The role of prestress and architecture of the cytoskeleton and deformability of cytoskeletal filaments in mechanics of adherent cells: a quantitative analysis

Long-distance propagation of forces in a cell

A fundamental question in the field of mechanotransduction is how forces propagate inside a cell. Recent experiments have shown that a force of a physiological magnitude, applied via a focal adhesion, can propagate a long distance into the cell. This observation disagrees with existing models that regard the cell as a homogeneous body. We show that this "action at a distance" results from the inhomogeneity in the cell: a prestressed and stiff actin bundle guides the propagation of forces over long distances. Our models highlight the enormous ratios of the prestress and the modulus of the actin bundle to the modulus of the cytoskeleton network. For a normal cell, the models predict that forces propagate over characteristic lengths comparable to the size of the cell. The characteristic lengths can be altered, however, by treatments of the cell. We provide experimental evidence and discuss biological implications.

Cytomechanical properties of papaver pollen tubes are altered after self-incompatibility challenge

Self-incompatibility (SI) in Papaver rhoeas triggers a ligand-mediated signal transduction cascade, resulting in the inhibition of incompatible pollen tube growth. Using a cytomechanical approach we have demonstrated that dramatic changes to the mechanical properties of incompatible pollen tubes are stimulated by SI induction. Microindentation revealed that SI resulted in a reduction of cellular stiffness and an increase in cytoplasmic viscosity. Whereas the former cellular response is likely to be the result of a drop in cellular turgor, we hypothesize that the latter is caused by as yet unidentified cross-linking events. F-actin rearrangements, a characteristic phenomenon for SI challenge in Papaver, displayed a spatiotemporal gradient along the pollen tube; this suggests that signal propagation occurs in a basipetal direction. However, unexpectedly, local application of SI inducing S-protein did not reveal any evidence for localized signal perception in the apical or subapical regions of the pollen tube. To our knowledge this represents the first mechanospatial approach to study signal propagation and cellular responses in a well-characterized plant cell system. Our data provide the first evidence for mechanical changes induced in the cytoplasm of a plant cell stimulated by a defined ligand.

Mechanical state of airway smooth muscle at very short lengths

Although the shortening of smooth muscle at physiological lengths is dominated by an interaction between external forces (loads) and internal forces, at very short lengths, internal forces appear to dominate the mechanical behavior of the active tissue. We tested the hypothesis that, under conditions of extreme shortening and low external force, the mechanical behavior of isolated canine tracheal smooth muscle tissue can be understood as a structure in which the force borne and exerted by the cross bridge and myofilament array is opposed by radially disposed connective tissue in the presence of an incompressible fluid matrix (cellular and extracellular). Strips of electrically stimulated tracheal muscle were allowed to shorten maximally under very low afterload, and large longitudinal sinusoidal vibrations (34 Hz, 1 s in duration, and up to 50% of the muscle length before vibration) were applied to highly shortened (active) tissue strips to produce reversible cross-bridge detachment. During the vibration, peak muscle force fell exponentially with successive forced elongations. After the episode, the muscle either extended itself or exerted a force against the tension transducer, depending on external conditions. The magnitude of this effect was proportional to the prior muscle stiffness and the amplitude of the vibration, indicating a recoil of strained connective tissue elements no longer opposed by cross-bridge forces. This behavior suggests that mechanical behavior at short lengths is dominated by tissue forces within a tensegrity-like structure made up of connective tissue, other extracellular matrix components, and active contractile elements.

Remodeling of the airway smooth muscle cell: are we built of glass?

