Dynamic Relation between Expansion and Cellular Turgor in Growing Grape (Vitis vinifera L.) Leaves

Measurements of the growth and water relations of expanding grape (Vitis vinifera L.) leaves have been used to determine the relationship between leaf expansion rate and leaf cell turgor. Direct measurement of turgor on the small (approximately 15 micrometer diameter) epidermal cells over the midvein of expanding grape leaves was made possible by improvements in the pressure probe technique. Leaf expansion rate and leaf water status were perturbed by environmentally induced changes in plant transpiration. After establishing a steady state growth rate, a step decrease in plant transpiration resulted in a rapid and large increase in leaf cell turgor (0.25 megapascal in 5 minutes), and leaf expansion rate. Subsequently, leaf expansion rate returned to the original steady state rate with no change in cell turgor. These results indicate that the expansion rate of leaves may not be strongly related to the turgor of the leaf cells, and that substantial control of leaf expansion rate, despite changes in turgor, may be part of normal plant function. It is suggested that a strictly physical interpretation of the parameters most commonly used to describe the relationship between turgor and growth in plant cells (cell wall extensibility and yield threshold) may be inappropriate when considering the process of plant cell expansion.     

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.     

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.     

Regulator or Driving Force? The Role of Turgor Pressure in Oscillatory Plant Cell Growth

Turgor generates the stress that leads to the expansion of plant cell walls during cellular growth. This has been formalized by the Lockhart equation, which can be derived from the physical laws of the deformation of viscoelastic materials. However, the experimental evidence for such a direct correlation between growth rate and turgor is inconclusive. This has led to challenges of the Lockhart model. We model the oscillatory growth of pollen tubes to investigate this relationship. We couple the Lockhart equation to the dynamical equations for the change in material properties. We find that the correct implementation of the Lockhart equation within a feedback loop leading to low amplitude oscillatory growth predicts that in this system changes in the global turgor do not influence the average growth rate in a linear manner, consistent with experimental observations. An analytic analysis of our model demonstrates in which regime the average growth rate becomes uncorrelated from the turgor pressure.     

Cell expansion-mediated organ growth is affected by mutations in three EXIGUA genes

Organ growth depends on two distinct, yet integrated, processes: cell proliferation and post-mitotic cell expansion. Although the regulatory networks of plant cell proliferation during organ growth have begun to be unveiled, the mechanisms regulating post-mitotic cell growth remain mostly unknown. Here, we report the characterization of three EXIGUA (EXI) genes that encode different subunits of the cellulose synthase complex specifically required for secondary cell wall formation. Despite this highly specific role of EXI genes, all the cells within the leaf, even those that do not have secondary walls, display small sizes in the exi mutants. In addition, we found a positive correlation between cell size and the DNA ploidy levels in exi mutant leaves, suggesting that both processes share some regulatory components. Our results are consistent with the hypothesis that the collapsed xylem vessels of the exi mutants hamper water transport throughout the plant, which, in turn, limits the turgor pressure levels required for normal post-mitotic cell expansion during leaf growth.     

Analysis of the dynamic and steady-state responses of growth rate and turgor pressure to changes in cell parameters

The physical analysis of plant cell enlargment is extended to show the dependence of turgor pressure and growth rate under steady-state conditions on the parameters which govern cell wall extension and water transport in growing cells and tissues, and to show the dynamic responses of turgor and growth rate to instantaneous changes in one of these parameters. The analysis is based on the fact that growth requires simultaneous water uptake and irreversible wall expansion. It shows that when a growing cell is perturbed from its steady-state growth rate, it will approach the steady-state rate with exponential kinetics. The half-time of the transient adjustment depends on the biophysical parameters governing both water transport and irreversible wall expansion. When wall extensibility is small compared to hydraulic conductance, the growth rate is controlled by the yielding properties of the cell wall, while the half-time for changes in growth rate is controlled by the water transport parameters. The reverse situation occurs when hydraulic conductance is lower than wall extensibility. The analysis also shows explicitly that turgor pressure is tightly coupled with growth rate when growth is controlled by both water transport and wall yielding parameters.     

