A model of crosslink kinetics in the expanding plant cell wall: yield stress and enzyme action

Expression responses of XTH genes in tomato and potato to environmental mechanical forces: focus on behavior in response to rainfall, wind and touch

Rainfall, wind and touch, as mechanical forces, were mimicked on 6-week-old soil-grown tomato and potato under controlled conditions. Expression level changes of xyloglucan endotransglucosylase/hydrolase genes (XTHs) of tomato (Solanum lycopersicum L. cv. Micro Tom; SlXTHs) and potato (Solanum tuberosum L. cv. Desirée; StXTHs) were analyzed in response to these mechanical forces. Transcription intensity of every SlXTHs of tomato was altered in response to rainfall, while the expression intensity of 72% and 64% of SlXTHs was modified by wind and touch, respectively. Ninety-one percent of StXTHs (32 out of 35) in potato responded to the rainfall, while 49% and 66% of the StXTHs were responsive to the wind and touch treatments, respectively. As previously demonstrated, all StXTHs were responsive to ultrasound treatment, and all were sensitive to one or more of the environmental mechanical factors examined in the current study. To our best knowledge, this is the first study to demonstrate that these ubiquitous mechanical environmental cues, such as rainfall, wind and touch, influence the transcription of most XTHs examined in both species.

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.

Mechanics and hydraulics of pollen tube growth

All kingdoms of life have evolved tip-growing cells able to mine their environment or deliver cargo to remote targets. The basic cellular processes supporting these functions are understood in increasing detail, but the multiple interactions between them lead to complex responses that require quantitative models to be disentangled. Here, I review the equations that capture the fundamental interactions between wall mechanics and cell hydraulics starting with a detailed presentation of James Lockhart's seminal model. The homeostatic feedbacks needed to maintain a steady tip velocity are then shown to offer a credible explanation for the pulsatile growth observed in some tip-growing cells. Turgor pressure emerges as a central variable whose role in the morphogenetic process has been a source of controversy for more than 50 yr. I argue that recasting Lockhart's work as a process of chemical stress relaxation can clarify how cells control tip growth and help us internalise the important but passive role played by turgor pressure in the morphogenetic process.

A Molecular Pinball Machine of the Plasma Membrane Regulates Plant Growth-A New Paradigm

Novel molecular pinball machines of the plasma membrane control cytosolic Ca²⁺ levels that regulate plant metabolism. The essential components involve: 1. an auxin-activated proton pump; 2. arabinogalactan glycoproteins (AGPs); 3. Ca²⁺ channels; 4. auxin-efflux "PIN" proteins. Typical pinball machines release pinballs that trigger various sound and visual effects. However, in plants, "proton pinballs" eject Ca²⁺ bound by paired glucuronic acid residues of numerous glycomodules in periplasmic AGP-Ca²⁺. Freed Ca²⁺ ions flow down the electrostatic gradient through open Ca²⁺ channels into the cytosol, thus activating numerous Ca²⁺-dependent activities. Clearly, cytosolic Ca²⁺ levels depend on the activity of the proton pump, the state of Ca²⁺ channels and the size of the periplasmic AGP-Ca²⁺ capacitor; proton pump activation is a major regulatory focal point tightly controlled by the supply of auxin. Auxin efflux carriers conveniently known as "PIN" proteins (null mutants are pin-shaped) pump auxin from cell to cell. Mechanosensitive Ca²⁺ channels and their activation by reactive oxygen species (ROS) are yet another factor regulating cytosolic Ca²⁺. Cell expansion also triggers proton pump/pinball activity by the mechanotransduction of wall stress via Hechtian adhesion, thus forming a Hechtian oscillator that underlies cycles of wall plasticity and oscillatory growth. Finally, the Ca²⁺ homeostasis of plants depends on cell surface external storage as a source of dynamic Ca²⁺, unlike the internal ER storage source of animals, where the added regulatory complexities ranging from vitamin D to parathormone contrast with the elegant simplicity of plant life. This paper summarizes a sixty-year Odyssey.

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.