Classical understanding of airway lumen narrowing in asthma has held that the isometric force generated by airway smooth muscle (ASM) must be at every instant in a static mechanical equilibrium with the external load against which the muscle has shortened. It has been established recently, however, that this balance of static forces does not apply in the setting of tidal loading as occurs during breathing and must give way to the broader concepts of (1). the perturbed contractile state that exists far from static equilibrium conditions and (2). mechanical plasticity of the ASM cell. Here we describe the hypothesis that the well-established static contractile state, the newly-elaborated perturbed contractile state, as well as the remarkable mechanical plasticity of the ASM cell, are all subsumed under a rubric that is at once surprising, unifying and mechanistic. The specific hypothesis suggested is that the ASM cell behaves as a glassy material [Phys. Rev. Lett. 87 (2001) 148102]. A glass is a material that has the disordered molecular state of a liquid and, at the same time, the rigidity of a solid. If the hypothesis is true, then the ability of the ASM cytoskeleton (CSK) to deform, to flow and to remodel would be determined by an effective temperature-called the noise temperature-representing the level of jostling (i.e. molecular noise or agitation) present in the intracellular microenvironment. The abilities of the CSK to deform, to flow and to reorganize represent basic biological processes that underlie a variety of higher cell functions. If supported by the data, therefore, this integrative hypothesis might have implications in medicine and biology that go beyond the immediate issues of smooth muscle shortening and its role in asthma.

Mechanisms governing the visco-elastic responses of living cells assessed by foam and tensegrity models

The visco-elastic properties of living cells, measured to date by various authors, vary considerably, depending on the experimental methods and/or on the theoretical models used. In the present study, two mechanisms thought to be involved in cellular visco-elastic responses were analysed, based on the idea that the cytoskeleton plays a fundamental role in cellular mechanical responses. For this purpose, the predictions of an open unit-cell model and a 30-element visco-elastic tensegrity model were tested, taking into consideration similar properties of the constitutive F-actin. The quantitative predictions of the time constant and viscosity modulus obtained by both models were compared with previously published experimental data obtained from living cells. The small viscosity modulus values (10(0)-10(3) Pa x s) predicted by the tensegrity model may reflect the combined contributions of the spatially rearranged constitutive filaments and the internal tension to the overall cytoskeleton response to external loading. In contrast, the high viscosity modulus values (10(3)-10(5) Pa x s) predicted by the unit-cell model may rather reflect the mechanical response of the cytoskeleton to the bending of the constitutive filaments and/or to the deformation of internal components. The present results suggest the existence of a close link between the overall visco-elastic response of micromanipulated cells and the underlying architecture.

A genetic screen for modifiers of the lats tumor suppressor gene identifies C-terminal Src kinase as a regulator of cell proliferation in Drosophila

Disrupting mechanisms that control cell proliferation, cell size and apoptosis can cause changes in animal and tissue size and contribute to diseases such as cancer. The LATS family of serine/threonine kinases control tissue size by regulating cell proliferation and function as tumor suppressor genes in both Drosophila and mammals. In order to understand the role of lats in size regulation, we performed a genetic modifier screen in Drosophila to identify components of the lats signaling pathway. Mutations in the Drosophila homolog of C-terminal Src kinase (dcsk) were identified as dominant modifiers of both lats gain-of-function and loss-of-function phenotypes. Homozygous dcsk mutants have enlarged tissue phenotypes similar to lats and FACS and immunohistochemistry analysis of these tissues revealed that dcsk also regulates cell proliferation during development. Animals having mutations in both dcsk and lats display cell overproliferation phenotypes more severe than either mutant alone, demonstrating these genes function together in vivo to regulate cell numbers. Furthermore, homozygous dcsk phenotypes can be partially suppressed by overexpression of lats, indicating that lats is a downstream mediator of dcsk function in vivo. Finally, we show that dCSK phosphorylates LATS in vitro at a conserved C-terminal tyrosine residue, which is critical for normal LATS function in vivo. Taken together, these results demonstrate a role for dCSK in regulating cell numbers during development by inhibiting cell proliferation and suggest that lats is one of the mediators of the dcsk phenotype.

