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.     

Dehomogenized Elastic Properties of Heterogeneous Layered Materials in AFM Indentation Experiments

Atomic force microscopy (AFM) is used to study mechanical properties of biological materials at submicron length scales. However, such samples are often structurally heterogeneous even at the local level, with different regions having distinct mechanical properties. Physical or chemical disruption can isolate individual structural elements but may alter the properties being measured. Therefore, to determine the micromechanical properties of intact heterogeneous multilayered samples indented by AFM, we propose the Hybrid Eshelby Decomposition (HED) analysis, which combines a modified homogenization theory and finite element modeling to extract layer-specific elastic moduli of composite structures from single indentations, utilizing knowledge of the component distribution to achieve solution uniqueness. Using finite element model-simulated indentation of layered samples with micron-scale thickness dimensions, biologically relevant elastic properties for incompressible soft tissues, and layer-specific heterogeneity of an order of magnitude or less, HED analysis recovered the prescribed modulus values typically within 10% error. Experimental validation using bilayer spin-coated polydimethylsiloxane samples also yielded self-consistent layer-specific modulus values whether arranged as stiff layer on soft substrate or soft layer on stiff substrate. We further examined a biophysical application by characterizing layer-specific microelastic properties of full-thickness mouse aortic wall tissue, demonstrating that the HED-extracted modulus of the tunica media was more than fivefold stiffer than the intima and not significantly different from direct indentation of exposed media tissue. Our results show that the elastic properties of surface and subsurface layers of microscale synthetic and biological samples can be simultaneously extracted from the composite material response to AFM indentation. HED analysis offers a robust approach to studying regional micromechanics of heterogeneous multilayered samples without destructively separating individual components before testing.     

Impacts of maturation on the micromechanics of the meniscus extracellular matrix

To elucidate how maturation impacts the structure and mechanics of meniscus extracellular matrix (ECM) at the length scale of collagen fibrils and fibers, we tested the micromechanical properties of fetal and adult bovine menisci via atomic force microscopy (AFM)-nanoindentation. For circumferential fibers, we detected significant increase in the effective indentation modulus, E_ind, with age. Such impact is in agreement with the increase in collagen fibril diameter and alignment during maturation, and is more pronounced in the outer zone, where collagen fibrils are more aligned and packed. Meanwhile, maturation also markedly increases the E_ind of radial tie fibers, but not those of intact surface or superficial layer. These results provide new insights into the effect of maturation on the assembly of meniscus ECM, and enable the design of new meniscus repair strategies by modulating local ECM structure and mechanical behaviors.     

Force microscopy of nonadherent cells: a comparison of leukemia cell deformability

Atomic force microscopy (AFM) has become an important tool for quantifying mechanical properties of biological materials ranging from single molecules to cells and tissues. Current AFM techniques for measuring elastic and viscoelastic properties of whole cells are based on indentation of cells firmly adhered to a substrate, but these techniques are not appropriate for probing nonadherent cells, such as passive human leukocytes, due to a lateral instability of the cells under load. Here we present a method for characterizing nonadherent cells with AFM by mechanically immobilizing them in microfabricated wells. We apply this technique to compare the deformability of human myeloid and lymphoid leukemia cells and neutrophils at low deformation rates, and we find that the cells are well described by an elastic model based on Hertzian mechanics. Myeloid (HL60) cells were measured to be a factor of 18 times stiffer than lymphoid (Jurkat) cells and six times stiffer than human neutrophils on average (E(infinity) = 855 +/- 670 Pa for HL60 cells, E(infinity) = 48 +/- 35 Pa for Jurkat cells, E(infinity) = 156 +/- 87 for neutrophils, mean +/- SD). This work demonstrates a simple method for extending AFM mechanical property measurements to nonadherent cells and characterizes properties of human leukemia cells that may contribute to leukostasis, a complication associated with acute leukemia.     

