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

A trachea-inspired bifurcated microfilter capturing viable circulating tumor cells via altered biophysical properties as measured by atomic force microscopy

Circulating tumor cells (CTCs), though exceedingly rare in the blood, are nonetheless becoming increasingly important in cancer diagnostics. Despite this keen interest and the growing number of potential clinical applications, there has been limited success in developing a CTC isolation platform that simultaneously optimizes recovery rates, purity, and cell compatibility. Herein, a novel tracheal carina-inspired bifurcated (TRAB) microfilter system is reported, which uses an optimal filter gap size satisfying both 100% theoretical recovery rate and purity, as determined by biomechanical analysis and fluid-structure interaction (FSI) simulations. Biomechanical properties are also used to clearly discriminate between cancer cells and leukocytes, whereby cancer cells are selectively bound to melamine microbeads, which increase the size and stiffness of these cells. Nanoindentation experiments are conducted to measure the stiffness of leukocytes as compared to the microbead-conjugated cancer cells, with these parameters then being used in FSI analyses to optimize the filter gap size. The simulation results show that given a flow rate of 100 μL min(-1), an 8 μm filter gap optimizes the recovery rate and purity. MCF-7 breast cancer cells with solid microbeads are spiked into 3 mL of whole blood and, by using this flow rate along with the optimized microfilter dimensions, the cell mixture passes through the TRAB filter, which achieves a recovery rate of 93% and purity of 59%. Regarding cell compatibility, it is verified that the isolation procedure does not adversely affect cell viability, thus also confirming that the re-collected cancer cells can be cultured for up to 8 days. This work demonstrates a CTC isolation technology platform that optimizes high recovery rates and cell purity while also providing a framework for functional cell studies, potentially enabling even more sensitive and specific cancer diagnostics.

Nano-mechanical compliance of Müller cells investigated by atomic force microscopy

It has been known that a single Müller cell displays a large variation in the cytoskeletal compositions along its cell body, suggesting different mechanical properties in different segments. Müller cells are thought to be involved in many retinal diseases such as retinoschisis, which can be facilitated by a mechanical stress. Thus, mapping of mechanical properties on localized nano-domains of Müller cells could provide essential information for understanding their structural functions in the retina and roles in their pathological progresses. Using Atomic Force Microscopy (AFM) - based bio-nano-mechanics, we have investigated the local variations of the mechanical properties of Müller cells in vitro. We have a particular interest in identifying elastic moduli in regions closer to three distinctive segments of the cells - process, endfoot, and soma. Using the modified spherical AFM probes, we were able to accurately determine mechanical properties, i.e., elastic moduli from the obtained force-distance curves. We found that the regions closer to soma were mechanically more compliant than regions closer to endfoot and process of Müller cells. We found that this lateral heterogeneity of the mechanical compliance within a single Müller cell is consistent with reports from other cell types. The local variation in mechanical compliances along a single Müller cell may support their diverse mechanical functions in the retina such as a soft mechanical embedding, mechanosensing, and neurotrophic functions for neurons.

Microactuator device for integrated measurement of epithelium mechanics

Mechanical forces are among important factors that drive cellular function and organization. We present a microfabricated device with on-chip actuation for mechanical testing of single cells. An integrated immersible electrostatic actuator system is demonstrated that applies calibrated forces to cells. We conduct stretching experiments by directly applying forces to epithelial cells adhered to device surfaces functionalized with collagen. We measure mechanical properties including stiffness, hysteresis and visco-elasticity of adherent cells.

Measuring the mechanical properties of living cells using atomic force microscopy

Mechanical properties of cells and extracellular matrix (ECM) play important roles in many biological processes including stem cell differentiation, tumor formation, and wound healing. Changes in stiffness of cells and ECM are often signs of changes in cell physiology or diseases in tissues. Hence, cell stiffness is an index to evaluate the status of cell cultures. Among the multitude of methods applied to measure the stiffness of cells and tissues, micro-indentation using an Atomic Force Microscope (AFM) provides a way to reliably measure the stiffness of living cells. This method has been widely applied to characterize the micro-scale stiffness for a variety of materials ranging from metal surfaces to soft biological tissues and cells. The basic principle of this method is to indent a cell with an AFM tip of selected geometry and measure the applied force from the bending of the AFM cantilever. Fitting the force-indentation curve to the Hertz model for the corresponding tip geometry can give quantitative measurements of material stiffness. This paper demonstrates the procedure to characterize the stiffness of living cells using AFM. Key steps including the process of AFM calibration, force-curve acquisition, and data analysis using a MATLAB routine are demonstrated. Limitations of this method are also discussed.

Experimental methods for the characterization of the frequency-dependent viscoelastic properties of soft materials

A characterization method based on Rayleigh wave propagation was developed for the quantification of the frequency-dependent viscoelastic properties of soft materials at high frequencies; i.e., up to 4 kHz. Planar harmonic surface waves were produced on the surface of silicone rubber samples. The phase and amplitude of the propagating waves were measured at different locations along the propagation direction, which allowed the calculation of the complex Rayleigh wavenumbers at each excitation frequency using a transfer function method. An inverse wave propagation problem was then solved to obtain the complex shear/elastic moduli from the measured wavenumbers. In a separate, related investigation, dynamic indentation tests using atomic force microscopy (AFM) were performed at frequencies up to 300 Hz. No systematic verification study is available for the AFM-based method, which can be used when the dimensions of the test samples are too small for other existing testing methods. The results obtained from the Rayleigh wave propagation and AFM-based indentation methods were compared with those from a well-established method, which involves the generation of standing longitudinal compression waves in rod-shaped test specimens. The results were cross validated and qualitatively confirmed theoretical expectations presented in the literature for the frequency-dependence of polymers.

