Interpreting atomic force microscopy nanoindentation of hierarchical biological materials using multi-regime analysis

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..

Synthetic and biopolymeric microgels: Review of similarities and difference in behaviour in bulk phases and at interfaces

This review discusses the current knowledge of interfacial and bulk interactions of biopolymeric microgels in relation to the well-established properties of synthetic microgels for applications as viscosity modifiers and Pickering stabilisers. We present a timeline showing the key milestones in designing microgels and their bulk/ interfacial performance. Poly(N-isopropylacrylamide) (pNIPAM) microgels have remained as the protagonist in the synthetic microgel domain whilst proteins or polysaccharides have been primarily used to fabricate biopolymeric microgels. Bulk properties of microgel dispersions are dominated by the volume fraction (ϕ) of the microgel particles, but ϕ is difficult to pinpoint, as addressed by many theoretical models. By evaluating recent experimental studies over the last five years, we find an increasing focus on the analysis of microgel elasticity as a key parameter in modulating their packing at the interfaces, within the provinces of both synthetic and biopolymeric systems. Production methods and physiochemical factors shown to influence microgel swelling in the aqueous phase can have a significant impact on their bulk as well as interfacial performance. Compared to synthetic microgels, biopolymer microgels show a greater tendency for polydispersity and aggregation and do not appear to have a core-corona structure. Comprehensive studies of biopolymeric microgels are still lacking, for example, to accurately determine their inter- and intra- particle interactions, whilst a wider variety of techniques need to be applied in order to allow comparisons to real systems of practical usage.

Soft Contact Mechanics with Gradient-Stiffness Surfaces

The stiffness in the top surface of many biological entities like cornea or articular cartilage, as well as chemically cross-linked synthetic hydrogels, can be significantly lower or more compliant than the bulk. When such a heterogeneous surface comes into contact, the contacting load is distributed differently from typical contact models. The mechanical response under indentation loading of a surface with a gradient of stiffness is a complex, integrated response that necessarily includes the heterogeneity. In this work, we identify empirical contact models between a rigid indenter and gradient elastic surfaces by numerically simulating quasi-static indentation. Three key case studies revealed the specific ways in which (I) continuous gradients, (II) laminate-layer gradients, and (III) alternating gradients generate new contact mechanics at the shallow-depth limit. Validation of the simulation-generated models was done by micro- and nanoindentation experiments on polyacrylamide samples synthesized to have a softer gradient surface layer. The field of stress and stretch in the subsurface as visualized from the simulations also reveals that the gradient layers become confined, which pushes the stretch fields closer to the surface and radially outward. Thus, contact areas are larger than expected, and average contact pressures are lower than predicted by the Hertz model. The overall findings of this work are new contact models and the mechanisms by which they change. These models allow a more accurate interpretation of the plethora of indentation data on surface gradient soft matter (biological and synthetic) as well as a better prediction of the force response to gradient soft surfaces. This work provides examples of how gradient hydrogel surfaces control the subsurface stress distribution and loading response.

Enabling Selectively Tunable Mechanical Properties of Graphene Oxide/Silk Fibroin/Cellulose Nanocrystal Bionanofilms

Enhancing and manipulating the mechanical properties of graphene oxide (GO)-based structures are challenging because the GO assembly is easily delaminated. We develop nacre-like bionanofilms whose in-plane mechanical properties can be manipulated through water vapor annealing without influencing their mechanical properties in the thickness direction. These bionanofilms are prepared from GO, silk fibroin (SF), and cellulose nanocrystals (CNCs) via a spin-assisted layer-by-layer assembly. The postannealing mechanical properties of the films are determined with atomic force microscopy (AFM) bending and nanoindentation, and it is confirmed that the mechanical properties of the bionanofilms are altered only in the in-plane direction. While AFM bending shows Young's moduli of 26.9, 36.3, 24.3, and 41.4 GPa for 15, 15 annealed, 30, and 30 annealed GO/SF/CNC trilayers, nanoindentation shows reduced moduli of 19.5 ± 2.6 and 19.5 ± 2.5 GPa before and after annealing, respectively. The unaltered mechanical properties of the bionanofilms along the thickness direction after annealing can be attributed to the CNC frame in the SF matrix acting as a support against stress in the thickness direction, while annealing reorganizes the bionanofilm structure. The tunability of the bionanofilms' mechanical properties in only one direction through structure manipulation can lead to various applications, such as e-skin, wearable sensors, and human-machine interaction devices.

