A genetic strategy for the dynamic and graded control of cell mechanics, motility, and matrix remodeling

Cellular mechanical properties have emerged as central regulators of many critical cell behaviors, including proliferation, motility, and differentiation. Although investigators have developed numerous techniques to influence these properties indirectly by engineering the extracellular matrix (ECM), relatively few tools are available to directly engineer the cells themselves. Here we present a genetic strategy for obtaining graded, dynamic control over cellular mechanical properties by regulating the expression of mutant mechanotransductive proteins from a single copy of a gene placed under a repressible promoter. With the use of constitutively active mutants of RhoA GTPase and myosin light chain kinase, we show that varying the expression level of either protein produces graded changes in stress fiber assembly, traction force generation, cellular stiffness, and migration speed. Using this approach, we demonstrate that soft ECMs render cells maximally sensitive to changes in RhoA activity, and that by modulating the ability of cells to engage and contract soft ECMs, we can dynamically control cell spreading, migration, and matrix remodeling. Thus, in addition to providing quantitative relationships between mechanotransductive signaling, cellular mechanical properties, and dynamic cell behaviors, this strategy enables us to control the physical interactions between cells and the ECM and thereby dictate how cells respond to matrix properties.     

The role of transmembrane proteins on force transmission in skeletal muscle

Lateral transmission of force from myofibers laterally to the surrounding extracellular matrix (ECM) via the transmembrane proteins between them is impaired in old muscles. Changes in geometrical and mechanical properties of ECM of skeletal muscle do not fully explain the impaired lateral transmission with aging. The objective of this study was to determine the role of transmembrane proteins on force transmission in skeletal muscle. In this study, a 2D finite element model of single muscle fiber composed of myofiber, ECM, and the transmembrane proteins between them was developed to determine how changes in spatial density and mechanical properties of transmembrane proteins affect the force transmission in skeletal muscle. We found that force transmission and stress distribution are not affected by mechanical stiffness of the transmembrane proteins due to its non-linear stress–strain relationship. Results also showed that the muscle fiber with insufficient transmembrane proteins near the end of muscle fiber transmitted less force than that with more proteins does. Higher stress was observed in myofiber, ECM, and proteins in the muscle fiber with fewer proteins.     

Viscoelastic retraction of single living stress fibers and its impact on cell shape, cytoskeletal organization, and extracellular matrix mechanics

Cells change their form and function by assembling actin stress fibers at their base and exerting traction forces on their extracellular matrix (ECM) adhesions. Individual stress fibers are thought to be actively tensed by the action of actomyosin motors and to function as elastic cables that structurally reinforce the basal portion of the cytoskeleton; however, these principles have not been directly tested in living cells, and their significance for overall cell shape control is poorly understood. Here we combine a laser nanoscissor, traction force microscopy, and fluorescence photobleaching methods to confirm that stress fibers in living cells behave as viscoelastic cables that are tensed through the action of actomyosin motors, to quantify their retraction kinetics in situ, and to explore their contribution to overall mechanical stability of the cell and interconnected ECM. These studies reveal that viscoelastic recoil of individual stress fibers after laser severing is partially slowed by inhibition of Rho-associated kinase and virtually abolished by direct inhibition of myosin light chain kinase. Importantly, cells cultured on stiff ECM substrates can tolerate disruption of multiple stress fibers with negligible overall change in cell shape, whereas disruption of a single stress fiber in cells anchored to compliant ECM substrates compromises the entire cellular force balance, induces cytoskeletal rearrangements, and produces ECM retraction many microns away from the site of incision; this results in large-scale changes of cell shape (> 5% elongation). In addition to revealing fundamental insight into the mechanical properties and cell shape contributions of individual stress fibers and confirming that the ECM is effectively a physical extension of the cell and cytoskeleton, the technologies described here offer a novel approach to spatially map the cytoskeletal mechanics of living cells on the nanoscale.     