Mapping cellular nanoscale viscoelasticity and relaxation times relevant to growth of living Arabidopsis thaliana plants using multifrequency AFM

The shapes of living organisms are formed and maintained by precise control in time and space of growth, which is achieved by dynamically fine-tuning the mechanical (viscous and elastic) properties of their hierarchically built structures from the nanometer up. Most organisms on Earth including plants grow by yield (under pressure) of cell walls (bio-polymeric matrices equivalent to extracellular matrix in animal tissues) whose underlying nanoscale viscoelastic properties remain unknown. Multifrequency atomic force microscopy (AFM) techniques exist that are able to map properties to a small subgroup of linear viscoelastic materials (those obeying the Kelvin-Voigt model), but are not applicable to growing materials, and hence are of limited interest to most biological situations. Here, we extend existing dynamic AFM methods to image linear viscoelastic behaviour in general, and relaxation times of cells of multicellular organisms in vivo with nanoscale resolution (~80 nm pixel size in this study), featuring a simple method to test the validity of the mechanical model used to interpret the data. We use this technique to image cells at the surface of living Arabidopsis thaliana hypocotyls to obtain topographical maps of storage E' = 120-200 MPa and loss E″ = 46-111 MPa moduli as well as relaxation times τ = 2.2-2.7 µs of their cell walls. Our results demonstrate that (taken together with previous studies) cell walls, despite their complex molecular composition, display a striking continuity of simple, linear, viscoelastic behaviour across scales-following almost perfectly the standard linear solid model-with characteristic nanometer scale patterns of relaxation times, elasticity and viscosity, whose values correlate linearly with the speed of macroscopic growth. We show that the time-scales probed by dynamic AFM experiments (microseconds) are key to understand macroscopic scale dynamics (e.g. growth) as predicted by physics of polymer dynamics.

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.

Phyllotaxis Turns Over a New Leaf-A New Hypothesis

Phyllotaxis describes the periodic arrangement of plant organs most conspicuously floral. Oscillators generally underlie periodic phenomena. A hypothetical algorithm generates phyllotaxis regulated by the Hechtian growth oscillator of the stem apical meristem (SAM) protoderm. The oscillator integrates biochemical and mechanical force that regulate morphogenetic gradients of three ionic species, auxin, protons and Ca2+. Hechtian adhesion between cell wall and plasma membrane transduces wall stress that opens Ca2+ channels and reorients auxin efflux "PIN" proteins; they control the auxin-activated proton pump that dissociates Ca2+ bound by periplasmic arabinogalactan proteins (AGP-Ca2+) hence the source of cytosolic Ca2+ waves that activate exocytosis of wall precursors, AGPs and PIN proteins essential for morphogenesis. This novel approach identifies the critical determinants of an algorithm that generates phyllotaxis spiral and Fibonaccian symmetry: these determinants in order of their relative contribution are: (1) size of the apical meristem and the AGP-Ca2+ capacitor; (2) proton pump activity; (3) auxin efflux proteins; (4) Ca2+ channel activity; (5) Hechtian adhesion that mediates the cell wall stress vector. Arguably, AGPs and the AGP-Ca2+ capacitor plays a decisive role in phyllotaxis periodicity and its evolutionary origins.

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 Statistical Model of Expansive Growth in Plant and Fungal Cells: The Case of Phycomyces

Expansive growth is a process by which walled cells of plants, algae, and fungi use turgor pressure to mediate irreversible wall deformation and regulate their shape and volume. The molecular structure of the primary cell wall must therefore perform multiple functions simultaneously, including providing structural support by combining elastic and irreversible deformation and facilitating the deposition of new material during growth. This is accomplished by a network of microfibrils and tethers composed of complex polysaccharides and proteins that can dynamically mediate the network topology via periodic detachment and reattachment events. Lockhart and Ortega have provided crucial macroscopic understanding of the expansive growth process through global biophysical models, but these models lack the connection to molecular processes that trigger network rearrangements in the wall. Interestingly, the helical growth of the fungal sporangiophores of Phycomyces blakesleeanus is attributed to a limited region (called the growth zone) where microfibrils are deposited, followed by reorientation and slip. Based on past evidence of dominant shear strain between microfibrils (slippage), we propose a mechanistic model of a network of sliding fibrils connected by tethers. A statistical approach is introduced to describe the population behavior of tethers that have elastic properties and the ability to break and reform in time. These properties are responsible for global cell wall mechanics such as creep and stress relaxation. Model predictions are compared with experiments from literature on stress relaxation and turgor pressure step up for the growing cells of P. blakesleeanus, which are later extended to incised pea (Pisum sativus L.) and the algae Chara corallina using the unique dimensionless number Πpe for each species. To our knowledge, this research is the first attempt to use a statistical approach to model the cell wall during expansive growth, and we believe it provides critical insights on cell wall dynamics at a molecular level.

