A Mechanical Model to Interpret Cell-Scale Indentation Experiments on Plant Tissues in Terms of Cell Wall Elasticity and Turgor Pressure

Cell wall dynamics: novel tools and research questions

Years ago, a classic textbook would define plant cell walls based on passive features. For instance, a sort of plant exoskeleton of invariable polysaccharide composition, and probably painted in green. However, currently, this view has been expanded to consider plant cell walls as active, heterogeneous, and dynamic structures with a high degree of complexity. However, what do we mean when we refer to a cell wall as a dynamic structure? How can we investigate the different implications of this dynamism? While the first question has been the subject of several recent publications, defining the ideal strategies and tools needed to address the second question has proven to be challenging due to the myriad of techniques available. In this review, we will describe the capacities of several methodologies to study cell wall composition, structure, and other aspects developed or optimized in recent years. Keeping in mind cell wall dynamism and plasticity, the advantages of performing long-term non-invasive live-imaging methods will be emphasized. We specifically focus on techniques developed for Arabidopsis thaliana primary cell walls, but the techniques could be applied to both secondary cell walls and other plant species. We believe this toolset will help researchers in expanding knowledge of these dynamic/evolving structures.

How do cells stiffen?

Cell stiffness is an important characteristic of cells and their response to external stimuli. In this review, we survey methods used to measure cell stiffness, summarize stimuli that alter cell stiffness, and discuss signaling pathways and mechanisms that control cell stiffness. Several pathological states are characterized by changes in cell stiffness, suggesting this property can serve as a potential diagnostic marker or therapeutic target. Therefore, we consider the effect of cell stiffness on signaling and growth processes required for homeostasis and dysfunction in healthy and pathological states. Specifically, the composition and structure of the cell membrane and cytoskeleton are major determinants of cell stiffness, and studies have identified signaling pathways that affect cytoskeletal dynamics both directly and by altered gene expression. We present the results of studies interrogating the effects of biophysical and biochemical stimuli on the cytoskeleton and other cellular components and how these factors determine the stiffness of both individual cells and multicellular structures. Overall, these studies represent an intersection of the fields of polymer physics, protein biochemistry, and mechanics, and identify specific mechanisms involved in mediating cell stiffness that can serve as therapeutic targets.

Non-autonomous stomatal control by pavement cell turgor via the K+ channel subunit AtKC1

Stomata optimize land plants' photosynthetic requirements and limit water vapor loss. So far, all of the molecular and electrical components identified as regulating stomatal aperture are produced, and operate, directly within the guard cells. However, a completely autonomous function of guard cells is inconsistent with anatomical and biophysical observations hinting at mechanical contributions of epidermal origins. Here, potassium (K+) assays, membrane potential measurements, microindentation, and plasmolysis experiments provide evidence that disruption of the Arabidopsis thaliana K+ channel subunit gene AtKC1 reduces pavement cell turgor, due to decreased K+ accumulation, without affecting guard cell turgor. This results in an impaired back pressure of pavement cells onto guard cells, leading to larger stomatal apertures. Poorly rectifying membrane conductances to K+ were consistently observed in pavement cells. This plasmalemma property is likely to play an essential role in K+ shuttling within the epidermis. Functional complementation reveals that restoration of the wild-type stomatal functioning requires the expression of the transgenic AtKC1 at least in the pavement cells and trichomes. Altogether, the data suggest that AtKC1 activity contributes to the building of the back pressure that pavement cells exert onto guard cells by tuning K+ distribution throughout the leaf epidermis.

