Atomic Force Microscopy Stiffness Tomography on Living Arabidopsis thaliana Cells Reveals the Mechanical Properties of Surface and Deep Cell-Wall Layers during Growth

Cell-wall mechanical properties play a key role in the growth and the protection of plants. However, little is known about genuine wall mechanical properties and their growth-related dynamics at subcellular resolution and in living cells. Here, we used atomic force microscopy (AFM) stiffness tomography to explore stiffness distribution in the cell wall of suspension-cultured Arabidopsis thaliana as a model of primary, growing cell wall. For the first time that we know of, this new imaging technique was performed on living single cells of a higher plant, permitting monitoring of the stiffness distribution in cell-wall layers as a function of the depth and its evolution during the different growth phases. The mechanical measurements were correlated with changes in the composition of the cell wall, which were revealed by Fourier-transform infrared (FTIR) spectroscopy. In the beginning and end of cell growth, the average stiffness of the cell wall was low and the wall was mechanically homogenous, whereas in the exponential growth phase, the average wall stiffness increased, with increasing heterogeneity. In this phase, the difference between the superficial and deep wall stiffness was highest. FTIR spectra revealed a relative increase in the polysaccharide/lignin content.     

A multiscale whole-cell theory for mechanosensitive migration on viscoelastic substrates

Increasing experimental evidence validates that both the elastic stiffness and viscosity of the extracellular matrix regulate mesenchymal cell behavior, such as the rational switch between durotaxis (cell migration to stiffer regions), anti-durotaxis (migration to softer regions), and adurotaxis (stiffness-insensitive migration). To reveal the mechanisms underlying the crossover between these motility regimes, we have developed a multiscale chemomechanical whole-cell theory for mesenchymal migration. Our framework couples the subcellular focal adhesion dynamics at the cell-substrate interface with the cellular cytoskeletal mechanics and the chemical signaling pathways involving Rho GTPase proteins. Upon polarization by the Rho GTPase gradients, our simulated cell migrates by concerted peripheral protrusions and contractions, a hallmark of the mesenchymal mode. The resulting cell dynamics quantitatively reproduces the experimental migration speed as a function of the uniform substrate stiffness and explains the influence of viscosity on the migration efficiency. In the presence of stiffness gradients and absence of chemical polarization, our simulated cell can exhibit durotaxis, anti-durotaxis, and adurotaxis respectively with increasing substrate stiffness or viscosity. The cell moves toward an optimally stiff region from softer regions during durotaxis and from stiffer regions during anti-durotaxis. We show that cell polarization through steep Rho GTPase gradients can reverse the migration direction dictated by the mechanical cues. Overall, our theory demonstrates that opposing durotactic behaviors emerge via the interplay between intracellular signaling and cell-medium mechanical interactions in agreement with experiments, thereby elucidating complex mechanosensing at the single-cell level.     

A close-up view of wood structure and properties across a growth ring of Norway spruce (Picea abies [L] Karst.)

A growth ring of an adult Norway spruce (Picea abies [L] Karst.) was analyzed to a high resolution at the single cell level with respect to structural and mechanical changes during the growth period. For this purpose structural characterization was performed by means of light microscopy, scanning electron microscopy and wide angle X-ray diffraction for investigating the geometry of cells, their cell wall fractions and cellulose microfibril angles (MFA). The mechanical properties were determined in microtensile tests on individual tracheids which had been taken from sequentially cut tangential slices. The results revealed pronounced differences in tensile stiffness between earlywood and latewood cells but only minor differences in tensile stiffness between the cell walls of both tissue types. These comparatively small changes in cell wall stiffness across the growth ring were caused by slight changes in MFA. The findings suggest that trees mainly vary cell size to optimize water transport and mechanical stability during the growth period and that modification of the cell wall organisation plays a minor role.     