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.

Dimensionless number is central to stress relaxation and expansive growth of the cell wall

Experiments demonstrate that both plastic and elastic deformation of the cell wall are necessary for wall stress relaxation and expansive growth of walled cells. A biophysical equation (Augmented Growth Equation) was previously shown to accurately model the experimentally observed wall stress relaxation and expansive growth rate. Here, dimensional analysis is used to obtain a dimensionless Augmented Growth Equation with dimensionless coefficients (groups of variables, or Π parameters). It is shown that a single Π parameter controls the wall stress relaxation rate. The Π parameter represents the ratio of plastic and elastic deformation rates, and provides an explicit relationship between expansive growth rate and the wall's mechanical properties. Values for Π are calculated for plant, algal, and fungal cells from previously reported experimental results. It is found that the Π values for each cell species are large and very different from each other. Expansive growth rates are calculated using the calculated Π values and are compared to those measured for plant and fungal cells during different growth conditions, after treatment with IAA, and in different developmental stages. The comparison shows good agreement and supports the claim that the Π parameter is central to expansive growth rate of walled cells.

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.

A continuous growth model for plant tissue

Morphogenesis in plants and animals involves large irreversible deformations. In plants, the response of the cell wall material to internal and external forces is determined by its mechanical properties. An appropriate model for plant tissue growth must include key features such as anisotropic and heterogeneous elasticity and cell dependent evaluation of mechanical variables such as turgor pressure, stress and strain. In addition, a growth model needs to cope with cell divisions as a necessary part of the growth process. Here we develop such a growth model, which is capable of employing not only mechanical signals but also morphogen signals for regulating growth. The model is based on a continuous equation for updating the resting configuration of the tissue. Simultaneously, material properties can be updated at a different time scale. We test the stability of our model by measuring convergence of growth results for a tissue under the same mechanical and material conditions but with different spatial discretization. The model is able to maintain a strain field in the tissue during re-meshing, which is of particular importance for modeling cell division. We confirm the accuracy of our estimations in two and three-dimensional simulations, and show that residual stresses are less prominent if strain or stress is included as input signal to growth. The approach results in a model implementation that can be used to compare different growth hypotheses, while keeping residual stresses and other mechanical variables updated and available for feeding back to the growth and material properties.

The Impact of Microfibril Orientations on the Biomechanics of Plant Cell Walls and Tissues

The microscopic structure and anisotropy of plant cell walls greatly influence the mechanical properties, morphogenesis, and growth of plant cells and tissues. The microscopic structure and properties of cell walls are determined by the orientation and mechanical properties of the cellulose microfibrils and the mechanical properties of the cell wall matrix. Viewing the shape of a plant cell as a square prism with the axis aligning with the primary direction of expansion and growth, the orientation of the microfibrils within the side walls, i.e. the parts of the cell walls on the sides of the cells, is known. However, not much is known about their orientation at the upper and lower ends of the cell. Here we investigate the impact of the orientation of cellulose microfibrils within the upper and lower parts of the plant cell walls by solving the equations of linear elasticity numerically. Three different scenarios for the orientation of the microfibrils are considered. We also distinguish between the microstructure in the side walls given by microfibrils perpendicular to the main direction of the expansion and the situation where the microfibrils are rotated through the wall thickness. The macroscopic elastic properties of the cell wall are obtained using homogenization theory from the microscopic description of the elastic properties of the cell wall microfibrils and wall matrix. It is found that the orientation of the microfibrils in the upper and lower parts of the cell walls affects the expansion of the cell in the lateral directions and is particularly important in the case of forces acting on plant cell walls and tissues.