Auxeticity in biosystems: an exemplification of its effects on the mechanobiology of heterogeneous living cells

Auxeticity (negative Poisson's ratio) is the unique mechanical property found in an extensive variety of materials, such as metals, graphene, composites, polymers, foams, fibers, ceramics, zeolites, silicates and biological tissues. The enhanced mechanical features of the auxetic materials have motivated scientists to design, engineer and manufacture man-made auxetic materials to fully leverage their capabilities in different fields of research applications, including aeronautics, medical, protective equipments, smart sensors, filter cleaning, and so on. Atomic force microscopy (AFM) indentation is one of the most widely used methods for characterizing the mechanical properties and response of the living cells. In this contribution, we highlight main consequences of auxeticity for biosystems and provide a representative example to quantify the effect of nucleus auxeticity on the force response of the embryonic stem cells. A parametric study has been conducted on a heterogeneous stem cell to evaluate the effect of nucleus diameter, nucleus elasticity, indenter's shape and location on the force-indentation curve. The developed model has also been validated with the recently reported experimental studies available in the literature. Our results suggest that the nucleus auxeticity plays a profound role in cell mechanics especially for large size nucleus. We also report the mechanical stresses induced within the hyperelastic cell model under different loading conditions that would be quite useful in decoding the interrelations between mechanical stimuli and cellular behavior of auxetic biosystems. Finally, current and potential areas of applications of our findings for regenerative therapies, tissue engineering, 3 D/4D bioprinting, and the development of meta-biomaterials are discussed.

Depletion of HP1α alters the mechanical properties of MCF7 nuclei

Within the nucleus of the eukaryotic cell, DNA is partitioned into domains of highly condensed, transcriptionally silent heterochromatin and less condensed, transcriptionally active euchromatin. Heterochromatin protein 1α (HP1α) is an architectural protein that establishes and maintains heterochromatin, ensuring genome fidelity and nuclear integrity. Although the mechanical effects of changes in the relative amount of euchromatin and heterochromatin brought about by inhibiting chromatin-modifying enzymes have been studied previously, here we measure how the material properties of the nuclei are modified after the knockdown of HP1α. These studies were inspired by the observation that poorly invasive MCF7 breast cancer cells become more invasive after knockdown of HP1α expression and that, indeed, in many solid tumors the loss of HP1α correlates with the onset of tumor cell invasion. Atomic force microscopy (AFM), optical tweezers (OT), and techniques based on micropipette aspiration (MA) were each used to characterize the mechanical properties of nuclei extracted from HP1α knockdown or matched control MCF7 cells. Using AFM or OT to locally indent nuclei, those extracted from MCF7 HP1α knockdown cells were found to have apparent Young's moduli that were significantly lower than nuclei from MCF7 control cells, consistent with previous studies that assert heterochromatin plays a major role in governing the mechanical response in such experiments. In contrast, results from pipette-based techniques in the spirit of MA, in which the whole nuclei were deformed and aspirated into a conical pipette, showed considerably less variation between HP1α knockdown and control, consistent with previous studies reporting that it is predominantly the lamins in the nuclear envelope that determine the mechanical response to large whole-cell deformations. The differences in chromatin organization observed by various microscopy techniques between the MCF7 control and HP1α knockdown nuclei correlate well with the results of our measured mechanical responses and our hypotheses regarding their origin.

Viscoelasticity of non-colloidal hydrogel particle suspensions at the liquid-solid transition

