are required for realistic and flexible root growth, likely orchestrated by the plant hormones auxin and cytokinin.

Physical models of plant development

The definition of shape in multicellular organisms is a major issue of developmental biology. It is well established that morphogenesis relies on genetic regulation. However, cells, tissues, and organism behaviors are also bound by the laws of physics, which limit the range of possible deformations organisms can undergo but also define what organisms must do to achieve specific shapes. Besides experiments, theoretical models and numerical simulations of growing tissues are powerful tools to investigate the link between genetic regulation and mechanics. Here, we provide an overview of the main mechanical models of plant morphogenesis developed so far, from subcellular scales to whole tissues. The common concepts and discrepancies between the various models are discussed.

Shade avoidance: phytochrome signalling and other aboveground neighbour detection cues

Plants compete with neighbouring vegetation for limited resources. In competition for light, plants adjust their architecture to bring the leaves higher in the vegetation where more light is available than in the lower strata. These architectural responses include accelerated elongation of the hypocotyl, internodes and petioles, upward leaf movement (hyponasty), and reduced shoot branching and are collectively referred to as the shade avoidance syndrome. This review discusses various cues that plants use to detect the presence and proximity of neighbouring competitors and respond to with the shade avoidance syndrome. These cues include light quality and quantity signals, mechanical stimulation, and plant-emitted volatile chemicals. We will outline current knowledge about each of these signals individually and discuss their possible interactions. In conclusion, we will make a case for a whole-plant, ecophysiology approach to identify the relative importance of the various neighbour detection cues and their possible interactions in determining plant performance during competition.

Brown algal morphogenesis: atomic force microscopy as a tool to study the role of mechanical forces

Over the last few years, a growing interest has been directed toward the use of macroalgae as a source of energy, food and molecules for the cosmetic and pharmaceutical industries. Besides this, macroalgal development remains poorly understood compared to other multicellular organisms. Brown algae (Phaeophyceae) form a monophyletic lineage of usually large multicellular algae which evolved independently from land plants. In their environment, they are subjected to strong mechanical forces (current, waves, and tide), in response to which they modify rapidly and reversibly their morphology. Because of their specific cellular features (cell wall composition, cytoskeleton organization), deciphering how they cope with these forces might help discover new control mechanisms of cell wall softening and cellulose synthesis. Despite the current scarcity in knowledge on brown algal cell wall dynamics and protein composition, we will illustrate, in the light of methods adapted to Ectocarpus siliculosus, to what extent atomic force microscopy can contribute to advance this field of investigation.

Mechanical control of morphogenesis at the shoot apex

Morphogenesis does not just require the correct expression of patterning genes; these genes must induce the precise mechanical changes necessary to produce a new form. Mechanical characterization of plant growth is not new; however, in recent years, new technologies and interdisciplinary collaborations have made it feasible in young tissues such as the shoot apex. Analysis of tissues where active growth and developmental patterning are taking place has revealed biologically significant variability in mechanical properties and has even suggested that mechanical changes in the tissue can feed back to direct morphogenesis. Here, an overview is given of the current understanding of the mechanical dynamics and its influence on cellular and developmental processes in the shoot apex. We are only starting to uncover the mechanical basis of morphogenesis, and many exciting questions remain to be answered.

