Tensile properties of single stress fibers isolated from cultured vascular smooth muscle cells

Filamentous network mechanics and active contractility determine cell and tissue shape

For both cells and tissues, shape is closely correlated with function presumably via geometry-dependent distribution of tension. In this study, we identify common shape determinants spanning cell and tissue scales. For cells whose sites of adhesion are restricted to small adhesive islands on a micropatterned substrate, shape resembles a sequence of inward-curved circular arcs. The same shape is observed for fibroblast-populated collagen gels that are pinned to a flat substrate. Quantitative image analysis reveals that, in both cases, arc radii increase with the spanning distance between the pinning points. Although the Laplace law for interfaces under tension predicts circular arcs, it cannot explain the observed dependence on the spanning distance. Computer simulations and theoretical modeling demonstrate that filamentous network mechanics and contractility give rise to a modified Laplace law that quantitatively explains our experimental findings on both cell and tissue scales. Our model in conjunction with actomyosin inhibition experiments further suggests that cell shape is regulated by two different control modes related to motor contractility and structural changes in the actin cytoskeleton.

Modeling neutrophil transport in pulmonary capillaries

Neutrophils can be retained in the pulmonary microvasculature due to their low deformability, resulting in having a higher concentration there than in the systemic circulation, even in normal lungs. It is thought that this high concentration of the cells facilitates their effective recruitment to sites of inflammation. Thus, in order to understand their role in the immune system in the lungs, where blood comes in contact with outer air via thin septa of alveoli, it is important to clarify their flow characteristics in the pulmonary capillary bed. However, in contrast to erythrocytes in systemic capillaries, little research has been performed on the flow of neutrophils in pulmonary capillaries. This may be partly because no complete rheological model of the cell has been established yet, and partly because pulmonary capillaries are very short and closely interconnected, forming a complicated three-dimensional network, in addition to difficulty in in vivo experimental observations. Moreover, the neutrophils change their mechanical properties and show active motion in response to some chemoattractants. In this article, various proposed rheological models of the neutrophil, flow models of a cell through a single capillary segment, and alveolar capillary network models are introduced, aiming at the numerical simulation of neutrophil transport in the pulmonary microvasculature.

Finite element modeling of 3D human mesenchymal stem cell-seeded collagen matrices exposed to tensile strain

The use of human mesenchymal stem cells (hMSCs) in tissue engineering is attractive due to their ability to extensively self-replicate and differentiate into a multitude of cell lineages. It has been experimentally established that hMSCs are influenced by chemical and mechanical signals. However, the combined chemical and mechanical in vitro culture conditions that lead to functional tissue require greater understanding. In this study, finite element models were created to evaluate the local loading conditions on bone marrow-derived hMSCs seeded in three-dimensional collagen matrices exposed to cyclic tensile strain. Mechanical property and geometry data used in the models were obtained experimentally from a previous study in our laboratory and from mechanical testing. Eight finite element models were created to simulate three-dimensional hMSC-seeded collagen matrices exposed to different levels of cyclic tensile strain (10% and 12%), culture media (complete growth and osteogenic differentiating), and durations of culture (7 and 14 days). Through finite element analysis, it was determined that globally applied uniaxial tensile strains of 10% and 12% resulted in local strains up to 18.3% and 21.8%, respectively. Model results were also compared to experimental studies in an attempt to explain observed differences between hMSC response to 10% and 12% cyclic tensile strain.

Rapid signal transduction in living cells is a unique feature of mechanotransduction

It is widely postulated that mechanotransduction is initiated at the local force-membrane interface by inducing local conformational changes of proteins, similar to soluble ligand-induced signal transduction. However, all published reports are limited in time scale to address this fundamental issue. Using a FRET-based cytosolic Src reporter in a living cell, we quantified changes of Src activities as a local stress via activated integrins was applied. The stress induced rapid (<0.3 s) activation of Src at remote cytoplasmic sites, which depends on the cytoskeletal prestress. In contrast, there was no Src activation within 12 s of soluble epidermal growth factor (EGF) stimulation. A 1.8-Pa stress over a focal adhesion activated Src to the same extent as 0.4 ng/ml EGF at long times (minutes), and the energy levels for mechanical stimulation and chemical stimulation were comparable. The effect of both stress and EGF was less than additive. Nanometer-scale cytoskeletal deformation analyses revealed that the strong activation sites of Src by stress colocalized with large deformation sites of microtubules, suggesting that microtubules are essential structures for transmitting stresses to activate cytoplasmic proteins. These results demonstrate that rapid signal transduction via the prestressed cytoskeleton is a unique feature of mechanotransduction.