Influence of tissue- and cell-scale extracellular matrix distribution on the mechanical properties of tissue-engineered cartilage

The insufficient load-bearing capacity of today’s tissue- engineered (TE) cartilage limits its clinical application. Generally, cartilage TE studies aim to increase the extracellular matrix (ECM) content, as this is thought to determine the load-bearing properties of the cartilage. However, there are apparent inconsistencies in the literature regarding the correlation between ECM content and mechanical properties of TE constructs. In addition to the amount of ECM, the spatial inhomogeneities in ECM distribution at the tissue scale as well as at the cell scale may affect the mechanical properties of TE cartilage. The relative importance of such structural inhomogeneities on mechanical behavior of TE cartilage is unknown. The aim of the present study was, therefore, to theoretically elucidate the influence of these inhomogeneities on the mechanical behavior of chondrocyte-agarose TE constructs. A validated non-linear fiber-reinforced poro-elastic swelling cartilage model that can accommodate for effects of collagen reinforcement and swelling by proteoglycans was used. At the tissue scale, ECM was gradually varied from predominantly localized in the periphery of the TE construct toward an ECM-rich inner core. The effect of these inhomogeneities in relation to the total amount of ECM was also evaluated. At the cell scale, ECM was gradually varied from localized in the pericellular area, toward equally distributed throughout the interterritorial area. Results from the tissue-scale model indicated that localization of ECM in either the construct periphery or in the inner core may reduce construct stiffness compared with that of constructs with homogeneous ECM. Such effects are more significant at high ECM amounts. At the cell scale, localization of ECM around the cells significantly reduced the overall stiffness, even at low ECM amounts. The compressive stiffness gradually increased when ECM distribution became more homogeneous and the osmotic swelling pressure in the interterritorial area increased. We conclude that for the same amount of ECM content in TE cartilage constructs, superior mechanical properties can be achieved with more homogeneous ECM distribution at both tissue and cell scale. Inhomogeneities at the cell scale are more important than those at the tissue scale.     

Micropatterned cell sheets with defined cell and extracellular matrix orientation exhibit anisotropic mechanical properties

For an arterial replacement graft to be effective, it must possess the appropriate strength in order to withstand long-term hemodynamic stress without failure, yet be compliant enough that the mismatch between the stiffness of the graft and the native vessel wall is minimized. The native vessel wall is a structurally complex tissue characterized by circumferentially oriented collagen fibers/cells and lamellar elastin. Besides the biochemical composition, the functional properties of the wall, including stiffness, depend critically on the structural organization. Therefore, it will be crucial to develop methods of producing tissues with defined structures in order to more closely mimic the properties of a native vessel. To this end, we sought to generate cell sheets that have specific ECM/cell organization using micropatterned polydimethylsiloxane (PDMS) substrates to guide cell organization and tissue growth. The patterns consisted of large arrays of alternating grooves and ridges. Adult bovine aortic smooth muscle cells cultured on these substrates in the presence of ascorbic acid produced ECM-rich sheets several cell layers thick in which both the cells and ECM exhibited strong alignment in the direction of the micropattern. Moreover, mechanical testing revealed that the sheets exhibited mechanical anisotropy similar to that of native vessels with both the stiffness and strength being significantly larger in the direction of alignment, demonstrating that the microscale control of ECM organization results in functional changes in macroscale material behavior.     

Extracellular matrix rigidity governs smooth muscle cell motility in a biphasic fashion

Increasing evidence suggests that mechanical cues inherent to the extracellular matrix (ECM) may be equally as critical as its chemical identity in regulating cell behavior. We hypothesized that the mechanical properties of the ECM directly regulate the motility of vascular smooth muscle cells (SMCs) and tested this hypothesis using polyacrylamide substrates with tunable mechanical properties. Quantification of the migration speed on uniformly compliant hydrogels spanning a range of stiffnesses (Young's moduli values from 1.0 to 308 kPa for acrylamide/bisacrylamide ratios between 5/0.1% and 15/1.2%, respectively) revealed a biphasic dependence on substrate compliance, suggesting the existence of an optimal substrate stiffness capable of supporting maximal migration. The value of this optimal stiffness shifted depending on the concentration of ECM protein covalently attached to the substrate. Specifically, on substrates presenting a theoretical density of 0.8 microg/cm(2) fibronectin, the maximum speed of 0.74 +/- 0.09 microm/min was achieved on a 51.9 kPa gel; on substrates presenting a theoretical density of 8.0 microg/cm(2) fibronectin, the maximum speed of 0.72 +/- 0.06 microm/min occurred on a softer 21.6 kPa gel. Pre-treatment of cells with Y27632, an inhibitor of the Rho/Rho-kinase (ROCK) pathway, reduced these observed maxima to values comparable to those on non-optimal stiffnesses. In parallel, quantification of TritonX-insoluble vinculin via Western blotting, coupled with qualitative fluorescent microscopy, revealed that the formation of focal adhesions and actin stress fibers also depends on ECM stiffness. Combined, these data suggest that the mechanical properties of the underlying ECM regulate Rho-mediated contractility in SMCs by disrupting a presumptive cell-ECM force balance, which in turn regulates cytoskeletal assembly and ultimately, cell migration.     

