Confocal microscopy-based three-dimensional cell-specific modeling for large deformation analyses in cellular mechanics

This study introduces a new confocal microscopy-based three-dimensional cell-specific finite element (FE) modeling methodology for simulating cellular mechanics experiments involving large cell deformations. Three-dimensional FE models of undifferentiated skeletal muscle cells were developed by scanning C2C12 myoblasts using a confocal microscope, and then building FE model geometries from the z-stack images. Strain magnitudes and distributions in two cells were studied when the cells were subjected to compression and stretching, which are used in pressure ulcer and deep tissue injury research to induce large cell deformations. Localized plasma membrane and nuclear surface area (NSA) stretches were observed for both the cell compression and stretching simulation configurations. It was found that in order to induce large tensile strains (>5%) in the plasma membrane and NSA, one needs to apply more than ～15% of global cell deformation in cell compression tests, or more than ～3% of tensile strains in the elastic plate substrate in cell stretching experiments. Utilization of our modeling can substantially enrich experimental cellular mechanics studies in classic cell loading designs that typically involve large cell deformations, such as static and cyclic stretching, cell compression, micropipette aspiration, shear flow and hydrostatic pressure, by providing magnitudes and distributions of the localized cellular strains specific to each setup and cell type, which could then be associated with the applied stimuli.     

Embryonic tissues as elasticoviscous liquids: II. Direct evidence for cell slippage in centrifuged aggregates

Certain embryonic cell aggregates display both solid-like and liquid-like properties in organ culture. When centrifuged against solid substrata, these aggregates undergo sudden initial deformations followed by more gradual shape changes. Thus, they are either compoundviscoelastic solids (in which cells first stretch rapidly, then slowly) or elasticoviscous liquids (in which cells first quickly stretch, but then gradually slide by one another). To distinguish between these alternatives, we have examined cell shapes in centrifugally deformed chick liver aggregates. Light and electron micrographs show that initially stretched cells within flattening aggregates gradually reassume their original undisturbed shapes during prolonged centrifugation. Therefore, although the cells themselves may react to stretching forces like elastic solids, they slowly slip past one another within aggregates to relax stretching forces, endowing the aggregates with liquid properties. Slow cell slippage can account not only for temporary elastic solidity and viscous liquid flow in cell aggregates, but also for stress-free changes in the positions and configurations of tissues migrating within developing embryos. Regulation of cell slippage properties may shift the morphogenetic dependence of embryonic tissues in successive developmental stages from intracellular to intercellular force-generating mechanisms, or vice versa.     

Cellular mechanics of wound formation in single cell layer under cyclic stretching

Wounds can be produced when cells and tissues are subjected to excessive forces, for instance, under pathological conditions or nonphysiological loading. However, the cellular behaviors in the wound formation process are not clear. Here we tested the behaviors of wound formation in the epithelial layer with an in-suit uniaxial stretching device. We found that the wound often nucleates at the position where the cells are dividing. The polarization direction of cells near the wound is preferentially along the wound edge, whereas the cells far from the wound are preferentially perpendicular to the stretching direction. The larger the wound area is, the higher is the aspect ratio of the cells around the wound. Increasing the cell density will strengthen the cell layer. The higher the cell density is, the smaller is the area of the wounds, and the weaker is the effect of stretching on the polarization of the cells. Furthermore, we built a coarse-grained cell model that can explicitly consider the elasticity and viscoelasticity of cells, cell-cell interaction, and cell active stress, by which we simulated the wound formation process and quantitatively analyzed the force and stress fields in the cell layer, particularly around the wound. These analyses reveal the cellular mechanisms of wound formation behaviors in the cell layer under stretching and shed useful light on tissue engineering and regenerative medicine for biomedical applications.     

Tensotaxis--a collective movement of embryonic cells up along the gradients of mechanical tensions]

We have examined the active collective movement of ectodermal cells from early gastrula of Xenopus laevis towards the point source of stretching, using techniques of videomicroscopy and scanning electron microscopy. We define this mode of cell movement as tensotaxis. This movement begins near the source of tension 5-10 min after the beginning of stretching and is spread in a relay fashion to more distant cells. As a result, a considerable fraction of observed cells more towards the source of stretching over a considerable territory at a rate of 0.6-3 mu/min. Subsequently, these movements are replaced by cell intercalation roughly oriented in the direction transverse to that of tissue stretching. It is proposed that tensotaxis is initiated by asymmetric deformation of the embryonic tissue due to the concentration (focusing) of a stretching force and contains both passive and active components. Data are presented supporting the view that, during normal development, tensotaxis may determine the movement of embryonic cells towards the blastopore and can also participate in other morphogenetic processes.     

