Quantitative analysis of the viscoelastic properties of thin regions of fibroblasts using atomic force microscopy

Nonlinear analysis of oscillatory indentation in elastic and viscoelastic solids

Determining the mechanical properties at micro- and nanometer length scales using nanoindentation or atomic force microscopy is important to many areas of science and engineering. Here we establish equations for obtaining storage and loss modulus from oscillatory indentations by performing a nonlinear analysis of conical and spherical indentation in elastic and viscoelastic solids. We show that, when the conical indenter is driven by a sinusoidal force, the square of displacement is a sinusoidal function of time, not the displacement itself, which is commonly assumed. Similar conclusions hold for spherical indentations. Well-known difficulties associated with measuring contact area and correcting thermal drift may be circumvented using the newly derived equations. These results may help improve methods of using oscillatory indentation for determining elastic and viscoelastic properties of solids.

Rheology of passive and adhesion-activated neutrophils probed by atomic force microscopy

The rheology of neutrophils in their passive and activated states plays a key role in determining their function in response to inflammatory stimuli. Atomic force microscopy was used to study neutrophil rheology by measuring the complex shear modulus G*(omega) of passive nonadhered rat neutrophils on poly(HEMA) and neutrophils activated through adhesion to glass. G*(omega) was measured over three frequency decades (0.1-102.4 Hz) by indenting the cells 500 nm with a spherical tip and then applying a 50-nm amplitude multi-frequency signal. G*(omega) of both passive and adhered neutrophils increased as a power law with frequency, with a coupling between elastic (G') and loss (G'') moduli. For passive neutrophils at 1.6 Hz, G' = 380 +/- 121 Pa, whereas G'' was fourfold smaller and the power law coefficient was of x = 1.184. Adhered neutrophils were over twofold stiffer with a lower slope (x = 1.148). This behavior was adequately described by the power law structural damping model but not by liquid droplet and Kelvin models. The increase in stiffness with frequency may modulate neutrophil transit, arrest, and transmigration in vascular microcirculation.

Cell migration through small gaps

Cell motility is a fundamental process associated with many phenomena in nature, such as immune response, wound healing, and cancer metastasis. In these processes, cells must squeeze through cell layers, and we characterize this ability to actively produce forces and simultaneously adapt their shapes. We have measured forward forces up to 15 nN that a migrating keratocyte was able to generate, in order to adjust its shape and successfully force its way under and past an obstacle. We also observed that 34 nN was capable of stalling the cell's forward motion. Furthermore, we measured that under compression stresses up to 1,165 pN/micro m2 (1,165 Pa), cell morphology, and velocity remained unchanged. Additionally, we found that keratocytes were able to compress themselves up to 80% vertically in order to squeeze through a gap as small as 500 nm.

Nanomechanical properties of individual chondrocytes and their developing growth factor-stimulated pericellular matrix

The nanomechanical properties of individual cartilage cells (chondrocytes) and their aggrecan and collagen-rich pericellular matrix (PCM) were measured via atomic force microscope nanoindentation using probe tips of two length scales (nanosized and micron-sized). The properties of cells freshly isolated from cartilage tissue (devoid of PCM) were compared to cells that were cultured for selected times (up to 28 days) in 3-D alginate gels which enabled PCM assembly and accumulation. Cells were immobilized and kept viable in pyramidal wells microfabricated into an array on silicon chips. Hertzian contact mechanics and finite element analyses were employed to estimate apparent moduli from the force versus depth curves. The effects of culture conditions on the resulting PCM properties were studied by comparing 10% fetal bovine serum to medium containing a combination of insulin growth factor-1 (IGF-1)+osteogenic protein-1 (OP-1). While both systems showed increases in stiffness with time in culture between days 7 and 28, the IGF-1+OP-1 combination resulted in a higher stiffness for the cell-PCM composite by day 28 and a higher apparent modulus of the PCM which is compared to the FBS cultured cells. These studies give insight into the temporal evolution of the nanomechanical properties of the pericellar matrix relevant to the biomechanics and mechanobiology of tissue-engineered constructs for cartilage repair.