Suspensions of soft particles transition from a viscous fluid to a soft material upon increases in phase volume. The criteria defining the transition to this jammed state are difficult to define due to the porous and deformable nature of soft particles. Here, we characterise the rheology of aqueous suspensions of industrially relevant non-colloidal, polydisperse, frictional agarose microgels and evaluate shear and viscoelastic behaviour across a range of phase volumes from the dilute regime to the highly concentrated regime. In order to model the viscoelastic response of suspensions without free fitting parameters, the random close packing volume fraction (φrcp) and the particle modulus are determined, respectively, from particle size distribution measurements and direct measurements of reduced elastic modulus of individual particles (Erp) using Atomic Force Microscopy. It is found that at φrcp, previously shown to correspond to divergence of the viscosity, also corresponds to the suspension transition from a viscous to viscoelastic fluid. However, the transition to a jammed solid-like state (φj) occurs at phase volumes exceeding this value (i.e. φj > φrcp). The suspension modulus and its sudden growth at φj are well-predicted by the Evans and Lips model that incorporates the Erp of the hydrogel particles. This rheological behaviour showing a dual transition is reminiscent of two families of systems: (i) colloidal suspensions and (ii) frictional-adhesive non-colloidal suspensions. However, it does not strictly follow either case. We propose that the width of the transition region is dictated by frictional contact, particle size distribution and particle modulus, and plan to further probe this in future work.

Visco-Hyperelastic Characterization of the Equine Immature Zona Pellucida

This article presents a very detailed study on the mechanical characterization of a highly nonlinear material, the immature equine zona pellucida (ZP) membrane. The ZP is modeled as a visco-hyperelastic soft matter. The Arruda–Boyce constitutive equation and the two-term Prony series are identified as the most suitable models for describing the hyperelastic and viscous components, respectively, of the ZP’s mechanical response. Material properties are identified via inverse analysis based on nonlinear optimization which fits nanoindentation curves recorded at different rates. The suitability of the proposed approach is fully demonstrated by the very good agreement between AFM data and numerically reconstructed force–indentation curves. A critical comparison of mechanical behavior of two immature ZP membranes (i.e., equine and porcine ZPs) is also carried out considering the information on the structure of these materials available from electron microscopy investigations documented in the literature.

Indentation probe with optical fibre array-based optical coherence tomography for material deformation

We present a new optomechanical probe for mechanical testing of soft matter. The probe consists of a micromachined cantilever equipped with an indenting sphere, and an array of 16 single‐mode optical fibres, which are connected to an optical coherence tomography (OCT) system that allows subsurface analysis of the sample during the indentation stroke. To test our device and its capability, we performed indentation on a PDMS‐based phantom. Our findings demonstrate that Common Path (CP)‐OCT via lensed optical fibres can be successfully combined with a microindentation sensor to visualise the phantom's deformation profile at different indentation depths and locations in real time.

Lay Description

This work presents a new approach to simultaneously perform micro‐indentation experiments and OCT imaging. An optical fiber array‐based sensor is used to develop a new hybrid tool where micro‐indentation is combined with optical coherence tomography. The sensor is therefore capable of compressing a sample with a small force and simultaneously collecting OCT depth profiles underneath and around the indentation point. This method offers the opportunity to characterize the mechanical properties of soft materials and simultaneously visualize their deformation profile. The ability to integrate OCT imaging with indentation technology is promising for the non‐invasive and precise characterization of different soft materials.

Theory and Practice in Measuring In-Vitro Extensibility of Growing Plant Cell Walls

This chapter summarizes four extensometer techniques for measuring cell wall extensibility in vitro and discusses how the results of these methods relate to the concept and ideal measurement of cell wall extensibility in the context of plant cell growth. These in-vitro techniques are particularly useful for studies of the molecular basis of cell wall extension. Measurements of breaking strength, elastic compliance and plastic compliance may be informative about changes in cell wall structure, whereas measurements of wall stress relaxation and creep are sensitive to both changes in wall structure and wall-loosening processes, such as those mediated by expansins and some lytic enzymes. A combination of methods is needed to obtain a broader view of cell wall behavior and properties connected with the concept of cell wall extensibility .

Discrete mechanical growth model for plant tissue

We present a discrete mechanical model to study plant development. The method is built up of mass points, springs and hinges mimicking the plant cell wall’s microstructure. To model plastic growth the resting lengths of springs are adjusted; when springs exceed a threshold length, new mass points, springs and hinges, are added. We formulate a stiffness tensor for the springs and hinges as a function of the fourth rank tensor of elasticity and the geometry of the mesh. This allows us to approximate the material law as a generalized orthotropic Hooke’s law, and control material properties during growth. The material properties of the model are illustrated in numerical simulations for finite strain and plastic growth. To solve the equations of motion of mass points we assume elastostatics and use Verlet integration. The method is demonstrated in simulations when anisotropic growth causes emergent residual strain fields in cell walls and a bending of tissue. The method can be used in multilevel models to study plant development, for example by coupling it to models for cytoskeletal, hormonal and gene regulatory processes.

