Stiffness characterization of anisotropic trabecular meshwork

Elevation of intraocular pressure has been correlated to changes in stiffness of trabecular meshwork (TM) in glaucomatous eyes although mechanical properties of the TM remain to be quantitatively determined. Data in the literature suggest that the TM cannot be considered mechanically as a uniform layer of isotropic elastic material, because the value of its Young’s modulus depends on the methods of measurements and can vary up to five orders of magnitude. To this end, we proposed a new theoretical framework for mechanical analysis of the TM, in which the inner wall of Schlemm’s canal and the juxtacanalicular tissue in the TM were treated as a uniform layer of isotropic elastic material, and the rest of the TM, i.e., the uveal and corneoscleral meshworks, were modeled as a uniform layer of transversely isotropic material. Using the model, we demonstrated that the large discrepancy in the apparent Young’s modulus reported in the literature could be caused by the anisotropy of the meshwork that was significantly stiffer in the longitudinal direction than in the transverse direction. The theoretical framework could be used to integrate existing data of the stiffness, investigate anisotropic behaviors of the tissues, and develop new methods to measure mechanical properties of the TM.     

Dynamic elastic modulus of porcine articular cartilage determined at two different levels of tissue organization by indentation-type atomic force microscopy

Cartilage stiffness was measured ex vivo at the micrometer and nanometer scales to explore structure-mechanical property relationships at smaller scales than has been done previously. A method was developed to measure the dynamic elastic modulus, |E(*)|, in compression by indentation-type atomic force microscopy (IT AFM). Spherical indenter tips (radius = approximately 2.5 microm) and sharp pyramidal tips (radius = approximately 20 nm) were employed to probe micrometer-scale and nanometer-scale response, respectively. |E(*)| values were obtained at 3 Hz from 1024 unloading response curves recorded at a given location on subsurface cartilage from porcine femoral condyles. With the microsphere tips, the average modulus was approximately 2.6 MPa, in agreement with available millimeter-scale data, whereas with the sharp pyramidal tips, it was typically 100-fold lower. In contrast to cartilage, measurements made on agarose gels, a much more molecularly amorphous biomaterial, resulted in the same average modulus for both indentation tips. From results of AFM imaging of cartilage, the micrometer-scale spherical tips resolved no fine structure except some chondrocytes, whereas the nanometer-scale pyramidal tips resolved individual collagen fibers and their 67-nm axial repeat distance. These results suggest that the spherical AFM tip is large enough to measure the aggregate dynamic elastic modulus of cartilage, whereas the sharp AFM tip depicts the elastic properties of its fine structure. Additional measurements of cartilage stiffness following enzyme action revealed that elastase digestion of the collagen moiety lowered the modulus at the micrometer scale. In contrast, digestion of the proteoglycans moiety by cathepsin D had little effect on |E(*)| at the micrometer scale, but yielded a clear stiffening at the nanometer scale. Thus, cartilage compressive stiffness is different at the nanometer scale compared to the overall structural stiffness measured at the micrometer and larger scales because of the fine nanometer-scale structure, and enzyme-induced structural changes can affect this scale-dependent stiffness differently.     

Indentation and adhesive probing of a cell membrane with AFM: theoretical model and experiments

In probing adhesion and cell mechanics by atomic force microscopy (AFM), the mechanical properties of the membrane have an important if neglected role. Here we theoretically model the contact of an AFM tip with a cell membrane, where direct motivation and data are derived from a prototypical ligand-receptor adhesion experiment. An AFM tip is functionalized with a prototypical ligand, SIRPalpha, and then used to probe its native receptor on red cells, CD47. The interactions prove specific and typical in force, and also show in detachment, a sawtooth-shaped disruption process that can extend over hundreds of nm. The theoretical model here that accounts for both membrane indentation as well as membrane extension in tip retraction incorporates membrane tension and elasticity as well as AFM tip geometry and stochastic disruption. Importantly, indentation depth proves initially proportional to membrane tension and does not follow the standard Hertz model. Computations of detachment confirm nonperiodic disruption with membrane extensions of hundreds of nm set by membrane tension. Membrane mechanical properties thus clearly influence AFM probing of cells, including single molecule adhesion experiments.     