A three-dimensional collagen-fiber network model of the extracellular matrix for the simulation of the mechanical behaviors and micro structures

The extracellular matrix (ECM) provides structural and biochemical support to cells and tissues, which is a critical factor for modulating cell dynamic behavior and intercellular communication. In order to further understand the mechanisms of the interactive relationship between cell and the ECM, we developed a three-dimensional (3D) collagen-fiber network model to simulate the micro structure and mechanical behaviors of the ECM and studied the stress–strain relationship as well as the deformation of the ECM under tension. In the model, the collagen-fiber network consists of abundant random distributed collagen fibers and some crosslinks, in which each fiber is modeled as an elastic beam and a crosslink is modeled as a linear spring with tensile limit, it means crosslinks will fail while the tensile forces exceed the limit of spring. With the given parameters of the beam and the spring, the simulated tensile stress–strain relation of the ECM highly matches the experimental results including damaged and failed behaviors. Moreover, by applying the maximal inscribed sphere method, we measured the size distribution of pores in the fiber network and learned the variation of the distribution with deformation. We also defined the alignment of the collagen-fibers to depict the orientation of fibers in the ECM quantitatively. By the study of changes of the alignment and the damaged crosslinks against the tensile strain, this paper reveals the comprehensive mechanisms of four stages of ‘toe’, ‘linear’, ‘damage’ and ‘failure’ in the tensile stress–strain relation of the ECM which can provide further insight in the study of cell-ECM interaction.     

Macrophage adhesion on fibronectin evokes an increase in the elastic property of the cell membrane and cytoskeleton: an atomic force microscopy study

Interactions between cells and microenvironments are essential to cellular functions such as survival, exocytosis and differentiation. Cell adhesion to the extracellular matrix (ECM) evokes a variety of biophysical changes in cellular organization, including modification of the cytoskeleton and plasma membrane. In fact, the cytoskeleton and plasma membrane are structures that mediate adherent contacts with the ECM; therefore, they are closely correlated. Considering that the mechanical properties of the cell could be affected by cell adhesion-induced changes in the cytoskeleton, the purpose of this study was to investigate the influence of the ECM on the elastic properties of fixed macrophage cells using atomic force microscopy. The results showed that there was an increase (~50 %) in the Young’s modulus of macrophages adhered to an ECM-coated substrate as compared with an uncoated glass substrate. In addition, cytochalasin D-treated cells had a 1.8-fold reduction of the Young’s modulus of the cells, indicating the contribution of the actin cytoskeleton to the elastic properties of the cell. Our findings show that cell adhesion influences the mechanical properties of the plasma membrane, providing new information toward understanding the influence of the ECM on elastic alterations of macrophage cell membranes.     

Effects of blocking integrin β1 and N-cadherin cellular interactions on mechanical properties of vascular smooth muscle cells

Experimental measurements of cellular mechanical properties have shown large variability in whole-cell mechanical properties between cells from a single population. This heterogeneity has been observed in many cell populations and with several measurement techniques but the sources are not yet fully understood. Cell mechanical properties are directly related to the composition and organization of the cytoskeleton, which is physically coupled to neighboring cells through adherens junctions and to underlying matrix through focal adhesion complexes. This high level of heterogeneity may be attributed to varying cellular interactions throughout the sample. We tested the effect of cell-cell and cell-matrix interactions on the mechanical properties of vascular smooth muscle cells (VSMCs) in culture by using antibodies to block N-cadherin and integrin β1 interactions. VSMCs were cultured on substrates of varying stiffness with and without tension. Under each of these conditions, cellular mechanical properties were characterized by performing atomic force microscopy (AFM) and cellular structure was analyzed through immunofluorescence imaging. As expected, VSMC mechanical properties were greatly affected by the underlying culture substrate and applied tension. Interestingly, the cell-to-cell variation in mechanical properties within each sample decreased significantly in the antibody conditions. Thus, the cells grown with blocking antibodies were more homogeneous in their mechanical properties on both glass and soft substrates. This suggests that diversified adhesion binding between cells and the ECM is responsible for a significant amount of mechanical heterogeneity that is observed in 2D cell culture studies.     

