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We present simulations of cell-cell adhesion as reported in a recent study [Liu et al., 2010, PNAS, 107(22), 9944-9] for two cells seeded on an array of micro-posts. The micro-post array allows for the measurement of forces exerted by the cell and these show that the cell-cell tugging stress is a constant and independent of the cell-cell junction area. In the current study, we demonstrate that a material model which includes the underlying cellular processes of stress fibre contractility and adhesion formation can capture these results. The simulations explain the experimentally observed phenomena whereby the cell-cell junction forces increase with junction size but the tractions exerted by the cell on the micro-post array are independent of the junction size. Further simulations on different types of micro-post arrays and cell phenotypes are presented as a guide to future experiments., (Copyright © 2014 Elsevier Ltd. All rights reserved.)

Actin stress fibers (SFs) generate intercellular tension and play important roles in cellular mechanotransduction processes and the regulation of various cellular functions. We recently found, in vascular smooth muscle cells (SMCs) cultured on a substrate, that the apical SFs running across the top surface of the nucleus have a mechanical connection with the cell nucleus and that their internal tension is transmitted directly to the nucleus. However, the effects of the connecting conditions and binding forces between SFs and the nucleus on force transmission processes are unclear at this stage. Here, we estimated the mechanical connection between apical SFs and the nucleus in SMCs, taking into account differences in the contractility of individual SFs, using experimental and numerical approaches. First, we classified apical SFs in SMCs according to their morphological characteristics: one subset appeared pressed onto the apical surface of the nucleus (pressed SFs), and the other appeared to be smoothly attached to the nuclear surface (attached SFs). We then dissected these SFs by laser irradiation to release the pretension, observed the dynamic behavior of the dissected SFs and the nucleus, and estimated the pretension of the SFs and the connection strength between the SFs and the nucleus by using a simple viscoelastic model. We found that pressed SFs generated greater contractile force and were more firmly connected to the nuclear surface than were attached SFs. We also observed line-like concentration of the nuclear membrane protein nesprin 1 and perinuclear DNA that was significantly located along the pressed SFs. These results indicate that the internal tension of pressed SFs is transmitted to the nucleus more efficiently than that of attached SFs, and that pressed SFs have significant roles in the regulation of the nuclear morphology and rearrangement of intranuclear DNA., (Copyright © 2014 Elsevier Ltd. All rights reserved.)

Cyclic uniaxial stretching of adherent nonmuscle cells induces the gradual reorientation of their actin stress fibers perpendicular to the stretch direction to an extent dependent on stretch frequency. By subjecting cells to various temporal waveforms of cyclic stretch, we revealed that stress fibers are much more sensitive to strain rate than strain frequency. By applying asymmetric waveforms, stress fibers were clearly much more responsive to the rate of lengthening than the rate of shortening during the stretch cycle. These observations were interpreted using a theoretical model of networks of stress fibers with sarcomeric structure. The model predicts that stretch waveforms with fast lengthening rates generate greater average stress fiber tension than that generated by fast shortening. This integrated approach of experiment and theory provides new insight into the mechanisms by which cells respond to matrix stretching to maintain tensional homeostasis., (Copyright © 2011 Elsevier Ltd. All rights reserved.)

It has been documented that mitosis orientation (MO) is guided by stress fibers (SFs), which are perpendicular to exogenous cyclic uniaxial stretch. However, the effect of mechanical forces on MO and the mechanism of stretch-induced SFs reorientation are not well elucidated to date. In the present study, we used murine 3T3 fibroblasts as a model, to investigate the effects of uniaxial stretch on SFO and MO utilizing custom-made stretch device. We found that cyclic uniaxial stretch induced both SFs and mitosis directions orienting perpendicularly to the stretch direction. The F-actin and myosin II blockages, which resulted in disoriented SFs and mitosis directions under uniaxial stretch, suggested a high correlation between SFO and MO. Y27632 (10 μM), ML7 (50 μM, or 75 μM), and blebbistatin (50 μM, or 75 μM) treatments resulted in SFO parallel to the principle stretch direction. Upon stimulating and inhibiting the phosphorylation of myosin light chain (p-MLC), we observed a monotonic proportion of SFO to the level of p-MLC. These results suggested that the level of cell contraction is crucial to the response of SFs, either perpendicular or parallel, to the external stretch. Showing the possible role of cell contractility in tuning SFO under external stretch, our experimental data are valuable to understand the predominant factor controlling SFO response to exogenous uniaxial stretch, and thus helpful for improving mechanical models., (Copyright © 2011 Elsevier Ltd. All rights reserved.)

Human endothelial cells derived from umbilical cord blood (hCB-ECs) represent a promising cell source for endothelialization of tissue engineered blood vessels. hCB-ECs cultured directly above human aortic smooth muscle cells (SMCs), which model native and tissue engineered blood vessels, produce a confluent endothelium that responds to flow like normal human aortic endothelial cells (HAECs). The objective of this study was to quantify the elastic modulus of hCB-ECs cocultured with SMCs under static and flow conditions using atomic force microscopy (AFM). Cytoskeleton structures were assessed by AFM cell surface imaging and immunofluorescence of F-actin. The elastic moduli of hCB-ECs and HAECs were similar and significantly smaller than the value for SMCs in monoculture under static conditions (p<0.05). In coculture, hCB-ECs and HAECs became significantly stiffer with moduli 160-180% larger than their corresponding values in monoculture. While the moduli of hCB-ECs and HAECs almost doubled in monoculture and flow condition, their corresponding values in coculture declined after exposure to flow. Both the number and diameter of cortical stress fiber per cell width increased in coculture and/or flow conditions, whereas the subcortical stress fiber density throughout the cell interior increased by a smaller amount. These findings indicate that changes to biomechanical properties in coculture and/or exposure to flow are correlated with changes in the cortical stress fiber density. For ECs, fluid shear stress appeared to have greater effect on the elastic modulus than the presence of SMCs and changes to the elastic modulus in coculture may be due to EC-SMC communication., (Copyright © 2011 Elsevier Ltd. All rights reserved.)

