Cell Growth and the Structure and Mechanical Properties of the Wall in Internodal Cells of Nitella opaca: II. MECHANICAL PROPERTIES OF THE WALLS

The internodal cells of Nitella opaca L. have been used in anattempt to assess the part which mechanical properties of thewall may play in the control of cell growth. It is shown thatthe wall is mechanically anisotropic in both its plastic andelastic properties, and evidence is presented which indicatesthat this arises from its anisotropy of structure. The degreeof anisotropy is greater in cells with a high growth-rate thanin those with a low growth-rate. Evidence is presented thatthis variation in properties with growth-rate is due wholly,or in part, to changes in the orientation of the crystallinecomponent, in the relative proportion of wall constituents,and in the condition of active groups of the wall components.The findings are in harmony with the theory that extension growthof the cell wall is due to ‘creep’, i.e. disturbancesof the molecular forces within the wall leading to a slow plasticyielding to turgor pressure.     

Loss of stability: a new look at the physics of cell wall behavior during plant cell growth

In this article we investigate aspects of turgor-driven plant cell growth within the framework of a model derived from the Eulerian concept of instability. In particular we explore the relationship between cell geometry and cell turgor pressure by extending loss of stability theory to encompass cylindrical cells. Beginning with an analysis of the three-dimensional stress and strain of a cylindrical pressure vessel, we demonstrate that loss of stability is the inevitable result of gradually increasing internal pressure in a cylindrical cell. The turgor pressure predictions based on this model differ from the more traditional viscoelastic or creep-based models in that they incorporate both cell geometry and wall mechanical properties in a single term. To confirm our predicted working turgor pressures, we obtained wall dimensions, elastic moduli, and turgor pressures of sequential internodal cells of intact Chara corallina plants by direct measurement. The results show that turgor pressure predictions based on loss of stability theory fall within the expected physiological range of turgor pressures for this plant. We also studied the effect of varying wall Poisson's ratio nu on extension growth in living cells, showing that while increasing elastic modulus has an understandably negative effect on wall expansion, increasing Poisson's ratio would be expected to accelerate wall expansion.     

Mechanical Response of Single Plant Cells to Cell Poking： A Numerical Simulation Model

Cell poking is an experimental technique that is widely used to study the mechanical properties of plant cells. A full understanding of the mechanical responses of plant cells to poking force Is helpful for experimental work. The aim of this study was to numerically investigate the stress distribution of the cell wall, cell turgor, and deformation of plant cells in response to applied poking force. Furthermore, the locations damaged during poking were analyzed. The model simulates cell poking, with the cell treated as a spherical, homogeneous, isotropic elastic membrane, filled with incompressible, highly viscous liquid. Equilibrium equations for the contact region and the non-contact regions were determined by using membrane theory. The boundary conditions and continuity conditions for the solution of the problem were found. The forcedeformation curve, turgor pressure and tension of the cell wall under cell poking conditions were obtained. The tension of the cell wall circumference was larger than that of the meridian. In general, maximal stress occurred at the equator around. When cell deformation increased to a certain level, the tension at the poker tip exceeded that of the equator. Breakage of the cell wall may start from the equator or the poker tip, depending on the deformation. A nonlinear model is suitable for estimating turgor, stress, and stiffness, and numerical simulation is a powerful method for determining plant cell mechanical properties.     

Loss of stability-a new model for stress relaxation in plant cell walls

This study addresses the mechanism of wall stress relaxation in growing plant cells. The current viscoelastic model of cell wall relaxation, which dates from the work of Preston, Cleland, Lockhart, and others in the 1960s, has serious shortcomings. It has been shown however that the theory of loss of stability (LOS) can be applied to materials in tension, leading to the conclusion that the relaxation of stresses in the walls of any pressure vessel is rigorously modeled using LOS. We propose that LOS also provides a more appropriate and versatile model of stress relaxation in growing plant cells. We argue that when treated as a manifestation of LOS, the regulation of cell turgor has a rigorous and demonstrable basis in the geometrical and physical properties of the cell wall and the cell's ability to import water. Thus plant cell growth can be regarded as an inherently self-limiting process, tunable by biochemical or structural means. Lastly, despite the current limitations of our model, we apply direct measurement of elastic modulus, wall thickness and cell radius obtained from cylindrical Chara corallina cells to generate an initial calculation of critical pressures in a hypothetical spherical cell with the same material properties.     