Computational model predicts cell orientation in response to a range of mechanical stimuli

To build anisotropic, mechanically functioning tissue, it is essential to understand how cells orient in response to mechanical stimuli. Therefore, a computational model was developed which predicts cell orientation, based on the actin stress fiber distribution inside the cell. In the model, the stress fiber distribution evolves dynamically according to the following: (1) Stress fibers contain polymerized actin. The total amount of depolymerized plus polymerized actin is constant. (2) Stress fibers apply tension to their environment. This active tension is maximal when strain rate and absolute strain are zero and reduces with increasing shortening rate and absolute strain. (3) A high active fiber stress in a direction leads to a large amount of fibers in this direction. (4) The cell is attached to a substrate; all fiber stresses are homogenized into a total cell stress, which is in equilibrium with substrate stress. This model predicts that on a substrate of anisotropic stiffness, fibers align in the stiffest direction. Under cyclic strain when the cellular environment is so stiff that no compaction occurs (1 MPa), the model predicts strain avoidance, which is more pronounced with increasing strain frequency or amplitude. Under cyclic strain when the cellular environment is so soft that cells can compact it (10 kPa), the model predicts a preference for the cyclically strained compared to the compacting direction. These model predictions all agree with experimental evidence. For the first time, a computational model predicts cell orientation in response to this range of mechanical stimuli using a single set of parameters.     

Experimental and Computational Investigation of the Role of Stress Fiber Contractility in the Resistance of Osteoblasts to Compression

The mechanical behavior of the actin cytoskeleton has previously been investigated using both experimental and computational techniques. However, these investigations have not elucidated the role the cytoskeleton plays in the compression resistance of cells. The present study combines experimental compression techniques with active modeling of the cell’s actin cytoskeleton. A modified atomic force microscope is used to perform whole cell compression of osteoblasts. Compression tests are also performed on cells following the inhibition of the cell actin cytoskeleton using cytochalasin-D. An active bio-chemo-mechanical model is employed to predict the active remodeling of the actin cytoskeleton. The model incorporates the myosin driven contractility of stress fibers via a muscle-like constitutive law. The passive mechanical properties, in parallel with active stress fiber contractility parameters, are determined for osteoblasts. Simulations reveal that the computational framework is capable of predicting changes in cell morphology and increased resistance to cell compression due to the contractility of the actin cytoskeleton. It is demonstrated that osteoblasts are highly contractile and that significant changes to the cell and nucleus geometries occur when stress fiber contractility is removed.     

Arterial Extracellular Matrix: A Mechanobiological Study of the Contributions and Interactions of Elastin and Collagen

The complex network structure of elastin and collagen extracellular matrix (ECM) forms the primary load bearing components in the arterial wall. The structural and mechanobiological interactions between elastin and collagen are important for properly functioning arteries. Here, we examined the elastin and collagen organization, realignment, and recruitment by coupling mechanical loading and multiphoton imaging. Two-photon excitation fluorescence and second harmonic generation methods were performed with a multiphoton video-rate microscope to capture real time changes to the elastin and collagen structure during biaxial deformation. Enzymatic removal of elastin was performed to assess the structural changes of the remaining collagen structure. Quantitative analysis of the structural changes to elastin and collagen was made using a combination of two-dimensional fast Fourier transform and fractal analysis, which allows for a more complete understanding of structural changes. Our study provides new quantitative evidence, to our knowledge on the sequential engagement of different arterial ECM components in response to mechanical loading. The adventitial collagen exists as large wavy bundles of fibers that exhibit fiber engagement after 20% strain. The medial collagen is engaged throughout the stretching process, and prominent elastic fiber engagement is observed up to 20% strain after which the engagement plateaus. The fiber orientation distribution functions show remarkably different changes in the ECM structure in response to mechanical loading. The medial collagen shows an evident preferred circumferential distribution, however the fiber families of adventitial collagen are obscured by their waviness at no or low mechanical strains. Collagen fibers in both layers exhibit significant realignment in response to unequal biaxial loading. The elastic fibers are much more uniformly distributed and remained relatively unchanged due to loading. Removal of elastin produces similar structural changes in collagen as mechanical loading. Our study suggests that the elastic fibers are under tension and impart an intrinsic compressive stress on the collagen.     