An AFM-based stiffness clamp for dynamic control of rigidity

Atomic force microscopy (AFM) has become a powerful tool for measuring material properties in biology and imposing mechanical boundary conditions on samples from single molecules to cells and tissues. Constant force or constant height can be maintained in an AFM experiment through feedback control of cantilever deflection, known respectively as a ‘force clamp’ or ‘position clamp’. However, stiffness, the third variable in the Hookean relation F = kx that describes AFM cantilever deflection, has not been dynamically controllable in the same way. Here we present and demonstrate a ‘stiffness clamp’ that can vary the apparent stiffness of an AFM cantilever. This method, employable on any AFM system by modifying feedback control of the cantilever, allows rapid and reversible tuning of the stiffness exposed to the sample in a way that can decouple the role of stiffness from force and deformation. We demonstrated the AFM stiffness clamp on two different samples: a contracting fibroblast cell and an expanding polyacrylamide hydrogel. We found that the fibroblast, a cell type that secretes and organizes the extracellular matrix, exhibited a rapid, sub-second change in traction rate (dF/dt) and contraction velocity (dx/dt) in response to step changes in stiffness between 1–100 nN/µm. This response was independent of the absolute contractile force and cell height, demonstrating that cells can react directly to changes in stiffness alone. In contrast, the hydrogel used in our experiment maintained a constant expansion velocity (dx/dt) over this range of stiffness, while the traction rate (dF/dt) changed with stiffness, showing that passive materials can also behave differently in different stiffness environments. The AFM stiffness clamp presented here, which is applicable to mechanical measurements on both biological and non-biological samples, may be used to investigate cellular mechanotransduction under a wide range of controlled mechanical boundary conditions.     

Measurement of cell adhesion force by vertical forcible detachment using an arrowhead nanoneedle and atomic force microscopy

The properties of substrates and extracellular matrices (ECM) are important factors governing the functions and fates of mammalian adherent cells. For example, substrate stiffness often affects cell differentiation. At focal adhesions, clustered–integrin bindings link cells mechanically to the ECM. In order to quantitate the affinity between cell and substrate, the cell adhesion force must be measured for single cells. In this study, forcible detachment of a single cell in the vertical direction using AFM was carried out, allowing breakage of the integrin–substrate bindings. An AFM tip was fabricated into an arrowhead shape to detach the cell from the substrate. Peak force observed in the recorded force curve during probe retraction was defined as the adhesion force, and was analyzed for various types of cells. Some of the cell types adhered so strongly that they could not be picked up because of plasma membrane breakage by the arrowhead probe. To address this problem, a technique to reinforce the cellular membrane with layer-by-layer nanofilms composed of fibronectin and gelatin helped to improve insertion efficiency and to prevent cell membrane rupture during the detachment process, allowing successful detachment of the cells. This method for detaching cells, involving cellular membrane reinforcement, may be beneficial for evaluating true cell adhesion forces in various cell types.     

Mechanical double layer model for Saccharomyces Cerevisiae cell wall

The elastic modulus of the Baker’s yeast (Saccharomyces cerevisiae) cell wall reported in studies using atomic force microscopy (AFM) is two orders of magnitude lower than that obtained using whole cell compression by micromanipulation. Using finite element modelling, it is shown that Hertz-Sneddon analysis cannot be applied to AFM indentation data for single layer core–shell structures. In addition, the Reissner solution for shallow homogeneous spheres is not appropriate for thick walls such as those of yeast cells. In order to explain yeast compression measurements at different length scales, a double layer wall model is presented considering a soft external layer composed of mannoproteins, and a stiff inner layer of β-glucan fibres and chitin. Under this model, previous AFM studies using sharp indenters provide reasonable estimates of the external layer elastic modulus, while micromanipulation provides the total stiffness of the cell wall. Data from both measurements are combined to estimate the mechanical properties of the inner stiff layer.     

