Stiffness of MDCK II Cells Depends on Confluency and Cell Size

Mechanical phenotyping of adherent cells has become a serious tool in cell biology to understand how cells respond to their environment and eventually to identify disease patterns such as the malignancy of cancer cells. In the steady state, homeostasis is of pivotal importance, and cells strive to maintain their internal stresses even in challenging environments and in response to external chemical and mechanical stimuli. However, a major problem exists in determining mechanical properties because many techniques, such as atomic force microscopy, that assess these properties of adherent cells locally can only address a limited number of cells and provide elastic moduli that vary substantially from cell to cell. The origin of this spread in stiffness values is largely unknown and might limit the significance of measurements. Possible reasons for the disparity are variations in cell shape and size, as well as biological reasons such as the cell cycle or polarization state of the cell. Here, we show that stiffness of adherent epithelial cells rises with increasing projected apical cell area in a nonlinear fashion. This size stiffening not only occurs as a consequence of varying cell-seeding densities, it can also be observed within a small area of a particular cell culture. Experiments with single adherent cells attached to defined areas via microcontact printing show that size stiffening is limited to cells of a confluent monolayer. This leads to the conclusion that cells possibly regulate their size distribution through cortical stress, which is enhanced in larger cells and reduced in smaller cells.     

Mechanical behavior of an individual adherent MLO-Y4 osteocyte under shear flow

Mechanical properties of a single cell and its mechanical response under stimulation play an important role in regulating interactions between cell and extracellular matrix and affecting mechanotransduction. Osteocytes exhibit solid-like viscoelastic behavior in response to the interstitial fluid shear resulting from tissue matrix deformation. This study intends to quantitatively describe the mechanical behavior of osteocytes combining in vitro experiment and fluid–structure interaction (FSI) finite element (FE) model. The cell is configured in the FSI FE model using the observed data from quasi-3D images. Instead of simply assigning the cellular viscoelastic parameters by statistical data, the mechanical parameters are determined by an iterative algorithm comparing the experimental and the computational results from the FE model. The viscoelastic parameters of osteocytes are obtained as: the equilibrium elasticity modulus \(k_{1}=0.15\pm 0.038\,\hbox {kPa}\), instantaneous elasticity modulus \((k_{1}+k_{2})=0.77\pm 0.23\,\hbox {kPa}\), viscosity coefficient \(\eta =1.38\pm 0.33\,\hbox {kPa}\,\hbox {s}\). A novel index to quantify the cell adhesion is also put forward. In addition, an interesting competition phenomenon is revealed on the cell surface concerning stress and strain, i.e., the place with high stress has low strain and that with low stress has high strain. The proposed method provides a novel technique to study the mechanical behavior of individual adherent cell in vitro. It is believed that this quantitative technique not only determines cell mechanical behavior but also helps elucidate the mechanism of mechanotransduction in various types of cells.     

Endothelial cells as mechanical transducers: Enzymatic activity and network formation under cyclic strain

Although it is established that endothelial cells can respond to external mechanical cues (e.g., alignment in the direction of fluid shear stress), the extent to which mechanical stress and strain applied via the endothelial cell substrate impact biomolecular and cellular processes is not well-understood. This issue is particularly important in the context of inflammation, vascular remodeling, and cancer progression, as each of these processes occurs concurrently with localized increases in strain and marked changes in molecules secreted by adjacent cells. Here, we systematically vary the level and duration of cyclic tensile strain applied to human dermal microvascular and bovine capillary endothelial cells via substrate deflection, and then correlate these cues with the secretion of extracellular matrix-degrading enzymes and a morphological transition from confluent monolayers to well-defined multicellular networks that resemble capillary tube-like structures. For a constant chemical environment, we find that super-physiological mechanical strain stimulates both endothelial cell secretion of latent matrix metalloprotease-2 and multicellular networks in a time- and strain-dependent manner. These results demonstrate coupling between the mechanical and biochemical states of microvascular endothelial cells, and indicate that elevated local stress may directly impact new capillary growth (angiogenesis) toward growing tumors and at capillary wall defect sites.     