Viscoelastic properties of zonal articular chondrocytes measured by atomic force microscopy

OBJECTIVE

Articular chondrocytes respond to chemical and mechanical signals depending on their zone of origin with respect to distance from the tissue surface. However, little is known of the zonal variations in cellular mechanical properties in cartilage. The goal of this study was to determine the zonal variations in the elastic and viscoelastic properties of porcine chondrocytes using atomic force microscopy (AFM), and to validate this method against micropipette aspiration.

METHODS

A theoretical solution for stress relaxation of a viscoelastic, incompressible, isotropic surface indented with a hard, spherical indenter (5 microm diameter) was derived and fit to experimental stress-relaxation data for AFM indentation of chondrocytes isolated from the superficial or middle/deep zones of cartilage.

RESULTS

The instantaneous moduli of chondrocytes were 0.55+/-0.23 kPa for superficial cells (S) and 0.29+/-0.14 kPa for middle/deep cells (M/D) (P<0.0001), and the relaxed moduli were 0.31+/-0.15 kPa (S) and 0.17+/-0.09 kPa (M/D) (P<0.0001). The apparent viscosities were 1.15+/-0.66 kPas (S) and 0.61+/-0.69 kPa-s (M/D) (P<0.0001). Results from the micropipette aspiration test showed similar cell moduli but higher apparent viscosities, indicating that mechanical properties measured by these two techniques are similar.

CONCLUSION

Our findings suggest that chondrocyte biomechanical properties differ significantly with the zone of origin, consistent with previous studies showing zonal differences in chondrocyte biosynthetic activity and gene expression. Given the versatility and dynamic testing capabilities of AFM, the ability to conduct stress-relaxation measurements using this technique may provide further insight into the viscoelastic properties of isolated cells.

Probing the viscoelastic response of glassy polymer films using atomic force microscopy

The mechanical properties of glassy films and glass surfaces have been studied using an atomic force microscope (AFM) through various imaging modes and measuring methods. In this paper, we discuss the viscoelastic response of a glassy surface probed using an AFM. We analyzed the force-distance curves measured on a glassy film or a glassy surface at temperatures near the glass transition temperature, Tg, using a Burgers model. We found that the material's characteristics of reversible anelastic response and viscous creep can be extracted from a force-distance curve. Anelastic response shifts the repulsive force-distance curve while viscous creep strongly affects the slope of the repulsive force-distance curve. When coupled with capillary force, due to the condensation of a thin layer of liquid film at the tip-surface joint, the anelasticity and viscous creep can alter the curve significantly in the attractive region.

Measurement and characterization of whole-cell mechanical behavior

An understanding of whole-cell mechanical behavior can provide insight into cellular responses to mechanical loading and diseases in which such responses are altered. However, this aspect of cellular mechanical behavior has received limited attention. In this study, we used the atomic force microscope (AFM) in conjunction with several mechanical characterization methods (Hertz contact theory, an exponential equation, and a parallel-spring recruitment model) to establish a mechanically rigorous method for measuring and characterizing whole-cell mechanical behavior in the deformation range 0-500 nm. Using MC3T3-E1 osteoblasts, measurement repeatability was assessed by performing multiple loading cycles on individual cells. Despite variability in measurements, repeatability of the measurement technique was statistically confirmed. The measurement technique also proved acceptable since only 5% of the total variance across all measurements was due to variations within measurements for a single cell. The parallel-spring recruitment model, a single-parameter model, accurately described the measured nonlinear force-deformation response (R2>0.99) while providing a mechanistic explanation of whole-cell mechanical behavior. Taken together, the results should improve the capabilities of the AFM to probe whole-cell mechanical behavior. In addition, the success of the parallel-spring recruitment model provides insight into the micromechanical basis of whole-cell behavior.