Structural models of tissue mechanics, in which the tissue is represented as a sum or integral of fiber contributions for a distribution of fiber orientations, are a popular tool to represent the complex mechanical behavior of soft tissues. A significant practical challenge, however, is evaluation of the integral that defines the stress. Numerical integration is accurate but computationally demanding, posing an impediment to incorporation of structural models into large-scale finite-element simulations. In this paper, a closed-form analytic evaluation of the integral is derived for fibers distributed according to a von Mises distribution and an exponential fiber stress-strain law.

Stress fibers are contractile bundles in the cytoskeleton that stabilize cell structure by exerting traction forces on the extracellular matrix. Individual stress fibers are molecular bundles composed of parallel actin and myosin filaments linked by various actin-binding proteins, which are organized end-on-end in a sarcomere-like pattern within an elongated three-dimensional network. While measurements of single stress fibers in living cells show that they behave like tensed viscoelastic fibers, precisely how this mechanical behavior arises from this complex supramolecular arrangement of protein components remains unclear. Here we show that computationally modeling a stress fiber as a multi-modular tensegrity network can predict several key behaviors of stress fibers measured in living cells, including viscoelastic retraction, fiber splaying after severing, non-uniform contraction, and elliptical strain of a puncture wound within the fiber. The tensegrity model can also explain how they simultaneously experience passive tension and generate active contraction forces; in contrast, a tensed cable net model predicts some, but not all, of these properties. Thus, tensegrity models may provide a useful link between molecular and cellular scale mechanical behaviors and represent a new handle on multi-scale modeling of living materials.

It is well documented that directed motion of cells is influenced by substrate stiffness. When cells are cultured on a substrate of graded stiffness, they tend to move from softer to stiffer regions--a process known as durotaxis. In this study, we propose a mathematical model of durotaxis described as an elastic stability phenomenon. We model the cytoskeleton (CSK) as a planar system of prestressed elastic line elements representing actin stress fibers (SFs), which are anchored via focal adhesions (FAs) at their end points to an elastic substrate of variable stiffness. The prestress in the SFs exerts a pulling force on FAs reducing thereby their chemical potential. Using Maxwell's global stability criterion, we obtain that the model stability increases as it is moved from a softer towards a stiffer region of the substrate. Numerical simulations reveal that elastic stability of SFs has a predominantly stabilizing effect, greater than the stabilizing effect of decreasing chemical potential of FAs. This is a novel finding which indicates that elasticity of the CSK plays an important role in cell migration and mechanosensing in general.

Stress fibers (SFs), a contractile bundle of actin filaments, play a critical role in mechanotransduction in adherent cells; yet, the mechanical properties of SFs are poorly understood. Here, we measured tensile properties of single SFs by in vitro manipulation with cantilevers. SFs were isolated from cultured vascular smooth muscle cells with a combination of low ionic-strength extraction and detergent extraction and were stretched until breaking. The breaking force and the Young's modulus (assuming that SFs were isotropic) were, on average, 377 nN and 1.45 MPa, which were approximately 600-fold greater and three orders of magnitude lower, respectively, than those of actin filaments reported previously. Strain-induced stiffening was observed in the force-strain curve. We also found that the extracted SFs shortened to approximately 80% of the original length in an ATP-independent manner after they were dislodged from the substrate, suggesting that SFs had preexisting strain in the cytoplasm. The force required for stretching the single SFs from the zero-stress length back to the original length was approximately 10 nN, which was comparable with the traction force level applied by adherent cells at single adhesion sites to maintain cell integrity. These results suggest that SFs can bear intracellular stresses that may affect overall cell mechanical properties and will impact interpretation of intracellular stress distribution and force-transmission mechanism in adherent cells.

We studied stress fiber orientation under a wide range of uniaxial cyclic deformations. We devised and validated a hypothesis consisting of two parts, as follows: (1) a stress fiber aligns to avoid a mechanical stimulus in the fiber direction under cyclic deformation. This means that, among all allowable directions, a stress fiber aligns in the direction which minimizes the stimulus, i. e., the summation of the changes in length of the stress fiber over one stretch cycle; and (2) there is a limit in the sensitivity of the cellular response to the mechanical stimulus. Due to this sensing limit, the orientation angle in stress fibers is distributed around the angle corresponding to the minimum stimulus. To validate this hypothesis, we approximated an anisotropic deformation of the membrane on which cells were to be cultured. We then obtained the relationships between the stretch range and the fiber angle in the undeformed state which minimize the mechanical stimuli, assuming that the membrane on which stress fibers and cells adhered was homogeneous and incompressible. Numerical simulation results showed that the proposed hypothesis described our previous experimental results well and was consistent with the experimental results in the literature. The simulation results, taking account of the second part of the hypothesis with a small value for the limit in sensitivity to the mechanical stimulus, could explain why cell orientation is distributed so widely with cyclic stretch ranges of <10%. The proposed hypothesis can be applied to various types of deformation because the mechanical stimulus is always sensed and accumulates under cyclic deformation without the necessity of a reference state to measure the stimulus.