Oxidized-LDL induce morphological changes and increase stiffness of endothelial cells

There is increasing evidence suggesting that oxidized low-density lipoproteins (ox-LDL) play a critical role in endothelial injury contributing to the age-related physio-pathological process of atherosclerosis. In this study, the effects of native LDL and ox-LDL on the mechanical properties of living human umbilical vein endothelial cells (HUVEC) were investigated by atomic force microscopy (AFM) force measurements. The contribution of filamentous actin (F-actin) and vimentin on cytoskeletal network organization were also examined by fluorescence microscopy. Our results revealed that ox-LDL had an impact on the HUVEC shape by interfering with F-actin and vimentin while native LDL showed no effect. AFM colloidal force measurements on living individual HUVEC were successfully used to measure stiffness of cells exposed to native and ox-LDL. AFM results demonstrated that the cell body became significantly stiffer when cells were exposed for 24 h to ox-LDL while cells exposed for 24 h to native LDL displayed similar rigidity to that of the control cells. Young's moduli of LDL-exposed HUVEC were calculated using two models. This study thus provides quantitative evidence on biomechanical mechanisms related to endothelial cell dysfunction and may give new insight on strategies aiming to protect endothelial function in atherosclerosis.     

Compressive nanomechanics of opposing aggrecan macromolecules

In this study, we have measured the nanoscale compressive interactions between opposing aggrecan macromolecules in near-physiological conditions, in order to elucidate the molecular origins of tissue-level cartilage biomechanical behavior. Aggrecan molecules from fetal bovine epiphyseal cartilage were chemically end-grafted to planar substrates, standard nanosized atomic force microscopy (AFM) probe tips (R(tip) approximately 50 nm), and larger colloidal probe tips (R(tip) approximately 2.5 microm). To assess normal nanomechanical interaction forces between opposing aggrecan layers, substrates with microcontact printed aggrecan were imaged using contact mode AFM, and aggrecan layer height (and hence deformation) was measured as a function of solution ionic strength (IS) and applied normal load. Then, using high-resolution force spectroscopy, nanoscale compressive forces between opposing aggrecan on the tip and substrate were measured versus tip-substrate separation distance in 0.001-1M NaCl. Nanosized tips enabled measurement of the molecular stiffness of 2-4 aggrecan while colloidal tips probed the nanomechanical properties of larger assemblies (approximately 10(4) molecules). The compressive stiffness of aggrecan was much higher when using a densely packed colloidal tip than the stiffness measured for using the nanosized tip with a few aggrecan, demonstrating the importance of lateral interactions to the normal nanomechanical properties. The measured stress at 0.1M NaCl (near-physiological ionic strength) increased sharply at aggrecan densities under the tip of approximately 40 mg/ml (physiological densities are approximately 20-80 mg/ml), corresponding to an average inter-GAG spacing of 4-5 Debye lengths (4-5 nm); this characteristic spacing is consistent with the onset of significant electrostatic interactions between GAG chains of opposing aggrecan molecules. Comparison of nanomechanical data to the predictions of Poisson-Boltzmann-based models further elucidated the regimes over which electrostatic and nonelectrostatic interactions affect aggrecan stiffness in compression. The most important aspects of this study include: the incorporation of experiments at two different length scales, the use of microcontact printing to enable quantification of aggrecan deformation and the corresponding nanoscale compressive stress vs. strain curve, the use of tips of differing functionality to provide insights into the molecular mechanisms of deformation, and the comparison of experimental data to the predictions of three increasingly refined Poisson-Boltzmann (P-B)-based theoretical models for the electrostatic double layer component of the interaction.     