Dynamic and structural signatures of lamellar actomyosin force generation

The regulation of cellular traction forces on the extracellular matrix is critical to cell adhesion, migration, proliferation, and differentiation. Diverse lamellar actin organizations ranging from contractile lamellar networks to stress fibers are observed in adherent cells. Although lamellar organization is thought to reflect the extent of cellular force generation, understanding of the physical behaviors of the lamellar actin cytoskeleton is lacking. To elucidate these properties, we visualized the actomyosin dynamics and organization in U2OS cells over a broad range of forces. At low forces, contractile lamellar networks predominate and force generation is strongly correlated to actomyosin retrograde flow dynamics with nominal change in organization. Lamellar networks build ～60% of cellular tension over rapid time scales. At high forces, reorganization of the lamellar network into stress fibers results in moderate changes in cellular tension over slower time scales. As stress fibers build and tension increases, myosin band spacing decreases and α-actinin bands form. On soft matrices, force generation by lamellar networks is unaffected, whereas tension-dependent stress fiber assembly is abrogated. These data elucidate the dynamic and structural signatures of the actomyosin cytoskeleton at different levels of tension and set a foundation for quantitative models of cell and tissue mechanics.     

Arterial Extracellular Matrix: A Mechanobiological Study of the Contributions and Interactions of Elastin and Collagen

The complex network structure of elastin and collagen extracellular matrix (ECM) forms the primary load bearing components in the arterial wall. The structural and mechanobiological interactions between elastin and collagen are important for properly functioning arteries. Here, we examined the elastin and collagen organization, realignment, and recruitment by coupling mechanical loading and multiphoton imaging. Two-photon excitation fluorescence and second harmonic generation methods were performed with a multiphoton video-rate microscope to capture real time changes to the elastin and collagen structure during biaxial deformation. Enzymatic removal of elastin was performed to assess the structural changes of the remaining collagen structure. Quantitative analysis of the structural changes to elastin and collagen was made using a combination of two-dimensional fast Fourier transform and fractal analysis, which allows for a more complete understanding of structural changes. Our study provides new quantitative evidence, to our knowledge on the sequential engagement of different arterial ECM components in response to mechanical loading. The adventitial collagen exists as large wavy bundles of fibers that exhibit fiber engagement after 20% strain. The medial collagen is engaged throughout the stretching process, and prominent elastic fiber engagement is observed up to 20% strain after which the engagement plateaus. The fiber orientation distribution functions show remarkably different changes in the ECM structure in response to mechanical loading. The medial collagen shows an evident preferred circumferential distribution, however the fiber families of adventitial collagen are obscured by their waviness at no or low mechanical strains. Collagen fibers in both layers exhibit significant realignment in response to unequal biaxial loading. The elastic fibers are much more uniformly distributed and remained relatively unchanged due to loading. Removal of elastin produces similar structural changes in collagen as mechanical loading. Our study suggests that the elastic fibers are under tension and impart an intrinsic compressive stress on the collagen.     

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 significance of alpha 5 beta 1 integrin dependent and independent actin cytoskelton organization in cell transformation and survival

Cell-matrix and cell-cell interactions are important physiological determinants of cell growth, survival and transformation. Cell adhesion to the extra cellular matrix (ECM) via integrins also crucially influences the organization of the cytoskeleton. It triggers a cascade of intracellular biochemical events, which regulate cell viability and growth. We have studied the relationship between cell attachment to the substratum and cytoskeletal organization and cell survival and transformation. Our results demonstrate that in the absence of attachment to the substratum, adhesion-dependent fibroblasts exhibit rapid loss of viability. However, a small percentage of cells survive even after remaining non-adherent for 16h. The adherent and non-adherent cells differ from one another both morphologically and physiologically. The latter show a loss of alpha5beta1 integrin expression on their surface and bind non-specifically to the substratum and ECM, thereby activating certain pathways more efficiently than adherent cells. We have also shown that non-adherent cells grow faster and have worse cytoskeletal organization after attachment to the substratum, and do not form focal adhesions or actin stress fibres. Hence, our data suggests that rat fibroblasts in prolonged suspension exhibit some properties that are comparable to cells undergoing transformation, by adapting integrin-dependent or independent signalling pathways for their survival.     