Slow, fast and furious: understanding the physics of plant movements

The ability of plants to move is central to many physiological processes from development to tropisms, from nutrition to reproduction. The movement of plants or plant parts occurs over a wide range of sizes and time scales. This review summarizes the main physical mechanisms plants use to achieve motility, highlighting recent work at the frontier of biology and physics on rapid movements. Emphasis is given to presenting in a single framework pioneering biological studies of water transport and growth with more recent physics research on poroelasticity and mechanical instabilities. First, the basic osmotic and hydration/dehydration motors are described that contribute to movement by growth and reversible swelling/shrinking of cells and tissues. The speeds of these water-driven movements are shown to be ultimately limited by the transport of water through the plant body. Some plant structures overcome this hydraulic limit to achieve much faster movement by using a mechanical instability. The principle is to impose an 'energy barrier' to the system, which can originate from geometrical constraint or matter cohesion, allowing elastic potential energy to be stored until the barrier is overcome, then rapidly transformed into kinetic energy. Three of these rapid motion mechanisms have been elucidated recently and are described here: the snapping traps of two carnivorous plants, the Venus flytrap and Utricularia, and the catapult of fern sporangia. Finally, movement mechanisms are reconsidered in the context of the timescale of important physiological processes at the cellular and molecular level.

QUIRKY interacts with STRUBBELIG and PAL OF QUIRKY to regulate cell growth anisotropy during Arabidopsis gynoecium development

Organ morphogenesis largely relies on cell division and elongation, which need to be both coordinated between cells and orchestrated with cytoskeleton dynamics. However, components that bridge the biological signals and the effectors that define cell shape remain poorly described. We have addressed this issue through the functional characterisation of QUIRKY (QKY), previously isolated as being involved in the STRUBBELIG (SUB) genetic pathway that controls cell-cell communication and organ morphogenesis in Arabidopsis. QKY encodes a protein containing multiple C2 domains and transmembrane regions, and SUB encodes an atypical LRR-receptor-like kinase. We show that twisting of the gynoecium observed in qky results from the abnormal division pattern and anisotropic growth of clustered cells arranged sporadically along the gynoecium. Moreover, the cortical microtubule (CMT) network of these cells is disorganised. A cross to botero, a katanin mutant in which the normal orientation of CMTs and anisotropic cell expansion are impaired, strongly reduces silique deviation, reinforcing the hypothesis of a role for QKY in CMT-mediated cell growth anisotropy. We also show that QKY is localised at the plasma membrane and functions in a multiprotein complex that includes SUB and PAL OF QUIRKY (POQ), a previously uncharacterised PB1-domain-containing protein that localises both at the plasma membrane and in intracellular compartments. Our data indicate that QKY and its interactors play central roles linking together cell-cell communication and cellular growth.

Another brick in the cell wall: biosynthesis dependent growth model

Expansive growth of plant cell is conditioned by the cell wall ability to extend irreversibly. This process is possible if (i) a tensile stress is developed in the cell wall due to the coupling effect between turgor pressure and the modulation of its mechanical properties through enzymatic and physicochemical reactions and if (ii) new cell wall elements can be synthesized and assembled to the existing wall. In other words, expansive growth is the result of coupling effects between mechanical, thermal and chemical energy. To have a better understanding of this process, models must describe the interplay between physical or mechanical variable with biological events. In this paper we propose a general unified and theoretical framework to model growth in function of energy forms and their coupling. This framework is based on irreversible thermodynamics. It is then applied to model growth of the internodal cell of Chara corallina modulated by changes in pressure and temperature. The results describe accurately cell growth in term of length increment but also in term of cell pectate biosynthesis and incorporation to the expanding wall. Moreover, the classical growth model based on Lockhart's equation such as the one proposed by Ortega, appears as a particular and restrictive case of the more general growth equation developed in this paper.

Growth response and acclimation of CO2 exchange characteristics to elevated temperatures in tropical tree seedlings