The first three minutes: smooth muscle contraction, cytoskeletal events, and soft glasses

Smooth muscle exhibits biophysical characteristics and physiological behaviors that are not readily explained by present paradigms of cytoskeletal and cross-bridge mechanics. There is increasing evidence that contractile activation of the smooth muscle cell involves an array of cytoskeletal processes that extend beyond cross-bridge cycling and the sliding of thick and thin filaments. We review here the evidence suggesting that the biophysical and mechanical properties of the smooth muscle cell reflect the integrated interactions of an array of highly dynamic cytoskeletal processes that both react to and transform the dynamics of cross-bridge interactions over the course of the contraction cycle. The activation of the smooth muscle cell is proposed to trigger dynamic remodeling of the actin filament lattice within cellular microdomains in response to local mechanical and pharmacological events, enabling the cell to adapt to its external environment. As the contraction progresses, the cytoskeletal lattice stabilizes, solidifies, and forms a rigid structure well suited for transmission of tension generated by the interaction of myosin and actin. The integrated molecular transitions that occur within the contractile cycle are interpreted in the context of microscale agitation mechanisms and resulting remodeling events within the intracellular microenvironment. Such an interpretation suggests that the cytoskeleton may behave as a glassy substance whose mechanical function is governed by an effective temperature.

Tensegrity I. Cell structure and hierarchical systems biology

In 1993, a Commentary in this journal described how a simple mechanical model of cell structure based on tensegrity architecture can help to explain how cell shape, movement and cytoskeletal mechanics are controlled, as well as how cells sense and respond to mechanical forces (J. Cell Sci. 104, 613-627). The cellular tensegrity model can now be revisited and placed in context of new advances in our understanding of cell structure, biological networks and mechanoregulation that have been made over the past decade. Recent work provides strong evidence to support the use of tensegrity by cells, and mathematical formulations of the model predict many aspects of cell behavior. In addition, development of the tensegrity theory and its translation into mathematical terms are beginning to allow us to define the relationship between mechanics and biochemistry at the molecular level and to attack the larger problem of biological complexity. Part I of this two-part article covers the evidence for cellular tensegrity at the molecular level and describes how this building system may provide a structural basis for the hierarchical organization of living systems--from molecule to organism. Part II, which focuses on how these structural networks influence information processing networks, appears in the next issue.

Microrheology of human lung epithelial cells measured by atomic force microscopy

Lung epithelial cells are subjected to large cyclic forces from breathing. However, their response to dynamic stresses is poorly defined. We measured the complex shear modulus (G(*)(omega)) of human alveolar (A549) and bronchial (BEAS-2B) epithelial cells over three frequency decades (0.1-100 Hz) and at different loading forces (0.1-0.9 nN) with atomic force microscopy. G(*)(omega) was computed by correcting force-indentation oscillatory data for the tip-cell contact geometry and for the hydrodynamic viscous drag. Both cell types displayed similar viscoelastic properties. The storage modulus G'(omega) increased with frequency following a power law with exponent approximately 0.2. The loss modulus G"(omega) was approximately 2/3 lower and increased similarly to G'(omega) up to approximately 10 Hz, but exhibited a steeper rise at higher frequencies. The cells showed a weak force dependence of G'(omega) and G"(omega). G(*)(omega) conformed to the power-law model with a structural damping coefficient of approximately 0.3, indicating a coupling of elastic and dissipative processes within the cell. Power-law behavior implies a continuum distribution of stress relaxation time constants. This complex dynamics is consistent with the rheology of soft glassy materials close to a glass transition, thereby suggesting that structural disorder and metastability may be fundamental features of cell architecture.

Toward a generalised tensegrity model describing the mechanical behaviour of the cytoskeleton structure

The control of many cell functions including growth, migration and mechanotransduction, depends crucially on stress-induced mechanical changes in cell shape and cytoskeleton (CSK) structure. Quantitative studies have been carried out on 6-bar tensegrity models to analyse several mechanical parameters involved in the mechanical responses of adherent cells (i.e. strain hardening, internal stress and scale effects). In the present study, we attempt to generalize some characteristic mechanical laws governing spherical tensegrity structures, with a view of evaluating the mechanical behaviour of the hierarchical multi-modular CSK-structure. The numerical results obtained by studying four different tensegrity models are presented in terms of power laws and point to the existence of unique and constant relationships between the overall structural stiffness and the local properties (length, number and internal stress) of the constitutive components.