Polyelectrolyte multilayers with a tunable Young's modulus: influence of film stiffness on cell adhesion

Mechanical properties of model and natural gels have recently been demonstrated to play an important role in various cellular processes such as adhesion, proliferation, and differentiation, besides events triggered by chemical ligands. Understanding the biomaterial/cell interface is particularly important in many tissue engineering applications and in implant surgery. One of the final goals would be to control cellular processes precisely at the biomaterial surface and to guide tissue regeneration. In this work, we investigate the substrate mechanical effect on cell adhesion for thin polyelectrolyte multilayer (PEM) films, which can be easily deposited on any type of material. The films were cross linked by means of a water-soluble carbodiimide (EDC), and the film elastic modulus was determined using the AFM nanoindentation technique with a colloidal probe. The Young's modulus could be varied over 2 orders of magnitude (from 3 to 400 kPa) for wet poly(L-lysine)/hyaluronan (PLL/HA) films by changing the EDC concentration. The chemical changes upon cross linking were characterized by means of Fourier transform infrared spectroscopy (FTIR). We demonstrated that the adhesion and spreading of human chondrosarcoma cells directly depend on the Young's modulus. These data indicate that, besides the chemical properties of the polyelectrolytes, the substrate mechanics of PEM films is an important parameter influencing cell adhesion and that PEM offer a new way to prepare thin films of tunable mechanical properties with large potential biomedical applications including drug release.

Imaging and probing cell mechanical properties with the atomic force microscope

This chapter describes the use of the atomic force microscope (AFM) to probe and map out regional variations in apparent elastic properties of living cells. The importance of mechanics in the field of cell biology is becoming more widely appreciated, and the AFM has unique advantages for cell mechanics applications. However, care must be taken in the acquisition, analysis, Band interpretation of AFM indentation data. To help make this powerful technique accessible to a broad range of investigators, detailed procedures are provided for all stages of the AFM experiment from sample preparation through data analysis and visualization.

Substrate rigidity regulates the formation and maintenance of tissues

The ability of cells to form tissues represents one of the most fundamental issues in biology. However, it is unclear what triggers cells to adhere to one another in tissues and to migrate once a piece of tissue is planted on culture surfaces. Using substrates of identical chemical composition but different flexibility, we show that this process is controlled by substrate rigidity: on stiff substrates, cells migrate away from one another and spread on surfaces, whereas on soft substrates they merge to form tissue-like structures. Similar behavior was observed not only with fibroblastic and epithelial cell lines but also explants from neonatal rat hearts. Cell compaction on soft substrates involves a combination of weakened adhesions to the substrate and myosin II-dependent contractile forces that drive cells toward one another. Our results suggest that tissue formation and maintenance is regulated by differential mechanical signals between cell-cell and cell-substrate interactions, which in turn elicit differential contractile forces and adhesions to determine the preferred direction of cell migration and association.

Membrane ripples of a living cell measured by non-interferometric widefield optical profilometry

We measured the membrane topography and dynamics on a living fibroblast by using the non-interferometric widefield optical profilometry (NIWOP) technique. With a water-immersion objective of a 0.75 numerical aperture, our NIWOP system provides depth resolution about 20 nm. The imaging speed could be as high as 5 frames/min. We directly observed and profiled the inward propagation of membrane ripples near the cell edge. To verify if the membrane activity was driven by the underlying cytoskeleton, we changed the structure of the cell cortex while observing the membrane topography. After dissolving the actin cortex by cytochalasin D, we found that the propagation of the membrane ripples disappeared and the edge of the cell shank. The non-contact NIWOP technique does not affect the motility and viability of cells and therefore is suitable for the studies on cell physiology related to membrane motions.

Elasticity and adhesion of resting and lipopolysaccharide-stimulated macrophages

Colloidal Force Microscopy was employed to study the viscoelastic and adhesive properties of macrophages upon stimulation with lipopolysaccharide (LPS). Force vs. distance measurements were performed. The adhesion of LPS-stimulated cells (separation force=37+/-3 nN) was almost twice as high as that of resting macrophages (16+/-1 nN). Upon retraction pulling of membrane tethers was observed. Tether lengths and forces at which rupture take place did not depend on stimulation. The reduced Young's modulus K, a measure of cytoskeleton elasticity, was three times lower than that of the control. The data show that LPS has profound effects on cytomechanical and adhesion properties of macrophages.