The Geometrical Model for Microfibril Deposition and the Influence of the Cell Wall Matrix

Abstract: A theory for cell wall deposition has been formulated consistent with present day experimental data on cell walls and cellular processes. This theory has a generic origin, geometrical constraints, as the underlying cause for the cell wall architecture. The theory has been worked out as a fully mathematical model, allowing for specific predictions of a qualitative and quantitative nature. The key point of the geometrical theory is the coupling of the trajectory of the cellulose microfibril synthases, i.e., rosettes, to their density. This coupling provides the cell with a mechanism for manipulating the cell wall texture by creating controlled local variations in the number of active synthases. In the present paper we show that the geometrical model can explain the helicoidal, crossed polylamellate, helical and axial wall textures, which are the basic textures found in plant cell walls. In addition, we discuss the role of cortical microtubules in the wall deposition process and how the cell wall matrix contributes to cell wall texture determination.     

Wall extensibility: its nature, measurement and relationship to plant cell growth

Expansive growth of plant cells is controlled principally by processes that loosen the wall and enable it to expand irreversibly. The central role of wall relaxation for cell expansion is reviewed. The most common methods for assessing the extension properties of plant cell walls ( wall extensibility') are described, categorized and assessed critically. What emerges are three fundamentally different approaches which test growing cells for their ability (a) to enlarge at different values of turgor, (b) to induce wall relaxation, and (c) to deform elastically or plastically in response to an applied tensile force. Analogous methods with isolated walls are similarly reviewed. The results of these different assays are related to the nature of plant cell growth and pertinent biophysical theory. I argue that the extensibilities' measured by these assays are fundamentally different from one another and that some are more pertinent to growth than others.     

A membrane model of plant cell extension

A theory is presented for the mechanics of plant cell wall extension and is based on the analogy of the cell wall with a membrane structure made of material capable of large non-linear deformations. These wall deformations may be elastic, elastic-plastic or visco-elastic. Mathematical analyses of such membrane structures show that there is, generally, a critical internal pressure at which dimensional instability occurs. This instability is characterized by a sudden drop in internal pressure accompanied by a large increase in the physical proportions of the membrane structure. The theory proposes that cell wall extension occurs when the cell turgor pressure reaches this critical instability value. The cell wall thus stretched is fixed by biochemical synthesis of wall material. Osmotic regulation re-establishes the turgor pressure and the instability cycle repeats itself as long as the critical instability pressure of the cell is below the osmotic pressure of the cell contents. Equalization of these pressures stops cell extension. The rate of cell extension depends on the frequency of the instability cycle and is thus dependent on the various rate processes associated with the instability cycle. The theory appears to be able to explain most of the known facts regarding cell extension such as the influence of temperature and the action of some growth substances.     

Biomechanical models of hyphal growth in actinomycetes

The tip growth of filamentary actinomycetes is investigated within the framework of large deformation membrane theory in which the cell wall is represented as a growing elastic membrane with geometry-dependent elastic properties. The model exhibits realistic hyphal shapes and indicates a self-similar tip growth mechanism consistent with that observed in experiments. It also demonstrates a simple mechanism for hyphal swelling and beading that is observed in the presence of a lysing agent.     

Biomechanics of plant growth

Growth of turgid cells, defined as an irreversible increase in cell volume and surface area, can be regarded as a physical process governed by the mechanical properties of the cell wall and the osmotic properties of the protoplast. Irreversible cell expansion is produced by creating a driving force for water uptake by decreasing the turgor through stress relaxation in the cell wall. This mechano-hydraulic process thus depends on and can be controlled by the mechanical properties of the wall, which in turn are subject to modification by wall loosening and wall stiffening reactions. The biochemical mechanisms of these changes in mechanical wall properties and their regulation by internal signals (e.g., hormones) or external signals (e.g., light, drought stress) are at present incompletely understood and subject to intensive research. These signals act on walls that have the properties of composite materials in which the molecular structure and spatial organization of polymers rather than the distribution of mechanical stresses dictate the allometry of cell and organ growth and thus cell and organ shape. The significance of cell wall architecture for allometric growth can be demonstrated by disturbing the oriented deposition of wall polymers with microtubule-interfering drugs such as colchicine. Elongating organs (e.g., cylindrical stems or coleoptiles) composed of different tissues with different mechanical properties exhibit longitudinal tissue tensions resulting in the transfer of wall stress from inner to peripheral cell layers that adopt control over organ growth. For physically analyzing the growth process leading to seed germination, the same mechanical and hydraulic parameters as in normal growth are principally appropriate. However, for covering the influences of the tissues that restrain embryo expansion (seed coat, endosperm), an additional force and a water permeability term must be considered.     