A prestressed cable network model of the adherent cell cytoskeleton

A prestressed cable network is used to model the deformability of the adherent cell actin cytoskeleton. The overall and microstructural model geometries and cable mechanical properties were assigned values based on observations from living cells and mechanical measurements on isolated actin filaments, respectively. The models were deformed to mimic cell poking (CP), magnetic twisting cytometry (MTC) and magnetic bead microrheometry (MBM) measurements on living adherent cells. The models qualitatively and quantitatively captured the fibroblast cell response to the deformation imposed by CP while exhibiting only some qualitative features of the cell response to MTC and MBM. The model for CP revealed that the tensed peripheral actin filaments provide the key resistance to indentation. The actin filament tension that provides mechanical integrity to the network was estimated at approximately 158 pN, and the nonlinear mechanical response during CP originates from filament kinematics. The MTC and MBM simulations revealed that the model is incomplete, however, these simulations show cable tension as a key determinant of the model response.

Cancer as a disease of epithelial-mesenchymal interactions and extracellular matrix regulation

Carcinogenesis - the process of cancer formation - is commonly discussed in terms of genetic alterations that lead to deregulation of cell growth. Recently, there has been a resurgence of interest in epigenetic factors and, in particular, the role of the stromal microenvironment and angiogenesis in tumor formation. In this article, cancer is presented as a disease of the developmental processes that govern how cells organize into tissues and tissues into organs. This histogenetic perspective raises the possibility that epithelial-mesenchymal interactions and the extracellular matrix (basement membrane) that is deposited through these interactions may actively contribute to the carcinogenic process. Experimental work is reviewed that confirms that extracellular matrix plays a key role in normal histodifferentiation during both epitheliogenesis and angiogenesis, and that epigenetic deregulation of cell-matrix interactions may actively promote tumor initiation and progression. The contributions of integrins, cytoskeleton, tensegrity and local variations in extracellular matrix mechanics to these processes are discussed, as are the implications of this work for future studies on cancer formation.

Mechanical signaling and the cellular response to extracellular matrix in angiogenesis and cardiovascular physiology

Great advances have been made in the identification of the soluble angiogenic factors, insoluble extracellular matrix (ECM) molecules, and receptor signaling pathways that mediate control of angiogenesis--the growth of blood capillaries. This review focuses on work that explores how endothelial cells integrate these chemical signals with mechanical cues from their local tissue microenvironment so as to produce functional capillary networks that exhibit specialized form as well as function. These studies have revealed that ECM governs whether an endothelial cell will switch between growth, differentiation, motility, or apoptosis programs in response to a soluble stimulus based on its ability to mechanically resist cell tractional forces and thereby produce cell and cytoskeletal distortion. Transmembrane integrin receptors play a key role in this mechanochemical transduction process because they both organize a cytoskeletal signaling complex within the focal adhesion and preferentially focus mechanical forces on this site. Molecular filaments within the internal cytoskeleton--microfilaments, microtubules, and intermediate filaments--also contribute to the cell's structural and functional response to mechanical stress through their role as discrete support elements within a tensegrity-stabilized cytoskeletal array. Importantly, a similar form of mechanical control also has been shown to be involved in the regulation of contractility in vascular smooth muscle cells and cardiac myocytes. Thus, the mechanism by which cells perform mechanochemical transduction and the implications of these findings for morphogenetic control are discussed in the wider context of vascular development and cardiovascular physiology.

A finite element model of cell deformation during magnetic bead twisting

Magnetic twisting cytometry probes mechanical properties of an adherent cell by applying a torque to a magnetic bead that is tightly bound to the cell surface. Here we have used a three-dimensional finite element model of cell deformation to compute the relationships between the applied torque and resulting bead rotation and lateral bead translation. From the analysis, we computed two coefficients that allow the cell elastic modulus to be estimated from measurements of either bead rotation or lateral bead translation, respectively, if the degree of bead embedding and the cell height are known. Although computed strains in proximity of the bead can be large, the relationships between applied torque and bead rotation or translation remain virtually linear up to bead rotations of 15 degrees, above which geometrical nonlinearities become significant. This appreciable linear range stands in contrast to the intrinsically nonlinear force-displacement relationship that is observed when cells are indented during atomic force microscopy. Finally, these computations support the idea that adhesive forces are sufficient to keep the bead firmly attached to the cell surface throughout the range of working torques.