Mapping nano-scale mechanical heterogeneity of primary plant cell walls

Nanoindentation experiments are performed using an atomic force microscope (AFM) to quantify the spatial distribution of mechanical properties of plant cell walls at nanometre length scales. At any specific location on the cell wall, a complex (non-linear) force-indentation response occurs that can be deconvoluted using a unique multiregime analysis (MRA). This allows an unambiguous evaluation of the local transverse elastic modulus of the wall. Nanomechanical measurements on suspension-cultured cells (SCCs), derived from Italian ryegrass (Lolium multiflorum) starchy endosperm, show three characteristic modes of deformation and a spatial distribution of elastic moduli across the surface. 'Soft' and 'hard' domains are found across length scales between 0.1 µm and 3 µm, which is well above a typical pore size of the polysaccharide mesh. The generality and wider applicability of this mechanical heterogeneity is verified through in planta characterization on leaf epidermal cells of Arabidopsis thaliana and L. multiflorum The outcomes of this research provide a basis for uncovering and quantifying the relationships between local wall composition, architecture, cell growth, and/or morphogenesis.

Shifting foundations: the mechanical cell wall and development

The cell wall has long been acknowledged as an important physical mediator of growth in plants. Recent experimental and modelling work has brought the importance of cell wall mechanics into the forefront again. These data have challenged existing dogmas that relate cell wall structure to cell/organ growth, that uncouple elasticity from extensibility, and those which treat the cell wall as a passive and non-stressed material. Within this review we describe experiments and models which have changed the ways in which we view the mechanical cell wall, leading to new hypotheses and research avenues. It has become increasingly apparent that while we often wish to simplify our systems, we now require more complex multi-scale experiments and models in order to gain further insight into growth mechanics. We are currently experiencing an exciting and challenging shift in the foundations of our understanding of cell wall mechanics in growth and development.

Relating the mechanics of the primary plant cell wall to morphogenesis

Regulation of the mechanical properties of the cell wall is a key parameter used by plants to control the growth behavior of individual cells and tissues. Modulation of the mechanical properties occurs through the control of the biochemical composition and the degree and nature of interlinking between cell wall polysaccharides. Preferentially oriented cellulose microfibrils restrict cellular expansive growth, but recent evidence suggests that this may not be the trigger for anisotropic growth. Instead, non-uniform softening through the modulation of pectin chemistry may be an initial step that precedes stress-induced stiffening of the wall through cellulose. Here we briefly review the major cell wall polysaccharides and their implication for plant cell wall mechanics that need to be considered in order to study the growth behavior of the primary plant cell wall.

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.

Monoclonal antibody-based analysis of cell wall remodeling during xylogenesis

Xylogenesis, a process by which woody tissues are formed, entails qualitative and quantitative changes in the cell wall. However, the molecular events that underlie these changes are not completely understood. Previously, we have isolated two monoclonal antibodies, referred to as XD3 and XD27, by subtractive screening of a phage-display library of antibodies raised against a wall fraction of Zinnia elegans xylogenic culture cells. Here we report the biochemical and immunohistochemical characterization of those antibodies. The antibody XD3 recognized (1→4)-β-D-galactan in pectin fraction. During xylogenesis, the XD3 epitope was localized to the primary wall of tracheary-element precursor cells, which undergo substantial cell elongation, and was absent from mature tracheary elements. XD27 recognized an arabinogalactan protein that was bound strongly to a germin-like protein. The XD27 epitope was localized to pre-lignified secondary walls of tracheary elements. Thus these cell-wall-directed monoclonal antibodies revealed two molecular events during xylogenesis. The biological significance of these events is discussed in relation to current views of the plant cell wall.

Multiscale models in the biomechanics of plant growth

Plant growth occurs through the coordinated expansion of tightly adherent cells, driven by regulated softening of cell walls. It is an intrinsically multiscale process, with the integrated properties of multiple cell walls shaping the whole tissue. Multiscale models encode physical relationships to bring new understanding to plant physiology and development.

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.