Cytoskeletal mechanics in airway smooth muscle cells

Mechanical properties and contractility of airway smooth muscle tissue are largely responsible for airway narrowing and airway hyperresponsiveness in asthma. To explain these pathological phenomena, investigators have studied the mechanical behaviour of airway smooth muscle cells and its relationship to the underlying cellular biophysical and biochemical mechanisms. During the past decade, a growing body of evidence has indicated that a deformable intracellular polymer network, known as the cytoskeleton, plays a major role in transmitting and distributing mechanical forces within the cell and in their conversion into biochemical responses. We review here evidence suggesting that the tensed and crosslinked cytoskeletal lattice, the contractile apparatus, and the cytoskeleton-extracellular matrix interactions are key determinants of mechanical properties and mechanosensing of airway smooth muscle cells, with the mechanical distending stress of the cytoskeleton playing the central role.

Propagation of mechanical stress through the actin cytoskeleton toward focal adhesions: model and experiment

We investigate both theoretically and experimentally how stress is propagated through the actin cytoskeleton of adherent cells and consequentially distributed at sites of focal adhesions (FAs). The actin cytoskeleton is modeled as a two-dimensional cable network with different lattice geometries. Both prestrain, resulting from actomyosin contractility, and central application of external force, lead to finite forces at the FAs that are largely independent of the lattice geometry, but strongly depend on the exact spatial distribution of the FAs. The simulation results compare favorably with experiments with adherent fibroblasts onto which lateral force is exerted using a microfabricated pillar. For elliptical cells, central application of external force along the long axis leads to two large stress regions located obliquely opposite to the pulling direction. For elliptical cells pulled along the short axis as well as for circular cells, there is only one region of large stress opposite to the direction of pull. If in the computer simulations FAs are allowed to rupture under force for elliptically elongated and circular cell shapes, then morphologies arise which are typical for migrating fibroblasts and keratocytes, respectively. The same effect can be obtained also by internally generated force, suggesting a mechanism by which cells can control their migration morphologies.

Time-dependent changes in smooth muscle cell stiffness and focal adhesion area in response to cyclic equibiaxial stretch

Observations from diverse studies on cell biomechanics and mechanobiology reveal that altered mechanical stimuli can induce significant changes in cytoskeletal organization, focal adhesion complexes, and overall mechanical properties. To investigate effects of short-term equibiaxial stretching on the transverse stiffness of and remodeling of focal adhesions in vascular smooth muscle cells, we developed a cell-stretching device that can be combined with both atomic force and confocal microscopy. Results demonstrate that cyclic 10%, but not 5%, equibiaxial stretching at 0.25 Hz significantly and rapidly alters both cell stiffness and focal adhesion associated paxillin and vinculin. Moreover, measured changes in stiffness and focal adhesion area from baseline values tend to correlate well over the durations of stretching studied. It is suggested that remodeling of focal adhesions plays a critical role in regulating cell stiffness by recruiting and anchoring actin filaments, and that cells rapidly remodel in an attempt to maintain a homeostatic biomechanical state when perturbed above a threshold value.

Brushes, cables, and anchors: recent insights into multiscale assembly and mechanics of cellular structural networks

The remarkable ability of living cells to sense, process, and respond to mechanical stimuli in their environment depends on the rapid and efficient interconversion of mechanical and chemical energy at specific times and places within the cell. For example, application of force to cells leads to conformational changes in specific mechanosensitive molecules which then trigger cellular signaling cascades that may alter cellular structure, mechanics, and migration and profoundly influence gene expression. Similarly, the sensitivity of cells to mechanical stresses is governed by the composition, architecture, and mechanics of the cellular cytoskeleton and extracellular matrix (ECM), which are in turn driven by molecular-scale forces between the constituent biopolymers. Understanding how these mechanochemical systems coordinate over multiple length and time scales to produce orchestrated cell behaviors represents a fundamental challenge in cell biology. Here, we review recent advances in our understanding of these complex processes in three experimental systems: the assembly of axonal neurofilaments, generation of tensile forces by actomyosin stress fiber bundles, and mechanical control of adhesion assembly.