Nanoindentation of Soft Biological Materials

Nanoindentation techniques, with high spatial resolution and force sensitivity, have recently been moved into the center of the spotlight for measuring the mechanical properties of biomaterials, especially bridging the scales from the molecular via the cellular and tissue all the way to the organ level, whereas characterizing soft biomaterials, especially down to biomolecules, is fraught with more pitfalls compared with the hard biomaterials. In this review we detail the constitutive behavior of soft biomaterials under nanoindentation (including AFM) and present the characteristics of experimental aspects in detail, such as the adaption of instrumentation and indentation response of soft biomaterials. We further show some applications, and discuss the challenges and perspectives related to nanoindentation of soft biomaterials, a technique that can pinpoint the mechanical properties of soft biomaterials for the scale-span is far-reaching for understanding biomechanics and mechanobiology.

Biomechanical Characterization at the Cell Scale: Present and Prospects

The rapidly growing field of mechanobiology demands for robust and reproducible characterization of cell mechanical properties. Recent achievements in understanding the mechanical regulation of cell fate largely rely on technological platforms capable of probing the mechanical response of living cells and their physico–chemical interaction with the microenvironment. Besides the established family of atomic force microscopy (AFM) based methods, other approaches include optical, magnetic, and acoustic tweezers, as well as sensing substrates that take advantage of biomaterials chemistry and microfabrication techniques. In this review, we introduce the available methods with an emphasis on the most recent advances, and we discuss the challenges associated with their implementation.

Layered Structure and Complex Mechanochemistry Underlie Strength and Versatility in a Bacterial Adhesive

While designing synthetic adhesives that perform in aqueous environments has proven challenging, microorganisms commonly produce bioadhesives that efficiently attach to a variety of substrates, including wet surfaces. The aquatic bacterium Caulobacter crescentus uses a discrete polysaccharide complex, the holdfast, to strongly attach to surfaces and resist flow. The holdfast is extremely versatile and has impressive adhesive strength. Here, we used atomic force microscopy in conjunction with superresolution microscopy and enzymatic assays to unravel the complex structure of the holdfast and to characterize its chemical constituents and their role in adhesion. Our data support a model whereby the holdfast is a heterogeneous material organized as two layers: a stiffer nanoscopic core layer wrapped into a sparse, far-reaching, flexible brush layer. Moreover, we found that the elastic response of the holdfast evolves after surface contact from initially heterogeneous to more homogeneous. From a composition point of view, besides N-acetyl-d-glucosamine (NAG), the only component that had been identified to date, our data show that the holdfast contains peptides and DNA. We hypothesize that, while polypeptides are the most important components for adhesive force, the presence of DNA mainly impacts the brush layer and the strength of initial adhesion, with NAG playing a primarily structural role within the core. The unanticipated complexity of both the structure and composition of the holdfast likely underlies its versatility as a wet adhesive and its distinctive strength. Continued improvements in understanding of the mechanochemistry of this bioadhesive could provide new insights into how bacteria attach to surfaces and could inform the development of new adhesives.IMPORTANCE There is an urgent need for strong, biocompatible bioadhesives that perform underwater. To strongly adhere to surfaces and resist flow underwater, the bacterium Caulobacter crescentus produces an adhesive called the holdfast, the mechanochemistry of which remains undefined. We show that the holdfast is a layered structure with a stiff core layer and a polymeric brush layer and consists of polysaccharides, polypeptides, and DNA. The DNA appears to play a role in the structure of the brush layer and initial adhesion, the peptides in adhesive strength, and the polysaccharides in the structure of the core. The complex, multilayer organization and diverse chemistry described here underlie the distinctive adhesive properties of the holdfast and will provide important insights into the mechanisms of bacterial adhesion and bioadhesive applications.