Mesenchymal stem cell mechanics from the attached to the suspended state

Human mesenchymal stem cells (hMSCs) are therapeutically useful cells that are typically expanded in vitro on stiff substrata before reimplantation. Here we explore MSC mechanical and structural changes via atomic force microscopy and optical stretching during extended passaging, and we demonstrate that cytoskeletal organization and mechanical stiffness of attached MSC populations are strongly modulated over >15 population doublings in vitro. Cytoskeletal actin networks exhibit significant coarsening, attendant with decreasing average mechanical compliance and differentiation potential of these cells, although expression of molecular surface markers does not significantly decline. These mechanical changes are not observed in the suspended state, indicating that the changes manifest themselves as alterations in stress fiber arrangement rather than cortical cytoskeleton arrangement. Additionally, optical stretching is capable of investigating a previously unquantified structural transition: remodeling-induced stiffening over tens of minutes after adherent cells are suspended. Finally, we find that optically stretched hMSCs exhibit power-law rheology during both loading and recovery; this evidence appears to be the first to originate from a biophysical measurement technique not involving cell-probe or cell-substratum contact. Together, these quantitative assessments of attached and suspended MSCs define the extremes of the extracellular environment while probing intracellular mechanisms that contribute to cell mechanical response.     

The effects of shear stress and metastatic phenotype on the detachment of transformed cells

A parallel-plate flow chamber was used to quantify the detachment of normal, transformed, and reverted rat fibroblasts from a confluent monolayer of normal fibroblasts. In this method, known shear stresses were applied to the adherent cells and the percent of cells detached from the monolayer was determined. Results indicate that the detachment of all cell types increased with increasing shear stress and detachment of highly metastatic ras-transformed cells was significantly higher than that of either nonmetastatic normal cells or transformed cells reverted with the Kirsten ras revertant (K-rev 1a) gene, which are lowly metastatic. From these results, it is concluded that a correlation exists between the metastatic phenotype of the cell and its ability to detach from normal cells.     

Spatiotemporal analysis of flow-induced intermediate filament displacement in living endothelial cells

The distribution of hemodynamic shear stress throughout the arterial tree is transduced by the endothelium into local cellular responses that regulate vasoactivity, vessel wall remodeling, and atherogenesis. Although the exact mechanisms of mechanotransduction remain unknown, the endothelial cytoskeleton has been implicated in transmitting extracellular force to cytoplasmic sites of signal generation via connections to the lumenal, intercellular, and basal surfaces. Direct observation of intermediate filament (IF) displacement in cells expressing green fluorescent protein-vimentin has suggested that cytoskeletal mechanics are rapidly altered by the onset of fluid shear stress. Here, restored images from time-lapse optical sectioning fluorescence microscopy were analyzed as a four-dimensional intensity distribution function that represented IF positions. A displacement index, related to the product moment correlation coefficient as a function of time and subcellular spatial location, demonstrated patterns of IF displacement within endothelial cells in a confluent monolayer. Flow onset induced a significant increase in IF displacement above the nucleus compared with that measured near the coverslip surface, and displacement downstream from the nucleus was larger than in upstream areas. Furthermore, coordinated displacement of IF near the edges of adjacent cells suggested the existence of mechanical continuity between cells. Thus, quantitative analysis of the spatiotemporal patterns of flow-induced IF displacement suggests redistribution of intracellular force in response to alterations in hemodynamic shear stress acting at the lumenal surface.     

A three-dimensional viscoelastic model for cell deformation with experimental verification

A three-dimensional viscoelastic finite element model is developed for cell micromanipulation by magnetocytometry. The model provides a robust tool for analysis of detailed strain/stress fields induced in the cell monolayer produced by forcing one microbead attached atop a single cell or cell monolayer on a basal substrate. Both the membrane/cortex and the cytoskeleton are modeled as Maxwell viscoelastic materials, but the structural effect of the membrane/cortex was found to be negligible on the timescales corresponding to magnetocytometry. Numerical predictions are validated against experiments performed on NIH 3T3 fibroblasts and previous experimental work. The system proved to be linear with respect to cytoskeleton mechanical properties and bead forcing. Stress and strain patterns were highly localized, suggesting that the effects of magnetocytometry are confined to a region extending <10 microm from the bead. Modulation of cell height has little effect on the results, provided the monolayer is >5 micro m thick. NIH 3T3 fibroblasts exhibited a viscoelastic timescale of approximately 1 s and a shear modulus of approximately 1000 Pa.     