Vascular adaptation and mechanical homeostasis at tissue, cellular, and sub-cellular levels

Blood vessels exhibit a remarkable ability to adapt throughout life that depends upon genetic programming and well-orchestrated biochemical processes. Findings over the past four decades demonstrate, however, that the mechanical environment experienced by these vessels similarly plays a critical role in governing their adaptive responses. This article briefly reviews, as illustrative examples, six cases of tissue level growth and remodeling, and then reviews general observations at cell-matrix, cellular, and sub-cellular levels, which collectively point to the existence of a "mechanical homeostasis" across multiple length and time scales that is mediated primarily by endothelial cells, vascular smooth muscle cells, and fibroblasts. In particular, responses to altered blood flow, blood pressure, and axial extension, disease processes such as cerebral aneurysms and vasospasm, and diverse experimental manipulations and clinical treatments suggest that arteries seek to maintain constant a preferred (homeostatic) mechanical state. Experiments on isolated microvessels, cell-seeded collagen gels, and adherent cells isolated in culture suggest that vascular cells and sub-cellular structures such as stress fibers and focal adhesions likewise seek to maintain constant a preferred mechanical state. Although much is known about mechanical homeostasis in the vasculature, there remains a pressing need for more quantitative data that will enable the formulation of an integrative mathematical theory that describes and eventually predicts vascular adaptations in response to diverse stimuli. Such a theory promises to deepen our understanding of vascular biology as well as to enable the design of improved clinical interventions and implantable medical devices.

Rheological behavior of living cells is timescale-dependent

The dynamic mechanical behavior of living cells has been proposed to result from timescale-invariant processes governed by the soft glass rheology theory derived from soft matter physics. But this theory is based on experimental measurements over timescales that are shorter than those most relevant for cell growth and function. Here we report results measured over a wider range of timescales which demonstrate that rheological behaviors of living cells are not timescale-invariant. These findings demonstrate that although soft glass rheology appears to accurately predict certain cell mechanical behaviors, it is not a unified model of cell rheology under biologically relevant conditions and thus, alternative mechanisms need to be considered.

Simple model of cytoskeletal fluctuations

The spontaneous motion of microbeads bound to the cytoskeleton of living cells is not an ordinary random walk. Unlike Brownian motion, the mean-square displacement undergoes a transition from subdiffusive to superdiffusive behavior with time. This transition is associated with characteristic changes of the turning angle distribution. Recent experimental data demonstrated that force fluctuations measured in an elastic hydrogel matrix beneath the cell correlate with the bead motion [C. Raupach, Phys. Rev. E 76, 011918 (2007)]. These data indicate that the bead trajectory is driven by motor forces originating from the actomyosin network and that cytoskeletal remodeling processes with short- and long-time dynamics are mainly responsible for the non-Brownian behavior. We show that the essential statistical properties of the spontaneous bead motion can be reproduced by a particle diffusing in a potential well with a slowly drifting minimum position. Based on this simple model, which can be solved analytically, we develop a biologically plausible numerical model of a tensed and continuously remodeling actomyosin network that accounts quantitatively for the measured data.

Constitutive material modeling of cell: a micromechanics approach

The variations in mechanical properties of cells obtained from experimental and theoretical studies can be overcome only through the development of a sound mathematical framework correlating the derived mechanical property with the cellular structure. Such a formulation accounting for the inhomogeneity of the cytoplasm due to stress fibers and actin cortex is developed in this work. The proposed model is developed using the Mori-Tanaka method of homogenization by treating the cell as a fiber-reinforced composite medium satisfying the continuum hypothesis. The validation of the constitutive model using finite element analysis on atomic force microscopy (AFM) and magnetic twisting cytometry (MTC) has been carried out and is found to yield good correlation with reported experimental results. It is observed from the study that as the volume fraction of the stress fiber increases, the stiffness of the cell increases and it alters the force displacement behavior for the AFM and MTC experiments. Through this model, we have also been able to find the stress fiber as a likely cause of the differences in the derived mechanical property from the AFM and MTC experiments. The correlation of the mechanical behavior of the cell with the cell composition, as obtained through this study, is an important observation in cell mechanics.

