Finite element modelling of the mechanical behaviour of onion epidermis with incorporation of nonlinear properties of cell walls and real tissue geometry

Regiospecific Cellulose Orientation and Anisotropic Mechanical Property in Plant Cell Walls

Cellulose microfibrils (CMFs) are a major load-bearing component in plant cell walls. Thus, their structures have been studied extensively with spectroscopic and microscopic characterization methods, but the findings from these two approaches were inconsistent, which hampers the mechanistic understanding of cell wall mechanics. Here, we report the regiospecific assembly of CMFs in the periclinal wall of plant epidermal cells. Using sum frequency generation spectroscopic imaging, we found that CMFs are highly aligned in the cell edge region where two cells form a junction, whereas they are mostly isotropic on average throughout the wall thickness in the flat face region of the epidermal cell. This subcellular-level heterogeneity in the CMF alignment provided a new perspective on tissue-level anisotropy in the tensile modulus of cell wall materials. This finding also has resolved a previous contradiction between the spectroscopic and microscopic imaging studies, which paves a foundation for better understanding of the cell wall architecture, especially structure-geometry relationships.

Measurement bruise volume of olive during impact test using FEM and quality evaluation of extracted olive oil

Mechanical damage is a phenomenon that always occurred in the postharvest process. Due to the inappropriate harvest and postharvest process of Olive that lead to the bruise phenomenon, the quality of the extracted olive oil reduces. In this study, the effect of olive damage on bruising volume and quality characteristics was investigated. Three different varieties of Yellow, Oily, and Fishemi in three stages of unripe, semiripe, and ripped were used. Also, three kinds of the surface of rubber, nylon, and foam for the drop test were considered. The tests were performed in laboratory mode and simulated. For all tests, with increasing maturity, the amount of stress and internal energy were decreased and the bruise volume was increased. The amount of bruise volume and bruise susceptibility were obtained, and the experimental and simulated conditions were compared. On the other hand, the quality characteristics of olive oil including free fatty acid (FFA), peroxide value (PV), k232 and K270 coefficients, total chlorophyll, total carotenoid, total phenol, and total flavonoid were measured. The results showed that the finite element and chemometric methods are acceptable methods for predicting the generated energy of the fruit during impact, the amount of bruising volume, as well as evaluating the quality of the extracted oil.

Determination of texture properties of banana fruit cells with an atomic force microscope: A case study on elastic modulus and stiffness

Characterization of biological materials with their elasto-mechanical properties is considered essential for understanding their nature. In addition, elasto-mechanical studies at the macroscale are frequently used to determine these characteristics by a resistance measurement such as the Magness-Taylor penetration test or compression test using an Instron Universal Mechanical Testing Machine. In this regard, the atomic force microscopy (AFM) was presented as a new method for identifying the alterations of elasto-mechanical properties at a nanoscale. Therefore, the present study estimated the elastic modulus and stiffness of the cell walls which were isolated from the banana mesocarp with AFM-based nanoindentation. Then, the elastic modulus of a cell and stiffness were determined by analyzing the force-separation curves using the theory of Hertz and the mechanics of Sneddon. Using two tips of the distinct radius of the curvature (10 and 10,000 nm), it was revealed that the tip geometry significantly affected the measured elasto-mechanical properties. Further, the elastic modulus was around 95 ± 45 and 18.5 ± 12.5 kPa for the sharper tip (R = 10 nm) and a bead (R = 10,000 nm) tips, respectively. Furthermore, a large variability was considered regarding the elasto-mechanical property (>100%) among the cells which were sampled from the same region in the fruit. Therefore, the AFM can be highly suitable for evaluating the structure-related properties of biological materials at the cellular and subcellular scales by combining nano elasto-mechanical properties with topography imaging.

Gradients of cell wall nano-mechanical properties along and across elongating primary roots of maize

To test the hypothesis that particular tissues can control root growth, we analysed the mechanical properties of cell walls belonging to different tissues of the apical part of the maize root using atomic force microscopy. The dynamics of properties during elongation growth were characterized in four consecutive zones of the root. Extensive immunochemical characterization and quantification were used to establish the polysaccharide motif(s) related to changes in cell wall mechanics. Cell transition from division to elongation was coupled to the decrease in the elastic modulus in all root tissues. Low values of moduli were retained in the elongation zone and increased in the late elongation zone. No relationship between the immunolabelling pattern and mechanical properties of the cell walls was revealed. When measured values of elastic moduli and turgor pressure were used in the computational simulation, this resulted in an elastic response of the modelled root and the distribution of stress and strain similar to those observed in vivo. In all analysed root zones, cell walls of the inner cortex displayed moduli of elasticity that were maximal or comparable with the maximal values among all tissues. Thus, we propose that the inner cortex serves as a growth-limiting tissue in maize roots.

