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.     

Indentation and adhesive probing of a cell membrane with AFM: theoretical model and experiments

In probing adhesion and cell mechanics by atomic force microscopy (AFM), the mechanical properties of the membrane have an important if neglected role. Here we theoretically model the contact of an AFM tip with a cell membrane, where direct motivation and data are derived from a prototypical ligand-receptor adhesion experiment. An AFM tip is functionalized with a prototypical ligand, SIRPalpha, and then used to probe its native receptor on red cells, CD47. The interactions prove specific and typical in force, and also show in detachment, a sawtooth-shaped disruption process that can extend over hundreds of nm. The theoretical model here that accounts for both membrane indentation as well as membrane extension in tip retraction incorporates membrane tension and elasticity as well as AFM tip geometry and stochastic disruption. Importantly, indentation depth proves initially proportional to membrane tension and does not follow the standard Hertz model. Computations of detachment confirm nonperiodic disruption with membrane extensions of hundreds of nm set by membrane tension. Membrane mechanical properties thus clearly influence AFM probing of cells, including single molecule adhesion experiments.     

Characterization of mechanical behavior of an epithelial monolayer in response to epidermal growth factor stimulation

Cell signaling often causes changes in cellular mechanical properties. Knowledge of such changes can ultimately lead to insight into the complex network of cell signaling. In the current study, we employed a combination of atomic force microscopy (AFM) and quartz crystal microbalance with dissipation monitoring (QCM-D) to characterize the mechanical behavior of A431 cells in response to epidermal growth factor receptor (EGFR) signaling. From AFM, which probes the upper portion of an individual cell in a monolayer of cells, we observed increases in energy dissipation, Young's modulus, and hysteresivity. Increases in hysteresivity imply a shift toward a more fluid-like mechanical ordering state in the bodies of the cells. From QCM-D, which probes the basal area of the monolayer of cells collectively, we observed decreases in energy dissipation factor. This result suggests a shift toward a more solid-like state in the basal areas of the cells. The comparative analysis of these results indicates a regionally specific mechanical behavior of the cell in response to EGFR signaling and suggests a correlation between the time-dependent mechanical responses and the dynamic process of EGFR signaling. This study also demonstrates that a combination of AFM and QCM-D is able to provide a more complete and refined mechanical profile of the cells during cell signaling.     

Disulfide bonds in the outer layer of keratin fibers confer higher mechanical rigidity: correlative nano-indentation and elasticity measurement with an AFM.

Nanomechanical properties of biological fibers are governed by the morphological features and chemically heterogeneous constituent subunits. However, very little experimental data exist for nanoscale correlation between heterogeneous subunits and their mechanical properties. We have used keratin-rich wool fibers as a model of composite biological fibers; a wool fiber is a simple two component cylindrical system consisting of a core cellular component surrounded by an outer cell layer and their ultrastructure and chemical composition are well-characterized. The core is 16-40 micrometer in diameter and rich in axially aligned keratin microfibrils. Outer cells have multiple laminar layers, 60-600 nm thick and distinctly rich in disulfide bonds. We used an atomic force microscope (AFM) to examine the nanomechanical properties of various structural components using complementary techniques of force-volume imaging and nano-indentation. AFM images of transverse sections of fibers were obtained in ambient environment, and the mechanical properties of several identified regions were examined. The outer cell layer showed a significantly higher mechanical stiffness than the internal cellular core region. Chemical reduction of disulfide bonds eliminated such dichotomy of mechanical strengths, indicating that the higher rigidity of the outer layer is attributed primarily to the presence of extensive disulfide bonding in the exo-cuticle. This is the first detailed correlative study of nano-indentation and regional elasticity measurements in composite biological systems, including mammalian biological fibers.     

Simple display system of mechanical properties of cells and their dispersion

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

Model of cellular mechanotransduction via actin stress fibers

Mechanical stresses due to blood flow regulate vascular endothelial cell structure and function and play a key role in arterial physiology and pathology. In particular, the development of atherosclerosis has been shown to correlate with regions of disturbed blood flow where endothelial cells are round and have a randomly organized cytoskeleton. Thus, deciphering the relation between the mechanical environment, cell structure, and cell function is a key step toward understanding the early development of atherosclerosis. Recent experiments have demonstrated very rapid (\(\sim \)100 ms) and long-distance (\(\sim \)10 \(\upmu \)m) cellular mechanotransduction in which prestressed actin stress fibers play a critical role. Here, we develop a model of mechanical signal transmission within a cell by describing strains in a network of prestressed viscoelastic stress fibers following the application of a force to the cell surface. We find force transmission dynamics that are consistent with experimental results. We also show that the extent of stress fiber alignment and the direction of the applied force relative to this alignment are key determinants of the efficiency of mechanical signal transmission. These results are consistent with the link observed experimentally between cytoskeletal organization, mechanical stress, and cellular responsiveness to stress. Based on these results, we suggest that mechanical strain of actin stress fibers under force constitutes a key link in the mechanotransduction chain.     