Comparison of the effects of cyclic stretching and compression on endothelial cell morphological responses

Recent results demonstrate the exquisite sensitivity of cell orientation responses to the pattern of imposed deformation. Cells undergoing pure in-plane uniaxial stretching orient differently than cells that are simply elongated--likely because the latter stimulus produces simultaneous compression in the unstretched direction. It is not known, however, if cells respond differently to pure stretching than to pure compression. This study was performed to address this issue. Human aortic endothelial cells were seeded on deformable silicone membranes and subjected to various magnitudes and rates of pure stretching or compression. The cell orientation and cytoskeletal stress fiber organization responses were examined. Both stretching and compression resulted in magnitude-dependent but not rate-dependent orientation responses away from the deforming direction. Compression produced a slower temporal response than stretching. However, stress fiber reorganization responses-early disruption followed by reassembly into parallel arrays along the cells' long axes were similar between the two stimuli. Moreover, the cell orientation and stress fiber responses appeared to be uncoupled since disruption of stress fibers was not required for the cell orientation. Moreover, parallel actin stress fibers were observed at oblique angles to the deforming direction indicating that stress fibers can reassemble when undergoing deformation.     

Spectroscopic study of human lung epithelial cells (A549) in culture: living cells versus dead cells

The noninvasive analysis of living cells grown on 3-dimensional scaffold materials is a key point in tissue engineering. In this work we show the capability of Raman spectroscopy for use as a noninvasive method to distinguish cells at different stages of the cell cycle and living cells from dead cells. The spectral differences between cells in different stages of the cell cycle are characterized mainly by variations in DNA vibrations at 782, 788, and 1095 cm(-1). The Raman spectrum of dead human lung derived (A549 line) cells indicates the breakdown of both phosphodiester bonds and DNA bases. The most sensitive peak for identifying dead cells is the 788 cm(-1) peak corresponding to DNA Obond;Pbond;O backbone stretching. The magnitude of this peak is reduced by 80% in the spectrum of dead cells. Changes in protein peaks suggest significant conformational changes; for example, the magnitude of the 1231 cm(-1) peak assigned to random coils is reduced by 63% for dead cells. The sharp peak of phenylalanine at 1005 cm(-1) drops to half, indicating a decrease of stable proteins associated with cell death. The differences in the 1190-1385 cm(-1) spectral region also suggest a decrease in the amount of nucleic acids and proteins. Using curve fitting, we quantify these spectral differences that can be used as markers of cell death.     

Stomatal mechanics: volume changes during opening

Abstract. The determination of guard cell lumen volume in relation to its geometric characteristic dimensions is presented. Stomatal movements can be divided into two stages: Spannungsphase and motorphase, with a transition point between them. During the Spannungsphase movement, the lumen volume increases as a result of the change in its geometric shape. At transition, the lumen volume is approximated by a portion of a circular tube with a rounded cross-section. The volume increase during the motorphase comes from three different sources: expansion by wall stretching, increasing inner cross-section of a guard cell by wall thinning, and polar expansion. The relationship between the aperture and the lumen volume is also established. The results set forth in this geometric model are essential to studies of the pressure interaction between a guard cell and its surrounding epidermal cells.     

Measurement of the Elastic Modulus for Red Cell Membrane Using a Fluid Mechanical Technique

Red cells which adhere to a surface in a parallel plate flow channel are stretched when acted on by a fluid shear stress. Three types of stretching are studied: whole cell stretching, the stretching of a red cell evagination, and tether (long, thin membrane process) stretching. In addition, the stretching of a large scale model cell attached to a surface is studied in a Couette flow channel. The results indicate that the uniaxial stretching of red cell membrane can be described by a linear stress-strain relationship. Simple theories developed from free body diagrams permit the calculation of a value for the modulus of elasticity of cell membrane in each of the three experiments. In all cases the value for the modulus is on the order of 10⁴ dyn/cm² for an assumed membrane thickness of 0.01 μm. It was also observed that red cell tethers steadily increase in length when the fluid shear stress is greater than approximately 1.5 dyn/cm² and tether lengths in excess of 200 μm have been achieved. Tethers appear to possess both fluid and elastic properties.     