Cell motility and local viscoelasticity of fibroblasts

Viscoelastic changes of the lamellipodial actin cytoskeleton are a fundamental element of cell motility. Thus, the correlation between the local viscoelastic properties of the lamellipodium (including the transitional region to the cell body) and the speed of lamellipodial extension is studied for normal and malignantly transformed fibroblasts. Using our atomic force microscopy-based microrheology technique, we found different mechanical properties between the lamellipodia of malignantly transformed fibroblasts (H-ras transformed and SV-T2 fibroblasts) and normal fibroblasts (BALB 3T3 fibroblasts). The average elastic constants, K, in the leading edge of SV-T2 fibroblasts (0.48 +/- 0.51 kPa) and of H-ras transformed fibroblasts (0.42 +/- 0.35 kPa) are significantly lower than that of BALB 3T3 fibroblasts (1.01 +/- 0.40 kPa). The analysis of time-lapse phase contrast images shows that the decrease in the elastic constant, K, for malignantly transformed fibroblasts is correlated with the enhanced motility of the lamellipodium. The measured mean speeds are 6.1 +/- 4.5 microm/h for BALB 3T3 fibroblasts, 13.1 +/- 5.2 microm/h for SV-T2 fibroblasts, and 26.2 +/- 11.5 microm/h for H-ras fibroblasts. Furthermore, the elastic constant, K, increases toward the cell body in many instances which coincide with an increase in actin filament density toward the cell body. The correlation between the enhanced motility and the decrease in viscoelastic moduli supports the Elastic Brownian Ratchet model for driving lamellipodia extension.

Probing mechanical properties of living cells by atomic force microscopy with blunted pyramidal cantilever tips

Atomic force microscopy (AFM) allows the acquisition of high-resolution images and the measurement of mechanical properties of living cells under physiological conditions. AFM cantilevers with blunted pyramidal tips are commonly used to obtain images of living cells. Measurement of mechanical properties with these tips requires a contact model that takes into account their blunted geometry. The aim of this work was to develop a contact model of a blunted pyramidal tip and to assess the suitability of pyramidal tips for probing mechanical properties of soft gels and living cells. We developed a contact model of a blunted pyramidal tip indenting an elastic half-space. We measured Young's modulus (E) and the complex shear modulus (G*= G' +i G" ) of agarose gels and A549 alveolar epithelial cells with pyramidal tips and compared them with those obtained with spherical tips. The gels exhibited an elastic behavior with almost coincident loading and unloading force curves and negligible values of G". E fell sharply with indentation up to approximately 300 nm , showing a linear regime for deeper indentations. A similar indentation dependence of E with twofold lower values at the linear regime was obtained with the spherical tip fitted with Hertz's model. The dependence of E on indentation in cells paralleled that found in gels. Cells exhibited viscoelastic behavior with G"/G' approximately 1/4 . Pyramidal tips commonly used for AFM imaging are suitable for probing mechanical properties of soft gels and living cells.

Characterizing single suspended cells by optorheology

The measurement of the mechanical properties of individual cells has received much attention in recent years. In this paper we describe the application of optically induced forces with an optical stretcher to perform step-stress experiments on individual suspended fibroblasts. The conversion from creep-compliance to frequency-dependent complex shear modulus reveals characteristic viscoelastic signatures of the underlying cytoskeleton and its dynamic molecular properties. Both normal and cancerous fibroblasts display a single stress relaxation time in the observed time and frequency space that can be related to the transient binding of actin crosslinking proteins. In addition, shear modulus and steady-state viscosity of the shell-like actin cortex as the main module resisting small deformations are extracted. These values in combination with insight into the cells' architecture are used to explain their different deformability. This difference can then be exploited to distinguish normal from cancerous cells. The nature of the optical stretcher as an optical trap allows easy incorporation in a microfluidic system with automatic trapping and alignment of the cells, and thus a high measurement throughput. This carries the potential for using the microfluidic optical stretcher to investigate cellular processes involving the cytoskeleton and to diagnose diseases related to cytoskeletal alterations.

Optical rheology of biological cells

A step stress deforming suspended cells causes a passive relaxation, due to a transiently cross-linked isotropic actin cortex underlying the cellular membrane. The fluid-to-solid transition occurs at a relaxation time coinciding with unbinding times of actin cross-linking proteins. Elastic contributions from slowly relaxing entangled filaments are negligible. The symmetric geometry of suspended cells ensures minimal statistical variability in their viscoelastic properties in contrast with adherent cells and thus is defining for different cell types. Mechanical stimuli on time scales of minutes trigger active structural responses.

