Elastic shell theory for plant cell wall stiffness reveals contributions of cell wall elasticity and turgor pressure in AFM measurement

Nanoparticles and plants: A focus on analytical characterization techniques

Nanotechnology has brought about significant progress through the use of goods based on nanomaterials. However, concerns remain about the accumulation of these materials in the environment and their potential toxicity to living organisms. Plants have the ability to take in nanomaterials (NMs), which can cause changes in their physiology and morphology. On the other hand, nanoparticles (NPs) have been used to increase plant development and control pests in agriculture by including them into agrochemicals. The challenges of the interaction, internalization, and accumulation of NMs within plant tissues are enormous, mainly because of the various characteristics of NMs and the absence of reliable analytical tools. As our knowledge of the interactions between NMs and plant cells expands, we are able to create novel NMs that are tailored, targeted, and designed to be safe, thus minimizing the environmental consequences of nanomaterials. This review provides a thorough examination and comparison of the main microscopy techniques, spectroscopic methods, and far-field super-resolution methodologies used to examine nanomaterials within the cell walls of plants.

Size Matters: Rethinking Hertz Model Interpretation for Cell Mechanics Using AFM

Cell mechanics are a biophysical indicator of cell state, such as cancer metastasis, leukocyte activation, and cell cycle progression. Atomic force microscopy (AFM) is a widely used technique to measure cell mechanics, where the Young modulus of a cell is usually derived from the Hertz contact model. However, the Hertz model assumes that the cell is an elastic, isotropic, and homogeneous material and that the indentation is small compared to the cell size. These assumptions neglect the effects of the cytoskeleton, cell size and shape, and cell environment on cell deformation. In this study, we investigated the influence of cell size on the estimated Young's modulus using liposomes as cell models. Liposomes were prepared with different sizes and filled with phosphate buffered saline (PBS) or hyaluronic acid (HA) to mimic the cytoplasm. AFM was used to obtain the force indentation curves and fit them to the Hertz model. We found that the larger the liposome, the lower the estimated Young's modulus for both PBS-filled and HA-filled liposomes. This suggests that the Young modulus obtained from the Hertz model is not only a property of the cell material but also depends on the cell dimensions. Therefore, when comparing or interpreting cell mechanics using the Hertz model, it is essential to account for cell size.

Two-layer elastic models for single-yeast compressibility with flat microlevers

Unicellular organisms such as yeast can survive in very different environments, thanks to a polysaccharide wall that reinforces their extracellular membrane. This wall is not a static structure, as it is expected to be dynamically remodeled according to growth stage, division cycle, environmental osmotic pressure and ageing. It is therefore of great interest to study the mechanics of these organisms, but they are more difficult to study than other mammalian cells, in particular because of their small size (radius of a few microns) and their lack of an adhesion machinery. Using flat cantilevers, we perform compression experiments on single yeast cells (S. cerevisiae) on poly-L-lysine-coated grooved glass plates, in the limit of small deformation using an atomic force microscope (AFM). Thanks to a careful decomposition of force-displacement curves, we extract local scaling exponents that highlight the non-stationary characteristic of the yeast behavior upon compression. Our multi-scale nonlinear analysis of the AFM force-displacement curves provides evidence for non-stationary scaling laws. We propose to model these phenomena based on a two-component elastic system, where each layer follows a different scaling law..

Quantifying turgor pressure in budding and fission yeasts based upon osmotic properties

Walled cells, such as plants, fungi, and bacteria cells, possess a high internal hydrostatic pressure, termed turgor pressure, that drives volume growth and contributes to cell shape determination. Rigorous measurement of turgor pressure, however, remains challenging, and reliable quantitative measurements, even in budding yeast are still lacking. Here, we present a simple and robust experimental approach to access turgor pressure in yeasts based upon the determination of isotonic concentration using protoplasts as osmometers. We propose three methods to identify the isotonic condition - three-dimensional cell volume, cytoplasmic fluorophore intensity, and mobility of a cytGEMs nano-rheology probe - that all yield consistent values. Our results provide turgor pressure estimates of 1.0 ± 0.1 MPa for Schizosaccharomyces pombe, 0.49 ± 0.01 MPa for Schizosaccharomyces japonicus, 0.5 ± 0.1 MPa for Saccharomyces cerevisiae W303a and 0.31 ± 0.03 MPa for Saccharomyces cerevisiae BY4741. Large differences in turgor pressure and nano-rheology measurements between the Saccharomyces cerevisiae strains demonstrate how fundamental biophysical parameters can vary even among wild-type strains of the same species. These side-by-side measurements of turgor pressure in multiple yeast species provide critical values for quantitative studies on cellular mechanics and comparative evolution.