Disentangling the link between leaf photosynthesis and turgor in fruit growth

Despite the importance of understanding plant growth, the mechanisms underlying how plant and fruit growth declines during drought remain poorly understood. Specifically, it remains unresolved whether carbon or water factors are responsible for limiting growth as drought progresses. We examine questions regarding the relative importance of water and carbon to fruit growth depending on the water deficit level and the fruit growth stage by measuring fruit diameter, leaf photosynthesis, and a proxy of cell turgor in olive (Olea europaea). Flow cytometry was also applied to determine the fruit cell division stage. We found that photosynthesis and turgor were related to fruit growth; specifically, the relative importance of photosynthesis was higher during periods of more intense cell division, while turgor had higher relative importance in periods where cell division comes close to ceasing and fruit growth is dependent mainly on cell expansion. This pattern was found regardless of the water deficit level, although turgor and growth ceased at more similar values of leaf water potential than photosynthesis. Cell division occurred even when fruit growth seemed to stop under water deficit conditions, which likely helped fruits to grow disproportionately when trees were hydrated again, compensating for periods with low turgor. As a result, the final fruit size was not severely penalized. We conclude that carbon and water processes are able to explain fruit growth, with importance placed on the combination of cell division and expansion. However, the major limitation to growth is turgor, which adds evidence to the sink limitation hypothesis.     

How to shape a cylinder: pollen tube as a model system for the generation of complex cellular geometry

Expansive growth in plant cells is a formidable problem for biophysical studies, and the mechanical principles governing the generation of complex cellular geometries are still poorly understood. Pollen, the male gametophyte stage of the flowering plants, is an excellent model system for the investigation of the mechanics of complex growth processes. The initiation of pollen tube growth requires first of all, the spatially confined formation of a protuberance. This process must be controlled by the mechanical properties of the cell wall, since turgor is a non-vectorial force. In the elongating tube, cell wall expansion is confined to the apex of the cell, requiring the tubular region to be stabilized against turgor-induced tensile stress. Tip focused surface expansion must be coordinated with the supply of cell wall material to this region requiring the precise, logistical control of intracellular transport processes. The advantage of such a demanding mechanism is the high efficiency it confers on the pollen tube in leading an invasive way of life.     

Actin filaments and microtubules of Arabidopsis suspension cells show different responses to changing turgor pressure

Past decades have brought great advances in understanding the relationship between turgor pressure and plant cell growth. New studies have provided evidence that turgor pressure acts as a stimulus for cell growth, and is also a developmental cue for post-embryonic organogenesis. However, the subcellular mechanisms underlying plant cell turgor pressure sensing remain unclear. Here, using the relatively simple undifferentiated cells from suspension cultures, we report real-time in vivo observations of the reorganization of microtubules and actin microfilaments induced by turgor pressure changes. We found that these two cytoskeletal elements differed in their reorganization patterns. Our results will be useful in the understanding of the relationship between the cytoskeleton, turgor pressure, and stress in plant cell morphogenesis.     