Probing the viscoelastic behavior of cultured airway smooth muscle cells with atomic force microscopy: stiffening induced by contractile agonist

Complex rheology of airway smooth muscle cells and its dynamic response during contractile stimulation involves many molecular processes, foremost of which are actomyosin cross-bridge cycling and actin polymerization. With an atomic force microscope, we tracked the spatial and temporal variations of the viscoelastic properties of cultured airway smooth muscle cells. Elasticity mapping identified stiff structural elements of the cytoskeletal network. Using a precisely positioned microscale probe, picoNewton forces and nanometer level indentation modulations were applied to cell surfaces at frequencies ranging from 0.5 to 100 Hz. The resulting elastic storage modulus (G') and dissipative modulus (G'') increased dramatically, with hysteresivity (eta = G''/G') showing a definitive decrease after stimulation with the contractile agonist 5-hydroxytryptamine. Frequency-dependent assays showed weak power-law structural damping behavior and universal scaling in support of the soft-glassy material description of cellular biophysics. Additionally, a high-frequency component of the loss modulus (attributed to cellular Newtonian viscosity) increased fourfold during the contractile process. The complex shear modulus showed a strong sensitivity to the degree of actin polymerization. Inhibitors of myosin light chain kinase activity had little effect on the stiffening response to contractile stimulation. Thus, our measurements appear to be particularly well suited for characterization of dynamic actin rheology during airway smooth muscle contraction.

Myotubes differentiate optimally on substrates with tissue-like stiffness: pathological implications for soft or stiff microenvironments

Contractile myocytes provide a test of the hypothesis that cells sense their mechanical as well as molecular microenvironment, altering expression, organization, and/or morphology accordingly. Here, myoblasts were cultured on collagen strips attached to glass or polymer gels of varied elasticity. Subsequent fusion into myotubes occurs independent of substrate flexibility. However, myosin/actin striations emerge later only on gels with stiffness typical of normal muscle (passive Young's modulus, E approximately 12 kPa). On glass and much softer or stiffer gels, including gels emulating stiff dystrophic muscle, cells do not striate. In addition, myotubes grown on top of a compliant bottom layer of glass-attached myotubes (but not softer fibroblasts) will striate, whereas the bottom cells will only assemble stress fibers and vinculin-rich adhesions. Unlike sarcomere formation, adhesion strength increases monotonically versus substrate stiffness with strongest adhesion on glass. These findings have major implications for in vivo introduction of stem cells into diseased or damaged striated muscle of altered mechanical composition.

Dynamic osmotic loading of chondrocytes using a novel microfluidic device

Many cells exhibit disparate responses to a mechanical stimulus depending on whether it is applied dynamically or statically. In this context, few studies have examined how cells respond to dynamic changes of the extracellular osmolality. In this study, we hypothesized that the cell size change response of cultured articular chondrocytes would be dependent on the frequency of applied osmotic loading. To test this hypothesis, we developed a novel microfluidic device, to apply hydrostatic pressure-driven dynamic osmotic loading by applying composition modulated flow, adapted from Tang and co-workers. This microfluidic device was used to study osmotic loads of +/-180 mOsm at a frequency up to 0.1 Hz with a constant minimal fluid-shear stress, and permit real-time monitoring of cell responses. Bovine articular chondrocytes were observed to exhibit increasing changes in cell volume with decreasing osmotic loading frequency. When the cell volume response was modeled by an exponential function, chondrocytes exhibited significantly different volume change responses to dynamic osmotic loading at 0.0125 Hz and static osmotic loading applied for a period of four minutes (Delta = +/-180 mOsm relative to the isotonic 360 mOsm). The intracellular calcium response at 0.0125 Hz was also monitored and compared with the response to static loading. Coupled with phenomenological or constitutive models, this novel approach could yield new information regarding cell material properties in response to dynamic loading that may contribute new insights into mechanisms of cellular homeostasis and mechanotransduction.