Mechanical properties of a mature biofilm from a wastewater system: from microscale to macroscale level

A fundamental understanding of biofilm mechanical stability is critical in order to describe detachment and develop biofouling control strategies. It is thus important to characterise the elastic deformation and flow behaviour of the biofilm under different modes of applied force. In this study, the mechanical properties of a mature wastewater biofilm were investigated with methods including macroscale compression and microscale indentation using atomic force microscopy (AFM). The mature biofilm was found to be mechanically isotropic at the macroscale level as its mechanical properties did not depend on the scales and modes of loading. However, the biofilm showed a tendency for mechanical inhomogeneity at the microscale level as indentation progressed deeper into the matrix. Moreover, it was observed that the adhesion force had a significant influence on the elastic properties of the biofilm at the surface, subjected to microscale tensile loading. These results are expected to inform a damage-based model for biofilm detachment.     

Non-Hertzian approach to analyzing mechanical properties of endothelial cells probed by atomic force microscopy

Detailed measurements of cell material properties are required for understanding how cells respond to their mechanical environment. Atomic force microscopy (AFM) is an increasingly popular measurement technique that uniquely combines subcellular mechanical testing with high-resolution imaging. However, the standard method of analyzing AFM indentation data is based on a simplified "Hertz" theory that requires unrealistic assumptions about cell indentation experiments. The objective of this study was to utilize an alternative "pointwise modulus" approach, that relaxes several of these assumptions, to examine subcellular mechanics of cultured human aortic endothelial cells (HAECs). Data from indentations in 2- to 5-microm square regions of cytoplasm reveal at least two mechanically distinct populations of cellular material. Indentations colocalized with prominent linear structures in AFM images exhibited depth-dependent variation of the apparent pointwise elastic modulus that was not observed at adjacent locations devoid of such structures. The average pointwise modulus at an arbitrary indentation depth of 200 nm was 5.6+/-3.5 kPa and 1.5+/-0.76 kPa (mean+/-SD, n=7) for these two material populations, respectively. The linear structures in AFM images were identified by fluorescence microscopy as bundles of f-actin, or stress fibers. After treatment with 4 microM cytochalasin B, HAECs behaved like a homogeneous linear elastic material with an apparent modulus of 0.89+/-0.46 kPa. These findings reveal complex mechanical behavior specifically associated with actin stress fibers that is not accurately described using the standard Hertz analysis, and may impact how HAECs interact with their mechanical environment.     

Effect of Age and Cytoskeletal Elements on the Indentation-Dependent Mechanical Properties of Chondrocytes

Articular cartilage chondrocytes are responsible for the synthesis, maintenance, and turnover of the extracellular matrix, metabolic processes that contribute to the mechanical properties of these cells. Here, we systematically evaluated the effect of age and cytoskeletal disruptors on the mechanical properties of chondrocytes as a function of deformation. We quantified the indentation-dependent mechanical properties of chondrocytes isolated from neonatal (1-day), adult (5-year) and geriatric (12-year) bovine knees using atomic force microscopy (AFM). We also measured the contribution of the actin and intermediate filaments to the indentation-dependent mechanical properties of chondrocytes. By integrating AFM with confocal fluorescent microscopy, we monitored cytoskeletal and biomechanical deformation in transgenic cells (GFP-vimentin and mCherry-actin) under compression. We found that the elastic modulus of chondrocytes in all age groups decreased with increased indentation (15–2000 nm). The elastic modulus of adult chondrocytes was significantly greater than neonatal cells at indentations greater than 500 nm. Viscoelastic moduli (instantaneous and equilibrium) were comparable in all age groups examined; however, the intrinsic viscosity was lower in geriatric chondrocytes than neonatal. Disrupting the actin or the intermediate filament structures altered the mechanical properties of chondrocytes by decreasing the elastic modulus and viscoelastic properties, resulting in a dramatic loss of indentation-dependent response with treatment. Actin and vimentin cytoskeletal structures were monitored using confocal fluorescent microscopy in transgenic cells treated with disruptors, and both treatments had a profound disruptive effect on the actin filaments. Here we show that disrupting the structure of intermediate filaments indirectly altered the configuration of the actin cytoskeleton. These findings underscore the importance of the cytoskeletal elements in the overall mechanical response of chondrocytes, indicating that intermediate filament integrity is key to the non-linear elastic properties of chondrocytes. This study improves our understanding of the mechanical properties of articular cartilage at the single cell level.     