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

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

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

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

Drug-induced changes of cytoskeletal structure and mechanics in fibroblasts: an atomic force microscopy study

The effect of various drugs affecting the integrity of different components of the cytoskeleton on the elasticity of two fibroblast cell lines was investigated by elasticity measurements with an atomic force microscope (AFM). Disaggregation of actin filaments always resulted in a distinct decrease in the cell's average elastic modulus indicating the crucial importance of the actin network for the mechanical stability of living cells. Disruption or chemical stabilization of microtubules did not affect cell elasticity. For the f-actin-disrupting drugs different mechanisms of drug action were observed. Cytochalasins B and D and Latrunculin A disassembled stress fibers. For Cytochalasin D this was accompanied by an aggregation of actin within the cytosol. Jasplakinolide disaggregated actin filaments but did not disassemble stress fibers. Fibrous structures found in AFM images and elasticity maps of fibroblasts could be identified as stress fibers by correlation of AFM data and fluorescence images.     

The orthotropic viscoelastic behavior of aortic elastin

In this paper, we studied the viscoelastic behaviors of isolated aortic elastin using combined modeling and experimental approaches. Biaxial stress relaxation and creep experiments were performed to study the time-dependent behavior of elastin. Experimental results reveal that stress relaxation preconditioning is necessary in order to obtain repeatable stress relaxation responses. Elastin exhibits less stress relaxation than intact or decellularized aorta. The rate of stress relaxation of intact and decellularized aorta is linearly dependent on the initial stress levels. The rate of stress relaxation for elastin increases linearly at stress levels below about 60 kPa; however, the rate changes very slightly at higher initial stress levels. Experimental results also show that creep response is negligible for elastin, and the intact or decellularized aorta. A quasi-linear viscoelasticity model was incorporated into a statistical mechanics based eight-chain microstructural model at the fiber level to simulate the orthotropic viscoelastic behavior of elastin. A user material subroutine was developed for finite element analysis. Results demonstrate that this model is suitable to capture both the orthotropic hyperelasticity and viscoelasticity of elastin.     

Computational and experimental investigation of local stress fiber orientation in uniaxially and biaxially constrained microtissues

The orientation of cells and associated F-actin stress fibers is essential for proper tissue functioning. We have previously developed a computational model that qualitatively describes stress fiber orientation in response to a range of mechanical stimuli. In this paper, the aim is to quantitatively validate the model in a static, heterogeneous environment. The stress fiber orientation in uniaxially and biaxially constrained microscale tissues was investigated using a recently developed experimental system. Computed and experimental stress fiber orientations were compared, while accounting for changes in orientation with location in the tissue. This allowed for validation of the model, and additionally, it showed how sensitive the stress fiber orientation in the experimental system is to the location where it is measured, i.e., the heterogeneity of the stress fiber orientation. Computed and experimental stress fiber orientations showed good quantitative agreement in most regions. A strong local alignment near the locations where boundary conditions were enforced was observed for both uniaxially and biaxially constrained tissues. Excepting these regions, in biaxially constrained tissues, no preferred orientation was found and the distribution was independent of location. The stress fiber orientation in uniaxially constrained tissues was more heterogeneous, and stress fibers mainly oriented in the constrained direction or along the free edge. These results indicate that the stress fiber orientation in these constrained microtissues is mainly determined by the local mechanical environment, as hypothesized in our model, and also that the model is a valid tool to predict stress fiber orientation in heterogeneously loaded tissues.     

An Improved Strategy for Generating Forces in Steered Molecular Dynamics: The Mechanical Unfolding of Titin,e2lip3 and Ubiquitin

One of the applications of Molecular Dynamics (MD) simulations is to explore the energetic barriers to mechanical unfolding of proteins such as occurs in response to the mechanical pulling of single molecules in Atomic Force Microscopy (AFM) experiments. Although Steered Molecular Dynamics simulations have provided microscopic details of the unfolding process during the pulling, the simulated forces required for unfolding are typically far in excess of the measured values. To rectify this, we have developed the Pulsed Unconstrained Fluctuating Forces (PUFF) method, which induces constant-momentum motions by applying forces directly to the instantaneous velocity of selected atoms in a protein system. The driving forces are applied in pulses, which allows the system to relax between pulses, resulting in more accurate unfolding force estimations than in previous methods. In the cases of titin, ubiquitin and e2lip3, the PUFF trajectories produce force fluctuations that agree quantitatively with AFM experiments. Another useful property of PUFF is that simulations get trapped if the target momentum is too low, simplifying the discovery and analysis of unfolding intermediates.     