Predictions of how tropical forests will respond to future climate change are constrained by the paucity of data on the performance of tropical species under elevated growth temperatures. In particular, little is known about the potential of tropical species to acclimate physiologically to future increases in temperature. Seedlings of 10 neo-tropical tree species from different functional groups were cultivated in controlled-environment chambers under four day/night temperature regimes between 30/22 °C and 39/31 °C. Under well-watered conditions, all species showed optimal growth at temperatures above those currently found in their native range. While non-pioneer species experienced catastrophic failure or a substantially reduced growth rate under the highest temperature regime employed (i.e. daily average of 35 °C), growth in three lowland pioneers showed only a marginal reduction. In a subsequent experiment, three species (Ficus insipida, Ormosia macrocalyx, and Ochroma pyramidale) were cultivated at two temperatures determined as sub- and superoptimal for growth, but which resulted in similar biomass accumulation despite a 6°C difference in growth temperature. Through reciprocal transfer and temperature adjustment, the role of thermal acclimation in photosynthesis and respiration was investigated. Acclimation potential varied among species, with two distinct patterns of respiration acclimation identified. The study highlights the role of both inherent temperature tolerance and thermal acclimation in determining the ability of tropical tree species to cope with enhanced temperatures.

Microtubules and biotic interactions

Plant microtubules undergo extensive reorganization in response to symbiotic and pathogenic organisms. During the development of successful symbioses with rhizobia and mycorrhizal fungi, novel microtubule arrays facilitate the progression of infection threads and hyphae, respectively, from the plant surface through epidermal and cortical cells. During viral and nematode infections, plant microtubules appear to be commandeered by the pathogen. Viruses use plant microtubules for intra and intercellular movement, as well as for interhost transmission. Nematodes manipulate spindle and phragmoplast microtubules to enhance mitosis and partial cytokinesis during the development of syncytia and giant cells. Pathogenic bacteria, fungi and oomycetes induce a range of alterations to microtubule arrays and dynamics. In many situations, the pathogen, or the elicitor or effector proteins derived from them, induce depolymerization of plant cortical microtubule arrays. In some cases, microtubule disruption is associated with the plant defence response and resistance. In other cases, microtubule depolymerization increases plant susceptibility to the invading pathogen. The reasons for this apparent inconsistency may depend on a number of factors, in particular on the identity of the organism orchestrating the microtubule changes. Overall, the weight of evidence indicates that microtubules play an important role in both the establishment of functional symbioses and in defence against invading pathogens. Research is beginning to unravel details about the nature of both the chemical and the mechanical signals to which the plant microtubule arrays respond during biotic interactions.

Dissecting the mechanism of abscisic acid-induced dynamic microtubule reorientation using live cell imaging

Abscisic acid (ABA) is involved in plant development and responses to environmental stress including the formation of longitudinal microtubule arrays in elongating cells, although the underlying mechanism for this is unknown. We explored ABA-induced microtubule reorientation in leek (Allium porrum L.) leaf epidermal cells transiently expressing a GFP-MBD microtubule reporter. After 14-18h incubation with ABA, the frequency of cells with longitudinal arrays of cortical microtubules along the outer epidermal wall increased with dose-dependency until saturation at 20μM. Time-course imaging of individual cells revealed a gradual increase in the occurrence of discordant, dynamic microtubules deviating from the normal transverse microtubule array within 2-4h of exposure to ABA, followed by reorientation into a completely longitudinal array within 5-8h. Approximately one-half of the ABA-induced reorientation occurred independently of cytoplasmic streaming following the application of cytochalasin D. Reorientation occurred also in the elongation zone of Arabidopsis root tips. Transient expression of AtEB1b-GFP reporter and analysis of 'comet' velocities in Allium revealed that the microtubule growth rate increased by 55% within 3h of exposure to ABA. ABA also increased the sensitivity of microtubules to depolymerisation by oryzalin and exacerbated oryzalin-induced radial swelling of Arabidopsis root tips. The swelling was further aggravated in AtPLDδ-null mutant, suggesting PLDδ plays a role in microtubule stability. We propose that ABA-induced reorientation of transverse microtubule array initially involves destabilisation of the array combined with the formation of dynamic, discordant microtubules.