Mechanical modelling quantifies the functional importance of outer tissue layers during root elongation and bending

Root elongation and bending require the coordinated expansion of multiple cells of different types. These processes are regulated by the action of hormones that can target distinct cell layers. We use a mathematical model to characterise the influence of the biomechanical properties of individual cell walls on the properties of the whole tissue. Taking a simple constitutive model at the cell scale which characterises cell walls via yield and extensibility parameters, we derive the analogous tissue-level model to describe elongation and bending. To accurately parameterise the model, we take detailed measurements of cell turgor, cell geometries and wall thicknesses. The model demonstrates how cell properties and shapes contribute to tissue-level extensibility and yield. Exploiting the highly organised structure of the elongation zone (EZ) of the Arabidopsis root, we quantify the contributions of different cell layers, using the measured parameters. We show how distributions of material and geometric properties across the root cross-section contribute to the generation of curvature, and relate the angle of a gravitropic bend to the magnitude and duration of asymmetric wall softening. We quantify the geometric factors which lead to the predominant contribution of the outer cell files in driving root elongation and bending.

Contributions of the mechanical properties of major structural polysaccharides to the stiffness of a cell wall network model

PREMISE OF THE STUDY

The molecular mechanisms regulating the expansive growth of the plant cell wall have yet to be fully understood. The recent development of a computational cell wall model allows quantitative examinations of hypothesized cell wall loosening mechanisms.

METHODS

Computational cell wall network (CWN) models were generated using cellulose microfibrils (CMFs), hemicelluloses (HCs), and their interactions (CMF-HC). For each component, a range of stiffness values, representing various situations hypothesized as potential cell-wall-loosening mechanisms, were used in the calculation of the overall stiffness of the computational CWN model. Thus, a critical mechanism of the loosening of the primary cell wall was investigated using a computational approach by modeling the molecular structure.

KEY RESULTS

The increase in the stiffness equivalent of the CMF-HC interaction results in an increase in the Young's modulus of the CWN. In the major growth direction, the CWN stiffness is most sensitive to the CMF-HC interaction (75%). HC stiffness contributes moderately (24%) to the change in the CWN stiffness, whereas the CMF contribution is marginal (1%). Minor growth direction exhibited a similar trend except that the contributions of CMFs and HCs are higher than for the major growth direction.

CONCLUSIONS

The stiffness of the CMF-HC interaction is the most critical mechanical component in altering stiffness of the CWN model, which supports the hypothesized mechanism of expansin's role in efficient loosening of the plant cell wall by disrupting HC binding to CMFs. The comparison to experiments suggests additional load-bearing mechanisms in CMF-HC interactions.

Mechanical consequences of cell-wall turnover in the elongation of a Gram-positive bacterium

A common feature of walled organisms is their exposure to osmotic forces that challenge the mechanical integrity of cells while driving elongation. Most bacteria rely on their cell wall to bear osmotic stress and determine cell shape. Wall thickness can vary greatly among species, with Gram-positive bacteria having a thicker wall than Gram-negative bacteria. How wall dimensions and mechanical properties are regulated and how they affect growth have not yet been elucidated. To investigate the regulation of wall thickness in the rod-shaped Gram-positive bacterium Bacillus subtilis, we analyzed exponentially growing cells in different media. Using transmission electron and epifluorescence microscopy, we found that wall thickness and strain were maintained even between media that yielded a threefold change in growth rate. To probe mechanisms of elongation, we developed a biophysical model of the Gram-positive wall that balances the mechanical effects of synthesis of new material and removal of old material through hydrolysis. Our results suggest that cells can vary their growth rate without changing wall thickness or strain by maintaining a constant ratio of synthesis and hydrolysis rates. Our model also indicates that steady growth requires wall turnover on the same timescale as elongation, which can be driven primarily by hydrolysis rather than insertion. This perspective of turnover-driven elongation provides mechanistic insight into previous experiments involving mutants whose growth rate was accelerated by the addition of lysozyme or autolysin. Our approach provides a general framework for deconstructing shape maintenance in cells with thick walls by integrating wall mechanics with the kinetics and regulation of synthesis and turnover.