Protocol for mapping the variability in cell wall mechanical bending behavior in living leaf pavement cells

Mechanical properties, size and geometry of cells, and internal turgor pressure greatly influence cell morphogenesis. Computational models of cell growth require values for wall elastic modulus and turgor pressure, but very few experiments have been designed to validate the results using measurements that deform the entire thickness of the cell wall. New wall material is synthesized at the inner surface of the cell such that full-thickness deformations are needed to quantify relevant changes associated with cell development. Here, we present an integrated, experimental-computational approach to analyze quantitatively the variation of elastic bending behavior in the primary cell wall of living Arabidopsis (Arabidopsis thaliana) pavement cells and to measure turgor pressure within cells under different osmotic conditions. This approach used laser scanning confocal microscopy to measure the 3D geometry of single pavement cells and indentation experiments to probe the local mechanical responses across the periclinal wall. The experimental results were matched iteratively using a finite element model of the experiment to determine the local mechanical properties and turgor pressure. The resulting modulus distribution along the periclinal wall was nonuniform across the leaf cells studied. These results were consistent with the characteristics of plant cell walls which have a heterogeneous organization. The results and model allowed the magnitude and orientation of cell wall stress to be predicted quantitatively. The methods also serve as a reference for future work to analyze the morphogenetic behaviors of plant cells in terms of the heterogeneity and anisotropy of cell walls.

Spherical depth-sensing nanoindentation of human anterior skull base bones: Establishment of a test protocol

The mechanical properties of anterior skull base (ASB) bones are not well understood due to their complex geometry and deep location. However, it is of particular interest for skull base surgeons to appraise the force range they can apply during procedures and know what kind of haptic feedback a simulation device should produce in order to be realistic for trainees. The aim of this study was to establish a measurement protocol to set the level of hydration state, temperature and curve analysis method for spherical depth sensing nanoindentation of ASB bones. A definitive screening design method was used to test the different possible combinations of these factors. Two samples of ASB bones from the heads of two human body donors (two specimens) were selected according to their microstructure as assessed by micro-CT (microtomography): low-porosity (16.87%, sphenoid bone) and high-porosity (79.85%, ethmoid bone). Depth measurement series of 36 nanoindentations (n = 288) were performed on specimen 1 according to the L8 Taguchi orthogonal array to study the effect of temperature (two levels: 20 or 37 °C), hydration state (dry or immerged in physiological saline sodium chloride), and loading curve analysis according to the Hertzian contact theory (fitting at the start or at the end). The mean values of reduced Young's (E*) modulus varied significantly depending on the hydration status and bone microstructure. In order to obtain the physiological properties of ASB bones, we thus propose performing immersion tests. To simplify the experimentation protocol, future experiments must include a room temperature level and a fit of the curve at the end of the load. A validation series was performed on the second specimen to assess the set of parameters. The E* in dry bone gave mean values of 994.68 MPa, versus 409.79 MPa in immerged bones (p < 0.00001). This is the first time a study has been carried out on ASB bones, defining the experimental parameters related to physiological conditions.

Cellular Heterogeneity in Pressure and Growth Emerges from Tissue Topology and Geometry

Cell-to-cell heterogeneity prevails in many systems, as exemplified by cell growth, although the origin and function of such heterogeneity are often unclear. In plants, growth is physically controlled by cell wall mechanics and cell hydrostatic pressure, alias turgor pressure. Whereas cell wall heterogeneity has received extensive attention, the spatial variation of turgor pressure is often overlooked. Here, combining atomic force microscopy and a physical model of pressurized cells, we show that turgor pressure is heterogeneous in the Arabidopsis shoot apical meristem, a population of stem cells that generates all plant aerial organs. In contrast with cell wall mechanical properties that appear to vary stochastically between neighboring cells, turgor pressure anticorrelates with cell size and cell neighbor number (local topology), in agreement with the prediction by our model of tissue expansion, which couples cell wall mechanics and tissue hydraulics. Additionally, our model predicts two types of correlations between pressure and cellular growth rate, where high pressure may lead to faster- or slower-than-average growth, depending on cell wall extensibility, yield threshold, osmotic pressure, and hydraulic conductivity. The meristem exhibits one of these two regimes, depending on conditions, suggesting that, in this tissue, water conductivity may contribute to growth control. Our results unravel cell pressure as a source of patterned heterogeneity and illustrate links between local topology, cell mechanical state, and cell growth, with potential roles in tissue homeostasis.