Mechanical Fluidity of Fully Suspended Biological Cells

Mechanical characteristics of single biological cells are used to identify and possibly leverage interesting differences among cells or cell populations. Fluidity—hysteresivity normalized to the extremes of an elastic solid or a viscous liquid—can be extracted from, and compared among, multiple rheological measurements of cells: creep compliance versus time, complex modulus versus frequency, and phase lag versus frequency. With multiple strategies available for acquisition of this nondimensional property, fluidity may serve as a useful and robust parameter for distinguishing cell populations, and for understanding the physical origins of deformability in soft matter. Here, for three disparate eukaryotic cell types deformed in the suspended state via optical stretching, we examine the dependence of fluidity on chemical and environmental influences at a timescale of ∼1 s. We find that fluidity estimates are consistent in the time and frequency domains under a structural damping (power-law or fractional-derivative) model, but not under an equivalent-complexity, lumped-component (spring-dashpot) model; the latter predicts spurious time constants. Although fluidity is suppressed by chemical cross-linking, we find that ATP depletion in the cell does not measurably alter the parameter, and we thus conclude that active ATP-driven events are not a crucial enabler of fluidity during linear viscoelastic deformation of a suspended cell. Finally, by using the capacity of optical stretching to produce near-instantaneous increases in cell temperature, we establish that fluidity increases with temperature—now measured in a fully suspended, sortable cell without the complicating factor of cell-substratum adhesion.     

Mechanical Fluidity of Fully Suspended Biological Cells

Mechanical characteristics of single biological cells are used to identify and possibly leverage interesting differences among cells or cell populations. Fluidity—hysteresivity normalized to the extremes of an elastic solid or a viscous liquid—can be extracted from, and compared among, multiple rheological measurements of cells: creep compliance versus time, complex modulus versus frequency, and phase lag versus frequency. With multiple strategies available for acquisition of this nondimensional property, fluidity may serve as a useful and robust parameter for distinguishing cell populations, and for understanding the physical origins of deformability in soft matter. Here, for three disparate eukaryotic cell types deformed in the suspended state via optical stretching, we examine the dependence of fluidity on chemical and environmental influences at a timescale of ∼1 s. We find that fluidity estimates are consistent in the time and frequency domains under a structural damping (power-law or fractional-derivative) model, but not under an equivalent-complexity, lumped-component (spring-dashpot) model; the latter predicts spurious time constants. Although fluidity is suppressed by chemical cross-linking, we find that ATP depletion in the cell does not measurably alter the parameter, and we thus conclude that active ATP-driven events are not a crucial enabler of fluidity during linear viscoelastic deformation of a suspended cell. Finally, by using the capacity of optical stretching to produce near-instantaneous increases in cell temperature, we establish that fluidity increases with temperature—now measured in a fully suspended, sortable cell without the complicating factor of cell-substratum adhesion.     

The role of viscoelasticity of collagen fibers in articular cartilage: theory and numerical formulation

The relative importance of fluid-dependent and fluid-independent transient mechanical behavior in articular cartilage was examined for tensile and unconfined compression testing using a fibril reinforced model. The collagen matrix of articular cartilage was modeled as viscoelastic using a quasi-linear viscoelastic formulation with strain-dependent elastic modulus, while the proteoglycan matrix was considered as linearly elastic. The collagen viscoelastic properties were obtained by fitting experimental data from a tensile test. These properties were used to investigate unconfined compression testing, and the sensitivity of the properties was also explored. It was predicted that the stress relaxation observed in tensile tests was not caused by fluid pressurization at the macroscopic level. A multi-step tensile stress relaxation test could be approximated using a hereditary integral in which the elastic fibrillar modulus was taken to be a linear function of the fibrillar strain. Applying the same formulation to the radial fibers in unconfined compression, stress relaxation could not be simulated if fluid pressurization were absent. Collagen viscoelasticity was found to slightly weaken fluid pressurization in unconfined compression, and this effect was relatively more significant at moderate strain rates. Therefore, collagen viscoelasticity appears to play an import role in articular cartilage in tensile testing, while fluid pressurization dominates the transient mechanical behavior in compression. Collagen viscoelasticity plays a minor role in the mechanical response of cartilage in unconfined compression if significant fluid flow is present.     