Plant Cell Growth in Tissue

Cell walls are part of the apoplasm pathway that transports water, solutes, and nutrients to cells within plant tissue. Pressures within the apoplasm (cell walls and xylem) are often different from atmospheric pressure during expansive growth of plant cells in tissue. The previously established Augmented Growth Equations are modified to evaluate the turgor pressure, water uptake, and expansive growth of plant cells in tissue when pressures within the apoplasm are lower and higher than atmospheric pressure. Analyses indicate that a step-down and step-up in pressure within the apoplasm will cause an exponential decrease and increase in turgor pressure, respectively, and the rates of water uptake and expansive growth each undergo a rapid decrease and increase, respectively, followed by an exponential return to their initial magnitude. Other analyses indicate that pressure within the apoplasm decreases exponentially to a lower value after a step-down in turgor pressure, which simulates its behavior after an increase in expansive growth rate. Also, analyses indicate that the turgor pressure decays exponentially to a constant value that is the sum of the critical turgor pressure and pressure within the apoplasm during stress relaxation experiments in which pressures within the apoplasm are not atmospheric pressure. Additional analyses indicate that when the turgor pressure is constant (clamped), a decrease in pressure within the apoplasm elicits an increase in elastic expansion followed by an increase in irreversible expansion rate. Some analytical results are supported by prior experimental research, and other analytical results can be verified with existing experimental methods.Cell walls perform many functions for plant, algal, and fungal cells. Physical and chemical protection from the environment and physical support for cells and organs are obvious functions. Cell walls also withstand the stresses imposed by turgor pressure and deform irreversibly and reversible (elastically) during expansive growth. Irreversible wall deformations during expansive growth control cell enlargement, size, and shape. Growing and mature (nongrowing) cell walls undergo elastic deformations after changes in turgor pressure caused by changes in water status and environmental conditions. Elastic wall deformations are fundamental to the water relations of plant, algal, and fungal cells. For plant cells in tissues and organs, cell walls are part of the apoplasm pathway that transports water, solutes, and nutrients to cells.Importantly, pressures within the apoplasm (cell walls and xylem) are frequently different from atmospheric pressure during expansive growth of plant cells in tissues and organs. Lower pressures (tensions) are related to transpiration rates from plant organs and to expansive growth of cells in plant organs, e.g. Boyer (1967, 2001), Molz and Boyer (1978), Nonami and Boyer (1987, 1993), Nonami and Hashimoto (1996), Passioura and Boyer (2003), Boyer and Silk (2004), Koch et al. (2004), Wiegers et al. (2009), and the references within. Higher pressures (root pressures) occur during the spring when the soil is well hydrated (e.g. Kramer, 1932). Bleeding sap from cuts and broken stems is evidence of root pressure. Also, higher pressures may occur diurnally, during the night when transpiration rates are low (e.g. Tang and Boyer, 2008). Guttation drops on leaves in the morning are evidence of these higher pressures.Prior research indicates that a significant amount of chemistry and molecular biology occur within cell walls undergoing irreversible deformation during expansive growth (e.g. Cosgrove, 2005; Boyer, 2009). Two questions arise. First, how do pressures within the wall that are different from atmospheric pressure affect the turgor pressure, water uptake, and growth rate of cells in plant organs such as roots, stems, and leaves? Second, how are relevant chemical reactions affected by lower and higher pressures within the wall? The analyses conducted in this article focus on the first question.Previously, equations derived by Lockhart (1965) for wall deformation and water uptake (Growth Equations) were augmented with terms for elastic wall deformation (Ortega, 1985) and transpiration (Ortega et al., 1988). In this article, the previously established Augmented Growth Equations (Ortega, 1985, 1990, 1994, 2004; Ortega et al., 1988; Geitmann and Ortega, 2009) are modified to evaluate the turgor pressure, water uptake, and expansive growth of plant cells in tissue when pressures within the apoplasm are lower and higher than atmospheric pressure. In addition, the pressure within the apoplasm is evaluated after turgor pressure in cells decrease, thus simulating the condition produced by an increase in expansive growth rate of cells in plant tissues and organs. Also, the modified equations are used to determine how the results of stress relaxation experiments conducted on growing plant organs are affected by pressures within the apoplasm that are not atmospheric pressure. Last, the expansive growth of a plant cell is evaluated when pressure within the apoplasm undergoes a semi-instantaneous change while the turgor pressure remains constant, i.e. clamped. Some analytical results are supported by prior experimental research, and some analytical results can be verified with existing experimental methods.     

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.     

Water relations and growth of tomato fruit pericarp tissue

The water relations of young tomato fruit pericarp tissue were examined and related to tissue expansion. The relationship between bulk turgor pressure and tissue expansion (as change in fresh mass or length of tissue) was determined in slices of pericarp cut from young, growing fruit by incubation in different osmotic concentrations of polyethylene glycol 6000 or mannitol. The bulk turgor of this tissue was low (about 0.2 MPa), even in fruit from plants that were otherwise fully turgid, whether measured psychrometrically or by length change in osmotic solutions. The rate of tissue growth at maximum turgor was less than that at moderate turgor unless calcium was added to the incubation medium. However, added calcium also decreased the rate of growth at lower turgor pressures. Yield turgor was < 0.1 MPa, but it was increased by the addition of calcium ions. Electrolyte leakage from tissue was greatest at maximum turgor pressure but was decreased by the addition of calcium ions or osmoticum. Tissue growth was unaffected by a range of plant growth regulators (IAA, abscisic acid, benzyladenine and GA₃) but was inhibited, particularly at high turgor, by low concentrations of malic or citric acid. The low turgor pressure of pericarp tissue could be due to the presence of apoplastic solutes within the pericarp, and evidence for this is discussed. Thus, fruit tissue may be able to maintain optimal expansion rates only at moderate turgor and low calcium concentration.     