Comparison of the viscoelastic properties of cells from different kidney cancer phenotypes measured with atomic force microscopy

The viscoelastic properties of human kidney cell lines from different tumor types (carcinoma (A-498) and adenocarcinoma (ACHN)) are compared to a non-tumorigenic cell line (RC-124). Our methodology is based on the mapping of viscoelastic properties (elasticity modulus E and apparent viscosity η) over the surface of tens of individual cells with atomic force microscopy (AFM). The viscoelastic properties are averaged over datasets as large as 15000 data points per cell line. We also propose a model to estimate the apparent viscosity of soft materials using the hysteresis observed in conventional AFM deflection-displacement curves, without any modification to the standard AFM apparatus. The comparison of the three cell lines show that the non-tumorigenic cells are less deformable and more viscous than cancerous cells, and that cancer cell lines have distinctive viscoelastic properties. In particular, we obtained that E(RC-124) > E(A-498) > E(ACHN) and η(RC-124) > η(A-498) > η(ACHN).

Atomic force microscopy reveals important differences in axonal resistance to injury

Axonal degeneration after traumatic brain injury and nerve compression is considered a common underlying cause of temporary as well as permanent disability. Because a proper functioning of neural network requires phase coherence of all components, even subtle changes in circuitry may lead to network failure. However, it is still not possible to determine which axons will recover or degenerate after injury. Several groups have studied the pressure threshold for axonal injury within a nerve, but difficulty accessing the injured region; insufficient imaging methods and the extremely small dimensions involved have prevented the evaluation of the response of individual axons to injury. We combined microfluidics with atomic force microscopy and in vivo imaging to estimate the threshold force required to 1), uncouple axonal transport without impairing axonal survival, and 2), compromise axonal survival in both individual and bundled axons. We found that rat hippocampal axons completely recover axonal transport with no detectable axonal loss when compressed with pressures up to 65 ± 30 Pa for 10 min, while dorsal root ganglia axons can resist to pressures up to 540 ± 220 Pa. We investigated the reasons for the differential susceptibility of hippocampal and DRG axons to mechanical injury and estimated the elasticity of live axons. We found that dorsal root ganglia axons have a 20% lower elastic modulus than hippocampal axons. Our results emphasize the importance of the integrity of the axonal cytoskeleton in deciding the axonal fate after damage and open up new avenues to improve injury diagnosis and to identify ways to protect axons.

Emergent complexity of the cytoskeleton: from single filaments to tissue

Despite their overwhelming complexity, living cells display a high degree of internal mechanical and functional organization which can largely be attributed to the intracellular biopolymer scaffold, the cytoskeleton. Being a very complex system far from thermodynamic equilibrium, the cytoskeleton's ability to organize is at the same time challenging and fascinating. The extensive amounts of frequently interacting cellular building blocks and their inherent multifunctionality permits highly adaptive behavior and obstructs a purely reductionist approach. Nevertheless (and despite the field's relative novelty), the physics approach has already proved to be extremely successful in revealing very fundamental concepts of cytoskeleton organization and behavior. This review aims at introducing the physics of the cytoskeleton ranging from single biopolymer filaments to multicellular organisms. Throughout this wide range of phenomena, the focus is set on the intertwined nature of the different physical scales (levels of complexity) that give rise to numerous emergent properties by means of self-organization or self-assembly.

Cell visco-elasticity measured with AFM and optical trapping at sub-micrometer deformations

The measurement of the elastic properties of cells is widely used as an indicator for cellular changes during differentiation, upon drug treatment, or resulting from the interaction with the supporting matrix. Elasticity is routinely quantified by indenting the cell with a probe of an AFM while applying nano-Newton forces. Because the resulting deformations are in the micrometer range, the measurements will be affected by the finite thickness of the cell, viscous effects and even cell damage induced by the experiment itself. Here, we have analyzed the response of single 3T3 fibroblasts that were indented with a micrometer-sized bead attached to an AFM cantilever at forces from 30–600 pN, resulting in indentations ranging from 0.2 to 1.2 micrometer. To investigate the cellular response at lower forces up to 10 pN, we developed an optical trap to indent the cell in vertical direction, normal to the plane of the coverslip. Deformations of up to two hundred nanometers achieved at forces of up to 30 pN showed a reversible, thus truly elastic response that was independent on the rate of deformation. We found that at such small deformations, the elastic modulus of 100 Pa is largely determined by the presence of the actin cortex. At higher indentations, viscous effects led to an increase of the apparent elastic modulus. This viscous contribution that followed a weak power law, increased at larger cell indentations. Both AFM and optical trapping indentation experiments give consistent results for the cell elasticity. Optical trapping has the benefit of a lower force noise, which allows a more accurate determination of the absolute indentation. The combination of both techniques allows the investigation of single cells at small and large indentations and enables the separation of their viscous and elastic components.

Effect of matrix on cardiomyocyte viscoelastic properties in 2D culture

Cardiomyocyte phenotype changes significantly in 2D culture systems depending on the substrate composition and organization. Given the variety of substrates that are used both for basic cardiac cell culture studies and for regenerative medicine applications, there is a critical need to understand how the different matrices influence cardiac cell mechanics. In the current study, the mechanical properties of neonatal rat cardiomyocytes cultured in a subconfluent layer upon aligned and unaligned collagen and fibronectin matrices were assessed over a two week period using atomic force microscopy. The elastic modulus was estimated by fitting the Hertz model to force curve data and the percent relaxation was determined from stress relaxation curves. The Quasilinear Viscoelastic (QLV) and Standard Linear Solid (SLS) models were fit to the stress relaxation data. Cardiomyocyte cellular mechanical properties were found to be highly dependent on matrix composition and organization as well as time in culture. It was observed that the cells stiffened and relaxed less over the first 3 to 5 days in culture before reaching a plateau in their mechanical properties. After day 5, cells on aligned matrices were stiffer than cells on unaligned matrices and cells on fibronectin matrices were stiffer than cells on collagen matrices. No such significant trends in percent relaxation measurements were observed but the QLV model fit the data very well. These results were correlated with observed changes in cellular structure associated with culture on the different substrates and analyzed for cell-to-cell variability.