The Influence of Physical and Physiological Cues on Atomic Force Microscopy-Based Cell Stiffness Assessment

Atomic force microscopy provides a novel technique for differentiating the mechanical properties of various cell types. Cell elasticity is abundantly used to represent the structural strength of cells in different conditions. In this study, we are interested in whether physical or physiological cues affect cell elasticity in Atomic force microscopy (AFM)-based assessments. The physical cues include the geometry of the AFM tips, the indenting force and the operating temperature of the AFM. All of these cues show a significant influence on the cell elasticity assessment. Sharp AFM tips create a two-fold increase in the value of the effective Young’s modulus (E_eff) relative to that of the blunt tips. Higher indenting force at the same loading rate generates higher estimated cell elasticity. Increasing the operation temperature of the AFM leads to decreases in the cell stiffness because the structure of actin filaments becomes disorganized. The physiological cues include the presence of fetal bovine serum or extracellular matrix-coated surfaces, the culture passage number, and the culture density. Both fetal bovine serum and the extracellular matrix are critical for cells to maintain the integrity of actin filaments and consequently exhibit higher elasticity. Unlike primary cells, mouse kidney progenitor cells can be passaged and maintain their morphology and elasticity for a very long period without a senescence phenotype. Finally, cell elasticity increases with increasing culture density only in MDCK epithelial cells. In summary, for researchers who use AFM to assess cell elasticity, our results provide basic and significant information about the suitable selection of physical and physiological cues.     

Simple display system of mechanical properties of cells and their dispersion

The mechanical properties of cells are unique indicators of their states and functions. Though, it is difficult to recognize the degrees of mechanical properties, due to small size of the cell and broad distribution of the mechanical properties. Here, we developed a simple virtual reality system for presenting the mechanical properties of cells and their dispersion using a haptic device and a PC. This system simulates atomic force microscopy (AFM) nanoindentation experiments for floating cells in virtual environments. An operator can virtually position the AFM spherical probe over a round cell with the haptic handle on the PC monitor and feel the force interaction. The Young's modulus of mesenchymal stem cells and HEK293 cells in the floating state was measured by AFM. The distribution of the Young's modulus of these cells was broad, and the distribution complied with a log-normal pattern. To represent the mechanical properties together with the cell variance, we used log-normal distribution-dependent random number determined by the mode and variance values of the Young's modulus of these cells. The represented Young's modulus was determined for each touching event of the probe surface and the cell object, and the haptic device-generating force was calculated using a Hertz model corresponding to the indentation depth and the fixed Young's modulus value. Using this system, we can feel the mechanical properties and their dispersion in each cell type in real time. This system will help us not only recognize the degrees of mechanical properties of diverse cells but also share them with others.     

Molecular dynamics study on deformation and mechanics of nanoscale Au/Cu multilayers under indentation

The effects of individual layer thickness, indentation velocity, and temperature on the mechanical properties and mechanics of nanoscale Au/Cu multilayers under indentation were studied using molecular dynamics simulations based on the many-body embedded-atom potential. The simulation results show that layer interfaces act as strong barriers that resist the propagation of dislocations, even at an extremely small individual layer thickness of 3 nm. The number of dislocations increases significantly and the growth of dislocations decreases with decreasing individual layer thickness. There is no clear relationship between the magnitude of the required indentation force and the number of film layers; however, the average required indentation force increases with increasing indentation velocity and decreasing temperature. During indentation at a relatively low velocity, dislocation propagation is more significant; the number of disordered atoms significantly increases at a relatively high indentation velocity.     