Characterization of cell elasticity correlated with cell morphology by atomic force microscope

Biomechanical properties of cells have been identified as an important factor in a broad range of biological processes. Based on measurements of mechanical properties by atomic force microscopy (AFM) particularly cell elasticity has been linked with human diseases, such as cancer. AFM has been widely used as a nanomechanical tool to probe the elasticity of living cells, however, standard methods for characterizing cell elasticity are still lacking. The local elasticity of a cell is conventionally used to represent the mechanical property of the cell. However, since cells have highly heterogeneous regions, elasticity mapping over the entire cell, rather than at a few points of measurement, is required. Using human aortic endothelial cells (HAECs) as a model, we have developed in this study a new method to evaluate cell elasticity more quantitatively. Based on the height information of the cell, a new characterization method was proposed to evaluate the elasticity of a cell. Using this method, elasticities of cells on different substrates were compared. Results showed that the elasticity of HAECs on softer substrate also has higher value compared to those on harder substrate given a certain height where the statistical distribution analysis confirmed that higher actin filaments density was located. Thus, the elasticity of small portions of a cell could not represent the entire cell property and may lead to invalid characterization. In order to gain a more comprehensive and detailed understanding of biomechanical properties for future clinical use, elasticity and cell morphology should therefore be correlated with discussion.     

Mechanical properties of zona pellucida hardening

We have investigated the changes in the mechanical properties of the zona pellucida (ZP), a multilayer glycoprotein coat that surrounds mammalian eggs, that occur after the maturation and fertilization process of the bovine oocyte by using atomic force spectroscopy. The response of the ZP to mechanical stress has been recovered according to a modified Hertz model. ZP of immature oocytes shows a pure elastic behavior. However, for ZPs of matured and fertilized oocyte, a transition from a purely elastic behavior, which occurs when low stress forces are applied, towards a plastic behavior has been observed. The high critical force necessary to induce deformations, which supports the noncovalent long interaction lifetimes of polymers, increases after the cortical reaction. Atomic force microscopy (AFM) images show that oocyte ZP surface appears to be composed mainly of a dense, random meshwork of nonuniformly arranged fibril bundles. More wrinkled surface characterizes matured oocytes compared with immature and fertilized oocytes. From a mechanical point of view, the transition of the matured ZP membrane toward fertilized ZP, through the hardening process, consists of the recovery of the elasticity of the immature ZP while maintaining a plastic transition that, however, occurs with a much higher force compared with that required in matured ZP.     

A computational model for understanding the micro-mechanics of collagen fiber network in the tunica adventitia

Abdominal aortic aneurysm is a prevalent cardiovascular disease with high mortality rates. The mechanical response of the arterial wall relies on the organizational and structural behavior of its microstructural components, and thus, a detailed understanding of the microscopic mechanical response of the arterial wall layers at loads ranging up to rupture is necessary to improve diagnostic techniques and possibly treatments. Following the common notion that adventitia is the ultimate barrier at loads close to rupture, in the present study, a finite element model of adventitial collagen network was developed to study the mechanical state at the fiber level under uniaxial loading. Image stacks of the rabbit carotid adventitial tissue at rest and under uniaxial tension obtained using multi-photon microscopy were used in this study, as well as the force–displacement curves obtained from previously published experiments. Morphological parameters like fiber orientation distribution, waviness, and volume fraction were extracted for one sample from the confocal image stacks. An inverse random sampling approach combined with a random walk algorithm was employed to reconstruct the collagen network for numerical simulation. The model was then verified using experimental stress–stretch curves. The model shows the remarkable capacity of collagen fibers to uncrimp and reorient in the loading direction. These results further show that at high stretches, collagen network behaves in a highly non-affine manner, which was quantified for each sample. A comprehensive parameter study to understand the relationship between structural parameters and their influence on mechanical behavior is presented. Through this study, the model was used to conclude important structure–function relationships that control the mechanical response. Our results also show that at loads close to rupture, the probability of failure occurring at the fiber level is up to 2%. Uncertainties in usually employed rupture risk indicators and the stochastic nature of the event of rupture combined with limited knowledge on the microscopic determinants motivate the development of such an analysis. Moreover, this study will advance the study of coupling microscopic mechanisms to rupture of the artery as a whole.