Mechanics-based classification rule for plants

The height of thick and solid plants, such as woody plants, is proportional to two-thirds of the power of their diameter at breast height. However, this rule cannot be applied to herbaceous plants that are thin and soft because the mechanisms supporting their bodies are fundamentally different. This study aims to clarify the rigidity control mechanism resulting from turgor pressure caused by internal water in herbaceous plants to formulate the corresponding scaling law. We modeled a herbaceous plant as a cantilever with the ground side as a fixed end, and the greatest height was formulated considering the axial tension force from the turgor pressure. The scaling law describing the relationship between the height and diameter in terms of the turgor pressure was theoretically derived. Moreover, we proposed a plant classification rule based on stress distribution.

Quantifying turgor pressure in budding and fission yeasts based upon osmotic properties

Walled cells, such as plants, fungi, and bacteria cells, possess a high internal hydrostatic pressure, termed turgor pressure, that drives volume growth and contributes to cell shape determination. Rigorous measurement of turgor pressure, however, remains challenging, and reliable quantitative measurements, even in budding yeast are still lacking. Here, we present a simple and robust experimental approach to access turgor pressure in yeasts based upon the determination of isotonic concentration using protoplasts as osmometers. We propose three methods to identify the isotonic condition - 3D cell volume, cytoplasmic fluorophore intensity, and mobility of a cytGEMs nano-rheology probe - that all yield consistent values. Our results provide turgor pressure estimates of 1.0 ± 0.1 MPa for S. pombe, 0.49 ± 0.01 MPa for S. japonicus, 0.5 ± 0.1 MPa for S. cerevisiae W303a and 0.31 ± 0.03 MPa for S. cerevisiae BY4741. Large differences in turgor pressure and nano-rheology measurements between the S. cerevisiae strains demonstrate how fundamental biophysical parameters can vary even among wildtype strains of the same species. These side-by-side measurements of turgor pressure in multiple yeast species provide critical values for quantitative studies on cellular mechanics and comparative evolution.

Measuring external primary cell wall elasticity of seedling roots using atomic force microscopy

Stiffness plays a central action in plant cell extension. Here, we present a protocol to detect changes in stiffness on the external epidermal cell wall of living plant roots using atomic force microscopy (AFM). We provide generalized instructions for collecting force-distance curves and analysis of stiffness using contact-based mechanical model. With this protocol, and some initial training in AFM, a user is able to perform indentation experiments on 4- and 5-day-old Arabidopsis thaliana and determine stiffness properties. For complete details on the use and execution of this protocol, please refer to Godon et al.¹.

Rigidity control mechanism by turgor pressure in plants

The bodies of herbaceous plants are slender, thin, and soft. These plants support their bodies through the action of turgor pressure associated with their internal water stores. The purpose of this study was to apply the principles of structural mechanics to clarify the underlying mechanism of rigidity control that is responsible for turgor pressure in plants and the reason behind the self-supporting ability of herbaceous plants. We modeled a plant a horizontally oriented thin-walled cylindrical cantilever with closed ends enclosing a cavity filled with water that is acted on by its own weight and by internal tension generated through turgor pressure. We derived an equation describing the plant's consequent deflection, introducing a dimensionless parameter to express the decrease in deflection associated with the action of turgor pressure. We found that the mechanical and physical characteristics of herbaceous plants that would appear to be counter-productive from a superficial perspective increase the deflection decreasing effect of turgor pressure.

Nano-structural stiffness measure for soft biomaterials of heterogeneous elasticity

Measuring the structural stiffness aims to reveal the impact of nanostructured components or various physiological circumstances on the elastic response of material to an external indentation. With a pyramidal tip at a nano-scale, we employed the atomic force microscopy (AFM) to indent the surfaces of two compositions of polyacrylamide gels with different softness and seedling roots of Arabidopsis thaliana. We found that the stiffness-depth curve derived from the measured force exhibits a heterogeneous character in elasticity. According to the tendency of stiffness-depth curve, we decomposed the responding force into depth-impact (F_C), Hookean (F_H) and tip-shape (F_S) components, called trimechanic, where F_S and its gradient should be offset at the surface or subsurfaces of the indented material. Thereby, trimechnic theory allows us to observe how the three restoring nanomechanics change with varied depth. Their strengths are represented by the respective spring constants (k_C, k_H, k_S) of three parallel-connected spring (3PCS) analogs to differentiate restoring nanomechansims of indented materials. The effective Young's modulus Ê and the total stiffness k_T (= k_H + k_S) globally unambiguously distinguish the softness between the two gel categories. Data fluctuations were observed in the elasticity parameters of individual samples, reflecting nanostructural variations in the gel matrix. Similar tendencies were found in the results from growing plant roots, though the data fluctuations are expectedly much more dramatic. The zone-wise representation of stiffness by the trimechanic-3PCS framework demonstrates a stiffness measure that reflects beneath nanostructures encountered by deepened depth. The trimechanic-3PCS framework can apply any mechanical model of power-law based force-depth relationship and is compatible with thin layer corrections. It provides a new paradigm for analyzing restoring nanomechanics of soft biomaterials in response to indenting forces.