Micro-Mechanical Characterization of Lung Tissue Using Atomic Force Microscopy

Matrix stiffness strongly influences growth, differentiation and function of adherent cells^1-3. On the macro scale the stiffness of tissues and organs within the human body span several orders of magnitude⁴. Much less is known about how stiffness varies spatially within tissues, and what the scope and spatial scale of stiffness changes are in disease processes that result in tissue remodeling. To better understand how changes in matrix stiffness contribute to cellular physiology in health and disease, measurements of tissue stiffness obtained at a spatial scale relevant to resident cells are needed. This is particularly true for the lung, a highly compliant and elastic tissue in which matrix remodeling is a prominent feature in diseases such as asthma, emphysema, hypertension and fibrosis. To characterize the local mechanical environment of lung parenchyma at a spatial scale relevant to resident cells, we have developed methods to directly measure the local elastic properties of fresh murine lung tissue using atomic force microscopy (AFM) microindentation. With appropriate choice of AFM indentor, cantilever, and indentation depth, these methods allow measurements of local tissue shear modulus in parallel with phase contrast and fluorescence imaging of the region of interest. Systematic sampling of tissue strips provides maps of tissue mechanical properties that reveal local spatial variations in shear modulus. Correlations between mechanical properties and underlying anatomical and pathological features illustrate how stiffness varies with matrix deposition in fibrosis. These methods can be extended to other soft tissues and disease processes to reveal how local tissue mechanical properties vary across space and disease progression.     

The synthesis of subendothelial matrix by bovine aortic endothelial cells in culture

Bovine aortic endothelial cells cultured on collagenous or plastic substrata continuously synthesize and deposit a subendothelial matrix, independently of whether the cells are in the logarithmic or the stationary phase of growth. This subendothelial matrix contains fibrillar and amorphous elements comparable with those observed in the subendothelium in vivo. Deposition of subendothelial matrix on a collagen gel substratum both started earlier and progressed at approximately double the rate than that on denatured collagen. The relative composition of the subendothelial matrix was assessed by sequential incubation with trypsin, elastase and collagenase (Jones et al., 1979). The subendothelial matrix deposited on collagen gels by early confluent cultures and late post-confluent cultures differed in their enzyme sensitivity. These age-related changes in the enzyme sensitivity of the subendothelial matrix were characteristic for each cloned cell population examined. Comparable variations in the composition of the subendothelial matrix were not observed when the cells were cultured on plastic or gelatin-coated dishes; the subendothelial matrix deposited on these two substrata contained considerably more trypsin-sensitive material and less elastase and collagenase-sensitive material than the matrix deposited on native collagen gels. Age-related changes in the enzyme sensitivity of the subendothelial matrix deposited on collagen gels was found to be a function of the time elapsed since confluence and it was not related to the time elapsed since plating or to the number of cells present.     

Relative microelastic mapping of living cells by atomic force microscopy.

The spatial and temporal changes of the mechanical properties of living cells reflect complex underlying physiological processes. Following these changes should provide valuable insight into the biological importance of cellular mechanics and their regulation. The tip of an atomic force microscope (AFM) can be used to indent soft samples, and the force versus indentation measurement provides information about the local viscoelasticity. By collecting force-distance curves on a time scale where viscous contributions are small, the forces measured are dominated by the elastic properties of the sample. We have developed an experimental approach, using atomic force microscopy, called force integration to equal limits (FIEL) mapping, to produce robust, internally quantitative maps of relative elasticity. FIEL mapping has the advantage of essentially being independent of the tip-sample contact point and the cantilever spring constant. FIEL maps of living Madine-Darby canine kidney (MDCK) cells show that elasticity is uncoupled from topography and reveal a number of unexpected features. These results present a mode of high-resolution visualization in which the contrast is based on the mechanical properties of the sample.     