Nanomechanics of pH-Responsive, Drug-Loaded, Bilayered Polymer Grafts

Stimuli-responsive polymer films play an important role in the development of smart antibacterial coatings. In this study, we consider complementary architectures of polyelectrolyte films, including a thin chitosan layer (CH), poly(acrylic acid) (PAA) brushes, and a bilayer structure of CH grafted to PAA brushes (CH/PAA) as possible candidates for targeted drug delivery platforms. Atomic force microscopy (AFM) was employed to study the structure-mechanical property relationship for these mono- and bi-layered polymer grafts at pH 7.4 and 4.0, corresponding to physiological and biofilm formation conditions, respectively. Herein, the surface interactions between polymer grafts and the negatively charged silica colloid attached to an AFM lever are considered as representative interactions between the antibacterial coating and a bacteria/biofilm. The bilayered structure of CH/PAA showed significantly reduced adhesive interactions in comparison to pure CH but slightly higher interactions in comparison to PAA films. Among PAA and CH/PAA films, upon grafting CH over the PAA brushes, the normal stiffness increased by 10-fold at pH 7.4 and 20-fold at pH 4.0. Notably, the study also showed that the addition of an antibiotic drug such as multicationic Tobramycin (TOB) impacts the mechanical properties of the antibacterial coatings. Competition between TOB and water molecules for the PAA chains is shown to determine the structural properties of PAA and CH/PAA films loaded with TOB. At high pH (7.4), the TOB molecules, which remain multicationic, strongly interact with polyanionic PAA, thereby reducing the film's compressibility. On the contrary, at low pH (4.0), the water molecules preferentially interact with TOB in comparison to uncharged PAA chains and, upon TOB release, results in a stronger film collapse together with an increase in adhesive interactions between the probe, the surface, and the elastic modulus of the film. The bacterial proliferation on these platforms when compared to the measured mechanical properties shows a direct correlation; hence, understanding nanomechanical properties can provide insights into designing new antibacterial polymer coatings.

Size Dependence of Nanoscale Wear of Silicon Carbide

Nanoscale, single-asperity wear of single-crystal silicon carbide (sc-SiC) and nanocrystalline silicon carbide (nc-SiC) is investigated using single-crystal diamond nanoindenter tips and nanocrystalline diamond atomic force microscopy (AFM) tips under dry conditions, and the wear behavior is compared to that of single-crystal silicon with both thin and thick native oxide layers. We discovered a transition in the relative wear resistance of the SiC samples compared to that of Si as a function of contact size. With larger nanoindenter tips (tip radius ≈ 370 nm), the wear resistances of both sc-SiC and nc-SiC are higher than that of Si. This result is expected from the Archard's equation because SiC is harder than Si. However, with the smaller AFM tips (tip radius ≈ 20 nm), the wear resistances of sc-SiC and nc-SiC are lower than that of Si, despite the fact that the contact pressures are comparable to those applied with the nanoindenter tips, and the plastic zones are well-developed in both sets of wear experiments. We attribute the decrease in the relative wear resistance of SiC compared to that of Si to a transition from a wear regime dominated by the materials' resistance to plastic deformation (i.e., hardness) to a regime dominated by the materials' resistance to interfacial shear. This conclusion is supported by our AFM studies of wearless friction, which reveal that the interfacial shear strength of SiC is higher than that of Si. The contributions of surface roughness and surface chemistry to differences in interfacial shear strength are also discussed.

Nanoindentation and finite element modelling of chitosan-alginate multilayer coated hydrogels

Composite soft materials are used as compounds for determining the effects of mechanical cues on cell behavior and cell encapsulation and for controlling drug release. The appropriate composite soft materials are conventionally prepared by selective deposition of polymers at the surface of an ionic hydrogel. In the present study we address the impact of a mechanically stratified two-layer structure of these materials on their overall mechanical characterization by applying a combination of nanoindentation, confocal microscopy and finite element modelling. We prepare covalent cross-linked hydrogels based on acrylamide (AAM) and including an anionic group, and impregnate them using a multilayer deposition strategy of alternating exposure to cationic chitosan and anionic alginate. The thickness of the chitosan-alginate layer on the hydrogels was determined to be 0.4 ± 0.05 μm for 4 bilayers, and 0.7 ± 0.1 μm for the 8 bilayer deposition procedure employing a fluorescently labelled chitosan and confocal microscopy. The force-indentation data for the AAM gels were highly reproducible, whereas 77% and 50% of the force-indentation data were reproducible following the 4 and 8 bilayer deposition. The main trends in the reproducible force-distance data were found to yield an apparent increased Young's modulus after the deposition. Finite element modelling showed that adaption of a homogeneous Young's modulus for the specimens with deposited layers yields approximately three times too low stiffness compared to the estimate of the mechanical properties of the outer part in the two-layered mechanical model. The thickness of the multilayer region determined by confocal microscopy was used in the model. This study shows that the mechanical layered property needs to be included in the interpretation of the nanoindentation data when there is a significant mechanical contrast.