A mechanics model for the compression of plant and vegetative tissues

The mechanics analysis of plant or vegetable tissue under a compressive stress has been developed based on large deformation elasticity theory. The tissue was treated as a lattice of regular perfect three-dimensional hexagonal cells. The cell walls were assumed to be impermeable under the time-scale of the loading. The cell walls of plants and vegetables are polymeric composite materials, consisting of a relatively amorphous matrix and a highly structured network of microfibrils embedded in the cell wall matrix. The micromechanical features of the individual cells have been related to the macroscopic properties of the whole tissue. The effects of microfibrillar stiffening factors k(1) and k(2), the cell wall matrix property alpha and the initial cell expansion ratio nu(i) on the compressive behaviour of a plant or vegetable tissue have been investigated. The predicted results have also been related to some experimental evidence.     

Viscoelastic properties of cell walls of single living plant cells determined by dynamic nanoindentation

Plant development results from controlled cell divisions, structural modifications, and reorganizations of the cell wall. Thereby, regulation of cell wall behaviour takes place at multiple length scales involving compositional and architectural aspects in addition to various developmental and/or environmental factors. The physical properties of the primary wall are largely determined by the nature of the complex polymer network, which exhibits time-dependent behaviour representative of viscoelastic materials. Here, a dynamic nanoindentation technique is used to measure the time-dependent response and the viscoelastic behaviour of the cell wall in single living cells at a micron or sub-micron scale. With this approach, significant changes in storage (stiffness) and loss (loss of energy) moduli are captured among the tested cells. The results reveal hitherto unknown differences in the viscoelastic parameters of the walls of same-age similarly positioned cells of the Arabidopsis ecotypes (Col 0 and Ws 2). The technique is also shown to be sensitive enough to detect changes in cell wall properties in cells deficient in the activity of the chromatin modifier ATX1. Extensive computational modelling of the experimental measurements (i.e. modelling the cell as a viscoelastic pressure vessel) is used to analyse the influence of the wall thickness, as well as the turgor pressure, at the positions of our measurements. By combining the nanoDMA technique with finite element simulations quantifiable measurements of the viscoelastic properties of plant cell walls are achieved. Such techniques are expected to find broader applications in quantifying the influence of genetic, biological, and environmental factors on the nanoscale mechanical properties of the cell wall.     

MECHANICAL BEHAVIOR OF PLANT TISSUES AS INFERRED FROM THE THEORY OF PRESSURIZED CELLULAR SOLIDS

The mechanical behavior of plant tissues and its dependency on tissue geometry and turgor pressure are analytically dealt with in terms of the theory of cellular solids. A cellular solid is any material whose matter is distributed in the form of beamlike struts or complete “cell” walls. Therefore, its relative density is less than one and typically less than 0.3. Relative density is the ratio of the density of the cellular solid to the density of its constitutive (“cell wall”) material. Relative density depends upon cell shape and the density of cell wall material. It largely influences the mechanical behavior of cellular solids. Additional important parameters to mechanical behavior are the elastic modulus of “cell walls” and the magnitude of internal “cell” pressure. Analyses indicate that two “stiffening” agents operate in natural cellular solids (plant tissues): 1) cell wall infrastructure and 2) the hydrostatic influence of the protoplasm within each cellular compartment. The elastic modulus measured from a living tissue sample is the consequence of both agents. Therefore, the mechanical properties of living tissues are dependent upon the magnitude of turgor pressure. High turgor pressure places cell walls into axial tension, reduces the magnitude of cell wall deformations under an applied stress, and hence increases the apparent elastic modulus of the tissue. In the absence of turgid protoplasts or in the case of dead tissues, the cell wall infrastructure will respond as a linear elastic, nonlinear elastic, or “densifying” material (under compression) dependent upon the magnitude of externally applied stress. Accordingly, it is proposed that no single tangent (elastic) modulus from a stress-strain curve of a plant tissue is sufficient to characterize the material properties of a sample. It is also suggested that when a modulus is calculated that it be referred to as the tissue composite modulus to distinguish it from the elastic modulus of a noncellular solid material.     