Adaptation of Tobacco Cells to NaCl

Cell lines of tobacco (Nicotiana tabacum L. var Wisconsin 38) were obtained which are adapted to grow in media with varying concentrations of NaCl, up to 35 grams per liter (599 millimolar). Salt-adapted cells exhibited enhanced abilities to gain both fresh and dry weight in the presence of NaCl compared to cells which were growing in medium without NaCl (unadapted cells). Tolerance of unadapted cells and cells adapted to 10 grams per liter NaCl was influenced by the stage of growth, with the highest degree of tolerance exhibited by cells in the exponential phase. Cell osmotic potential and turgor varied through the growth cycle of unadapted cells and cells at all levels of adaptation, with maximum turgor occurring at approximately the onset of exponential fresh weight accumulation.

Adaptation to NaCl led to reduced cell expansion and fresh weight gain, while dry weight gain remained unaffected. This reduction in cell expansion was not due to failure of the cells to maintain turgor since cells adapted to NaCl underwent osmotic adjustment in excess of the change in water potential caused by the addition of NaCl to the medium. Tolerance of the adapted cells, as indicated by fresh or dry weight gain, did not increase proportionately with the increase in turgor. Adaptation of these glycophytic cells to NaCl appears to involve mechanisms which result in an altered relationship between turgor and cell expansion.

     

Channelling auxin action: modulation of ion transport by indole-3-acetic acid

The growth hormone auxin is a key regulator of plant cell division and elongation. Since plants lack muscles, processes involved in growth and movements rely on turgor formation, and thus on the transport of solutes and water. Modern electrophysiological techniques and molecular genetics have shed new light on the regulation of plant ion transporters in response to auxin. Guard cells, hypocotyls and coleoptiles have advanced to major model systems in studying auxin action. This review will therefore focus on the molecular mechanism by which auxin modulates ion transport and cell expansion in these model cell types.     

Acid-induced wall loosening is confined to the accelerating region of the root growing zone

The aims of this study were to quantify developmental differences in acid growth along the root axis and to determine whether these differences were due to alterations in cell turgor or cell wall properties. The apoplast pH of maize roots growing in hydroponics was altered from pH 7.0 to pH 3.4 using 2 mol m^-3 citrate-phosphate buffer or unbuffered solutions. Whole root elongation rate rapidly increased and measurement of the local growth profile indicated that this increase in growth occurred in young cells in the accelerating zone (apical 0-4 mm) while more proximal growing cells were unaffected. Unbuffered solutions of identical pH produced qualitatively similar results. Single cell turgor pressures were unchanged between pH treatments both longitudinally and radially in the root tip. This suggests that the rapid acid-induced changes in growth rate were due to an increase in cell wall loosening. Single cell osmotic pressure and water potential were not significantly different between pH treatments. Acid pH caused net solute import at the root tip to increase 3- to 4-fold, which, coupled with the maintenance of turgor and osmotic pressure, indicated that solute import was not limiting expansion. Thus, acidic solutions cause an increase in growth in accelerating but not decelerating regions. It has been shown for the first time that acid growth in intact, growing roots is not due to differences in turgor, assigning these changes to cell wall properties. Possible cell wall biochemical alterations are discussed.     

Growth Physics in Nitella: a Method for Continuous in Vivo Analysis of Extensibility Based on a Micro-manometer Technique for Turgor Pressure

The view that the plant cell grows by the yielding of the cell wall to turgor pressure can be expressed in the equation: rate = cell extensibility × turgor. All growth rate responses can in principle be resolved into changes in the 2 latter variables. Extensibility will relate primarily to the yielding properties of the cell wall, turgor primarily to solute uptake or production. Use of this simple relationship in vivo requires that at least 2 of the 3 variables be measured in a growing cell. Extensibility is not amenable to direct measurement. Data on rate and turgor for single Nitella cells can, however, be continuously gathered to permit calculation of extensibility (rate/turgor). Rate is accurately obtained from measurements on time-lapse film. Turgor is estimated in the same cell, to within 0.1 atm or less, by measurement of the ability of the cell to compress gas trapped in the closed end of a capillary the open end of which is in the cell vacuole. The method is independent of osmotic equilibrium. It operates continuously for several days, over a several fold increase in cell length, and has response time of less than one minute. Rapid changes in turgor brought on by changes in tonicity of the medium, show that extensibility, as defined above, is not constant but has a value of zero unless the cell has about 80% of normal turgor. Because elastic changes are small, extensibility relates to growth. Over long periods of treatment in a variety of osmotica the threshold value for extensibility and growth is seen to fall to lower values to permit resumption of growth at reduced turgor. A brief period of rapid growth (5× normal) follows the return to normal turgor. All variables then become normal and the cycle can be repeated. The cell remains essentially at osmotic equilibrium, even while growing at 5× the normal rate. The method has potential for detailed in vivo analyses of “wall softening.”     