Dissecting the contribution of actin and vimentin intermediate filaments to mechanical phenotype of suspended cells using high-throughput deformability measurements and computational modeling

Mechanical cell properties play an important role in many basic biological functions, including motility, adhesion, proliferation and differentiation. There is a growing body of evidence that the mechanical cell phenotype can be used for detection and, possibly, treatment of various diseases, including cancer. Understanding of pathological mechanisms requires investigation of the relationship between constitutive properties and major structural components of cells, i.e., the nucleus and cytoskeleton. While the contribution of actin und microtubules to cellular rheology has been extensively studied in the past, the role of intermediate filaments has been scarcely investigated up to now. Here, for the first time we compare the effects of drug-induced disruption of actin and vimentin intermediate filaments on mechanical properties of suspended NK cells using high-throughput deformability measurements and computational modeling. Although, molecular mechanisms of actin and vimentin disruption by the applied cytoskeletal drugs, Cytochalasin-D and Withaferin-A, are different, cell softening in both cases can be attributed to reduction of the effective density and stiffness of filament networks. Our experimental data suggest that actin and vimentin deficient cells exhibit, in average, 41% and 20% higher deformability in comparison to untreated control. 3D Finite Element simulation is performed to quantify the contribution of cortical actin and perinuclear vimentin to mechanical phenotype of the whole cell. Our simulation provides quantitative estimates for decreased filament stiffness in drug-treated cells and predicts more than two-fold increase of the strain magnitude in the perinuclear vimentin layer of actin deficient cells relatively to untreated control. Thus, the mechanical function of vimentin becomes particularly essential in motile and proliferating cells that have to dynamically remodel the cortical actin network. These insights add functional cues to frequently observed overexpression of vimentin in diverse types of cancer and underline the role of vimentin targeting drugs, such as Withaferin-A, as a potent cancerostatic supplement.     

Atomic Force Microscopy of Biological Membranes

Atomic force microscopy (AFM) is an ideal method to study the surface topography of biological membranes. It allows membranes that are adsorbed to flat solid supports to be raster-scanned in physiological solutions with an atomically sharp tip. Therefore, AFM is capable of observing biological molecular machines at work. In addition, the tip can be tethered to the end of a single membrane protein, and forces acting on the tip upon its retraction indicate barriers that occur during the process of protein unfolding. Here we discuss the fundamental limitations of AFM determined by the properties of cantilevers, present aspects of sample preparation, and review results achieved on reconstituted and native biological membranes.     

Comparison of atomic force microscopy interaction forces between bacteria and silicon nitride substrata for three commonly used immobilization methods

Atomic force microscopy (AFM) has emerged as a powerful technique for mapping the surface morphology of biological specimens, including bacterial cells. Besides creating topographic images, AFM enables us to probe both physicochemical and mechanical properties of bacterial cell surfaces on a nanometer scale. For AFM, bacterial cells need to be firmly anchored to a substratum surface in order to withstand the friction forces from the silicon nitride tip. Different strategies for the immobilization of bacteria have been described in the literature. This paper compares AFM interaction forces obtained between Klebsiella terrigena and silicon nitride for three commonly used immobilization methods, i.e., mechanical trapping of bacteria in membrane filters, physical adsorption of negatively charged bacteria to a positively charged surface, and glutaraldehyde fixation of bacteria to the tip of the microscope. We have shown that different sample preparation techniques give rise to dissimilar interaction forces. Indeed, the physical adsorption of bacterial cells on modified substrata may promote structural rearrangements in bacterial cell surface structures, while glutaraldehyde treatment was shown to induce physicochemical and mechanical changes on bacterial cell surface properties. In general, mechanical trapping of single bacterial cells in filters appears to be the most reliable method for immobilization.     

Sanguinarine Decreases Cell Stiffness and Traction Force and Inhibits the Reactivity of Airway Smooth Muscle Cells in Culture