Measuring the elastic properties of living cells through the analysis of current-displacement curves in scanning ion conductance microscopy

Knowledge of mechanical properties of living cells is essential to understand their physiological and pathological conditions. To measure local cellular elasticity, scanning probe techniques have been increasingly employed. In particular, non-contact scanning ion conductance microscopy (SICM) has been used for this purpose; thanks to the application of a hydrostatic pressure via the SICM pipette. However, the measurement of sample deformations induced by weak pressures at a short distance has not yet been carried out. A direct quantification of the applied pressure has not been also achieved up to now. These two issues are highly relevant, especially when one addresses the investigation of thin cell regions. In this paper, we present an approach to solve these problems based on the use of a setup integrating SICM, atomic force microscopy, and optical microscopy. In particular, we describe how we can directly image the pipette aperture in situ. Additionally, we can measure the force induced by a constant hydrostatic pressure applied via the pipette over the entire probe-sample distance range from a remote point to contact. Then, we demonstrate that the sample deformation induced by an external pressure applied to the pipette can be indirectly and reliably evaluated from the analysis of the current-displacement curves. This method allows us to measure the linear relationship between indentation and applied pressure on uniformly deformable elastomers of known Young's modulus. Finally, we apply the method to murine fibroblasts and we show that it is sensitive to local and temporally induced variations of the cell surface elasticity.

In situ mechanical analysis of myofibrillar perturbation and aging on soft, bilayered Drosophila myocardium

Drosophila melanogaster is a genetically malleable organism with a short life span, making it a tractable system in which to study mechanical effects of genetic perturbation and aging on tissues, e.g., impaired heart function. However, Drosophila heart-tube studies can be hampered by its bilayered structure: a ventral muscle layer covers the contractile cardiomyocytes. Here we propose an atomic force microscopy-based analysis that uses a linearized-Hertz method to measure individual mechanical components of soft composite materials. The technique was verified using bilayered polydimethylsiloxane. We further demonstrated its biological utility via its ability to resolve stiffness changes due to RNA interference to reduce myofibrillar content or due to aging in Drosophila myocardial layers. This protocol provides a platform to assess the mechanics of soft biological composite systems and, to our knowledge, for the first time, permits direct measurement of how genetic perturbations, aging, and disease can impact cardiac function in situ.

AFM nano-mechanics and calcium dynamics of prostate cancer cells with distinct metastatic potential

BACKGROUND

Despite recent advances, it is not clear to correlate the mechanical compliances and the metastatic potential of cancer cells. In this study, we investigated combined signatures of mechanical compliances, adhesions, and calcium dynamics correlated with the metastatic potential of cancer cells.

SCOPE OF REVIEW

We used the lowly (LNCaP) and highly (CL-1, CL-2) metastatic human prostate cancer cells. The AFM-based nanomechanics was performed to determine the elastic moduli and the cell-to-substrate adhesion. The intracellular calcium dynamics was evaluated by fluorescence spectroscopy. Cell migration and the distribution of cytoskeleton were evaluated using the wounded monolayer model and immunofluorescence, respectively. The elastic moduli, the calcium dynamics, and the migratory ability are greater in CL-1 and CL-2 than LNCaP. CL-1 and CL-2 also display a significantly larger area of cell-to-substrate adhesions while the LNCaP displays a limited adhesion. These properties were slightly reduced in CL-2 compared with CL-1 cells. The enhanced elastic moduli and calcium dynamics found in CL-1 and CL-2 can be consistently explained by the intensified tensile stress generated by actin cytoskeletons anchored at more focal adhesion sites.

MAJOR CONCLUSIONS

Although the suppressed mechanical compliance of highly metastatic cells may not support the enhanced cancer metastasis, the enhanced adhesion and calcium dynamics are favorable for invasion and extra-vasation required for malignant progression.

GENERAL SIGNIFICANCE

Our results suggest that the mechanical compliance alone may fail to indicate the metastatic progression, but the combined biomechanical signatures of mechanical compliance, adhesion, and calcium dynamics can provide critical clues to determine the metastatic potential of cells.

High-resolution microrheology in the pericellular matrix of prostate cancer cells

Many cells express a membrane-coupled external mechanical layer, the pericellular matrix (PCM), which often contains long-chain polymers. Its role and properties are not entirely known, but its functions are believed to include physical protection, mechanosensing, chemical signalling or lubrication. The viscoelastic response of the PCM, with polysaccharides as the main structural components, is therefore crucial for the understanding of its function. We have here applied microrheology, based on optically trapped micrometre-sized colloids, to the PCM of cultured PC3 prostate cancer cells. This technology allowed us to measure the extremely soft response of the PCM, with approximately 1 µm height resolution. Exogenously added aggrecan, a hyaluronan-binding proteoglycan, caused a remarkable increase in thickness of the viscoelastic layer and also triggered filopodia-like protrusions. The viscoelastic response of the PCM, however, did not change significantly.