A cellular tensegrity model to analyse the structural viscoelasticity of the cytoskeleton

This study describes the viscoelastic properties of a refined cellular-tensegrity model composed of six rigid bars connected to a continuous network of 24 viscoelastic pre-stretched cables (Voigt bodies) in order to analyse the role of the cytoskeleton spatial rearrangement on the viscoelastic response of living adherent cells. This structural contribution was determined from the relationships between the global viscoelastic properties of the tensegrity model, i.e., normalized viscosity modulus (eta(*)), normalized elasticity modulus (E(*)), and the physical properties of the constitutive elements, i.e., their normalized length (L(*)) and normalized initial internal tension (T(*)). We used a numerical method to simulate the deformation of the structure in response to different types of loading, while varying by several orders of magnitude L(*) and T(*). The numerical results obtained reveal that eta(*) remains almost independent of changes in T(*) (eta(*) proportional, variant T(*+0.1)), whereas E(*) increases with approximately the square root of the internal tension T(*) (from E(*) proportional, variant T(*+0.3) to E(*) proportional, variant T(*+0.7)). Moreover, structural viscosity eta(*) and elasticity E(*) are both inversely proportional to the square of the size of the structure (eta(*) proportional, variant L(*-2) and E(*) proportional, variant L(*-2)). These structural properties appear consistent with cytoskeleton (CSK) mechanical properties measured experimentally by various methods which are specific to the CSK micromanipulation in living adherent cells. Present results suggest, for the first time, that the effect of structural rearrangement of CSK elements on global CSK behavior is characterized by a faster cellular mechanical response relatively to the CSK element response, which thus contributes to the solidification process observed in adherent cells. In extending to the viscoelastic properties the analysis of the mechanical response of the cellular 30-element tensegrity model, the present study contributes to the understanding of recent results on the cellular-dynamic response and allows to reunify the scattered data reported for the viscoelastic properties of living adherent cells.

Assessment of mechanical properties of adherent living cells by bead micromanipulation: comparison of magnetic twisting cytometry vs optical tweezers

We compare the measurements of viscoelastic properties of adherent alveolar epithelial cells by two micromanipulation techniques: (i) magnetic twisting cytometry and (ii) optical tweezers, using microbeads of same size and similarly attached to F-actin. The values of equivalent Young modulus E, derived from linear viscoelasticity theory, become consistent when the degree of bead immersion in the cell is taken into account. E-values are smaller in (i) than in (ii): approximately 34-58 Pa vs approximately 29-258 Pa, probably because higher stress in (i) reinforces nonlinearity and cellular plasticity. Otherwise, similar relaxation time constants, around 2 s, suggest similar dissipative mechanisms.

Mechanical properties of hepatocellular carcinoma cells

AIM: To study the viscoelastic properties of human hepatocytes and hepatocellular carcinoma (HCC) cells under cytoskeletal perturbation, and to further to study the viscoelastic properties and the adhesive properties of mouse hepatoma cells (HTC) in different cell cycle.

METHODS: Micropipette aspiration technique was adopted to measure viscoelastic coefficients and adhesion force to collagen coated surface of the cells. Three kinds of cytoskeleton perturbing agents, colchicines (Col), cytochalasin D (CD) and vinblastine (VBL), were used to treat HCC cells and hepatocytes and the effects of these treatment on cell viscoelastic coefficients were investigated. The experimental results were analyzed with a three-element standard linear solid. Further, the viscoelastic properties of HTC cells and the adhesion force of different cycle HTC cells were also investigated. The synchronous G₁ and S phase cells were achieved through thymine-2-desoryriboside and colchicines sequential blockage method and thymine-2-desoryriboside blockage method respectively.