Theoretical Considerations and a Mathematical Model for the Analysis of the Biomechanical Response of Human Keratinized Oral Mucosa

Removable complete and partial dentures are supported by the residual alveolar ridges consisting of mucosa, submucosa, periosteum, and bone. An understanding of the biomechanical behavior of the oral mucosa is essential in order to improve the denture-bearing foundations for complete and partially edentulous patients. The purpose of this paper was to examine the biomechanical behavior of the soft tissues supporting a removable denture and develop a model for that reason. Keratinized oral mucosa blocks with their underlying bone were harvested from the maxillary palatal area adjacent to the edentulous ridges of a cadaver. The compressive response of the oral mucosa was tested by using atomic force microscopy. The specimens were first scanned in order their topography to be obtained. The mechanical properties of the specimens were tested using a single crystal silicon pyramidal tip, which traversed toward the keratinized oral mucosa specimens. Loading-unloading cycles were registered and four mathematical models were tested using MATLAB to note which one approximates the force-displacement curve as close as possible: a. spherical, b. conical, c. third order polynomial, d. Murphy (fourth order polynomial, non-linear Hertzian based). The third order polynomial model showed the best accuracy in representing the force-displacement data of the tested specimens. A model was developed in order to analyze the biomechanical behavior of the human oral keratinized mucosa and obtain information about its mechanical properties.

AFM Investigation of Liquid-Filled Polymer Microcapsules Elasticity

Elasticity of polymer microcapsules (MCs) filled with a liquid fluorinated core is studied by atomic force microscopy (AFM). Accurately characterized spherical tips are employed to obtain the Young's moduli of MCs having four different shell thicknesses. We show that those moduli are effective ones because the samples are composites. The strong decrease of the effective MC elasticity (from 3.0 to 0.1 GPa) as the shell thickness decreases (from 200 to 10 nm) is analyzed using a novel numerical approach. This model describes the evolution of the elasticity of a coated half-space according to the contact radius, the thickness of the film, and the elastic moduli of bulk materials. This numerical model is consistent with the experimental data and allows simulating the elastic behavior of MCs at high frequencies (5 MHz). While the quasi-static elasticity of the MCs is found to be very dependent on the shell thickness, the high frequency (5 MHz) elastic behavior of the core leads to a stable behavior of the MCs (from 2.5 to 3 GPa according to the shell thickness). Finally, the effect of thermal annealing on the MCs elasticity is investigated. The Young's modulus is found to decrease because of the reduction of the shell thickness due to the loss of the polymer.

Mapping nano-scale mechanical heterogeneity of primary plant cell walls

Nanoindentation experiments are performed using an atomic force microscope (AFM) to quantify the spatial distribution of mechanical properties of plant cell walls at nanometre length scales. At any specific location on the cell wall, a complex (non-linear) force-indentation response occurs that can be deconvoluted using a unique multiregime analysis (MRA). This allows an unambiguous evaluation of the local transverse elastic modulus of the wall. Nanomechanical measurements on suspension-cultured cells (SCCs), derived from Italian ryegrass (Lolium multiflorum) starchy endosperm, show three characteristic modes of deformation and a spatial distribution of elastic moduli across the surface. 'Soft' and 'hard' domains are found across length scales between 0.1 µm and 3 µm, which is well above a typical pore size of the polysaccharide mesh. The generality and wider applicability of this mechanical heterogeneity is verified through in planta characterization on leaf epidermal cells of Arabidopsis thaliana and L. multiflorum The outcomes of this research provide a basis for uncovering and quantifying the relationships between local wall composition, architecture, cell growth, and/or morphogenesis.