Mechanobiology in lung epithelial cells: measurements, perturbations, and responses

Epithelial cells of the lung are located at the interface between the environment and the organism and serve many important functions including barrier protection, fluid balance, clearance of particulate, initiation of immune responses, mucus and surfactant production, and repair following injury. Because of the complex structure of the lung and its cyclic deformation during the respiratory cycle, epithelial cells are exposed to continuously varying levels of mechanical stresses. While normal lung function is maintained under these conditions, changes in mechanical stresses can have profound effects on the function of epithelial cells and therefore the function of the organ. In this review, we will describe the types of stresses and strains in the lungs, how these are transmitted, and how these may vary in human disease or animal models. Many approaches have been developed to better understand how cells sense and respond to mechanical stresses, and we will discuss these approaches and how they have been used to study lung epithelial cells in culture. Understanding how cells sense and respond to changes in mechanical stresses will contribute to our understanding of the role of lung epithelial cells during normal function and development and how their function may change in diseases such as acute lung injury, asthma, emphysema, and fibrosis.

Measuring the elastic properties of living cells with atomic force microscopy indentation

Atomic force microscopy (AFM) is a powerful and versatile tool for probing the mechanical properties of biological samples. This chapter describes the procedures for using AFM indentation to measure the elastic moduli of living cells. We include step-by-step instructions for cantilever calibration and data acquisition using a combined AFM/optical microscope system, as well as a detailed protocol for data analysis. Our protocol is written specifically for the BioScope™ Catalyst™ AFM system (Bruker AXS Inc.); however, most of the general concepts can be readily translated to other commercial systems.

Viscoelastic property mapping with contact resonance force microscopy

We demonstrate the accurate nanoscale mapping of near-surface loss and storage moduli on a polystyrene-polypropylene blend with contact resonance force microscopy (CR-FM). These viscoelastic properties are extracted from spatially resolved maps of the contact resonance frequency and quality factor of the AFM cantilever. We consider two methods of data acquisition: (i) discrete stepping between mapping points and (ii) continuous scanning. For point mapping and low-speed scanning, the values of the relative loss and storage modulus are in good agreement with the time-temperature superposition of low-frequency dynamic mechanical analysis measurements to the high frequencies probed by CR-FM.

Poroelasticity of cartilage at the nanoscale

Atomic-force-microscopy-based oscillatory loading was used in conjunction with finite element modeling to quantify and predict the frequency-dependent mechanical properties of the superficial zone of young bovine articular cartilage at deformation amplitudes, δ, of ~15 nm; i.e., at macromolecular length scales. Using a spherical probe tip (R ~ 12.5 μm), the magnitude of the dynamic complex indentation modulus, |E*|, and phase angle, φ, between the force and tip displacement sinusoids, were measured in the frequency range f ~ 0.2-130 Hz at an offset indentation depth of δ(0) ~ 3 μm. The experimentally measured |E*| and φ corresponded well with that predicted by a fibril-reinforced poroelastic model over a three-decade frequency range. The peak frequency of phase angle, f(peak), was observed to scale linearly with the inverse square of the contact distance between probe tip and cartilage, 1/d(2), as predicted by linear poroelasticity theory. The dynamic mechanical properties were observed to be independent of the deformation amplitude in the range δ = 7-50 nm. Hence, these results suggest that poroelasticity was the dominant mechanism underlying the frequency-dependent mechanical behavior observed at these nanoscale deformations. These findings enable ongoing investigations of the nanoscale progression of matrix pathology in tissue-level disease.

Atomic force microscopy and its contribution to understanding the development of the nervous system

While our understanding of the influence of biochemical signaling on cell functioning is increasing rapidly, the consequences of mechanical signaling are currently poorly understood. However, cells of the nervous system respond to their mechanical environment; their mechanosensitivity has important implications for development and disease. Atomic force microscopy provides a powerful technique to investigate the mechanical interaction of cells with their environment with high resolution. This method can be used to obtain high-resolution surface topographies, stiffness maps, and apply well-defined forces to samples at different length scales. This review summarizes recent advances of atomic force microscopy, provides an overview about state-of-the-art measurements, and suggests directions for future applications to investigate the involvement of mechanics in the development of the nervous system.

Growth cones as soft and weak force generators

Many biochemical processes in the growth cone finally target its biomechanical properties, such as stiffness and force generation, and thus permit and control growth cone movement. Despite the immense progress in our understanding of biochemical processes regulating neuronal growth, growth cone biomechanics remains poorly understood. Here, we combine different experimental approaches to measure the structural and mechanical properties of a growth cone and to simultaneously determine its actin dynamics and traction force generation. Using fundamental physical relations, we exploited these measurements to determine the internal forces generated by the actin cytoskeleton in the lamellipodium. We found that, at timescales longer than the viscoelastic relaxation time of τ = 8.5 ± 0.5 sec, growth cones show liquid-like characteristics, whereas at shorter time scales they behaved elastically with a surprisingly low elastic modulus of E = 106 ± 21 Pa. Considering the growth cone's mechanical properties and retrograde actin flow, we determined the internal stress to be on the order of 30 pN per μm(2). Traction force measurements confirmed these values. Hence, our results indicate that growth cones are particularly soft and weak structures that may be very sensitive to the mechanical properties of their environment.

Time-dependent nanomechanics of cartilage

In this study, atomic force microscopy-based dynamic oscillatory and force-relaxation indentation was employed to quantify the time-dependent nanomechanics of native (untreated) and proteoglycan (PG)-depleted cartilage disks, including indentation modulus E(ind), force-relaxation time constant τ, magnitude of dynamic complex modulus |E(∗)|, phase angle δ between force and indentation depth, storage modulus E', and loss modulus E″. At ∼2 nm dynamic deformation amplitude, |E(∗)| increased significantly with frequency from 0.22 ± 0.02 MPa (1 Hz) to 0.77 ± 0.10 MPa (316 Hz), accompanied by an increase in δ (energy dissipation). At this length scale, the energy dissipation mechanisms were deconvoluted: the dynamic frequency dependence was primarily governed by the fluid-flow-induced poroelasticity, whereas the long-time force relaxation reflected flow-independent viscoelasticity. After PG depletion, the change in the frequency response of |E(∗)| and δ was consistent with an increase in cartilage local hydraulic permeability. Although untreated disks showed only slight dynamic amplitude-dependent behavior, PG-depleted disks showed great amplitude-enhanced energy dissipation, possibly due to additional viscoelastic mechanisms. Hence, in addition to functioning as a primary determinant of cartilage compressive stiffness and hydraulic permeability, the presence of aggrecan minimized the amplitude dependence of |E(∗)| at nanometer-scale deformation.