Microelastic mapping of living endothelial cells exposed to shear stress in relation to three-dimensional distribution of actin filaments

The surface topography and local elastic moduli of endothelial cells exposed to shear stress were measured using atomic force microscopy. Bovine aortic endothelial cells were exposed to shear stress of 2Pa for 6, 12 or 24h. In addition, a confocal laser-scanning microscope used in conjunction with the atomic force microscope was used to observe the actin filament structure of these endothelial cells to elucidate the relationship between mechanical properties and cytoskeletal structure. The elastic modulus, calculated using the Hertz model, was measured at 50x50 points at 1mum intervals within 40min. For endothelial cells sheared for 6h and 12h, the elastic modulus at the upstream region was found to be higher than that at the downstream region. For endothelial cells sheared for 24h, the elastic modulus at both the upstream and downstream regions increased. Fluorescent images showed thick, elongated actin filaments oriented in the direction of flow at the ventral surface of the cells. In the middle plane of the cells, actin filaments developed around the nucleus, while in the upper plane, short, thick actin filaments were observed but thick stress fibers were not present. The high elastic modulus came from the stress fibers. These results indicate that the higher elastic modulus observed in the upstream and downstream regions of sheared endothelial cells is mainly due to the development of stress fibers at the ventral surface and middle plane of the cell.

A theoretical model for F-actin remodeling in vascular smooth muscle cells subjected to cyclic stretch

A constrained mixture theory model was developed and used to estimate remodeling of F-actin in vascular smooth muscle cells that were subjected to 10% equibiaxial stretching for up to 30min. The model was based on a synthesis of data on time-dependent changes in atomic force microscopy measured cell stiffness and immunofluorescence measured focal adhesion associated vinculin as well as data on stress fiber stiffness and pre-stretch. Results suggest that an observed acute (after 2min of stretching) increase in cell stiffness is consistent with an increased stretch of the originally present F-actin plus an assembly of new F-actin having nearly homeostatic values of stretch. Moreover, the subsequent (after 30min of stretching) decrease in cell stiffness back towards the baseline value is consistent with a replacement of the overstretched original filaments with the new (reassembled), less stretched filaments. That is, overall cell response is consistent with a recently proposed concept of "tensional homeostasis" whereby cells seek to maintain constant certain mechanical factors via a remodeling of intracellular and transmembrane proteins. Although there is a need to refine the model based on more comprehensive data sets, using multiple experimental approaches, the present results suggest that a constrained mixture theory can capture salient features of the dynamics of F-actin remodeling and that it offers some advantages over many past methods of modeling, particularly those based on classical linearized viscoelasticity.

Microtubules can bear enhanced compressive loads in living cells because of lateral reinforcement

Cytoskeletal microtubules have been proposed to influence cell shape and mechanics based on their ability to resist large-scale compressive forces exerted by the surrounding contractile cytoskeleton. Consistent with this, cytoplasmic microtubules are often highly curved and appear buckled because of compressive loads. However, the results of in vitro studies suggest that microtubules should buckle at much larger length scales, withstanding only exceedingly small compressive forces. This discrepancy calls into question the structural role of microtubules, and highlights our lack of quantitative knowledge of the magnitude of the forces they experience and can withstand in living cells. We show that intracellular microtubules do bear large-scale compressive loads from a variety of physiological forces, but their buckling wavelength is reduced significantly because of mechanical coupling to the surrounding elastic cytoskeleton. We quantitatively explain this behavior, and show that this coupling dramatically increases the compressive forces that microtubules can sustain, suggesting they can make a more significant structural contribution to the mechanical behavior of the cell than previously thought possible.

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.