Cellulose orientation determines mechanical anisotropy in onion epidermis cell walls

The role of cellulose microfibril orientation in determining cell wall mechanical anisotropy and in the control of the wall plastic versus elastic properties was studied in the adaxial epidermis of onion bulb scales using the constant-load (creep) test. The mean or net cellulose orientation in the outer periclinal wall of the epidermis was parallel to the long axis of the cells. In vitro cell wall extensibility was 30-90% higher in the direction perpendicular to the net microfibril orientation than parallel to it. This was the case for the size of the initial deformation occurring just after the load application and for the rate of time-dependent creep. Loading/unloading experiments confirmed the presence of a real irreversible component in cell wall extension. The plastic component of the time-dependent deformation was higher perpendicular to the net cellulose orientation than parallel to it. An acid buffer (pH 4.5) increased the creep rate by 25-30% but this response was not related to cellulose orientation. The present data provide direct evidence that the net orientation of cellulose microfibrils confers mechanical anisotropy to the walls of seed plants, a characteristic that may be relevant to understanding anisotropic cell growth.     

Measuring the stiffness of bacterial cells from growth rates in hydrogels of tunable elasticity

Although bacterial cells are known to experience large forces from osmotic pressure differences and their local microenvironment, quantitative measurements of the mechanical properties of growing bacterial cells have been limited. We provide an experimental approach and theoretical framework for measuring the mechanical properties of live bacteria. We encapsulated bacteria in agarose with a user-defined stiffness, measured the growth rate of individual cells and fit data to a thin-shell mechanical model to extract the effective longitudinal Young's modulus of the cell envelope of Escherichia coli (50-150 MPa), Bacillus subtilis (100-200 MPa) and Pseudomonas aeruginosa (100-200 MPa). Our data provide estimates of cell wall stiffness similar to values obtained via the more labour-intensive technique of atomic force microscopy. To address physiological perturbations that produce changes in cellular mechanical properties, we tested the effect of A22-induced MreB depolymerization on the stiffness of E. coli. The effective longitudinal Young's modulus was not significantly affected by A22 treatment at short time scales, supporting a model in which the interactions between MreB and the cell wall persist on the same time scale as growth. Our technique therefore enables the rapid determination of how changes in genotype and biochemistry affect the mechanical properties of the bacterial envelope.     

Poroelastic Mechanical Effects of Hemicelluloses on Cellulosic Hydrogels under Compression

Hemicelluloses exhibit a range of interactions with cellulose, the mechanical consequences of which in plant cell walls are incompletely understood. We report the mechanical properties of cell wall analogues based on cellulose hydrogels to elucidate the contribution of xyloglucan or arabinoxylan as examples of two hemicelluloses displaying different interactions with cellulose. We subjected the hydrogels to mechanical pressures to emulate the compressive stresses experienced by cell walls in planta. Our results revealed that the presence of either hemicellulose increased the resistance to compression at fast strain rates. However, at slow strain rates, only xyloglucan increased composite strength. This behaviour could be explained considering the microstructure and the flow of water through the composites confirming their poroelastic nature. In contrast, small deformation oscillatory rheology showed that only xyloglucan decreased the elastic moduli. These results provide evidence for contrasting roles of different hemicelluloses in plant cell wall mechanics and man-made cellulose-based composite materials.     

A computational approach for inferring the cell wall properties that govern guard cell dynamics

Guard cells dynamically adjust their shape in order to regulate photosynthetic gas exchange, respiration rates and defend against pathogen entry. Cell shape changes are determined by the interplay of cell wall material properties and turgor pressure. To investigate this relationship between turgor pressure, cell wall properties and cell shape, we focused on kidney‐shaped stomata and developed a biomechanical model of a guard cell pair. Treating the cell wall as a composite of the pectin‐rich cell wall matrix embedded with cellulose microfibrils, we show that strong, circumferentially oriented fibres are critical for opening. We find that the opening dynamics are dictated by the mechanical stress response of the cell wall matrix, and as the turgor rises, the pectinaceous matrix stiffens. We validate these predictions with stomatal opening experiments in selected Arabidopsis cell wall mutants. Thus, using a computational framework that combines a 3D biomechanical model with parameter optimization, we demonstrate how to exploit subtle shape changes to infer cell wall material properties. Our findings reveal that proper stomatal dynamics are built on two key properties of the cell wall, namely anisotropy in the form of hoop reinforcement and strain stiffening.     