Extreme hardening of PDMS thin films due to high compressive strain and confined thickness

Polymers confined to small dimensions and that undergo high strains can show remarkable nonlinear mechanics, which must be understood to accurately predict the functioning of nanoscale polymer devices. In this paper we describe the determination of the mechanical properties of ultrathin polydimethylsiloxane (PDMS) films undergoing large strains, using atomic force microscope (AFM) indentation with a spherical tip. The PDMS was molded into extremely thin films of variable thickness and adhered to a hard substrate. We found that for films below 1 μm in thickness the Young's modulus increased with decreasing sample thickness with a power law exponent of 1.35. Furthermore, as the soft PDMS film was indented, significant strain hardening was observed as the indentation depth approached 45% of the sample thickness. To properly quantify the nonlinear mechanical measurements, we utilized a pointwise Hertzian model which assumes only piecewise linearity on the part of the probed material. This analysis revealed three regions within the material. A linear region with a constant Young's modulus was seen for compression up to 45% strain. At strains higher than 45%, a marked increase in Young's modulus was measured. The onset of strain induced stiffening is well modeled by finite element modeling and occurs as stress contours expanding from the probe and the substrate overlap. A third region of mechanical variation occurred at small indentations of less than 10 nm. The pointwise Young's modulus at small indentations was several orders of magnitude higher than that in the linear elasticity region; we studied and ruled out causes responsible for this phenomenon. In total, these effects can cause thin elastomer films to become extremely stiff such that the measured Young's modulus is over a 100-fold higher than the bulk PDMS. Therefore, the mechanics of a polymer can be changed by adjusting the geometry of a material, in addition to changing the material itself. In addition to understanding the mechanics of thin polymer films, this work provides an excellent test of experimental techniques to measure the mechanics of other nonlinear and heterogeneous materials such as biological cells.

Real-time monitoring of cell elasticity reveals oscillating myosin activity

The cytoskeleton is the physical and biochemical interface for a large variety of cellular processes. Its complex regulation machinery is involved upstream and downstream in various signaling pathways. The cytoskeleton determines the mechanical properties of a cell. Thus, cell elasticity could serve as a parameter reflecting the behavior of the system rather than reflecting the specific properties of isolated components. In this study, we used atomic force microscopy to perform real-time monitoring of cell elasticity unveiling cytoskeletal dynamics of living bronchial epithelial cells. In resting cells, we found a periodic activity of the cytoskeleton. Amplitude and frequency of this spontaneous oscillation were strongly affected by intracellular calcium. Experiments reveal that basal cell elasticity and superimposed elasticity oscillations are caused by the collective action of myosin motor proteins. We characterized the cell as a mechanically multilayered structure, and followed cytoskeletal dynamics in the different layers with high time resolution. In conclusion, the collective activities of the myosin motor proteins define overall mechanical cell dynamics, reflecting specific changes of the chemical and mechanical environment.

The role of the cytoskeleton in volume regulation and beading transitions in PC12 neurites

We present investigations on volume regulation and beading shape transitions in PC12 neurites, conducted using a flow-chamber technique. By disrupting the cell cytoskeleton with specific drugs, we investigate the role of its individual components in the volume regulation response. We find that microtubule disruption increases both swelling rate and maximum volume attained, but does not affect the ability of the neurite to recover its initial volume. In addition, investigation of axonal beading-also known as pearling instability-provides additional clues on the mechanical state of the neurite. We conclude that volume recovery is driven by passive diffusion of osmolites, and propose that the initial swelling phase is mechanically slowed down by microtubules. Our experiments provide a framework to investigate the role of cytoskeletal mechanics in volume homeostasis.

Biomechanics of single cortical neurons

This study presents experimental results and computational analysis of the large strain dynamic behavior of single neurons in vitro with the objective of formulating a novel quantitative framework for the biomechanics of cortical neurons. Relying on the atomic force microscopy (AFM) technique, novel testing protocols are developed to enable the characterization of neural soma deformability over a range of indentation rates spanning three orders of magnitude, 10, 1, and 0.1 μm s(-1). Modified spherical AFM probes were utilized to compress the cell bodies of neonatal rat cortical neurons in load, unload, reload and relaxation conditions. The cell response showed marked hysteretic features, strong non-linearities, and substantial time/rate dependencies. The rheological data were complemented with geometrical measurements of cell body morphology, i.e. cross-diameter and height estimates. A constitutive model, validated by the present experiments, is proposed to quantify the mechanical behavior of cortical neurons. The model aimed to correlate empirical findings with measurable degrees of (hyper)elastic resilience and viscosity at the cell level. The proposed formulation, predicated upon previous constitutive model developments undertaken at the cortical tissue level, was implemented in a three-dimensional finite element framework. The simulated cell response was calibrated to the experimental measurements under the selected test conditions, providing a novel single cell model that could form the basis for further refinements.

