In vivo extraction of Arabidopsis cell turgor pressure using nanoindentation in conjunction with finite element modeling

Turgor pressure in plant cells is involved in many important processes. Stable and normal turgor pressure is required for healthy growth of a plant, and changes in turgor pressure are indicative of changes taking place within the plant tissue. The ability to quantify the turgor pressure of plant cells in vivo would provide opportunities to understand better the process of pressure regulation within plants, especially when plant stress is considered, and to understand the role of turgor pressure in cellular signaling. Current experimental methods do not separate the influence of the turgor pressure from the effects associated with deformation of the cell wall when estimates of turgor pressure are made. In this paper, nanoindentation measurements are combined with finite element simulations to determine the turgor pressure of cells in vivo while explicitly separating the cell‐wall properties from the turgor pressure effects. Quasi‐static cyclic tests with variable depth form the basis of the measurements, while relaxation tests at low depth are used to determine the viscoelastic material properties of the cell wall. Turgor pressure is quantified using measurements on Arabidopsis thaliana under three pressure states (control, turgid and plasmolyzed) and at various stages of plant development. These measurements are performed on cells in vivo without causing damage to the cells, such that pressure changes may be studied for a variety of conditions to provide new insights into the biological response to plant stress conditions.     

Single Cell Wall Nonlinear Mechanics Revealed by a Multiscale Analysis of AFM Force-Indentation Curves

Individual plant cells are rather complex mechanical objects. Despite the fact that their wall mechanical strength may be weakened by comparison with their original tissue template, they nevertheless retain some generic properties of the mother tissue, namely the viscoelasticity and the shape of their walls, which are driven by their internal hydrostatic turgor pressure. This viscoelastic behavior, which affects the power-law response of these cells when indented by an atomic force cantilever with a pyramidal tip, is also very sensitive to the culture media. To our knowledge, we develop here an original analyzing method, based on a multiscale decomposition of force-indentation curves, that reveals and quantifies for the first time the nonlinearity of the mechanical response of living single plant cells upon mechanical deformation. Further comparing the nonlinear strain responses of these isolated cells in three different media, we reveal an alteration of their linear bending elastic regime in both hyper- and hypotonic conditions.     

An anisotropic-viscoplastic model of plant cell morphogenesis by tip growth

Plant cell morphogenesis depends critically on two processes: the deposition of new wall material at the cell surface and the mechanical deformation of this material by the stresses resulting from the cell's turgor pressure. We developed a model of plant cell morphogenesis that is a first attempt at integrating these two processes. The model is based on the theories of thin shells and anisotropic viscoplasticity. It includes three sets of equations that give the connection between wall stresses, wall strains and cell geometry. We present an algorithm to solve these equations numerically. Application of this simulation approach to the morphogenesis of tip-growing cells illustrates how the viscoplastic properties of the cell wall affect the shape of the cell at steady state. The same simulation approach was also used to reproduce morphogenetic transients such as the initiation of tip growth and other non-steady changes in cell shape. Finally, we show that the mechanical anisotropy built into the model is required to account for observed patterns of wall expansion in plant cells.     

The pollen tube: a soft shell with a hard core

Plant cell expansion is controlled by a fine‐tuned balance between intracellular turgor pressure, cell wall loosening and cell wall biosynthesis. To understand these processes, it is important to gain in‐depth knowledge of cell wall mechanics. Pollen tubes are tip‐growing cells that provide an ideal system to study mechanical properties at the single cell level. With the available approaches it was not easy to measure important mechanical parameters of pollen tubes, such as the elasticity of the cell wall. We used a cellular force microscope (CFM) to measure the apparent stiffness of lily pollen tubes. In combination with a mechanical model based on the finite element method (FEM), this allowed us to calculate turgor pressure and cell wall elasticity, which we found to be around 0.3 MPa and 20–90 MPa, respectively. Furthermore, and in contrast to previous reports, we showed that the difference in stiffness between the pollen tube tip and the shank can be explained solely by the geometry of the pollen tube. CFM, in combination with an FEM‐based model, provides a powerful method to evaluate important mechanical parameters of single, growing cells. Our findings indicate that the cell wall of growing pollen tubes has mechanical properties similar to rubber. This suggests that a fully turgid pollen tube is a relatively stiff, yet flexible cell that can react very quickly to obstacles or attractants by adjusting the direction of growth on its way through the female transmitting tissue.     