The fluid shear stress distribution on the membrane of leukocytes in the microcirculation

Recent in-vivo and in-vitro evidence indicates that fluid shear stress on the membrane of leukocytes has a powerful control over several aspects of their cell function. This evidence raises a question about the magnitude of the fluid shear stress on leukocytes in the circulation. The flow of plasma on the surface of a leukocyte at a very low Reynolds number is governed by the Stokes equation for the motion of a Newtonian fluid. We numerically estimated the distribution of fluid shear stress on a leukocyte membrane in a microvessel for the cases when the leukocyte is freely suspended, as well as rolling along or attached to a microvessel wall. The results indicate that the fluid shear stress distribution on the leukocyte membrane is nonuniform with a sharp increase when the leukocyte makes membrane attachment to the microvessel wall. In a microvessel (10 microns diameter), the fluid shear stress on the membrane of a freely suspended leukocyte (8 microns diameter) is estimated to be several times larger than the wall shear stress exerted by the undisturbed Poiseuille flow, and increases on an adherent leukocyte up to ten times. High temporal stress gradients are present in freely suspended leukocytes in shear flow due to cell rotation, which are proportional to the local shear rate. In comparison, the temporal stress gradients are reduced on the membrane of leukocytes that are rolling or firmly adhered to the endothelium. High temporal gradients of shear stress are also present on the endothelial wall. At a plasma viscosity of 1 cPoise, the peak shear stresses for suspended and adherent leukocytes are of the order of 10 dyn/cm2 and 100 dyn/cm2, respectively.     

Surface ATPase activity at cell-cell contacts in hepatic parenchymal cells and in cAMP-treated hepatoma cells in monolayer culture.

Histochemical investigation shows that ATPase activity is located intensively on the surface of cell contacts in hepatoma cells grown in confluent monolayer culture. Dibutyryl cyclic AMP and theophylline-treated hepatoma cells which exhibit contact-inhibited growth show the absence of localization of intense ATPase activity at cell-cell contacts. However, after removal of these additives the activity fully recovers to the intense level of control cells, when the release of cells from contact inhibition of growth occurs. Cultured hepatic parenchymal cells in monolayer have little or no ATPase activity at their surface immediately after contacts are established, and again after growth to a confluent state. In a different type of hepatoma cell which is less malignant and forms a small tissue mass or island, cell surface ATPase activity at cell-cell contacts in an island is very weak or scarcely detected even when cells are not treated with dibutyryl cyclic AMP and theophylline.     

Modelling biological cell attachment and growth on adherent surfaces

A mathematical model, in the form of an integro-partial differential equation, is presented to describe the dynamics of cells being deposited, attaching and growing in the form of a monolayer across an adherent surface. The model takes into account that the cells suspended in the media used for the seeding have a distribution of sizes, and that the attachment of cells restricts further deposition by fragmenting the parts of the domain unoccupied by cells. Once attached the cells are assumed to be able to grow and proliferate over the domain by a process of infilling of the interstitial gaps; it is shown that without cell proliferation there is a slow build up of the monolayer but if the surface is conducive to cell spreading and proliferation then complete coverage of the domain by the monolayer can be achieved more rapidly. Analytical solutions of the model equations are obtained for special cases, and numerical solutions are presented for parameter values derived from experiments of rat mesenchymal stromal cells seeded onto thin layers of collagen-coated polyethylene terephthalate electrospun fibers. The model represents a new approach to describing the deposition, attachment and growth of cells over adherent surfaces, and should prove useful for studying the dynamics of the seeding of biomaterials.     