Micromechanical regulation in cardiac myocytes and fibroblasts: implications for tissue remodeling

Cells of the myocardium are at home in one of the most mechanically dynamic environments in the body. At the cellular level, pulsatile stimuli of chamber filling and emptying are experienced as cyclic strains (relative deformation) and stresses (force per unit area). The intrinsic characteristics of tension-generating myocytes and fibroblasts thus have a continuous mechanical interplay with their extrinsic surroundings. This review explores the ways that the micromechanics at the scale of single cardiac myocytes and fibroblasts have been measured, modeled, and recapitulated in vitro in the context of adaptation. Both types of cardiac cells respond to externally applied strain, and many of the intracellular mechanosensing pathways have been identified with the careful manipulation of experimental variables. In addition to strain, the extent of loading in myocytes and fibroblasts is also regulated by cues from the microenvironment such as substrate surface chemistry, stiffness, and topography. Combinations of these structural cues in three dimensions are needed to mimic the micromechanical complexity derived from the extracellular matrix of the developing, healthy, or pathophysiologic heart. An understanding of cardiac cell micromechanics can therefore inform the design and composition of tissue engineering scaffolds or stem cell niches for future applications in regenerative medicine.

AFM stiffness nanotomography of normal, metaplastic and dysplastic human esophageal cells

The mechanical stiffness of individual cells is important in tissue homeostasis, cell growth, division and motility, and the epithelial-mesenchymal transition in the initiation of cancer. In this work, a normal squamous cell line (EPC2) and metaplastic (CP-A) as well as dysplastic (CP-D) Barrett's Esophagus columnar cell lines are studied as a model of pre-neoplastic progression in the human esophagus. We used the combination of an atomic force microscope (AFM) with a scanning confocal fluorescence lifetime imaging microscope to study the mechanical properties of single adherent cells. Sixty four force indentation curves were taken over the nucleus of each cell in an 8 x 8 grid pattern. Analyzing the force indentation curves, indentation depth-dependent Young's moduli were found for all cell lines. Stiffness tomograms demonstrate distinct differences between the mechanical properties of the studied cell lines. Comparing the stiffness for indentation forces of 1 nN, most probable Young's moduli were calculated to 4.7 kPa for EPC2 (n = 18 cells), 3.1 kPa for CP-A (n = 10) and 2.6 kPa for CP-D (n = 19). We also tested the influence of nuclei and nucleoli staining organic dyes on the mechanical properties of the cells. For stained EPC2 cells (n = 5), significant stiffening was found (9.9 kPa), while CP-A cells (n = 5) showed no clear trend (2.9 kPa) and a slight softening was observed (2.1 kPa) in the case of CP-D cells (n = 16). Some force-indentation curves show non-monotonic discontinuities with segments of negative slope, resembling a sawtooth pattern. We found the incidence of these 'breakthrough events' to be highest in the dysplastic CP-D cells, intermediate in the metaplastic CP-A cells and lowest in the normal EPC2 cells. This observation suggests that the microscopic explanation for the increased compliance of cancerous and pre-cancerous cells may lie in their susceptibility to 'crumble and yield' rather than their ability to 'bend and flex'.

Probing the mechanical properties of TNF-α stimulated endothelial cell with atomic force microscopy

TNF-α (tumor necrosis factor-α) is a potent pro-inflammatory cytokine that regulates the permeability of blood and lymphatic vessels. The plasma concentration of TNF-α is elevated (> 1 pg/mL) in several pathologies, including rheumatoid arthritis, atherosclerosis, cancer, pre-eclampsia; in obese individuals; and in trauma patients. To test whether circulating TNF-α could induce similar alterations in different districts along the vascular system, three endothelial cell lines, namely HUVEC, HPMEC, and HCAEC, were characterized in terms of 1) mechanical properties, employing atomic force microscopy; 2) cytoskeletal organization, through fluorescence microscopy; and 3) membrane overexpression of adhesion molecules, employing ELISA and immunostaining. Upon stimulation with TNF-α (10 ng/mL for 20 h), for all three endothelial cells, the mechanical stiffness increased by about 50% with a mean apparent elastic modulus of E ~5 ± 0.5 kPa (~3.3 ± 0.35 kPa for the control cells); the density of F-actin filaments increased in the apical and median planes; and the ICAM-1 receptors were overexpressed compared with controls. Collectively, these results demonstrate that sufficiently high levels of circulating TNF-α have similar effects on different endothelial districts, and provide additional information for unraveling the possible correlations between circulating pro-inflammatory cytokines and systemic vascular dysfunction.

Local rheology of human neutrophils investigated using atomic force microscopy

During the immune response, neutrophils display localized mechanical events by interacting with their environment through the micro-vascular transit, trans-endothelial, and trans-epithelial migration. Nano-mechanical studies of human neutrophils on localized nano-domains could provide the essential information for understanding their immune responsive functions. Using the Atomic Force Microscopy (AFM)-based micro-rheology, we have investigated rheological properties of the adherent human neutrophils on local nano-domains. We have applied the modified Hertz model to obtain the viscoelastic moduli from the relatively thick body regions of the neutrophils. In addition, by using more advanced models to account for the substrate effects, we have successfully characterized the rheological properties of the thin leading and tail regions as well. We found a regional difference in the mechanical compliances of the adherent neutrophils. The central regions of neutrophils were significantly stiffer (1,548 ± 871 Pa) than the regions closer to the leading edge (686 ± 801 Pa), while the leading edge and the tail (494 ± 537 Pa) regions were mechanically indistinguishable. The frequency-dependent elastic and viscous moduli also display a similar regional difference. Over the studied frequency range (100 to 300 Hz), the complex viscoelastic moduli display the partial rubber plateau behavior where the elastic moduli are greater than the viscous moduli for a given frequency. The non-disparaging viscous modulus indicates that the neutrophils display a viscoelastic dynamic behavior rather than a perfect elastic behavior like polymer gels. In addition, we found no regional difference in the structural damping coefficient between the leading edge and the cell body. Thus, we conclude that despite the lower loss and storage moduli, the leading edges of the human neutrophils display partially elastic properties similar to the cell body. These results suggest that the lower elastic moduli in the leading edges are more favorable for the elastic fluctuation of actin filaments, which supports the polymerization of the actin filaments leading to the active protrusion during the immune response.