RESULTS: The elastic coefficients, but not viscous coefficient of HCC cells (K₁ = 103.6 ± 12.6 N·m^-2, K₂ = 42.5 ± 10.4 N·m^-2, μ = 4.5 ± 1.9 Pa·s), were significantly higher than the corresponding value for hepatocytes (K₁ = 87.5 ± 12.1 N·m^-2, K₂ = 33.3 ± 10.3 N·m^-2, μ = 5.9 ± 3.0 Pa·s, P < 0.01). Upon treatment with CD, the viscoelastic coefficients of both hepatocytes and HCC cells decreased consistently, with magnitudes for the decrease in elastic coefficients of HCC cells (K₁: 68.7 N·m^-2 to 81.7 N·m^-2, 66.3% to 78.9%; K₂: 34.5 N·m^-2 to 37.1 N·m^-2, 81.2% to 87.3%, P < 0.001) larger than those for normal hepatocytes (K₁: 42.6 N·m^-2 to 49.8 N·m^-2, 48.7% to 56.9%; K₂: 17.2 N·m^-2 to 20.4 N·m^-2, 51.7% to 61.3%, P < 0.001). There was a little decrease in the viscous coefficient of HCC cells (2.0 to 3.4 Pa•s, 44.4 to 75.6%, P < 0.001) than that for hepatocytes (3.0 to 3.9 Pa•s, 50.8 to 66.1% P < 0.001). Upon treatment with Col and VBL, the elastic coefficients of hepatocytes generally increased or tended to increase while those of HCC cells decreased. HTC cells with 72.1% of G₁ phase and 98.9% of S phase were achieved and high K₁, K₂ value and low μ value were the general characteristics of HTC cells. G₁ phase cells had higher K₁ value and lower μ value than S phase cells had, and G₁ phase HTC cells had stronger adhesive forces [(275.9 ± 232.8) × 10^-10 N] than S phase cells [(161.2 ± 120.4) × 10^-10 N, P < 0.001).

CONCLUSION: The difference in both the pattern and the magnitude of the effect of cytoskeletal perturbing agent on the viscoelastic properties between HCC cells and hepatocytes may reflect differences in the state of the cytoskeleton structure and function and in the sensitivity to perturbing agent treatment between these two types of cells. Change in the viscoelastic properties of cancer cells may affect significantly tumor cell invasion and metastasis as well as interactions between tumor cells and their micro-mechanical environments.

Three-dimensional cellular deformation analysis with a two-photon magnetic manipulator workstation

The ability to apply quantifiable mechanical stresses at the microscopic scale is critical for studying cellular responses to mechanical forces. This necessitates the use of force transducers that can apply precisely controlled forces to cells while monitoring the responses noninvasively. This paper describes the development of a micromanipulation workstation integrating two-photon, three-dimensional imaging with a high-force, uniform-gradient magnetic manipulator. The uniform-gradient magnetic field applies nearly uniform forces to a large cell population, permitting statistical quantification of select molecular responses to mechanical stresses. The magnetic transducer design is capable of exerting over 200 pN of force on 4.5-microm-diameter paramagnetic particles and over 800 pN on 5.0-microm ferromagnetic particles. These forces vary within +/-10% over an area 500 x 500 microm2. The compatibility with the use of high numerical aperture (approximately 1.0) objectives is an integral part of the workstation design allowing submicron-resolution, three-dimensional, two-photon imaging. Three-dimensional analyses of cellular deformation under localized mechanical strain are reported. These measurements indicate that the response of cells to large focal stresses may contain three-dimensional global deformations and show the suitability of this workstation to further studying cellular response to mechanical stresses.

Cell prestress. I. Stiffness and prestress are closely associated in adherent contractile cells

The tensegrity hypothesis holds that the cytoskeleton is a structure whose shape is stabilized predominantly by the tensile stresses borne by filamentous structures. Accordingly, cell stiffness must increase in proportion with the level of the tensile stress, which is called the prestress. Here we have tested that prediction in adherent human airway smooth muscle (HASM) cells. Traction microscopy was used to measure the distribution of contractile stresses arising at the interface between each cell and its substrate; this distribution is called the traction field. Because the traction field must be balanced by tensile stresses within the cell body, the prestress could be computed. Cell stiffness (G) was measured by oscillatory magnetic twisting cytometry. As the contractile state of the cell was modulated with graded concentrations of relaxing or contracting agonists (isoproterenol or histamine, respectively), the mean prestress ((t)) ranged from 350 to 1,900 Pa. Over that range, cell stiffness increased linearly with the prestress: G (Pa) = 0.18(t) + 92. While this association does not necessarily preclude other interpretations, it is the hallmark of systems that secure shape stability mainly through the prestress. Regardless of mechanism, these data establish a strong association between stiffness of HASM cells and the level of tensile stress within the cytoskeleton.