Impacts of hematite nanoparticle exposure on biomechanical, adhesive, and surface electrical properties of Escherichia coli cells

Despite a wealth of studies examining the toxicity of engineered nanomaterials, current knowledge on their cytotoxic mechanisms (particularly from a physical perspective) remains limited. In this work, we imaged and quantitatively characterized the biomechanical (hardness and elasticity), adhesive, and surface electrical properties of Escherichia coli cells with and without exposure to hematite nanoparticles (NPs) in an effort to advance our understanding of the cytotoxic impacts of nanomaterials. Both scanning electron microscopy (SEM) and atomic force microscopy (AFM) showed that E. coli cells had noticeable deformation with hematite treatment for 45 min with a statistical significance. The hematite-treated cells became significantly harder or stiffer than untreated ones, as evidenced by indentation and spring constant measurements. The average indentation of the hematite-treated E. coli cells was 120 nm, which is significantly lower (P < 0.01) than that of the untreated cells (approximately 400 nm). The spring constant of hematite-treated E. coli cells (0.28 ± 0.11 nN/nm) was about 20 times higher than that of untreated ones (0.01 ± 0.01 nN/nm). The zeta potential of E. coli cells, measured by dynamic light scattering (DLS), was shown to shift from -4 ± 2 mV to -27 ± 8 mV with progressive surface adsorption of hematite NPs, a finding which is consistent with the local surface potential measured by Kelvin probe force microscopy (KPFM). Overall, the reported findings quantitatively revealed the adverse impacts of nanomaterial exposure on physical properties of bacterial cells and should provide insight into the toxicity mechanisms of nanomaterials.     

Probing elasticity and adhesion of live cells by atomic force microscopy indentation

Atomic force microscopy (AFM) indentation has become an important technique for quantifying the mechanical properties of live cells at nanoscale. However, determination of cell elasticity modulus from the force–displacement curves measured in the AFM indentations is not a trivial task. The present work shows that these force–displacement curves are affected by indenter-cell adhesion force, while the use of an appropriate indentation model may provide information on the cell elasticity and the work of adhesion of the cell membrane to the surface of the AFM probes. A recently proposed indentation model (Sirghi, Rossi in Appl Phys Lett 89:243118, 2006), which accounts for the effect of the adhesion force in nanoscale indentation, is applied to the AFM indentation experiments performed on live cells with pyramidal indenters. The model considers that the indentation force equilibrates the elastic force of the cell cytoskeleton and the adhesion force of the cell membrane. It is assumed that the indenter-cell contact area and the adhesion force decrease continuously during the unloading part of the indentation (peeling model). Force–displacement curves measured in indentation experiments performed with silicon nitride AFM probes with pyramidal tips on live cells (mouse fibroblast Balb/c3T3 clone A31-1-1) in physiological medium at 37°C agree well with the theoretical prediction and are used to determine the cell elasticity modulus and indenter-cell work of adhesion. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

On atomic force microscopy and the constitutive behavior of living cells

Atomic force microscopy (AFM) is one of many new technologies available to study the mechanical properties and mechanobiological responses of living cells. Despite the widespread usage of this technology, there has been little attempt to develop new theoretical frameworks to interpret the associated data. Rather, most analyses rely on the classical Hertz solution for the indentation of an elastic half-space within the context of linearized elasticity. In contrast, we propose a fully nonlinear, constrained mixture model for adherent cells that allows one to account separately for the contributions of the three primary structural constituents of the cytoskeleton. Moreover, we extend a prior solution for a small indentation superimposed on a finite equibiaxial extension by incorporating in this mixture model for the special case of an initially random distribution of constituents (actin, intermediate filaments, and microtubules). We submit that this theoretical framework will allow an improved interpretation of indentation force-depth data from a sub-class of atomic force microscopy tests and will serve as an important analytical check for future finite element models. The latter will be necessary to exploit further the capabilities of both atomic force microscopy and nonlinear mixture theories for cell behavior.     