Cells in 3D matrices under interstitial flow: Effects of extracellular matrix alignment on cell shear stress and drag forces

Interstitial flow is an important regulator of various cell behaviors both in vitro and in vivo, yet the forces that fluid flow imposes on cells embedded in a 3D extracellular matrix (ECM), and the effects of matrix architecture on those forces, are not well understood. Here, we demonstrate how fiber alignment can affect the shear and pressure forces on the cell and ECM. Using computational fluid dynamics simulations, we show that while the solutions of the Brinkman equation accurately estimate the average fluid shear stress and the drag forces on a cell within a 3D fibrous medium, the distribution of shear stress on the cellular surface as well as the peak shear stresses remain intimately related to the pericellular fiber architecture and cannot be estimated using bulk-averaged properties. We demonstrate that perpendicular fiber alignment of the ECM yields lower shear stress and pressure forces on the cells and higher stresses on the ECM, leading to decreased permeability, while parallel fiber alignment leads to higher stresses on cells and increased permeability, as compared to a cubic lattice arrangement. The Spielman–Goren permeability relationships for fibrous media agreed well with CFD simulations of flow with explicitly considered fibers. These results suggest that the experimentally observed active remodeling of ECM fibers by fibroblasts under interstitial flow to a perpendicular alignment could serve to decrease the shear and drag forces on the cell.     

Spatial Mapping of the Biomechanical Properties of the Pericellular Matrix of Articular Cartilage Measured In Situ via Atomic Force Microscopy

In articular cartilage, chondrocytes are surrounded by a narrow region called the pericellular matrix (PCM), which is biochemically, structurally, and mechanically distinct from the bulk extracellular matrix (ECM). Although multiple techniques have been used to measure the mechanical properties of the PCM using isolated chondrons (the PCM with enclosed cells), few studies have measured the biomechanical properties of the PCM in situ. The objective of this study was to quantify the in situ mechanical properties of the PCM and ECM of human, porcine, and murine articular cartilage using atomic force microscopy (AFM). Microscale elastic moduli were quantitatively measured for a region of interest using stiffness mapping, or force-volume mapping, via AFM. This technique was first validated by means of elastomeric models (polyacrylamide or polydimethylsiloxane) of a soft inclusion surrounded by a stiff medium. The elastic properties of the PCM were evaluated for regions surrounding cell voids in the middle/deep zone of sectioned articular cartilage samples. ECM elastic properties were evaluated in regions visually devoid of PCM. Stiffness mapping successfully depicted the spatial arrangement of moduli in both model and cartilage surfaces. The modulus of the PCM was significantly lower than that of the ECM in human, porcine, and murine articular cartilage, with a ratio of PCM to ECM properties of ∼0.35 for all species. These findings are consistent with previous studies of mechanically isolated chondrons, and suggest that stiffness mapping via AFM can provide a means of determining microscale inhomogeneities in the mechanical properties of articular cartilage in situ.     

A mathematical model of the coupled mechanisms of cell adhesion,contraction and spreading

Recent research has shown that cell spreading is highly dependent on the contractility of its cytoskeleton and the mechanical properties of the environment it is located in. The dynamics of such process is critical for the development of tissue engineering strategy but is also a key player in wound contraction, tissue maintenance and angiogenesis. To better understand the underlying physics of such phenomena, the paper describes a mathematical formulation of cell spreading and contraction that couples the processes of stress fiber formation, protrusion growth through actin polymerization at the cell edge and dynamics of cross-membrane protein (integrins) enabling cell-substrate attachment. The evolving cell’s cytoskeleton is modeled as a mixture of fluid, proteins and filaments that can exchange mass and generate contraction. In particular, besides self-assembling into stress fibers, actin monomers able to polymerize into an actin meshwork at the cell’s boundary in order to push the membrane forward and generate protrusion. These processes are possible via the development of cell-substrate attachment complexes that arise from the mechano-sensitive equilibrium of membrane proteins, known as integrins. After deriving the governing equation driving the dynamics of cell evolution and spreading, we introduce a numerical solution based on the extended finite element method, combined with a level set formulation. Numerical simulations show that the proposed model is able to capture the dependency of cell spreading and contraction on substrate stiffness and chemistry. The very good agreement between model predictions and experimental observations suggests that mechanics plays a strong role into the coupled mechanisms of contraction, adhesion and spreading of adherent cells.     

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.