Cell prestress. II. Contribution of microtubules

The tensegrity model hypothesizes that cytoskeleton-based microtubules (MTs) carry compression as they balance a portion of cell contractile stress. To test this hypothesis, we used traction force microscopy to measure traction at the interface of adhering human airway smooth muscle cells and a flexible polyacrylamide gel substrate. The prediction is that if MTs balance a portion of contractile stress, then, upon their disruption, the portion of stress balanced by MTs would shift to the substrate, thereby causing an increase in traction. Measurements were done first in maximally activated cells (10 microM histamine) and then again after MTs had been disrupted (1 microM colchicine). We found that after disruption of MTs, traction increased on average by approximately 13%. Because in activated cells colchicine induced neither an increase in intracellular Ca(2+) nor an increase in myosin light chain phosphorylation as shown previously, we concluded that the observed increase in traction was a result of load shift from MTs to the substrate. In addition, energy stored in the flexible substrate was calculated as work done by traction on the deformation of the substrate. This result was then utilized in an energetic analysis. We assumed that cytoskeleton-based MTs are slender elastic rods supported laterally by intermediate filaments and that MTs buckle as the cell contracts. Using the post-buckling equilibrium theory of Euler struts, we found that energy stored during buckling of MTs was quantitatively consistent with the measured increase in substrate energy after disruption of MTs. This is further evidence supporting the idea that MTs are intracellular compression-bearing elements.

Mechanotransduction: all signals point to cytoskeleton, matrix, and integrins

Mechanical stresses modulate cell function by either activating or tuning signal transduction pathways. Mechanotransduction, the process by which cells convert mechanical stimuli into a chemical response, occurs both in cells specialized for sensing mechanical cues and in parenchymal cells whose primary function is not mechanosensory. However, common among the various responses to mechanical stress is the importance of direct or indirect connections between the internal cytoskeleton, the extracellular matrix (ECM), and traditional signal transducing molecules. In many instances, these elements converge at focal adhesions, sites of structural attachment between the cytoskeleton and ECM that are anchored by cell surface integrin receptors. Alenghat and Ingber discuss the accumulating evidence for the central role of cytoskeleton, ECM, and integrin-anchored focal adhesions in several mechanotransduction pathways.

Cell mechanics: mechanical response, cell adhesion, and molecular deformation

As the basic unit of life, the cell is a biologically complex system, the understanding of which requires a combination of various approaches including biomechanics. With recent progress in cell and molecular biology, the field of cell mechanics has grown rapidly over the last few years. This review synthesizes some of these recent developments to foster new concepts and approaches, and it emphasizes molecular-level understanding. The focuses are on the common themes and interconnections in three related areas: (a) the responses of cells to mechanical forces, (b) the mechanics and kinetics of cell adhesion, and (c) the deformation of biomolecules. Specific examples are also given to illustrate the quantitative modeling used in analyzing biological processes and physiological functions.

Mechanical behavior in living cells consistent with the tensegrity model

Alternative models of cell mechanics depict the living cell as a simple mechanical continuum, porous filament gel, tensed cortical membrane, or tensegrity network that maintains a stabilizing prestress through incorporation of discrete structural elements that bear compression. Real-time microscopic analysis of cells containing GFP-labeled microtubules and associated mitochondria revealed that living cells behave like discrete structures composed of an interconnected network of actin microfilaments and microtubules when mechanical stresses are applied to cell surface integrin receptors. Quantitation of cell tractional forces and cellular prestress by using traction force microscopy confirmed that microtubules bear compression and are responsible for a significant portion of the cytoskeletal prestress that determines cell shape stability under conditions in which myosin light chain phosphorylation and intracellular calcium remained unchanged. Quantitative measurements of both static and dynamic mechanical behaviors in cells also were consistent with specific a priori predictions of the tensegrity model. These findings suggest that tensegrity represents a unified model of cell mechanics that may help to explain how mechanical behaviors emerge through collective interactions among different cytoskeletal filaments and extracellular adhesions in living cells.