Orientation of Smooth Muscle-Derived A10 Cells in Culture by Cyclic Stretching: Relationship between Stress Fiber Rearrangement and Cell Reorientation

Mechanical stress causes various responses in cells both in vivo and in vitro. Realignment of cells and stress fibers is one of the remarkable phenomena that are induced by the stress. However, the mechanism by which their realignment is controlled is largely unknown. In this study, effects of mechanical stretch on the morphology of cultured cells were examined using a cyclic and reciprocal cell stretching apparatus. A10 cells, a cell line derived from rat aortic smooth muscle, were used as a model, since they are spindle-shaped and have remarkable stress fibers aligned along the longitudinal cell axis. Therefore, the orientation of the cell and stress fibers could be easily identified. When the cells were cultured on elastic silicone membranes and subjected to cyclic and reciprocal stretch with an amplitude of 20% at a frequency of 60 cycles per minute, actin stress fibers were aligned obliquely to the direction of stretching with angles of 50 to 70 degrees within about 15 min after the onset of stretching. Then, after 1-3 hr of cyclic stretching, the long axes of a majority of the cells were also reoriented to similar directions to the stress fibers. The stretch-induced cell reorientation was blocked by 1 muM cytochalasin B, but not by colcemid. These results indicate that the orientation of cells and actin filaments are closely related and actin filaments play a critical role in the early step of the cell reorientation.     

Deformation analyses in cell and developmental biology. Part I--Formal methodology

This study presents a computational approach for the deformation analyses of problems in cell and developmental biology. Cells and embryos are viewed mechanically as axisymmetric shell-like bodies containing a body of incompressible material. The analysis approach is based on the finite element method. It is comprised of three finite element ingredients: an axisymmetric shell/membrane element valid for modeling finite bending, shearing and stretching; a volume constraint algorithm for modeling the membrane-bound incompressible material; and a contact algorithm for modeling the mechanical interactions between deformable bodies. Part II of this study will demonstrate how these three ingredients can be applied to analyze mechanical experiments on cells. This same method is also useful for simulating embryonic shape changes during development.     

The cell cycle thermal-inactivation sensitive stage of Schizosaccharomyces pombe is independent of 2-phenylethanol-induced changes in S phase location

Synchronous cultures of the fission yeast Schizosaccharomyces pombe 972 h⁻¹ are most sensitive to killing by 15 min, 49 °C pulses during a stage stretching from nuclear division through short G1 and S phases to a point early in G2. In this work the cell cycle position of the S phase has been altered by growing the cells in the presence of 2-phenylethanol. The heat sensitivity of these cells was greater at all stages of the cell cycle compared with the cells grown without 2-phenylethanol. However, the position of the most heat sensitive stage in the cell cycle was unaltered. This heat sensitive stage did not include S phase in the cells grown with 2-phenylethanol.     

Specificity of endothelial cell reorientation in response to cyclic mechanical stretching

Evidence suggests that cellular responses to mechanical stimuli depend specifically on the type of stimuli imposed. For example, when subjected to fluid shear stress, endothelial cells align along the flow direction. In contrast, in response to cyclic stretching, cells align away from the stretching direction. However, a few aspects of this cell alignment response remain to be clarified: (1) Is the cell alignment due to actual cell reorientation or selective cell detachment? (2) Does the resulting cell alignment represent a response of the cells to elongation or shortening, or both? (3) Does the cell alignment depend on the stretching magnitude or rate, or both? Finally, the role of the actin cytoskeleton and microtubules in the cell alignment response remains unclear. To address these questions, we grew human aortic endothelial cells on deformable silicone membranes and subjected them to three types of cyclic stretching: simple elongation, pure uniaxial stretching and equi-biaxial stretching. Examination of the same cells before and after stretching revealed that they reoriented. Cells subjected to either simple elongation or pure uniaxial stretching reoriented specifically toward the direction of minimal substrate deformation, even though the directions for the two types of stretching differed by only about 20°. At comparable stretching durations, the extent of cell reorientation was more closely related to the stretching magnitude than the stretching rate. The actin cytoskeleton of the endothelial cell subjected to either type of stretching was reorganized into parallel arrays of actin filaments (i.e., stress fibers) aligned in the direction of the minimal substrate deformation. Furthermore, in response to equi-biaxial stretching, the actin cytoskeleton was remodeled into a “tent-like” structure oriented out of the membrane plane—again towards the direction of the minimal substrate deformation. Finally, abolishing microtubules prevented neither the formation of stress fibers nor cell reorientation. Thus, endothelial cells respond very specifically to the type of deformation imposed upon them.     