Pattern formation in auxin flux

The plant hormone auxin is fundamental for plant growth, and its spatial distribution in plant tissues is critical for plant morphogenesis. We consider a leading model of the polar auxin flux, and study in full detail the stability of the possible equilibrium configurations. We show that the critical states of the auxin transport process are composed of basic building blocks, which are isolated in a background of auxin depleted cells, and are not geometrically regular in general. The same model was considered recently through a continuous limit and a coupling to the von Karman equations, to model the interplay of biochemistry and mechanics during plant growth. Our conclusions might be of interest in this setting, since, for example, we establish the existence of Lyapunov functions for the auxin flux, proving in this way the convergence of pure transport processes toward the set of equilibrium points.

Phyllotaxis

The precise arrangement of plant organs, also called phyllotaxis, has fascinated scientists from multiple disciplines. Whereas early work focused on morphological observations of phyllotaxis, recent findings have started to reveal the mechanisms behind this process, showing how molecular regulation and biochemical gradients interact with physical components to generate such precise patterns of growth. Here, I review new insights into the regulation of phyllotactic patterning and provide an overview of the various factors that can drive these robust growth patterns.

Brown algae as a model for plant organogenesis

Brown algae are an extremely interesting, but surprisingly poorly explored, group of organisms. They are one of only five eukaryotic lineages to have independently evolved complex multicellularity, which they express through a wide variety of morphologies ranging from uniseriate branched filaments to complex parenchymatous thalli with multiple cell types. Despite their very distinct evolutionary history, brown algae and land plants share a striking amount of developmental features. This has led to an interest in several aspects of brown algal development, including embryogenesis, polarity, cell cycle, asymmetric cell division and a putative role for plant hormone signalling. This review describes how investigations using brown algal models have helped to increase our understanding of the processes controlling early embryo development, in particular polarization, axis formation and asymmetric cell division. Additionally, the diversity of life cycles in the brown lineage and the emergence of Ectocarpus as a powerful model organism, are affording interesting insights on the molecular mechanisms underlying haploid-diploid life cycles. The use of these and other emerging brown algal models will undoubtedly add to our knowledge on the mechanisms that regulate development in multicellular photosynthetic organisms.

Venus flytrap biomechanics: forces in the Dionaea muscipula trap

Biomechanics of morphing structures in the Venus flytrap has attracted the attention of scientists during the last 140 years. The trap closes in a tenth of a second if a prey touches a trigger hair twice. The driving force of the closing process is most likely due to the elastic curvature energy stored and locked in the leaves, which is caused by a pressure differential between the upper and lower layers of the leaf. The trap strikes, holds and compresses the prey. We have developed new methods for measuring all these forces involved in the hunting cycle. We made precise calibration of the piezoelectric sensor and performed direct measurements of the average impact force of the trap closing using a high speed video camera for the determination of time constants. The new equation for the average impact force was derived. The impact average force between rims of two lobes in the Venus flytrap was found equal to 149 mN and the corresponding pressure between the rims was about 41 kPa. Direct measurements of the constriction force in the trap of Dionaea muscipula was performed during gelatin digestion. This force increases in the process of digestion from zero to 450 mN with maximal constriction pressure created by the lobes reaching to 9 kPa. The insects and different small prey have little chance to escape after the snap of the trap. The prey would need to overpower the "escaping" force which is very strong and can reach up to 4N.

Cracking the elusive alignment hypothesis: the microtubule-cellulose synthase nexus unraveled

Directed plant cell growth is governed by deposition and alterations of cell wall components under turgor pressure. A key regulatory element of anisotropic growth, and hence cell shape, is the directional deposition of cellulose microfibrils. The microfibrils are synthesized by plasma membrane-located cellulose synthase complexes that co-align with and move along cortical microtubules. That the parallel relation between cortical microtubules and extracellular microfibrils is causal has been named the alignment hypothesis. Three recent studies revealed that the previously identified pom2 mutant codes for a large cellulose synthases interacting (CSI1) protein which also binds cortical microtubules. This review summarizes these findings, provides structure-function models and discusses the inferred mechanisms in the context of plant growth.