My body is a cage: mechanisms and modulation of plant cell growth

388 I. 388 II. 389 III. 389 IV. 390 V. 391 VI. 393 VII. 394 VIII. 398 399 References 399 SUMMARY: The wall surrounding plant cells provides protection from abiotic and biotic stresses, and support through the action of turgor pressure. However, the presence of this strong elastic wall also prevents cell movement and resists cell growth. This growth can be likened to extending a house from the inside, using extremely high pressures to push out the walls. Plants must increase cell volume in order to explore their environment, acquire nutrients and reproduce. Cell wall material must stretch and flow in a controlled manner and, concomitantly, new cell wall material must be deposited at the correct rate and site to prevent wall and cell rupture. In this review, we examine biomechanics, cell wall structure and growth regulatory networks to provide a 'big picture' of plant cell growth.

Stress and strain provide positional and directional cues in development

The morphogenesis of organs necessarily involves mechanical interactions and changes in mechanical properties of a tissue. A long standing question is how such changes are directed on a cellular scale while being coordinated at a tissular scale. Growing evidence suggests that mechanical cues are participating in the control of growth and morphogenesis during development. We introduce a mechanical model that represents the deposition of cellulose fibers in primary plant walls. In the model both the degree of material anisotropy and the anisotropy direction are regulated by stress anisotropy. We show that the finite element shell model and the simpler triangular biquadratic springs approach provide equally adequate descriptions of cell mechanics in tissue pressure simulations of the epidermis. In a growing organ, where circumferentially organized fibers act as a main controller of longitudinal growth, we show that the fiber direction can be correlated with both the maximal stress direction and the direction orthogonal to the maximal strain direction. However, when dynamic updates of the fiber direction are introduced, the mechanical stress provides a robust directional cue for the circumferential organization of the fibers, whereas the orthogonal to maximal strain model leads to an unstable situation where the fibers reorient longitudinally. Our investigation of the more complex shape and growth patterns in the shoot apical meristem where new organs are initiated shows that a stress based feedback on fiber directions is capable of reproducing the main features of in vivo cellulose fiber directions, deformations and material properties in different regions of the shoot. In particular, we show that this purely mechanical model can create radially distinct regions such that cells expand slowly and isotropically in the central zone while cells at the periphery expand more quickly and in the radial direction, which is a well established growth pattern in the meristem.

Leaf development: a cellular perspective

Through its photosynthetic capacity the leaf provides the basis for growth of the whole plant. In order to improve crops for higher productivity and resistance for future climate scenarios, it is important to obtain a mechanistic understanding of leaf growth and development and the effect of genetic and environmental factors on the process. Cells are both the basic building blocks of the leaf and the regulatory units that integrate genetic and environmental information into the developmental program. Therefore, to fundamentally understand leaf development, one needs to be able to reconstruct the developmental pathway of individual cells (and their progeny) from the stem cell niche to their final position in the mature leaf. To build the basis for such understanding, we review current knowledge on the spatial and temporal regulation mechanisms operating on cells, contributing to the formation of a leaf. We focus on the molecular networks that control exit from stem cell fate, leaf initiation, polarity, cytoplasmic growth, cell division, endoreduplication, transition between division and expansion, expansion and differentiation and their regulation by intercellular signaling molecules, including plant hormones, sugars, peptides, proteins, and microRNAs. We discuss to what extent the knowledge available in the literature is suitable to be applied in systems biology approaches to model the process of leaf growth, in order to better understand and predict leaf growth starting with the model species Arabidopsis thaliana.

On the role of stress anisotropy in the growth of stems

We review the role of anisotropic stress in controlling the growth anisotropy of stems. Instead of stress, growth anisotropy is usually considered in terms of compliance. Anisotropic compliance is typical of cell walls, because they contain aligned cellulose microfibrils, and it appears to be sufficient to explain the growth anisotropy of an isolated cell. Nevertheless, a role for anisotropic stress in the growth of stems is indicated by certain growth responses that appear too rapid to be accounted for by changes in cell-wall compliance and because the outer epidermal wall of most growing stems has microfibrils aligned axially, an arrangement that would favour radial expansion based on cell-wall compliance alone. Efforts to quantify stress anisotropy in the stem have found that it is predominantly axial, and large enough in principle to explain the elongation of the epidermis, despite its axial microfibrils. That the epidermis experiences a stress deriving from the inner tissue, the so-called 'tissue stress', has been widely recognized; however, the origin of the dominant axial direction remains obscure. Based on geometry, an isolated cylindrical cell should have an intramural stress anisotropy favouring the transverse direction. Explanations for tissue stress have invoked differential elastic moduli, differential plastic deformation (so-called differential growth), and a phenomenon analogous to the maturation stress generated by secondary cell walls. None of these explanations has been validated. We suggest that understanding the role of stress anisotropy in plant growth requires a deeper understanding of the nature of stress in hierarchical, organic structures.