     

Micromechanical modeling of the epimysium of the skeletal muscles

A micromechanical model has been developed to investigate the mechanical properties of the epimysium. In the present model, the collagen fibers in the epimysium are embedded randomly in the ground substance. Two parallel wavy collagen fibers and the surrounding ground substance are used as the repeat unit (unit cell), and the epimysium is considered as an aggregate of unit cells. Each unit cell is distributed in the epimysium with some different angle to the muscle fiber direction. The model allows the progressive straightening of the collagen fiber as well as the effects of fiber reorientation. The predictions of the model compare favorably against experiment. The effects of the collagen fiber volume fraction, collagen fiber waviness at the rest length and the mechanical properties of the collagen fibers and the ground substance are analyzed. This model allows the analysis of mechanical behavior of most soft tissues if appropriate experimental data are available.     

Analyzing valve interstitial cell mechanics and geometry with spatial statistics

Understanding cell geometric and mechanical properties is crucial to understanding how cells sense and respond to their local environment. Moreover, changes to cell mechanical properties under varied micro-environmental conditions can both influence and indicate fundamental changes to cell behavior. Atomic Force Microscopy (AFM) is a well established, powerful tool to capture geometric and mechanical properties of cells. We have previously demonstrated substantial functional and behavioral differences between aortic and pulmonary valve interstitial cells (VIC) using AFM and subsequent models of VIC mechanical response. In the present work, we extend these studies by demonstrating that to best interpret the spatially distributed AFM data, the use of spatial statistics is required. Spatial statistics includes formal techniques to analyze spatially distributed data, and has been used successfully in the analysis of geographic data. Thus, spatially mapped AFM studies of cell geometry and mechanics are analogous to more traditional forms of geospatial data. We are able to compare the spatial autocorrelation of stiffness in aortic and pulmonary valve interstitial cells, and more accurately capture cell geometry from height recordings. Specifically, we showed that pulmonary valve interstitial cells display higher levels of spatial autocorrelation of stiffness than aortic valve interstitial cells. This suggests that aortic VICs form different stress fiber structures than their pulmonary counterparts, in addition to being more highly expressed and stiffer on average. Thus, the addition of spatial statistics can contribute to our fundamental understanding of the differences between cell types. Moving forward, we anticipate that this work will be meaningful to enhance direct analysis of experimental data and for constructing high fidelity computational of VICs and other cell models.     

AFM-based dual nano-mechanical phenotypes for cancer metastasis

An enhanced mechanical compliance is considered to be a mechanical indicator for metastatic cancer cells. Our study using atomic force microscopy (AFM) revealed that breast cancer cells agreed well with this hypothesis. However, prostate cancer cells displayed a reverse correlation; less metastatic prostate cancer cells were more mechanically compliant. Two-dimensional AFM force spectroscopy was performed to characterize dual mechanical properties—the cell–substrate adhesion as well as the mechanical compliance. Interestingly, prostate cancer cells displayed a strong positive correlation between the cell–substrate adhesion and metastatic potential. However, there was no clearly observable correlation between the cell–substrate adhesion and the metastatic potential despite variations in mechanical compliance of breast cancer cells. These results suggest that the correlation between the dual mechanical signatures and metastatic potential be uniquely identified for cancer cells originating from different organs. We postulate that this correlation could reveal which step of cancer progression is favorable in terms of physical interaction between cancer cells and micro-environments. We expect that based on the “seed and soil hypothesis”, the identification of the dual mechanical phenotypes, could provide a new insight for understanding how a dominant metastatic site is determined for cancer cells originating from specific organs.     

Micromechanics modeling of Haversian cortical bone properties.

A finite-element micromechanics model for Haversian cortical bone tissue has been developed and studied. The model is an extension of two-dimensional micromechanics techniques for fiber-reinforced composite materials. Haversian systems, or secondary osteons, are considered to be the fiber component, and interstitial lamellar bone the matrix material. The cement line is included as an 'interphase' component along the fiber/matrix interface. The model assumes a regular repeatable spacing of the longitudinally aligned continuous fibers and is, therefore, restricted to approximating Haversian cortical bone in its present form. Haversian porosity is modeled explicitly by incorporating a hollow fiber to represent the Haversian canal. Solutions have been obtained by applying uniform macroscopic stresses to the boundaries of the repeating unit cell model. Macroscopic mechanical property predictions correspond reasonably well with the experimental data for cortical bone, but are necessarily dependent on the input properties for each constituent, which are not well established. The predicted variation in the elastic modulus with porosity is not as sensitive as that observed experimentally. Stresses within the constituents can also be modeled with this method and are demonstrated to deviate from the macroscopic applied stress levels.