Nano-indentation reveals a potential role for gradients of cell wall stiffness in directional movement of the resurrection plant Selaginella lepidophylla

As a physical response to water loss during drought, inner Selaginella lepidophylla stems curl into a spiral shape to prevent photoirradiation damage to their photosynthetic surfaces. Curling is reversible and involves hierarchical deformation, making S. lepidophylla an attractive model with which to study water-responsive actuation. Investigation at the organ and tissue level has led to the understanding that the direction and extent of stem curling can be partially attributed to stiffness gradients between adaxial and abaxial stem sides at the nanoscale. Here, we examine cell wall elasticity to understand how it contributes to the overall stem curling. We compare the measured elastic moduli along the stem length and between adaxial and abaxial stem sides using atomic force microscopy nano-indentation testing. We show that changes in cortex secondary cell wall development lead to cell wall stiffness gradients from stem tip to base, and also between adaxial and abaxial stem sides. Changes in cortical cell wall morphology and secondary cell wall composition are suggested to contribute to the observed stiffness gradients.

An Automated Confocal Micro-Extensometer Enables in Vivo Quantification of Mechanical Properties with Cellular Resolution

How complex developmental-genetic networks are translated into organs with specific 3D shapes remains an open question. This question is particularly challenging because the elaboration of specific shapes is in essence a question of mechanics. In plants, this means how the genetic circuitry affects the cell wall. The mechanical properties of the wall and their spatial variation are the key factors controlling morphogenesis in plants. However, these properties are difficult to measure and investigating their relation to genetic regulation is particularly challenging. To measure spatial variation of mechanical properties, one must determine the deformation of a tissue in response to a known force with cellular resolution. Here, we present an automated confocal micro-extensometer (ACME), which greatly expands the scope of existing methods for measuring mechanical properties. Unlike classical extensometers, ACME is mounted on a confocal microscope and uses confocal images to compute the deformation of the tissue directly from biological markers, thus providing 3D cellular scale information and improved accuracy. Additionally, ACME is suitable for measuring the mechanical responses in live tissue. As a proof of concept, we demonstrate that the plant hormone gibberellic acid induces a spatial gradient in mechanical properties along the length of the Arabidopsis thaliana hypocotyl.

Nonlinear compliance of elastic layers to indentation

Thin samples adherent to a rigid substrate are considerably less compliant to indentation when compared to specimens that are not geometrically confined. Analytical corrections to this so-called substrate effect exist for various types of indenters but are not applicable when large deformations are possible, as is the case in biological materials. To overcome this limitation, we construct a nonlinear scaling model characterized by one single exponent, which we explore employing a parametric finite element analysis. The model is based on asymptotes of two length scales in relation to the sample thickness, i.e., indentation depth and radius of the contact area. For small indentation depth, we require agreement with analytical, linear models, whereas for large indentation depth and extensive contact area, we recognize similarity to uniaxial deformation, indicating a divergent force required to indent nonlinear materials. In contrast, we find linear materials not to be influenced by the substrate effect beyond first order, implying that nonlinear effects originating from either the material or geometric confinement are clearly separated only in thin samples. Furthermore, in this regime the scaling model can be derived by following a heuristic argument extending a linear model to large indentation depths. Lastly, in a large indentation setting where the contact is small in comparison with sample thickness, we observe nonlinear effects independent of material type that we attribute to a higher-order influence of geometrical confinement. In this regime, we define a scalar as the ratio of strains along principal axes as obtained by comparison with the case of a point force on a half-space. We find this scalar to be in quantitative agreement with the scaling exponent, indicating an approach to distinguish between nonlinear effects in the scaling model. While we conjecture our findings to be applicable to other flat-ended indenters, we focus on the case of a flat-ended cylinder in normal contact with a thin layer. The analytical solution for small indentation associated with this problem has been given by Hayes et al. (J Biomech 5:541-551, 1972), for which we provide a convenient numerical implementation.