Airway hyperresponsiveness (AHR) is the cardinal character of asthma, which involves the biomechanical properties such as cell stiffness and traction force of airway smooth muscle cells (ASMCs). Therefore, these biomechanical properties comprise logical targets of therapy. β2-adrenergic agonist is currently the mainstream drug to target ASMCs in clinical practice for treating asthma. However, this drug is known for side effects such as desensitization and non-responsiveness in some patients. Therefore, it is desirable to search for new drug agents to be alternative of β2-adrenergic agonist. In this context, sanguinarine, a natural product derived from plants such as bloodroots, that has been reported to relax gut smooth muscle emerges as a potential candidate. So far, it is unknown whether sanguinarine can regulate the biomechanical properties of ASMCs and reactivity of ASMCs to irritants. Thus, we tested the hypothesis that sanguinarine reduce the contractile potentials of ASMCs in culture. To do so, the primary cultured rat ASMCs were first treated with different concentration of sanguinarine. Then, cell stiffness, traction force, fiber distribution, and calcium signaling of the ASMCs were evaluated by optical magnetic twisting cytometry, Fourier transform traction microscopy, atomic force microscopy, and Fluo-4/AM based fluorescence confocal scanning microscopy, respectively. The results indicated that sanguinarine (0.05 and 0.5 μmol/L) significantly decreased cell stiffness and traction force, inhibited reactivity of ASMCs to histamine, and disrupted the fiber structures in ASMCs in dose-dependent manner. These findings establish that sanguinarine can indeed change the biomechanical properties of ASMCs and may be used to treat AHR in asthma.     

Comparison of Atomic Force Microscopy Interaction Forces between Bacteria and Silicon Nitride Substrata for Three Commonly Used Immobilization Methods

Atomic force microscopy (AFM) has emerged as a powerful technique for mapping the surface morphology of biological specimens, including bacterial cells. Besides creating topographic images, AFM enables us to probe both physicochemical and mechanical properties of bacterial cell surfaces on a nanometer scale. For AFM, bacterial cells need to be firmly anchored to a substratum surface in order to withstand the friction forces from the silicon nitride tip. Different strategies for the immobilization of bacteria have been described in the literature. This paper compares AFM interaction forces obtained between Klebsiella terrigena and silicon nitride for three commonly used immobilization methods, i.e., mechanical trapping of bacteria in membrane filters, physical adsorption of negatively charged bacteria to a positively charged surface, and glutaraldehyde fixation of bacteria to the tip of the microscope. We have shown that different sample preparation techniques give rise to dissimilar interaction forces. Indeed, the physical adsorption of bacterial cells on modified substrata may promote structural rearrangements in bacterial cell surface structures, while glutaraldehyde treatment was shown to induce physicochemical and mechanical changes on bacterial cell surface properties. In general, mechanical trapping of single bacterial cells in filters appears to be the most reliable method for immobilization.     

Exploring the mechanical behavior of single intermediate filaments

Intermediate filaments (IFs) are structural elements of eukaryotic cells with distinct mechanical properties. Tissue integrity is severely impaired, in particular in skin and muscle, when IFs are either absent or malfunctioning due to mutations. Our knowledge on the mechanical properties of IFs is mainly based on tensile testing of macroscopic fibers and on the rheology of IF networks. At the single filament level, the only piece of data available is a measure of the persistence length of vimentin IFs. Here, we have employed an atomic force microscopy (AFM) based protocol to directly probe the mechanical properties of single cytoplasmic IFs when adsorbed to a solid support in physiological buffer environment. Three IF types were studied in vitro: recombinant murine desmin, recombinant human keratin K5/K14 and neurofilaments isolated from rat brains, which are composed of the neurofilament triplet proteins NF-L, NF-M and NF-H. Depending on the experimental conditions, the AFM tip was used to laterally displace or to stretch single IFs on the support they had been adsorbed to. Upon applying force, IFs were stretched on average 2.6-fold. The maximum stretching that we encountered was 3.6-fold. A large reduction of the apparent filament diameter was observed concomitantly. The observed mechanical properties therefore suggest that IFs may indeed function as mechanical shock absorbers in vivo.     

If Cell Mechanics Can Be Described by Elastic Modulus: Study of Different Models and Probes Used in Indentation Experiments