The role of pectin in plant morphogenesis

The presence of a polysaccharidic cell wall distinguishes plant cells from animal cells and is responsible for fundamental mechanistic differences in organ development between the two kingdoms. Due to the presence of this wall, plant cells are unable to crawl and contract. On the other hand, plant cell size can increase by several orders of magnitude and cell shape can change from a simple polyhedron or cube to extremely intricate. This expansive cellular growth is regulated by the interaction between the cell wall and the intracellular turgor pressure. One of the principal cell wall components involved in temporal and spatial regulation of the growth process is pectin. Through biochemical changes to pectin composition and biochemical configuration, the properties of this material can be altered to trigger specific developmental processes. Here, the roles of pectin in three systems displaying rapid growth - the elongation zone of the root, the tip region of the pollen tube, and organ primordia formation at the shoot apical meristem - are reviewed.     

A plant cell division algorithm based on cell biomechanics and ellipse-fitting

Background and Aims

The importance of cell division models in cellular pattern studies has been acknowledged since the 19th century. Most of the available models developed to date are limited to symmetric cell division with isotropic growth. Often, the actual growth of the cell wall is either not considered or is updated intermittently on a separate time scale to the mechanics. This study presents a generic algorithm that accounts for both symmetrically and asymmetrically dividing cells with isotropic and anisotropic growth. Actual growth of the cell wall is simulated simultaneously with the mechanics.

Methods

The cell is considered as a closed, thin-walled structure, maintained in tension by turgor pressure. The cell walls are represented as linear elastic elements that obey Hooke''s law. Cell expansion is induced by turgor pressure acting on the yielding cell-wall material. A system of differential equations for the positions and velocities of the cell vertices as well as for the actual growth of the cell wall is established. Readiness to divide is determined based on cell size. An ellipse-fitting algorithm is used to determine the position and orientation of the dividing wall. The cell vertices, walls and cell connectivity are then updated and cell expansion resumes. Comparisons are made with experimental data from the literature.

Key Results

The generic plant cell division algorithm has been implemented successfully. It can handle both symmetrically and asymmetrically dividing cells coupled with isotropic and anisotropic growth modes. Development of the algorithm highlighted the importance of ellipse-fitting to produce randomness (biological variability) even in symmetrically dividing cells. Unlike previous models, a differential equation is formulated for the resting length of the cell wall to simulate actual biological growth and is solved simultaneously with the position and velocity of the vertices.

Conclusions

The algorithm presented can produce different tissues varying in topological and geometrical properties. This flexibility to produce different tissue types gives the model great potential for use in investigations of plant cell division and growth in silico.     

Not-so-tip-growth

In tip-growing plant cells such as pollen tubes and root hairs, surface expansion is confined to the cell apex. Vesicles containing pectic cell wall material are delivered to this apical region to provide the material necessarily to build the expanding cell wall. Quantification of wall expansion reveals that the surface expansion rates are not highest at the pole but instead in an annular region around the pole. These findings raise the question of the precise localization of exocytosis events in these cells. Recently, we used spatio-temporal image correlation spectroscopy (STICS) in combination with high temporal resolution confocal imaging to characterize the intracellular movement of vesicles in growing pollen tubes. These observations, together with the analysis of FRAP (fluorescence recovery after photobleaching) experiments, indicate that exocytosis is likely to occur predominantly in the same annular region where wall expansion rates are greatest. Therefore, tip growth in plant cells does not seem to happen exactly at the tip.Key words: tip growth, pollen tube, exocytosis, cell wall, expansion, root hair, plant cell growth, allometric growth, cytomechanics, cell mechanics, vesicle transport     

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.