Robust organizational principles of protrusive biopolymer networks in migrating living cells

Cell migration is associated with the dynamic protrusion of a thin actin-based cytoskeletal extension at the cell front, which has been shown to consist of two different substructures, the leading lamellipodium and the subsequent lamellum. While the formation of the lamellipodium is increasingly well understood, organizational principles underlying the emergence of the lamellum are just beginning to be unraveled. We report here on a 1D mathematical model which describes the reaction-diffusion processes of a polarized actin network in steady state, and reproduces essential characteristics of the lamellipodium-lamellum system. We observe a steep gradient in filament lengths at the protruding edge, a local depolymerization maximum a few microns behind the edge, as well as a differential dominance of the network destabilizer ADF/cofilin and the stabilizer tropomyosin. We identify simple and robust organizational principles giving rise to the derived network characteristics, uncoupled from the specifics of any molecular implementation, and thus plausibly valid across cell types. An analysis of network length dependence on physico-chemical system parameters implies that to limit array treadmilling to cellular dimensions, network growth has to be truncated by mechanisms other than aging-induced depolymerization, e.g., by myosin-associated network dissociation at the transition to the cell body. Our work contributes to the analytical understanding of the cytoskeletal extension's bisection into lamellipodium and lamellum and sheds light on how cells organize their molecular machinery to achieve motility.

Mechanical properties of cells and ageing

Mechanical properties are fundamental properties of the cells and tissues of living organisms. The mechanical properties of a single cell as a biocomposite are determined by the interdependent combination of cellular components mechanical properties. Quantitative estimate of the cell mechanical properties depends on a cell state, method of measurement, and used theoretical model. Predominant tendency for the majority of cells with ageing is an increase of cell stiffness and a decrease of cell ability to undergo reversible large deformations. The mechanical signal transduction in old cells becomes less effective than that in young cells, and with ageing, the cells lose the ability of the rapid functional rearrangements of cellular skeleton. The article reviews the theoretical and experimental facts touching the age-related changes of the mechanical properties of cellular components and cells in the certain systems of an organism (the blood, the vascular system, the musculoskeletal system, the lens, and the epithelium). In fact, the cell mechanical parameters (including elastic modulii) can be useful as specific markers of cell ageing.

Atomic force microscopy in mechanobiology: measuring microelastic heterogeneity of living cells

Recent findings clearly demonstrate that cells feel mechanical forces, and respond by altering their -phenotype and modulating their mechanical environment. Atomic force microscope (AFM) indentation can be used to mechanically stimulate cells and quantitatively characterize their elastic properties, providing critical information for understanding their mechanobiological behavior. This review focuses on the experimental and computational aspects of AFM indentation in relation to cell biomechanics and pathophysiology. Key aspects of the indentation protocol (including preparation of substrates, selection of indentation parameters, methods for contact point detection, and further post-processing of data) are covered. Historical perspectives on AFM as a mechanical testing tool as well as studies of cell mechanics and physiology are also highlighted.

Can common adhesion molecules and microtopography affect cellular elasticity? A combined atomic force microscopy and optical study

The phenomenon that cells respond to chemical and topographic cues in their surroundings has been widely examined and exploited in many fields ranging from basic life science research to biomedical therapeutics. Adhesion promoting molecules such as poly-L-lysine (PLL) and fibronectin (Fn) are commonly used for in vitro cell assays to promote cell spreading/proliferation on tissue culture plastic and to enhance the biocompatibility of biomedical devices. Likewise, engineered topography is often used to guide cell growth and differentiation. Little is known about how these cues affect the biomechanical properties of cells and subsequent cell function. In this study we have applied atomic force microscopy (AFM) to investigate these biomechanical properties. In the first stage of the study we formulated a rigorous approach to quantify cellular elasticity using AFM. Operational factors, including indentation depth and speed, and mathematical models for data fitting have been systematically evaluated. We then quantified how PLL, Fn and microtopography affected cellular elasticity and the organization of the cytoskeleton. Cellular elasticity after 1 day in culture was greater on a Fn-coated surface as compared to PLL or glass. These statistically significant differences disappeared after two more days in culture. In contrast, the significantly higher elasticity associated with cells grown on micrometric grooves remained for at least 3 days. This work sheds light on the apparently simple but debatable questions: "Are engineered chemical cues eventually masked by a cell's own matrix proteins and so only exert short-term influence? Does engineered topography as well as engineered chemistry affect cell elasticity?"

Age-dependent regional mechanical properties of the rat hippocampus and cortex

Age-dependent outcomes following traumatic brain injury motivate the study of brain injury biomechanics in experimental animal models at different stages of development. Finite element models of the rat brain are used to better understand the mechanical mechanisms behind these age-dependent outcomes; however, age- and region-specific rat brain tissue mechanical properties are required for biofidelity in modeling. Here, we have used the atomic force microscope (AFM) to measure region-dependent mechanical properties for subregions of the cortex and hippocampus in P10, P17, and adult rats. Apparent elastic modulus increased nonlinearly with indentation strain, and a nonlinear Ogden hyperelastic model was used to fit the force-deflection data. Subregional heterogeneous distributions of mechanical properties changed significantly with age. Apparent elastic modulus was also found to increase overall with age, increasing by >100% between P10 and adult rats. Unconfined compression tests (epsilon=-0.3) were performed on whole slices of the hippocampus and cortex of P10, P17, and adult rats to verify the mechanical properties measured with the AFM. Mean apparent elastic modulus at an indentation strain of 30% from AFM measurements for each region and age correlated well with the long-term elastic modulus measured from 30% unconfined compression tests (slope not significantly different from 1, p>0.05). Protein, lipid, and sulfated glycosaminoglycan content of the brain increased with age and were positively correlated with tissue stiffness, whereas water content decreased with age and was negatively correlated with tissue stiffness. These correlations can be used to hypothesize mechanistic models for describing the mechanical behavior of brain tissue as well as to predict relative differences between brain tissue mechanical properties of other species, at different ages, and for different regions based on differences in tissue composition.