Estimates of biomechanical forces in Magnaporthe grisea

The mechanical actions of the fungus Magnaporthe grisea raise many intriguing questions concerning the forces involved. These include: (1) the material properties of the appressorial wall; (2) the strength of the adhesive that keeps the appressorium anchored to the rice leaf surface; and (3) the forces involved in the penetration process whereby a peg is driven through the host cell wall. In this paper we give order of magnitude estimates for all three of these quantities. A simple Young-Laplace law type argument is used to show that the appressorial wall elastic modulus is of order 10–100 MPa; and an adaptation of standard adhesion theory indicates a lower bound on the strength of the appressorial adhesive to be of the order 500 J/m². Drawing on ideas from plasticity theory and ballistics, estimates of the penetration force raise interesting questions about experiments performed on the penetration of inert substrates by the fungus.     

The Modification of Cell Wall Properties by Expression of Recombinant Resilin in Transgenic Plants

Plant tissue is composed of many different types of cells. Plant cells required to withstand mechanical pressure, such as vessel elements and fibers, have a secondary cell wall consisting of polysaccharides and lignin, which strengthen the cell wall structure and stabilize the cell shape. Previous attempts to alter the properties of the cell wall have mainly focused on reducing the amount of lignin or altering its structure in order to ease its extraction from raw woody materials for the pulp and paper and biorefinery industries. In this work, we propose the in vivo modification of the cell wall structure and mechanical properties by the introduction of resilin, an elastic protein that is able to crosslink with lignin monomers during cell wall synthesis. The effects of resilin were studied in transgenic eucalyptus plants. The protein was detected within the cell wall and its expression led to an increase in the elastic modulus of transgenic stems. In addition, transgenic stems displayed a higher yield point and toughness, indicating that they were able to absorb more energy before breaking.     

Influence of fermentation medium composition on physicochemical surface properties of Lactobacillus acidophilus

The effect of the simple and complex basic components of a fermentation medium on the surface properties of Lactobacillus acidophilus NCC2628 is studied by physicochemical methods, such as electrophoresis, interfacial adhesion, and X-ray photonelectron spectroscopy, and by transmission electron microscopy. Starting from an optimized complete medium, the effect of carbohydrates, peptones, and yeast extracts on the physicochemical properties of the cell wall is systematically investigated by consecutively omitting one of the principal components from the fermentation medium at the time. The physicochemical properties and structure of the bacterial cell wall remain largely unchanged if the carbohydrate content of the fermentation medium is strongly reduced, although the concentration of surface proteins increases slightly. Both peptone and yeast extract have a considerable influence on the bacterial cell wall, as witnessed by changes in surface charge, hydrophobicity, and the nitrogen-to-carbon ratio. Both zeta potential and the cell wall hydrophobicity show a positive correlation with the nitrogen-to-carbon ratio of the bacterial surfaces, indicative of the important role of surface proteins in the overall surface physical chemistry. The hydrophobicity of the cell wall, which is low for the cultures grown in the complete medium and in the absence of carbohydrates, becomes fairly high for the cultures grown in the medium without peptones and the medium without yeast extract. UV spectrophotometry and sodium dodecyl sulfate-polyacrylamide gel electrophoresis combined with liquid chromatography-tandem mass spectrometry are used to analyze the effect of medium composition on LiCl-extractable cell wall proteins, confirming the major change in protein composition of the cell wall for the culture fermented in the medium without peptones. In particular, it is found that expression of the S-layer protein is dependent on the protein source of the fermentation medium.     