Myosin-II-Mediated Directional Migration of Dictyostelium Cells in Response to Cyclic Stretching of Substratum

Living cells are constantly subjected to various mechanical stimulations, such as shear flow, osmotic pressure, and hardness of substratum. They must sense the mechanical aspects of their environment and respond appropriately for proper cell function. Cells adhering to substrata must receive and respond to mechanical stimuli from the substrata to decide their shape and/or migrating direction. In response to cyclic stretching of the elastic substratum, intracellular stress fibers in fibroblasts and endothelial, osteosarcoma, and smooth muscle cells are rearranged perpendicular to the stretching direction, and the shape of those cells becomes extended in this new direction. In the case of migrating Dictyostelium cells, cyclic stretching regulates the direction of migration, and not the shape, of the cell. The cells migrate in a direction perpendicular to that of the stretching. However, the molecular mechanisms that induce the directional migration remain unknown. Here, using a microstretching device, we recorded green fluorescent protein (GFP)-myosin-II dynamics in Dictyostelium cells on an elastic substratum under cyclic stretching. Repeated stretching induced myosin II localization equally on both stretching sides in the cells. Although myosin-II-null cells migrated randomly, myosin-II-null cells expressing a variant of myosin II that cannot hydrolyze ATP migrated perpendicular to the stretching. These results indicate that Dictyostelium cells accumulate myosin II at the portion of the cell where a large strain is received and migrate in a direction other than that of the portion where myosin II accumulated. This polarity generation for migration does not require the contraction of actomyosin.     

The effects of mechanical stress on the growth, differentiation, and paracrine factor production of cardiac stem cells

Stem cell therapies have been clinically employed to repair the injured heart, and cardiac stem cells are thought to be one of the most potent stem cell candidates. The beating heart is characterized by dynamic mechanical stresses, which may have a significant impact on stem cell therapy. The purpose of this study is to investigate how mechanical stress affects the growth and differentiation of cardiac stem cells and their release of paracrine factors. In this study, human cardiac stem cells were seeded in a silicon chamber and mechanical stress was then induced by cyclic stretch stimulation (60 cycles/min with 120% elongation). Cells grown in non-stretched silicon chambers were used as controls. Our result revealed that mechanical stretching significantly reduced the total number of surviving cells, decreased Ki-67-positive cells, and increased TUNEL-positive cells in the stretched group 24 hrs after stretching, as compared to the control group. Interestingly, mechanical stretching significantly increased the release of the inflammatory cytokines IL-6 and IL-1β as well as the angiogenic growth factors VEGF and bFGF from the cells in 12 hrs. Furthermore, mechanical stretching significantly reduced the percentage of c-kit-positive stem cells, but increased the expressions of cardiac troponin-I and smooth muscle actin in cells 3 days after stretching. Using a traditional stretching model, we demonstrated that mechanical stress suppressed the growth and proliferation of cardiac stem cells, enhanced their release of inflammatory cytokines and angiogenic factors, and improved their myogenic differentiation. The development of this in vitro approach may help elucidate the complex mechanisms of stem cell therapy for heart failure.     

Kinetochore stretching inactivates the spindle assembly checkpoint

The spindle assembly checkpoint (SAC) monitors the attachment of microtubules to the kinetochore and inhibits anaphase when microtubule binding is incomplete. The SAC might also respond to tension; however, how cells can sense tension and whether its detection is important to satisfy the SAC remain controversial. We generated a HeLa cell line in which two components of the kinetochore, centromere protein A and Mis12, are labeled with green and red fluorophores, respectively. Live cell imaging of these cells reveals repetitive cycles of kinetochore extension and recoiling after biorientation. Under conditions in which kinetochore stretching is suppressed, cells fail to silence the SAC and enter anaphase after a delay, regardless of centromere stretching. Monitoring cyclin B levels as a readout for anaphase-promoting complex/cyclosome activity, we find that suppression of kinetochore stretching delays and decelerates cyclin B degradation. These observations suggest that the SAC monitors stretching of kinetochores rather than centromeres and that kinetochore stretching promotes silencing of the SAC signal.     

Mechanical stretching stimulates smooth muscle cell growth, nuclear protein import, and nuclear pore expression through mitogen-activated protein kinase activation

Although it is known that mechanical stretching of cells can induce significant increases in cell growth and shape, the intracellular signaling pathways that induce this response at the level of the cell nucleus is unknown. The transport of molecules from the cell cytoplasm to the nucleoplasm through the nuclear pore is a key pathway through which gene expression can be controlled in some conditions. It is presently unknown if mechanical stimuli can induce changes in nuclear pore expression and/or function. The purpose of the present investigation was to determine if mechanical stretching of a cell will alter nuclear protein import and the mechanisms that may be responsible. Vascular smooth muscle cells that were mechanically stretched exhibited an increase in proliferating cell nuclear antigen expression, cell number, and cell size within 24-48 h. Cells were microinjected with marker proteins for nuclear import. Nuclear protein import was significantly stimulated in stretched cells when compared with control. This was associated with an increase in the expression of nuclear pore proteins as detected by Western blots. Inhibition of the MAPK pathway blocked the stretch-induced stimulation of both cell proliferation and nuclear protein import. We conclude that nuclear protein import and nuclear pore density can adapt to mechanical stimuli during the process of cell growth through a MAPK-mediated mechanism.     