Cancer cell viscoelasticity measurement by quantitative phase and flow stress induction

Cell viscoelastic properties are affected by the cell cycle, differentiation, and pathological processes such as malignant transformation. Therefore, evaluation of the mechanical properties of the cells proved to be an approach to obtaining information on the functional state of the cells. Most of the currently used methods for cell mechanophenotyping are limited by low robustness or the need for highly expert operation. In this paper, the system and method for viscoelasticity measurement using shear stress induction by fluid flow is described and tested. Quantitative phase imaging (QPI) is used for image acquisition because this technique enables one to quantify optical path length delays introduced by the sample, thus providing a label-free objective measure of morphology and dynamics. Viscosity and elasticity determination were refined using a new approach based on the linear system model and parametric deconvolution. The proposed method allows high-throughput measurements during live-cell experiments and even through a time lapse, whereby we demonstrated the possibility of simultaneous extraction of shear modulus, viscosity, cell morphology, and QPI-derived cell parameters such as circularity or cell mass. Additionally, the proposed method provides a simple approach to measure cell refractive index with the same setup, which is required for reliable cell height measurement with QPI, an essential parameter for viscoelasticity calculation. Reliability of the proposed viscoelasticity measurement system was tested in several experiments including cell types of different Young/shear modulus and treatment with cytochalasin D or docetaxel, and an agreement with atomic force microscopy was observed. The applicability of the proposed approach was also confirmed by a time-lapse experiment with cytochalasin D washout, whereby an increase of stiffness corresponded to actin repolymerization in time.     

Cellular force microscopy for in vivo measurements of plant tissue mechanics

Although growth and morphogenesis are controlled by genetics, physical shape change in plant tissue results from a balance between cell wall loosening and intracellular pressure. Despite recent work demonstrating a role for mechanical signals in morphogenesis, precise measurement of mechanical properties at the individual cell level remains a technical challenge. To address this challenge, we have developed cellular force microscopy (CFM), which combines the versatility of classical microindentation techniques with the high automation and resolution approaching that of atomic force microscopy. CFM's large range of forces provides the possibility to map the apparent stiffness of both plasmolyzed and turgid tissue as well as to perform micropuncture of cells using very high stresses. CFM experiments reveal that, within a tissue, local stiffness measurements can vary with the level of turgor pressure in an unexpected way. Altogether, our results highlight the importance of detailed physically based simulations for the interpretation of microindentation results. CFM's ability to be used both to assess and manipulate tissue mechanics makes it a method of choice to unravel the feedbacks between mechanics, genetics, and morphogenesis.     

Local Viscoelastic Properties of Live Cells Investigated Using Dynamic and Quasi-Static Atomic Force Microscopy Methods

The measurement of viscoelasticity of cells in physiological environments with high spatio-temporal resolution is a key goal in cell mechanobiology. Traditionally only the elastic properties have been measured from quasi-static force-distance curves using the atomic force microscope (AFM). Recently, dynamic AFM-based methods have been proposed to map the local in vitro viscoelastic properties of living cells with nanoscale resolution. However, the differences in viscoelastic properties estimated from such dynamic and traditional quasi-static techniques are poorly understood. In this work we quantitatively reconstruct the local force and dissipation gradients (viscoelasticity) on live fibroblast cells in buffer solutions using Lorentz force excited cantilevers and present a careful comparison between mechanical properties (local stiffness and damping) extracted using dynamic and quasi-static force spectroscopy methods. The results highlight the dependence of measured viscoelastic properties on both the frequency at which the chosen technique operates as well as the interactions with subcellular components beyond certain indentation depth, both of which are responsible for differences between the viscoelasticity property maps acquired using the dynamic AFM method against the quasi-static measurements.     

Local Viscoelastic Properties of Live Cells Investigated Using Dynamic and Quasi-Static Atomic Force Microscopy Methods

The measurement of viscoelasticity of cells in physiological environments with high spatio-temporal resolution is a key goal in cell mechanobiology. Traditionally only the elastic properties have been measured from quasi-static force-distance curves using the atomic force microscope (AFM). Recently, dynamic AFM-based methods have been proposed to map the local in vitro viscoelastic properties of living cells with nanoscale resolution. However, the differences in viscoelastic properties estimated from such dynamic and traditional quasi-static techniques are poorly understood. In this work we quantitatively reconstruct the local force and dissipation gradients (viscoelasticity) on live fibroblast cells in buffer solutions using Lorentz force excited cantilevers and present a careful comparison between mechanical properties (local stiffness and damping) extracted using dynamic and quasi-static force spectroscopy methods. The results highlight the dependence of measured viscoelastic properties on both the frequency at which the chosen technique operates as well as the interactions with subcellular components beyond certain indentation depth, both of which are responsible for differences between the viscoelasticity property maps acquired using the dynamic AFM method against the quasi-static measurements.     