Investigation of PDMS based bi-layer elasticity via interpretation of apparent Young's modulus

As the need of new methods for the investigation of thin films on various kinds of substrates becomes greater, a novel approach based on AFM nanoindentation is explored. Substrates of polydimethylsiloxane (PDMS) coated by a layer of hard material are probed with an AFM tip in order to obtain the force profile as a function of the indentation. The equivalent elasticity of those composite systems is interpreted using a new numerical approach, the Coated Half-Space Indentation Model of Elastic Response (CHIMER), in order to extract the thicknesses of the upper layer. Two kinds of coating are investigated. First, chitosan films of known thicknesses between 30 and 200 nm were probed in order to test the model. A second type of samples is produced by oxygen plasma oxidation of the PDMS substrate, which results in the growth of a relatively homogeneous oxide layer. The local nature of this protocol enables measurements at long oxidation time, where the apparition of cracks prevents other kinds of measurements.

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

Morphogenesis in plants is directly linked to the mechanical elements of growing tissues, namely cell wall and inner cell pressure. Studies of these structural elements are now often performed using indentation methods such as atomic force microscopy. In these methods, a probe applies a force to the tissue surface at a subcellular scale and its displacement is monitored, yielding force-displacement curves that reflect tissue mechanics. However, the interpretation of these curves is challenging as they may depend not only on the cell probed, but also on neighboring cells, or even on the whole tissue. Here, we build a realistic three-dimensional model of the indentation of a flower bud using SOFA (Simulation Open Framework Architecture), in order to provide a framework for the analysis of force-displacement curves obtained experimentally. We find that the shape of indentation curves mostly depends on the ratio between cell pressure and wall modulus. Hysteresis in force-displacement curves can be accounted for by a viscoelastic behavior of the cell wall. We consider differences in elastic modulus between cell layers and we show that, according to the location of indentation and to the size of the probe, force-displacement curves are sensitive with different weights to the mechanical components of the two most external cell layers. Our results confirm most of the interpretations of previous experiments and provide a guide to future experimental work.

Plant cell wall extensibility: connecting plant cell growth with cell wall structure, mechanics, and the action of wall-modifying enzymes

The advent of user-friendly instruments for measuring force/deflection curves of plant surfaces at high spatial resolution has resulted in a recent outpouring of reports of the 'Young's modulus' of plant cell walls. The stimulus for these mechanical measurements comes from biomechanical models of morphogenesis of meristems and other tissues, as well as single cells, in which cell wall stress feeds back to regulate microtubule organization, auxin transport, cellulose deposition, and future growth directionality. In this article I review the differences between elastic modulus and wall extensibility in the context of cell growth. Some of the inherent complexities, assumptions, and potential pitfalls in the interpretation of indentation force/deflection curves are discussed. Reported values of elastic moduli from surface indentation measurements appear to be 10- to >1000-fold smaller than realistic tensile elastic moduli in the plane of plant cell walls. Potential reasons for this disparity are discussed, but further work is needed to make sense of the huge range in reported values. The significance of wall stress relaxation for growth is reviewed and connected to recent advances and remaining enigmas in our concepts of how cellulose, hemicellulose, and pectins are assembled to make an extensible cell wall. A comparison of the loosening action of α-expansin and Cel12A endoglucanase is used to illustrate two different ways in which cell walls may be made more extensible and the divergent effects on wall mechanics.

Nanomechanics of Cells and Biomaterials Studied by Atomic Force Microscopy

The behavior and mechanical properties of cells are strongly dependent on the biochemical and biomechanical properties of their microenvironment. Thus, understanding the mechanical properties of cells, extracellular matrices, and biomaterials is key to understanding cell function and to develop new materials with tailored mechanical properties for tissue engineering and regenerative medicine applications. Atomic force microscopy (AFM) has emerged as an indispensable technique for measuring the mechanical properties of biomaterials and cells with high spatial resolution and force sensitivity within physiologically relevant environments and timescales in the kPa to GPa elastic modulus range. The growing interest in this field of bionanomechanics has been accompanied by an expanding array of models to describe the complexity of indentation of hierarchical biological samples. Furthermore, the integration of AFM with optical microscopy techniques has further opened the door to a wide range of mechanotransduction studies. In recent years, new multidimensional and multiharmonic AFM approaches for mapping mechanical properties have been developed, which allow the rapid determination of, for example, cell elasticity. This Progress Report provides an introduction and practical guide to making AFM-based nanomechanical measurements of cells and surfaces for tissue engineering applications.