基于AFM的活体状态外泌体纳米结构及机械特性研究(英文)

外泌体在细胞生理病理活动过程中起着重要的调控作用,研究外泌体的行为特性对于揭示生命活动及疾病发生发展的内在机理具有重要的基础意义.然而由于缺乏合适的观测手段及方法,目前对于活体状态下外泌体结构及特性的认知仍然很不足.原子力显微镜(AFM)的发明为研究溶液环境下天然状态生物样本提供了强大的技术工具,已成为生物学重要研究手段.本文利用AFM对单个活体状态外泌体的纳米结构及机械特性进行了研究.通过多聚赖氨酸静电吸附作用将从淋巴瘤患者骨髓中分离的外泌体吸附至基底,在溶液环境下实现了对单个活体状态外泌体的高质量AFM形貌成像并通过与空气中成像结果进行对比揭示了空气干燥处理对外泌体形貌的影响.在此基础上,分别利用AFM压痕试验和多参数成像技术实现了对单个活体状态外泌体机械特性的定量测量和可视化表征.最后基于所建立的方法技术揭示了化学处理后外泌体结构和机械特性的动态变化.研究结果为研究纳米尺度下活体状态外泌体的结构及特性,以更好理解天然状态外泌体的生理行为提供了新的方法和思路,对于外泌体研究具有潜在积极的意义.     

Cell dynamic adhesion and elastic properties probed with cylindrical atomic force microscopy cantilever tips

Cell adhesion is required for essential biological functions such as migration, tissue formation and wound healing, and it is mediated by individual molecules that bind specifically to ligands on other cells or on the extracellular matrix. Atomic force microscopy (AFM) has been successfully used to measure cell adhesion at both single molecule and whole cell levels. However, the measurement of inherent cell adhesion properties requires a constant cell-probe contact area during indentation, a requirement which is not fulfilled in common pyramidal or spherical AFM tips. We developed a procedure using focused ion beam (FIB) technology by which we modified silicon pyramidal AFM cantilever tips to obtain flat-ended cylindrical tips with a constant and known area of contact. The tips were validated on elastic gels and living cells. Cylindrical tips showed a fairly linear force-indentation behaviour on both gels and cells for indentations >200 nm. Cylindrical tips coated with ligands were used to quantify inherent dynamic cell adhesion and elastic properties. Force, work of adhesion and elasticity showed a marked dynamic response. In contrast, the deformation applied to the cells before rupture was fairly constant within the probed dynamic range. Taken together, these results suggest that the dynamic adhesion strength is counterbalanced by the dynamic elastic response to keep a constant cell deformation regardless of the applied pulling rate.     

Heterogeneous cell mechanical properties: an atomic force microscopy study.

Atomic force microscopy (AFM) is a non-invasive microscopy to explore living biological systems like cells in liquid environment. Thus AFM is an appropriate tool to investigate surface chemical modification and its influence on biological systems. In particular, control over biomaterial surface chemistry can result in a regulated cell response. This report investigates the influence of adhesive and non-adhesive surfaces on the cell morphology and the influence of the cytoskeleton structure on the local mechanical properties. In this study, the main work concerns a thorough investigation of the height images obtained with an AFM as therecorded images provide the evolution of the mechanical properties of the cell as function of its local structure. Information on the cell elasticity due to the cytoskeleton organization is deduced when comparing the AFM tip indentation depth versus the distance between the cytoskeleton bundles for the different samples.     

Effects of temperature and cellular interactions on the mechanics and morphology of human cancer cells investigated by atomic force microscopy

Cell mechanics plays an important role in cellular physiological activities. Recent studies have shown that cellular mechanical properties are novel biomarkers for indicating the cell states. In this article, temperature-controllable atomic force microscopy(AFM) was applied to quantitatively investigate the effects of temperature and cellular interactions on the mechanics and morphology of human cancer cells. First, AFM indenting experiments were performed on six types of human cells to investigate the changes of cellular Young's modulus at different temperatures and the results showed that the mechanical responses to the changes of temperature were variable for different types of cancer cells. Second, AFM imaging experiments were performed to observe the morphological changes in living cells at different temperatures and the results showed the significant changes of cell morphology caused by the alterations of temperature. Finally, by co-culturing human cancer cells with human immune cells, the mechanical and morphological changes in cancer cells were investigated. The results showed that the co-culture of cancer cells and immune cells could cause the distinct mechanical changes in cancer cells, but no significant morphological differences were observed. The experimental results improved our understanding of the effects of temperature and cellular interactions on the mechanics and morphology of cancer cells.