Roles of Cellulose and Xyloglucan in Determining the Mechanical Properties of Primary Plant Cell Walls

The primary cell walls of growing and fleshy plant tissue mostly share a common set of molecular components, cellulose, xyloglucan (XyG), and pectin, that are required for both inherent strength and the ability to respond to cell expansion during growth. To probe molecular mechanisms underlying material properties, cell walls and analog composites from Acetobacter xylinus have been measured under small deformation and uniaxial extension conditions as a function of molecular composition. Small deformation oscillatory rheology shows a common frequency response for homogenized native cell walls, their sequential extraction residues, and bacterial cellulose alone. This behavior is characteristic of structuring via entanglement of cellulosic rods and is more important than cross-linking with XyG in determining shear moduli. Compared with cellulose alone, composites with XyG have lower stiffness and greater extensibility in uniaxial tension, despite being highly cross-linked at the molecular level. It is proposed that this is due to domains of cross-linked cellulose behaving as mechanical elements, whereas cellulose alone behaves as a mat of individual fibrils. The implication from this work is that XyG/cellulose networks provide a balance of extensibility and strength required by primary cell walls, which is not achievable with cellulose alone.     

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.     

Relative crystallinity of plant biomass: studies on assembly, adaptation and acclimation

Plant biomechanical design is central to cell shape, morphogenesis, reproductive performance and protection against environmental and mechanical stress. The cell wall forms the central load bearing support structure for plant design, yet a mechanistic understanding of its synthesis is incomplete. A key tool for studying the structure of cellulose polymorphs has been x-ray diffraction and fourier transform infrared spectroscopy (FTIR). Relative crystallinity index (RCI) is based on the x-ray diffraction characteristics of two signature peaks and we used this technique to probe plant assembly, adaptation and acclimation. Confocal microscopy was used to visualize the dynamics of cellulose synthase in transgenic Arabidopsis plants expressing a homozygous YFP::CESA6. Assembly: RCI values for stems and roots were indistinguishable but leaves had 23.4 and 21.6% lower RCI than stems and roots respectively. Adaptation: over 3-fold variability in RCI was apparent in leaves from 35 plant species spanning Ordovician to Cretaceous periods. Within this study, RCI correlated positively with leaf geometric constraints and with mass per unit area, suggestive of allometry. Acclimation: biomass crystallinity was found to decrease under conditions of thigmomorphogenesis in Arabidopsis. Further, in etiolated pea hypocotyls, RCI values also decreased compared to plants that were grown in light, consistent with alterations in FTIR cellulose fingerprint peaks and live cell imaging experiments revealing rapid orientation of the YFP::cellulose synthase-6 array in response to light. Herein, results and technical challenges associated with the structure of the cell wall that gives rise to sample crystallinity are presented and examined with respect to adaptation, acclimation and assembly in ecosystem-level processes.     

Mechanical effects of plant cell wall enzymes on cellulose/xyloglucan composites

Xyloglucan-acting enzymes are believed to have effects on type I primary plant cell wall mechanical properties. In order to get a better understanding of these effects, a range of enzymes with different in vitro modes of action were tested against cell wall analogues (bio-composite materials based on Acetobacter xylinus cellulose and xyloglucan). Tomato pericarp xyloglucan endo transglycosylase (tXET) and nasturtium seed xyloglucanase (nXGase) were produced heterologously in Pichia pastoris. Their action against the cell wall analogues was compared with that of a commercial preparation of Trichoderma endo-glucanase (EndoGase). Both 'hydrolytic' enzymes (nXGase and EndoGase) were able to depolymerise not only the cross-link xyloglucan fraction but also the surface-bound fraction. Consequent major changes in cellulose fibril architecture were observed. In mechanical terms, removal of xyloglucan cross-links from composites resulted in increased stiffness (at high strain) and decreased visco-elasticity with similar extensibility. On the other hand, true transglycosylase activity (tXET) did not affect the cellulose/xyloglucan ratio. No change in composite stiffness or extensibility resulted, but a significant increase in creep behaviour was observed in the presence of active tXET. These results provide direct in vitro evidence for the involvement of cell wall xyloglucan-specific enzymes in mechanical changes underlying plant cell wall re-modelling and growth processes. Mechanical consequences of tXET action are shown to be complimentary to those of cucumber expansin.     