Invited review: engineering approaches to cytoskeletal mechanics

An outstanding problem in cell biology is how cells sense mechanical forces and how those forces affect cellular functions. Various biophysical and biochemical mechanisms have been invoked to answer this question. A growing body of evidence indicates that the deformable cytoskeleton (CSK), an intracellular network of interconnected filamentous biopolymers, provides a physical basis for transducing mechanical signals into biochemical signals. Therefore, to understand how mechanical forces regulate cellular functions, it is important to know how cells respond to changes in the CSK force balance and to identify the underlying mechanisms that control transmission of mechanical forces throughout the CSK and bring it to equilibrium. Recent developments of new experimental techniques for measuring cell mechanical properties and novel theoretical models of cellular mechanics make it now possible to identify and quantitate the contributions of various CSK structures to the overall balance of mechanical forces in the cell. This review focuses on engineering approaches that have been used in the past two decades in studies of the mechanics of the CSK.

Mechanical properties of cultured human airway smooth muscle cells from 0.05 to 0.4 Hz

We investigated the rheological properties of living human airway smooth muscle cells in culture and monitored the changes in rheological properties induced by exogenous stimuli. We oscillated small magnetic microbeads bound specifically to integrin receptors and computed the storage modulus (G') and loss modulus (G") from the applied torque and the resulting rotational motion of the beads as determined from their remanent magnetic field. Under baseline conditions, G' increased weakly with frequency, whereas G" was independent of the frequency. The cell was predominantly elastic, with the ratio of G" to G' (defined as eta) being approximately 0. 35 at all frequencies. G' and G" increased together after contractile activation and decreased together after deactivation, whereas eta remained unaltered in each case. Thus elastic and dissipative stresses were coupled during changes in contractile activation. G' and G" decreased with disruption of the actin fibers by cytochalasin D, but eta increased. These results imply that the mechanisms for frictional energy loss and elastic energy storage in the living cell are coupled and reside within the cytoskeleton.

Contribution of intermediate filaments to cell stiffness, stiffening, and growth

It has been shown previously that intermediate filament (IF) gels in vitro exhibit stiffening at high-applied stress, and it was suggested that this stiffening property of IFs might be important for maintaining cell integrity at large deformations (Janmey PA, Evtenever V, Traub P, and Schliwa M, J Cell Biol 113: 155-160, 1991). In this study, the contribution of IFs to cell mechanical behavior was investigated by measuring cell stiffness in response to applied stress in adherent wild-type and vimentin-deficient fibroblasts using magnetic twisting cytometry. It was found that vimentin-deficient cells were less stiff and exhibited less stiffening than wild-type cells, except at the lowest applied stress (10 dyn/cm(2)) where the difference in the stiffness was not significant. Similar results were obtained from measurements on wild-type fibroblasts and endothelial cells after vimentin IFs were disrupted by acrylamide. If, however, cells were plated over an extended period of time (16 h), they exhibited a significantly greater stiffness before than after acrylamide, even at the lowest applied stress. A possible reason could be that the initially slack IFs became fully extended due to a high degree of cell spreading and thus contributed to the transmission of mechanical stress across the cell. Taken together, these findings were consistent with the notion that IFs play important roles in the mechanical properties of the cell during large deformation. The experimental data also showed that depleting or disrupting IFs reduced, but did not entirely abolish, cell stiffening. This residual stiffening might be attributed to the effect of geometrical realignment of cytoskeletal filaments in the direction of applied load. It was also found that vimentin-deficient cells exhibited a slower rate of proliferation and DNA synthesis than wild-type cells. This could be a direct consequence of the absence of the intracellular IFs that may be necessary for efficient mediation of mechanical signals within the cell. Taken together, results of this study suggest that IFs play important roles in the mechanical properties of cells and in cell growth.