Surface ATPase activity at cell-cell contacts in hepatic parenchymal cells and in cAMP-treated hepatoma cells in monolayer culture

Summary Histochemical investigation shows that ATPase activity is located intensively on the surface of cell contacts in hepatoma cells grown in confluent monolayer culture. Dibutyryl cyclic AMP and theophylline-treated hepatoma cells which exhibit contact-inhibited growth show the absence of localization of intense ATPase activity at cell-cell contacts. However, after removal of these additives the activity fully recovers to the intense level of control cells, when the release of cells from contact inhibition of growth occurs. Cultured hepatic parenchymal cells in monolayer have little or no ATPase activity at their surface immediately after contacts are established, and again after growth to a confluent state. In a different type of hepatoma cell which is less malignant and forms a small tissue mass or island, cell surface ATPase activity at cell-cell contacts in an island is very weak or scarcely detected even when cells are not treated with dibutyryl cyclic AMP and theophylline.     

Direct measurement of shear strain in adherent vascular endothelial cells exposed to fluid shear stress

Functional and morphological responses of endothelial cells (ECs) to fluid shear stress are thought to be mediated by several mechanosensitive molecules. However, how the force due to fluid shear stress applied to the apical surface of ECs is transmitted to the mechanosensors is poorly understood. In the present paper, we performed an analysis of an intracellular mechanical field by observation of the deformation behaviors of living ECs exposed to shear stress with a novel experimental method. Lateral images of human umbilical vein ECs before and after the onset of flow were obtained by confocal microscopy, and image correlation and finite element analysis were performed for quantitative analyses of subcellular strain due to shear stress. The shear strain of the cells changed from 1.06 ± 1.09% (mean ± SD) to 4.67 ± 1.79% as the magnitude of the shear stress increased from 2 to 10 Pa. The nuclei of ECs also exhibited shear deformation, which was similar to that observed in cytoplasm, suggesting that nuclei transmit forces from apical to intracellular components, as well as cytoskeletons. The obtained strain-stress relation resulted in a mean shear modulus of 213 Pa for adherent ECs. These results provide a mechanical perspective on the investigation of flow-sensing mechanisms of ECs.     

Oxidative stress response induced in rat primary hepatocyte monolayers by mechanical removal of adherent cells

We show that mechanical separation of adherent rat primary hepatocytes after the monolayer-forming stage causes the induction of the oxidative stress genes HO-1 (haem oxygenase) and MnSOD (manganese superoxide dismutase). The procedures for enzymatically breaking up liver tissue structure and isolating hepatocytes do not cause HO-1 and MnSOD activation. Only after a 3-h incubation, during which hepatocytes form a monolayer on culture dishes, does the hydrodynamic shearing away of necrotic cells sticking to the monolayer surface activate these two genes. Analysis of this injury-response pathway shows that oxidative stress and mitochondrial dysfunction play a role, as activation can be repressed by antioxidants and by respiratory inhibitors. Recovery of the cells takes a further 24-h incubation during which HO-1 and MnSOD expression returns to basal levels.     

Cell poking: quantitative analysis of indentation of thick viscoelastic layers.

A recently introduced device, the cell poker, measures the force required to indent the exposed surface of a cell adherent to a rigid substratum. The cell poker has provided phenomenological information about the viscoelastic properties of several different types of cells, about mechanical changes triggered by external stimuli, and about the role of the cytoskeleton in these mechanical functions. Except in special cases, however, it has not been possible to extract quantitative estimates of viscosity and elasticity moduli from cell poker measurements. This paper presents cell poker measurements of well characterized viscoelastic polymeric materials, polydimethylsiloxanes of different degrees of polymerization, in a simple shape, a flat, thick layer, which for our purposes can be treated as a half space. Analysis of the measurements in terms of a linear viscoelasticity theory yields viscosity values for three polymer samples in agreement with those determined by measurements on a macroscopic scale. Theoretical analysis further indicates that the measured limiting static elasticity of the layers may result from the tension generated at the interface between the polymer and water. This work demonstrates the possibility of obtaining quantitative viscoelastic material properties from cell poker measurements and represents the first step in extending these quantitative studies to more complicated structures including cells.     