Radiometric and spectrophotometric in vitro assays of glycosyltransferases involved in plant cell wall carbohydrate biosynthesis

Most of the glycosyltransferases (GTs) that catalyze the formation of plant cell wall carbohydrates remain to be biochemically characterized. This can be achieved only if specific assays are available for these enzymes. Here we present a protocol for in vitro assays of processive and nonprocessive membrane-bound GTs. The assays are either based on the use of radioactive nucleotide sugars (NDP sugars; e.g., UDP-[U-(14)C]glucose) and the quantification of the radiolabeled monosaccharides incorporated into soluble or insoluble carbohydrates, or on the coupling of the GT reaction with that of pyruvate kinase (PK) and the oxidation of NADH by lactate dehydrogenase (LDH). The radiometric assays are more suitable for exploratory work on poorly characterized enzymes, whereas the spectrophotometric assays require the availability of highly enriched GTs. Both assays can be performed within 1 d, depending on the number of fractions to be assayed or reaction mixtures to be tested.

A revised architecture of primary cell walls based on biomechanical changes induced by substrate-specific endoglucanases

Xyloglucan is widely believed to function as a tether between cellulose microfibrils in the primary cell wall, limiting cell enlargement by restricting the ability of microfibrils to separate laterally. To test the biomechanical predictions of this "tethered network" model, we assessed the ability of cucumber (Cucumis sativus) hypocotyl walls to undergo creep (long-term, irreversible extension) in response to three family-12 endo-β-1,4-glucanases that can specifically hydrolyze xyloglucan, cellulose, or both. Xyloglucan-specific endoglucanase (XEG from Aspergillus aculeatus) failed to induce cell wall creep, whereas an endoglucanase that hydrolyzes both xyloglucan and cellulose (Cel12A from Hypocrea jecorina) induced a high creep rate. A cellulose-specific endoglucanase (CEG from Aspergillus niger) did not cause cell wall creep, either by itself or in combination with XEG. Tests with additional enzymes, including a family-5 endoglucanase, confirmed the conclusion that to cause creep, endoglucanases must cut both xyloglucan and cellulose. Similar results were obtained with measurements of elastic and plastic compliance. Both XEG and Cel12A hydrolyzed xyloglucan in intact walls, but Cel12A could hydrolyze a minor xyloglucan compartment recalcitrant to XEG digestion. Xyloglucan involvement in these enzyme responses was confirmed by experiments with Arabidopsis (Arabidopsis thaliana) hypocotyls, where Cel12A induced creep in wild-type but not in xyloglucan-deficient (xxt1/xxt2) walls. Our results are incompatible with the common depiction of xyloglucan as a load-bearing tether spanning the 20- to 40-nm spacing between cellulose microfibrils, but they do implicate a minor xyloglucan component in wall mechanics. The structurally important xyloglucan may be located in limited regions of tight contact between microfibrils.

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.

Energetics and forces of the Dionaea muscipula trap closing

The Venus flytrap is the most famous carnivorous plant. The electrical stimulus between a midrib and a lobe closes the Venus flytrap upper leaf in 0.3s without mechanical stimulation of trigger hairs. Here we present results for direct measurements of the closing force of the trap of Dionaea muscipula Ellis after mechanical or electrical stimulation of the trap using the piezoelectric thin film or Fuji Prescale indicating sensor film. The closing force was 0.14N and the corresponding pressure between rims of two lobes was 38 kPa. We evaluated theoretically using the Hydroelastic Curvature Model and compared with experimental data velocity, acceleration and kinetic energy from the time dependencies of distance between rims of lobes during the trap closing. The Charge Stimulation Method was used for trap electrostimulation between the midrib and lobes. From the dependence of voltage between two Ag/AgCl electrodes in the midrib and one of the lobes, we estimated electrical charge, current, resistance, electrical energy and electrical power dependencies on time during electrostimulation of the trap.