One-dimensional steady continuum model of retraction of pseudopod in leukocytes

A one-dimensional steady state continuum mechanics model of retraction of pseudopod in leukocytes is developed. The retracting pseudopod is assumed to move bodily toward the main cell body, the bulk motion of which can be represented by cytoplasmic flow within a typical stream tube through the leukocyte. The stream tube is approximated by a frictionless tube with prescribed geometry. The passive rheological properties of cytoplasm in the main cell body and in the pseudopod are modeled, respectively, by Maxwell fluid and Hookean solid. The two regions are assumed to be separated by a sharp interface at which actin gel solates and thereby changes its rheological properties as it flows from the pseudopod to the main cell body. The driving mechanism responsible for the active retraction motion is hypothesized to be a spontaneous deformation of the actin gel, analogous but not necessarily equal to the well known actin-myosin interaction. This results in an active contractile stress being developed in the pseudopod as well as in the cell cortex. The transverse traction pulls against the inclined wall of the stream tube and is transduced into an axial stress gradient, which in turn drives the flow. The tension on the tube wall is picked up by the prestressed cortical shell. Governing equations and boundary conditions are derived. A solution is obtained. Sample data are computed. Comparison of the theory with experiments shows that the model is compatible to the observations.     

Mechanical properties of plant cell walls probed by relaxation spectra

Transformants and mutants with altered cell wall composition are expected to display a biomechanical phenotype due to the structural role of the cell wall. It is often quite difficult, however, to distinguish the mechanical behavior of a mutant's or transformant's cell walls from that of the wild type. This may be due to the plant's ability to compensate for the wall modification or because the biophysical method that is often employed, determination of simple elastic modulus and breakstrength, lacks the resolving power necessary for detecting subtle mechanical phenotypes. Here, we apply a method, determination of relaxation spectra, which probes, and can separate, the viscoelastic properties of different cell wall components (i.e. those properties that depend on the elastic behavior of load-bearing wall polymers combined with viscous interactions between them). A computer program, BayesRelax, that deduces relaxation spectra from appropriate rheological measurements is presented and made accessible through a Web interface. BayesRelax models the cell wall as a continuum of relaxing elements, and the ability of the method to resolve small differences in cell wall mechanical properties is demonstrated using tuber tissue from wild-type and transgenic potatoes (Solanum tuberosum) that differ in rhamnogalacturonan I side chain structure.     

Control of Auxin-induced Stem Elongathn by the Epidermis

Segments of the 4th and 5th internodes of light-grown pea seedlings were used for the study of control of stem elongation. With 5th internodes, at low turgor as well as at water saturation auxin primarily appeared to cause a change in cell wall properties of the epidermis but it showed little effect on expansion af the inner tissue. This was confirmed by comparison of expansion between peeled and unpeeled segments, split tests and by measurements of stress-relaxation properties of the epidermal cell wall. Segments with the central part re-moved elongated well in response to auxin, but the isolated epidermis showed neither auxin-induced elongation nor cell wall loosening. A fungal β-1,3-glucanase appeared, at least partly, to have a similar effect as that of auxin on elongation, by changing cell wall properties of the epidermal cell wall. Peeled segments of 4th internodes expanded very little and auxin had little effect on their epidermal cell wall properties.     

Mathematical modelling of the cellular mechanics of plants

The complex mechanical behaviour of plant tissues reflects the complexity of their structure and material properties. Modelling has been widely used in studies of how cell walls, single cells and tissue respond to loading, both externally applied loading and loads on the cell wall resulting from changes in the pressure within fluid-filled cells. This paper reviews what approaches have been taken to modelling and simulation of cell wall, cell and tissue mechanics, and to what extent models have been successful in predicting mechanical behaviour. Advances in understanding of cell wall ultrastructure and the control of cell growth present opportunities for modelling to clarify how growth-related mechanical properties arise from wall polymeric structure and biochemistry.     

Feedback from the wall

The ability of cells to perceive changes in the composition and mechanical properties of their cell wall is crucial for plants to achieve coordinated growth and development. Evidence is accumulating to show that the plant cell wall, like its yeast counterpart, is capable of triggering multiple signalling pathways. The components of the cell wall that are responsible for initiating these signal responses remain unknown; however, recent technological advances in cell wall analysis may now facilitate the identification of these components and accelerate the characterisation of changes that occur in cell wall mutants.