Texture of Hot-Air-Dried Persimmon (Diospyros kaki) Chips: Instrumental, Sensory, and Consumer Input for Product Development

Persimmon (Diospyros kaki) is an underutilized tree fruit. Previous studies have shown the feasibility of making a hot-air-dried, chip-style product from persimmon. However, the texture of this type of product has not been explored or connected to consumer preference. Thus, for dried samples representing 37 cultivars, this study aimed to (1) predict trained sensory panel texture attributes from instrumental measurements, (2) predict consumer liking from instrumental measurements and sensory texture attributes, and (3) elucidate whether astringency type affects dried product texture. Partial least-squares regression models of fair-to-good quality predicted all measured sensory texture attributes (except Tooth Packing) from instrumental measurements. Modeling also identified that consumer preference is for a moist, smooth texture. Lastly, while astringency type has significant (p < 0.05) effects on several individual texture attributes, astringency type should not be used a priori to screen-in or -out persimmon cultivars for processing into a hot-air-dried product.

Methods to quantify primary plant cell wall mechanics

The primary plant cell wall is a dynamically regulated composite material of multiple biopolymers that forms a scaffold enclosing the plant cells. The mechanochemical make-up of this polymer network regulates growth, morphogenesis, and stability at the cell and tissue scales. To understand the dynamics of cell wall mechanics, and how it correlates with cellular activities, several experimental frameworks have been deployed in recent years to quantify the mechanical properties of plant cells and tissues. Here we critically review the application of biomechanical tool sets pertinent to plant cell mechanics and outline some of their findings, relevance, and limitations. We also discuss methods that are less explored but hold great potential for the field, including multiscale in silico mechanical modeling that will enable a unified understanding of the mechanical behavior across the scales. Our overview reveals significant differences between the results of different mechanical testing techniques on plant material. Specifically, indentation techniques seem to consistently report lower values compared with tensile tests. Such differences may in part be due to inherent differences among the technical approaches and consequently the wall properties that they measure, and partly due to differences between experimental conditions.

Discrete element modelling of tomato tissue deformation and failure at the cellular scale

Bruise damage in fruit results from cell wall failure and inter-cellular separation. Despite the importance of the micro-mechanics of plant tissue with respect to its integrity, it remains largely unquantified and poorly understood, due to many difficulties during experimental characterization. In this article, a 3D micro-mechanical plant tissue model that is able to model cell rupture and inter-cellular debonding and thus provide more insight into the micro-mechanics was developed. The model is based on the discrete element method (DEM) and represents the tissue as a mass-spring system. Each plant cell is represented as a deformable visco-elastoplastic triangulated mesh under turgor pressure. To model cell wall rupture, it is assumed that a spring connection in the wall breaks at a certain critical stretch ratio and that a ruptured cell is turgorless. The inter-cellular contact model assumes brittle fracture between a cell's node and an adjacent cell's triangle when their bond distance exceeds a critical value. A high-speed tomato fruit cell compression test was simulated and the modelled force-strain curve compares well with the experimental data, including for strains above the elastic limit. By varying the shape of the cell in the compression simulation it was shown that the force-strain curve is highly dependent on the cell shape and thus parameter fitting procedures based on a spherical cell model will be inaccurate. Furthermore, the wall stiffness and thickness showed a positive linear relationship with the force at cell bursting. Besides simulating compression tests of single cells, we also simulated tensile and compression tests on small tissue specimens. Realistic tissue structures of tomato mesocarp tissue were generated by a novel method using DEM simulations of deformable cells in a shrinking cylinder. The cell area, volume and anisotropy distributions of the virtual tissue compared well with micro-CT images of real tomato mesocarp tissue (normalized root mean square error values smaller than 3%). The tissue compression and tensile test simulations demonstrated an important influence of the inter-cellular bonding energy and tissue porosity on the tissue failure characteristics and elastic modulus.

Compression simulations of plant tissue in 3D using a mass-spring system approach and discrete element method

A hybrid model based on a mass-spring system methodology coupled with the discrete element method (DEM) was implemented to simulate the deformation of cellular structures in 3D. Models of individual cells were constructed using the particles which cover the surfaces of cell walls and are interconnected in a triangle mesh network by viscoelastic springs. The spatial arrangement of the cells required to construct a virtual tissue was obtained using Poisson-disc sampling and Voronoi tessellation in 3D space. Three structural features were included in the model: viscoelastic material of cell walls, linearly elastic interior of the cells (simulating compressible liquid) and a gas phase in the intercellular spaces. The response of the models to an external load was demonstrated during quasi-static compression simulations. The sensitivity of the model was investigated at fixed compression parameters with variable tissue porosity, cell size and cell wall properties, such as thickness and Young's modulus, and a stiffness of the cell interior that simulated turgor pressure. The extent of the agreement between the simulation results and other models published is discussed. The model demonstrated the significant influence of tissue structure on micromechanical properties and allowed for the interpretation of the compression test results with respect to changes occurring in the structure of the virtual tissue. During compression virtual structures composed of smaller cells produced higher reaction forces and therefore they were stiffer than structures with large cells. The increase in the number of intercellular spaces (porosity) resulted in a decrease in reaction forces. The numerical model was capable of simulating the quasi-static compression experiment and reproducing the strain stiffening observed in experiment. Stress accumulation at the edges of the cell walls where three cells meet suggests that cell-to-cell debonding and crack propagation through the contact edge of neighboring cells is one of the most prevalent ways for tissue to rupture.