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.

Vertex-element models for anisotropic growth of elongated plant organs

New tools are required to address the challenge of relating plant hormone levels, hormone responses, wall biochemistry and wall mechanical properties to organ-scale growth. Current vertex-based models (applied in other contexts) can be unsuitable for simulating the growth of elongated organs such as roots because of the large aspect ratio of the cells, and these models fail to capture the mechanical properties of cell walls in sufficient detail. We describe a vertex-element model which resolves individual cells and includes anisotropic non-linear viscoelastic mechanical properties of cell walls and cell division whilst still being computationally efficient. We show that detailed consideration of the cell walls in the plane of a 2D simulation is necessary when cells have large aspect ratio, such as those in the root elongation zone of Arabidopsis thaliana, in order to avoid anomalous transverse swelling. We explore how differences in the mechanical properties of cells across an organ can result in bending and how cellulose microfibril orientation affects macroscale growth. We also demonstrate that the model can be used to simulate growth on realistic geometries, for example that of the primary root apex, using moderate computational resources. The model shows how macroscopic root shape can be sensitive to fine-scale cellular geometries.

Architecture-based multiscale computational modeling of plant cell wall mechanics to examine the hydrogen-bonding hypothesis of the cell wall network structure model

A primary plant cell wall network was computationally modeled using the finite element approach to study the hypothesis of hemicellulose (HC) tethering with the cellulose microfibrils (CMFs) as one of the major load-bearing mechanisms of the growing cell wall. A computational primary cell wall network fragment (10 × 10 μm) comprising typical compositions and properties of CMFs and HC was modeled with well-aligned CMFs. The tethering of HC to CMFs is modeled in accordance with the strength of the hydrogen bonding by implementing a specific load-bearing connection (i.e. the joint element). The introduction of the CMF-HC interaction to the computational cell wall network model is a key to the quantitative examination of the mechanical consequences of cell wall structure models, including the tethering HC model. When the cell wall network models with and without joint elements were compared, the hydrogen bond exhibited a significant contribution to the overall stiffness of the cell wall network fragment. When the cell wall network model was stretched 1% in the transverse direction, the tethering of CMF-HC via hydrogen bonds was not strong enough to maintain its integrity. When the cell wall network model was stretched 1% in the longitudinal direction, the tethering provided comparable strength to maintain its integrity. This substantial anisotropy suggests that the HC tethering with hydrogen bonds alone does not manifest sufficient energy to maintain the integrity of the cell wall during its growth (i.e. other mechanisms are present to ensure the cell wall shape).

Multiscale systems analysis of root growth and development: modeling beyond the network and cellular scales

Over recent decades, we have gained detailed knowledge of many processes involved in root growth and development. However, with this knowledge come increasing complexity and an increasing need for mechanistic modeling to understand how those individual processes interact. One major challenge is in relating genotypes to phenotypes, requiring us to move beyond the network and cellular scales, to use multiscale modeling to predict emergent dynamics at the tissue and organ levels. In this review, we highlight recent developments in multiscale modeling, illustrating how these are generating new mechanistic insights into the regulation of root growth and development. We consider how these models are motivating new biological data analysis and explore directions for future research. This modeling progress will be crucial as we move from a qualitative to an increasingly quantitative understanding of root biology, generating predictive tools that accelerate the development of improved crop varieties.

Comparative structure and biomechanics of plant primary and secondary cell walls

Recent insights into the physical biology of plant cell walls are reviewed, summarizing the essential differences between primary and secondary cell walls and identifying crucial gaps in our knowledge of their structure and biomechanics. Unexpected parallels are identified between the mechanism of expansion of primary cell walls during growth and the mechanisms by which hydrated wood deforms under external tension. There is a particular need to revise current "cartoons" of plant cell walls to be more consistent with data from diverse approaches and to go beyond summarizing limited aspects of cell walls, serving instead as guides for future experiments and for the application of new techniques.