Polar growth in pollen tubes is associated with spatially confined dynamic changes in cell mechanical properties

Cellular morphogenesis involves changes to cellular size and shape which in the case of walled cells implies the mechanical deformation of the extracellular matrix. So far, technical challenges have made quantitative mechanical measurements of this process at subcellular scale impossible. We used micro-indentation to investigate the dynamic changes in the cellular mechanical properties during the onset of spatially confined growth activities in plant cells. Pollen tubes are cellular protuberances that have a strictly unidirectional growth pattern. Micro-indentation of these cells revealed that the initial formation of a cylindrical protuberance is preceded by a local reduction in cellular stiffness. Similar cellular softening was observed before the onset of a rapid growth phase in cells with oscillating growth pattern. These findings provide the first quantitative cytomechanical data that confirm the important role of the mechanical properties of the cell wall for local cellular growth processes. They are consistent with a conceptual model that explains pollen tube oscillatory growth based on the relationship between turgor pressure and tensile resistance in the apical cell wall. To further confirm the significance of cell mechanics, we artificially manipulated the mechanical cell wall properties as well as the turgor pressure. We observed that these changes affected the oscillation profile and were able to induce oscillatory behavior in steadily growing tubes.     

Turgor pressure, membrane tension and the control of exocytosis in higher plants

Both turgor pressure and differences in membrane tension are capable of providing an energy input into exocytosis, the process of fusion of Golgi vesicles with the cell membrane in plants. It is shown that the contribution of turgor pressure is much larger than that of membrane tension, so that the exocytotic process is not likely on thermodynamic grounds to be reversible unless another source of energy is made available. However, recycling of membrane material as flattened, empty vesicles is energetically possible and is likely to be favoured when the magnitude of membrane tension in the cell membrane is low. Thus the outward flows of membrane and cell wall material are in principle linked to turgor, whereas membrane tension influences the inward flow of membrane material.     

More than a leak sealant. The mechanical properties of callose in pollen tubes

While callose is a well-known permeability barrier and leak sealant in plant cells, it is largely unknown whether this cell wall polymer can also serve as a load-bearing structure. Since callose occurs in exceptionally large amounts in pollen, we assessed its role for resisting tension and compression stress in this cell. The effect of callose digestion in Solanum chacoense and Lilium orientalis pollen grains demonstrated that, depending on the species, this cell wall polymer represents a major stress-bearing structure at the aperture area of germinating grains. In the pollen tube, it is involved in cell wall resistance to circumferential tension stress, and despite its absence at the growing apex, callose is indirectly involved in the establishment of tension stress resistance in this area. To investigate whether or not callose is able to provide mechanical resistance against compression stress, we subjected pollen tubes to local deformation by microindentation. The data revealed that lowering the amount of callose resulted in reduced cellular stiffness and increased viscoelasticity, thus indicating clearly that callose is able to resist compression stress. Whether this function is relevant for pollen tube mechanics, however, is unclear, as stiffened growth medium caused a decrease in callose deposition. Together, our data provide clear evidence for the capacity of cell wall callose to resist tension and compression stress, thus demonstrating that this amorphous cell wall substance can have a mechanical role in growing plant cells.     

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.     

Tissue stresses in growing plant organs

Rapidly growing plant organs (e.g. coleopties, hypocotyls, or internodes) are composed of tissues that differ with respect to the thickness, structure, and extensibility of their cell walls. The thick, relatively inextensible outer wall of the epidermal cells contains both transverse and longitudinally oriented cellulose-microfibrils. The orientation of microfibrils of the thin, extensible walls of the parenchyma cells seems to be predominantly transverse. In many growing organs (i.e. leafstalks), the outer epidermal wall is supported by a thickened inner epidermal wall and by thick-walled subepidermal collenchyma tissue. Owing to the turgor pressure of the cells the peripheral walls are under tension, while the extensible inner tissue is under compression. As a corollary, the longitudinal tensile stress of the rigid peripheral wall is high whereas that of the internal walls is lowered. The physical stress between the tissues has been described by Sachs in 1865 as 'tissue tension'. The term 'tissue stress'. however, seems to be more appropriate since it comprises both tension and compression. Hitherto no method has been developed to measure tissue stresses directly as force per unit cross-sectional area. One can demonstrate the existence of tissue stresses by separation of the tissues (splitting, peeling) and determining the resulting strain of the isolated organ fragments. Based on such experiments it has been shown that rapid growth is always accompanied by the existence of longitudinal tissue stresses.