Disentangling loosening from softening: insights into primary cell wall structure

How cell wall elasticity, plasticity, and time‐dependent extension (creep) relate to one another, to plant cell wall structure and to cell growth remain unsettled topics. To examine these issues without the complexities of living tissues, we treated cell‐free strips of onion epidermal walls with various enzymes and other agents to assess which polysaccharides bear mechanical forces in‐plane and out‐of‐plane of the cell wall. This information is critical for integrating concepts of wall structure, wall material properties, tissue mechanics and mechanisms of cell growth. With atomic force microscopy we also monitored real‐time changes in the wall surface during treatments. Driselase, a potent cocktail of wall‐degrading enzymes, removed cellulose microfibrils in superficial lamellae sequentially, layer‐by‐layer, and softened the wall (reduced its mechanical stiffness), yet did not induce wall loosening (creep). In contrast Cel12A, a bifunctional xyloglucanase/cellulase, induced creep with only subtle changes in wall appearance. Both Driselase and Cel12A increased the tensile compliance, but differently for elastic and plastic components. Homogalacturonan solubilization by pectate lyase and calcium chelation greatly increased the indentation compliance without changing tensile compliances. Acidic buffer induced rapid cell wall creep via endogenous α‐expansins, with negligible effects on wall compliances. We conclude that these various wall properties are not tightly coupled and therefore reflect distinctive aspects of wall structure. Cross‐lamellate networks of cellulose microfibrils influenced creep and tensile stiffness whereas homogalacturonan influenced indentation mechanics. This information is crucial for constructing realistic molecular models that define how wall mechanics and growth depend on primary cell wall structure.     

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.     

Toward a biophysical theory of organogenesis: Birefringence observations on regenerating leaves in the succulent,Graptopetalum paraguayense E. Walther

Polarity shifts occur during organogenesis. The histological criterion for polarity is the direction of cell division. The biophysical criterion is the orientation of reinforcing cellulose microfibrils which lie normal to the organ axis and which determine the preferred growth direction. Using cell pattern to deduce cell lineage, and polarized light to study cellulose alignment, both aspects of polarity were examined in the epidermis of regenerating G. paraguayense. In this system new leaves and a stem arise from parallel cell files on a mature leaf. Large (90°) shifts in polarity occur in regions of the epidermis to give the new organs radial symmetry in the surface plane (files radiating from a pole). Study of the shifts in the epidermis showed that, during certain stages, shifts in the division direction are accompanied by shifts in the cellulose deposition direction, as expected. The new cellulose orientation is parallel to the new cross wall. During normal organ extension, however, shifts in division direction do not bring on changes in cellulose pattern. Thus the coupling between the two kinds of polarity is facultative. This variable relation is used in a biophysical model which can account for the reorganization of cell file pattern and cellulose reinforcement pattern into the radial symmetry of the new organ.     

Building an extensible cell wall

This article recounts, from my perspective of four decades in this field, evolving paradigms of primary cell wall structure and the mechanism of surface enlargement of growing cell walls. Updates of the structures, physical interactions, and roles of cellulose, xyloglucan, and pectins are presented. This leads to an example of how a conceptual depiction of wall structure can be translated into an explicit quantitative model based on molecular dynamics methods. Comparison of the model’s mechanical behavior with experimental results provides insights into the molecular basis of complex mechanical behaviors of primary cell wall and uncovers the dominant role of cellulose–cellulose interactions in forming a strong yet extensible network.

The ordered synthesis and bundling of cellulose microfibrils leads to a strong yet extensible surface network whose organization and physical properties are modulated by pliant matrix polysaccharides.