Dynamic reorientation of cultured cells and stress fibers under mechanical stress from periodic stretching.

Cell lines derived from rat aorta and frog kidney were cultured on elastic membrane, and mechanical stress was given to the cells by stretching the membrane periodically. Cell reorientation oblique to the direction of stretching occurred as a result of the rapid withdrawal of cell periphery located along the direction of stretching and gradual extension of the cell membrane toward the direction oblique to the direction of stretching. Dynamic reorganization of stress fibers in living cells was visualized by labeling stress fibers with TRITC(3)-actin or EGFP-tagged moesin fragments with actin-binding ability. Stress fibers aligned in the direction of stretching disappeared soon after the start of stretching and then obliquely reoriented stress fibers appeared. The stretch-induced reorientation of cultured cells was suppressed by an inhibitor of stretch-activated (SA) cation channels and by a Ca(2+) chelator. However, the rearrangement of stress fibers was not affected by these agents. From these results, we suggest that Ca(2+) influx via SA channels is involved in stretch-induced cell reorientation but stress fiber rearrangement is independent of SA channels. Therefore, cell reorientation does not simply depend on the arrangement of stress fibers but may be controlled by some additional mechanism(s) which is regulated by calcium signaling.     

A mathematical model of cell reorientation in response to substrate stretching

It is well documented that in response to substrate stretching adhering cells alter their orientation. Generally, the cells reorient away from the direction of the maximum substrate strain, depending upon the magnitude of the substrate strain and the state of cell contractility. Theoretical models from the literature can describe only some aspects of this phenomenon. In the present study, we developed a more comprehensive mathematical model of cell reorientation than the current models. Using the framework of theory of non-linear elasticity, we found that the problem of cell reorientation was a stability problem, with the global (Maxwell's) criterion for stability. For the case of uniaxial substrate stretching, we showed that cells would orient away from the direction of substrate strain such that the angle between the cell long axis and the direction of the substrate strain would increase with increasing magnitude of the strain. We also showed that at a given substrate strain this angle would be greater in cells having greater contractile strain. These results are consistent with experimental observations reported in the literature.     

A new cell-based FE model for the mechanics of embryonic epithelia

In order to overcome a significant stiffening artefact associated with current finite element (FE) models for the mechanics of embryonic epithelia, two new FE formulations were developed. Cell–cell interfacial tensions γ are represented by constant-force rod elements as in previous models. However, the viscosity of the cytoplasm with its embedded organelles and filament networks is modeled using viscous triangular elements, it is modeled using either radial and circumferential dashpots or an orthogonal dashpot system rather than the viscous triangular elements typical of previous two-dimensional FE models. The models are tested against tissue (epithelium) stretching because it gives rise to significant changes in cell shape and against cell sorting because it involves high rates of cell rearrangement. The orthogonal dashpot system is found to capture cell size and shape effects well, give the model cells characteristics that are consistent with those of real cells, provide high computational efficiency and hold promise for future three-dimensional analyses.     

Alignment and proliferation of MC3T3-E1 osteoblasts in microgrooved silicone substrata subjected to cyclic stretching

Previous studies have shown that many types of cells align in microgrooves in static cultures. However, whether cells remain aligned and also proliferate in microgrooves under stretching conditions has not been determined. We grew MC3T3-E1 osteoblasts in deformable silicone dishes containing microgrooves oriented in the stretch direction. We found that with or without 4% stretching, cells aligned in microgrooves of all sizes, with the groove and ridge widths ranged from 1 to 6microm, but the same groove depth of about 1.6microm. In addition, actin cytoskeleton and nuclei became highly aligned in the microgrooves with and without 4% cyclic stretching. To further examine whether MC3T3-E1 osteoblasts proliferate in microgrooves with cyclic stretching, we grew the cells in six-well silicone dishes containing microgrooves in three wells and smooth surfaces in other three wells. After 4% cyclic stretching for 3, 4, and 7 days, we found that cell numbers in the microgrooves were not significantly different (p>0.05) from those on the smooth surface (p>0.05). Taken together, these results show that MC3T3-E1 osteoblasts can align and proliferate in microgrooves with 4% cyclic stretching. We suggest that the silicone microgrooves can be a useful tool to study the phenotype of MC3T3-E1 osteoblasts under controlled substrate strains. The silicone microgrooves can also be useful for delivering defined substrate strains to other adherent cells in cultures.