Here we investigated the question whether cells, being highly heterogeneous objects, could be described with the elastic modulus (effective Young’s modulus) in a self-consistent way. We performed a comparative analysis of the elastic modulus derived from the indentation data obtained with atomic force microscopy (AFM) on human cervical epithelial cells (both normal and cancerous). Both sharp (cone) and dull (2500-nm radius sphere) AFM probes were used. The indentation data were processed through different elastic models. The cell was approximated as a homogeneous elastic medium that had either 1), smooth hemispherical boundary (Hertz/Sneddon models) or 2), the boundary covered with a layer of glycocalyx and membrane protrusions (“brush” models). Consistency of these approximations was investigated. Specifically, we tested the independence of the elastic modulus of the indentation depth, which is assumed in these models. We demonstrated that only one model showed consistency in treating cells as a homogeneous elastic medium, namely, the brush model, when processing the indentation data collected with the dull AFM probe. The elastic modulus demonstrated strong depth dependence in all models: Hertz/Sneddon models (no brush taken into account), and when the brush model was applied to the data collected with sharp conical probes. We conclude that it is possible to describe the elastic properties of the cell body by means of an effective elastic modulus, used in a self-consistent way, when using the brush model to analyze data collected with a dull AFM probe. The nature of these results is discussed.     

If Cell Mechanics Can Be Described by Elastic Modulus: Study of Different Models and Probes Used in Indentation Experiments

Here we investigated the question whether cells, being highly heterogeneous objects, could be described with the elastic modulus (effective Young’s modulus) in a self-consistent way. We performed a comparative analysis of the elastic modulus derived from the indentation data obtained with atomic force microscopy (AFM) on human cervical epithelial cells (both normal and cancerous). Both sharp (cone) and dull (2500-nm radius sphere) AFM probes were used. The indentation data were processed through different elastic models. The cell was approximated as a homogeneous elastic medium that had either 1), smooth hemispherical boundary (Hertz/Sneddon models) or 2), the boundary covered with a layer of glycocalyx and membrane protrusions (“brush” models). Consistency of these approximations was investigated. Specifically, we tested the independence of the elastic modulus of the indentation depth, which is assumed in these models. We demonstrated that only one model showed consistency in treating cells as a homogeneous elastic medium, namely, the brush model, when processing the indentation data collected with the dull AFM probe. The elastic modulus demonstrated strong depth dependence in all models: Hertz/Sneddon models (no brush taken into account), and when the brush model was applied to the data collected with sharp conical probes. We conclude that it is possible to describe the elastic properties of the cell body by means of an effective elastic modulus, used in a self-consistent way, when using the brush model to analyze data collected with a dull AFM probe. The nature of these results is discussed.     

Analysis of indentation: implications for measuring mechanical properties with atomic force microscopy.

Indentation using the atomic force microscope (AFM) has potential to measure detailed micromechanical properties of soft biological samples. However, interpretation of the results is complicated by the tapered shape of the AFM probe tip, and its small size relative to the depth of indentation. Finite element models (FEMs) were used to examine effects of indentation depth, tip geometry, and material nonlinearity and heterogeneity on the finite indentation response. Widely applied infinitesimal strain models agreed with FEM results for linear elastic materials, but yielded substantial errors in the estimated properties for nonlinear elastic materials. By accounting for the indenter geometry to compute an apparent elastic modulus as a function of indentation depth, nonlinearity and heterogeneity of material properties may be identified. Furthermore, combined finite indentation and biaxial stretch may reveal the specific functional form of the constitutive law--a requirement for quantitative estimates of material constants to be extracted from AFM indentation data.     

Mechanism of the reconstruction of aqueous outflow drainage

Glaucoma is the leading cause of irreversible blindness worldwide. The reconstruction of aqueous outflow drainage (RAOD) has recently been proposed to aid in restoring aqueous outflow drainage in primary open-angle glaucoma. However, the mechanism of RAOD remains to be fully understood. Based on literature review and research studies, the potential mechanisms of RAOD are the following: (i) Circumferential dilation of the Schlemm’s canal (SC) and surrounding collector channels. (ii) Instant formation of microcracks through RAOD procedures. (iii) Formation of more pores, and local detachment between the SC endothelium (SCE) and basement membrane. (iv) Activation of stem cells by constant mechanical stress caused by the tensional suture placed at the anterior part of the SC. (v) Reversal of trabecular meshwork (TM) herniation. (vi) Mobilization of the reserve of the aqueous drainage. (vii) Change of SCE phenotype. (viii) Mechanosensing and mechanotransducing of TM.