Characterization of 3-D collagen hydrogels for functional cell-based biosensing

To address the growing demand for functional cell-based assay technologies with accelerated drug discovery applications, we have proposed the use of human neuroblastoma cells (IMR-32) immobilized in three-dimensional (3-D) collagen hydrogel matrices. The gel protects weakly adherent cells from fluid mechanical forces while providing a more physiologically relevant 3-D environment. Hydrogels made up of collagen, between 0.5 and 1.0mg/ml, exhibited mechanical stability adequate to withstand fluid mechanical forces (<0.11 mN) typical of automated commercial fluid transfer equipment. Collagen-entrapped cells visualized with the aid of confocal microscopy and a potentiometric-sensitive dye, TMRM, exhibited round morphology in comparison to flat morphology typical of cells in two-dimensional (2-D) monolayer cultures. Morphological differentiation characterized by neurite extension and cell aggregation was observed for both 2-D and 3-D cultures. Differentiated IMR-32 cells failed to develop a resting membrane potential typical of excitable cells. Free intracellular calcium was monitored with Calcium Green-1. Depolarization-induced Ca 2+influx was only observed with differentiated 3-D cells unlike 2-D cells, where calcium flux was observed in both differentiated and undifferentiated cells. Taken together, the results revealed that collagen hydrogels (0.5 mg/ml collagen) were suitable structural supports for weakly adherent cells. However, for voltage-dependent calcium channel function applications, further investigations are needed to explain the difference between 2-D monolayer and 3-D collagen-entrapped cells.     

Application of multiple forms of mechanical loading to human osteoblasts reveals increased ATP release in response to fluid flow in 3D cultures and differential regulation of immediate early genes

ATP is actively released into the extracellular environment from a variety of cell types in response to mechanical stimuli. This is particularly true in bone where mechanically induced ATP release leads to immediate early gene activation to regulate bone remodelling; however there is no consensus as to which mechanical stimuli stimulate osteoblasts the most. To elucidate which specific type(s) of mechanical stimuli induce ATP release and gene activation in human osteoblasts, we performed an array of experiments using different mechanical stimuli applied to both monolayer and 3D cultures of the same osteoblast cell type, SaOS-2. ATP release from osteoblasts cultured in monolayer significantly increased in response to turbulent fluid flow, laminar fluid flow and substrate strain. No significant change in ATP release could be detected in 3D osteoblast cultures in response to cyclic or static compressive loading of osteoblast-seeded scaffolds, whilst turbulent fluid flow increased ATP release from 3D cultures of osteoblasts to a greater degree than observed in monolayer cultures. Cox-2 expression quantified using real time PCR was significantly lower in cells subjected to turbulent fluid flow whereas c-fos expression was significantly higher in cells subjected to strain. Load-induced signalling via c-fos was further investigated using a SaOS-2 c-fos luciferase reporter cell line and increased in response to substrate strain and turbulent fluid flow in both monolayer and 3D, with no significant change in response to laminar fluid flow or 3D compressive loading. The results of this study demonstrate for the first time strain-induced ATP release from osteoblasts and that turbulent fluid flow in 3D up regulates the signals required for bone remodelling.     

Volumetric stress-strain analysis of optohydrodynamically suspended biological cells

Ongoing investigations are exploring the biomechanical properties of isolated and suspended biological cells in pursuit of understanding single-cell mechanobiology. An optical tweezer with minimal applied laser power has positioned biologic cells at the geometric center of a microfluidic cross-junction, creating a novel optohydrodynamic trap. The resulting fluid flow environment facilitates unique multiaxial loading of single cells with site-specific normal and shear stresses resulting in a physical albeit extensional state. A recent two-dimensional analysis has explored the cytoskeletal strain response due to these fluid-induced stresses [Wilson and Kohles, 2010, "Two-Dimensional Modeling of Nanomechanical Stresses-Strains in Healthy and Diseased Single-Cells During Microfluidic Manipulation," J Nanotechnol Eng Med, 1(2), p. 021005]. Results described a microfluidic environment having controlled nanometer and piconewton resolution. In this present study, computational fluid dynamics combined with multiphysics modeling has further characterized the applied fluid stress environment and the solid cellular strain response in three dimensions to accompany experimental cell stimulation. A volumetric stress-strain analysis was applied to representative living cell biomechanical data. The presented normal and shear stress surface maps will guide future microfluidic experiments as well as provide a framework for characterizing cytoskeletal structure influencing the stress to strain response.