Modeling receptor-mediated endocytosis of polymer-functionalized iron oxide nanoparticles by human macrophages

Although systemically applied nanoparticles are quickly taken up by phagocytic cells, mainly macrophages, the interactions between engineered nanoparticles and macrophages are still not well defined. We therefore analyzed the uptake of diagnostically used carboxydextran-coated superparamagnetic iron oxide nanoparticles of 60 nm (SPIO) and 20 nm (USPIO) by human macrophages. By pharmacological and in vitro knockdown approaches, the principal uptake mechanism for both particles was identified as clathrin-mediated, scavenger receptor A-dependent endocytosis. We developed a mathematical model of the uptake process that allows determination of key parameters of endocytosis, including the rate of uptake, the number of nanoparticles per cell in saturation, the mean uptake time, and the correlation between the number of internalized nanoparticles and their extracellular concentration. The calculated parameters correlate well with experimental data obtained by confocal microscopy. Moreover, the model predicts the individual and collective wrapping times of different nanoparticles, describes the relation between cytoskeletal forces, membrane elasticity and the uptake time. We also introduced a new physical parameter 'a' governing the collective uptake process, a reflecting minimal linear spacing between simultaneously acting neighboring endocytotic pits.

Critical review: cellular mechanobiology and amoeboid migration

Cell motility is important for tissue homeostasis and plays a central role in various pathologies, notably inflammation and cancer. Research into the critical processes involved in cell migration has so far mostly focused on cell adhesion and proteolytic degradation of the extracellular matrix. However, pharmacological interference with these processes only partially blocks cell motility in vivo. In this review we summarize the arising evidence that the mechanical properties of the cell body have a major role to play in cell motility--especially in a low-adhesion, amoeboid-like migration mode in three-dimensional tissue structures. We summarize the processes determining cell mechanics and discuss relevant measurement technologies including their applications in medical cell biology.

Surface morphology and mechanical properties of fibroblasts from scleroderma patients

Overproduction of extracellular matrix components by fibroblasts plays a key role in the pathogenesis of scleroderma. To investigate whether these functional alterations are accompanied by changes in the mechanical properties and morphology of fibroblast, atomic force microscopy was applied to dermal fibroblasts derived either from scleroderma patients or from healthy donors. No significant morphological differences could be observed among the different cell strains showing long cytoskeleton fibres similar in length and irregularly distributed protrusions on the cell surface. In contrast, significant differences in cellular stiffness of dermal fibroblasts derived from scleroderma lesions were detected. Compared to fibroblasts from healthy donors, diseased cells were characterized by a reduced elastic constant both when the global and local mechanical properties were probed. The altered stiffness of scleroderma fibroblasts may be important in the pathogenesis of the disease as it could lead to the abnormal response of fibroblasts to mechanical stimuli.

Continuous depth-sensing nano-mechanical characterization of living, fixed and dehydrated cells attached on a glass substrate

Continuous depth-sensing nano-indentation on living, fixed and dehydrated fibroblast cells was performed using a dynamic contact module and vertically measured from a pre-contact state to the glass substrate. The nano-indentation tip-on-cell approaches took advantage of finding a contact surface, followed by obtaining a continuous nano-mechanical profile along the nano-indentation depths. In the experiment, serial indentations from the leading edge, i.e., the lamellipodium to nucleus regions of living, fixed and dehydrated fibroblast cells were examined. Nano-indentations on a living cell anchored upon glass substrate were competent in finding the tip-on-cell contact surfaces and cell heights. For the result on the fixed and the dehydrated cells, cellular nano-mechanical properties were clearly characterized by continuous harmonic contact stiffness (HCS) measurements. The relations of HCS versus measured displacement, varied from the initial tip-on-cell contact to the glass substrate, were presumably divided into three stages, respectively induced by cellular intrinsic behavior, the substrate-dominant property, and the substrate property. This manifestation is beneficial to elucidate how the underlying substrate influences the interpretation of the nano-mechanical property of thin soft matter on a hard substrate. These findings, based upon continuous depth-sensing nano-indentations, are presumably valuable as a reference to related work, e.g., accomplished by atomic force microscopy.

Power-law rheology analysis of cells undergoing micropipette aspiration

Accurate quantification of the mechanical properties of living cells requires the combined use of experimental techniques and theoretical models. In this paper, we investigate the viscoelastic response of suspended NIH 3T3 fibroblasts undergoing micropipette aspiration using power-law rheology model. As an important first step, we examine the pipette size effect on cell deformation and find that pipettes larger than ~7 μm are more suitable for bulk rheological measurements than smaller ones and the cell can be treated as effectively continuum. When the large pipettes are used to apply a constant pressure to a cell, the creep deformation is better fitted with the power-law rheology model than with the liquid drop or spring-dashpot models; magnetic twisting cytometry measurement on the rounded cell confirms the power-law behavior. This finding is further extended to suspended cells treated with drugs targeting their cytoskeleton. As such, our results suggest that the application of relatively large pipettes can provide more effective assessment of the bulk material properties as well as support application of power-law rheology to cells in suspension.