The stiffening of the cell walls observed during physiological softening of pears

The Young's modulus of the primary cell walls of pears decreases linearly during the pre-harvest on-tree maturation and increases during postharvest storage, and does not correlate with firmness of fruit. The determination of mechanical properties of cell walls is indispensable for understanding the mechanism of physiological softening and deterioration of quality of fruits during postharvest storage. The Young's modulus of the primary cell walls from pear fruit (Pyrus communis L., cultivars 'Conference' and 'Xenia') during pre-harvest maturation and postharvest storage in an ambient atmosphere at 2 °C followed by shelf life was studied using atomic force microscopy (AFM). The results were related to the firmness of fruits, galacturonic acid content in water, chelator, sodium carbonate and insoluble pectin fractions, polygalacturonase and pectin methylesterase activities. The Young's modulus of the primary cell walls decreased linearly during the last month of pre-harvest maturation from 3.2 ± 1.8 to 1.1 ± 0.7 MPa for 'Conference' and from 1.9 ± 1.2 to 0.2 ± 0.1 MPa for 'Xenia' which correlated with linear firmness decrease. During postharvest storage the cell wall Young's modulus increased while firmness continued to decrease. Correlation analysis for the entire period of the experiment showed a lack of straightforward relation between the Young's modulus of primary cell walls and fruit firmness. The Young's modulus of cell walls correlated negatively either with galacturonic acid content in sodium carbonate soluble pectin ('Conference') or with insoluble pectin fractions ('Xenia') and positively with polygalacturonase activity. It was therefore evidenced that covalently linked pectins play the key role for the stiffness of fruit cell walls. Based on the obtained results, the model explaining the fruit transition from firm and crispy to soft and mealy was proposed.

Spatial organization of cellulose microfibrils and matrix polysaccharides in primary plant cell walls as imaged by multichannel atomic force microscopy

We used atomic force microscopy (AFM), complemented with electron microscopy, to characterize the nanoscale and mesoscale structure of the outer (periclinal) cell wall of onion scale epidermis - a model system for relating wall structure to cell wall mechanics. The epidermal wall contains ~100 lamellae, each ~40 nm thick, containing 3.5-nm wide cellulose microfibrils oriented in a common direction within a lamella but varying by ~30 to 90° between adjacent lamellae. The wall thus has a crossed polylamellate, not helicoidal, wall structure. Montages of high-resolution AFM images of the newly deposited wall surface showed that single microfibrils merge into and out of short regions of microfibril bundles, thereby forming a reticulated network. Microfibril direction within a lamella did not change gradually or abruptly across the whole face of the cell, indicating continuity of the lamella across the outer wall. A layer of pectin at the wall surface obscured the underlying cellulose microfibrils when imaged by FESEM, but not by AFM. The AFM thus preferentially detects cellulose microfibrils by probing through the soft matrix in these hydrated walls. AFM-based nanomechanical maps revealed significant heterogeneity in cell wall stiffness and adhesiveness at the nm scale. By color coding and merging these maps, the spatial distribution of soft and rigid matrix polymers could be visualized in the context of the stiffer microfibrils. Without chemical extraction and dehydration, our results provide multiscale structural details of the primary cell wall in its near-native state, with implications for microfibrils motions in different lamellae during uniaxial and biaxial extensions.

Prediction of water loss and viscoelastic deformation of apple tissue using a multiscale model

A two-dimensional multiscale water transport and mechanical model was developed to predict the water loss and deformation of apple tissue (Malus × domestica Borkh. cv. 'Jonagold') during dehydration. At the macroscopic level, a continuum approach was used to construct a coupled water transport and mechanical model. Water transport in the tissue was simulated using a phenomenological approach using Fick's second law of diffusion. Mechanical deformation due to shrinkage was based on a structural mechanics model consisting of two parts: Yeoh strain energy functions to account for non-linearity and Maxwell's rheological model of visco-elasticity. Apparent parameters of the macroscale model were computed from a microscale model. The latter accounted for water exchange between different microscopic structures of the tissue (intercellular space, the cell wall network and cytoplasm) using transport laws with the water potential as the driving force for water exchange between different compartments of tissue. The microscale deformation mechanics were computed using a model where the cells were represented as a closed thin walled structure. The predicted apparent water transport properties of apple cortex tissue from the microscale model showed good agreement with the experimentally measured values. Deviations between calculated and measured mechanical properties of apple tissue were observed at strains larger than 3%, and were attributed to differences in water transport behavior between the experimental compression tests and the simulated dehydration-deformation behavior. Tissue dehydration and deformation in the high relative humidity range ( > 97% RH) could, however, be accurately predicted by the multiscale model. The multiscale model helped to understand the dynamics of the dehydration process and the importance of the different microstructural compartments (intercellular space, cell wall, membrane and cytoplasm) for water transport and mechanical deformation.