Glass transition and rheological redundancy in F-actin solutions

Heavy water induces bundling in entangled actin networks

Heavy water is known to affect many different biological systems, with the most striking effects observed at the cellular level. Many dynamic processes, such as migration or invasion, but also central processes of cell proliferation are measurably inhibited by the presence of deuterium oxide (D2O). Furthermore, individual cell deformabilities are significantly decreased upon D2O treatment. In order to understand the origin of these effects, we studied entangled filamentous actin networks, a commonly used model system for the cytoskeleton, which is considered a central functional element for dynamic cellular processes. Using bulk shear rheology to extract rheological signatures of reconstituted actin networks at varying concentrations of D2O, we found a non-monotonic behavior, which is explainable by a drastic change in the actin network architecture. Applying light scattering and fluorescence microscopy, we were able to demonstrate that the presence of deuterium oxide induces bundling in reconstituted entangled networks of filamentous actin. This constitutes an entirely novel and previously undescribed actin bundling mechanism.

Activity-dependent glassy cell mechanics Ⅰ: Mechanical properties measured with active microrheology

Active microrheology was conducted in living cells by applying an optical-trapping force to vigorously fluctuating tracer beads with feedback-tracking technology. The complex shear modulus G(ω)=G'(ω)-iG″(ω) was measured in HeLa cells in an epithelial-like confluent monolayer. We found that G(ω)∝(-iω)1/2 over a wide range of frequencies (1 Hz < ω/2π < 10 kHz). Actin disruption and cell-cycle progression from G1 to S and G2 phases only had a limited effect on G(ω) in living cells. On the other hand, G(ω) was found to be dependent on cell metabolism; ATP-depleted cells showed an increased elastic modulus G'(ω) at low frequencies, giving rise to a constant plateau such that G(ω)=G0+A(-iω)1/2. Both the plateau and the additional frequency dependency ∝(-iω)1/2 of ATP-depleted cells are consistent with a rheological response typical of colloidal jamming. On the other hand, the plateau G0 disappeared in ordinary metabolically active cells, implying that living cells fluidize their internal states such that they approach the critical jamming point.

Nonlinear mechanics of human mitotic chromosomes

In preparation for mitotic cell division, the nuclear DNA of human cells is compacted into individualized, X-shaped chromosomes¹. This metamorphosis is driven mainly by the combined action of condensins and topoisomerase IIα (TOP2A)^2,3, and has been observed using microscopy for over a century. Nevertheless, very little is known about the structural organization of a mitotic chromosome. Here we introduce a workflow to interrogate the organization of human chromosomes based on optical trapping and manipulation. This allows high-resolution force measurements and fluorescence visualization of native metaphase chromosomes to be conducted under tightly controlled experimental conditions. We have used this method to extensively characterize chromosome mechanics and structure. Notably, we find that under increasing mechanical load, chromosomes exhibit nonlinear stiffening behaviour, distinct from that predicted by classical polymer models⁴. To explain this anomalous stiffening, we introduce a hierarchical worm-like chain model that describes the chromosome as a heterogeneous assembly of nonlinear worm-like chains. Moreover, through inducible degradation of TOP2A⁵ specifically in mitosis, we provide evidence that TOP2A has a role in the preservation of chromosome compaction. The methods described here open the door to a wide array of investigations into the structure and dynamics of both normal and disease-associated chromosomes.

The force loading rate drives cell mechanosensing through both reinforcement and cytoskeletal softening

Cell response to force regulates essential processes in health and disease. However, the fundamental mechanical variables that cells sense and respond to remain unclear. Here we show that the rate of force application (loading rate) drives mechanosensing, as predicted by a molecular clutch model. By applying dynamic force regimes to cells through substrate stretching, optical tweezers, and atomic force microscopy, we find that increasing loading rates trigger talin-dependent mechanosensing, leading to adhesion growth and reinforcement, and YAP nuclear localization. However, above a given threshold the actin cytoskeleton softens, decreasing loading rates and preventing reinforcement. By stretching rat lungs in vivo, we show that a similar phenomenon may occur. Our results show that cell sensing of external forces and of passive mechanical parameters (like tissue stiffness) can be understood through the same mechanisms, driven by the properties under force of the mechanosensing molecules involved.

Cells in Slow Motion: Apparent Undercooling Increases Glassy Behavior at Physiological Temperatures

Solvent conditions are unexpectedly sufficient to drastically and reversibly slow down cells. In vitro on the molecular level, protein-solvent interactions drastically change in the presence of heavy water (D₂ O) and its stronger hydrogen bonds. Adding D₂ O to the cell medium of living cells increases the molecular intracellular viscosity. While cell morphology and phenotype remain unchanged, cellular dynamics transform into slow motion in a changeable manner. This is exemplified in the slowdown of cell proliferation and migration, which is caused by a reversible gelation of the cytoplasm. In analogy to the time-temperature superposition principle, where temperature is replaced by D₂ O, an increase in viscosity slows down the effective time. Actin networks, crucial structures in the cytoplasm, switch from a power-law-like viscoelastic to a more rubber-like elastic behavior. The resulting intracellular resistance and dissipation impair cell movement. Since cells are highly adaptive non-equilibrium systems, they usually respond irreversibly from a thermodynamic perspective. D₂ O induced changes, however, are fully reversible and their effects are independent of signaling as well as expression. The stronger hydrogen bonds lead to glass-like, drawn-out intramolecular dynamics, which may facilitate longer storage times of biological matter, for instance, during transport of organ transplants.

Cytoskeletal prestress: The cellular hallmark in mechanobiology and mechanomedicine

Increasing evidence demonstrates that mechanical forces, in addition to soluble molecules, impact cell and tissue functions in physiology and diseases. How living cells integrate mechanical signals to perform appropriate biological functions is an area of intense investigation. Here, we review the evidence of the central role of cytoskeletal prestress in mechanotransduction and mechanobiology. Elevating cytoskeletal prestress increases cell stiffness and reinforces cell stiffening, facilitates long-range cytoplasmic mechanotransduction via integrins, enables direct chromatin stretching and rapid gene expression, spurs embryonic development and stem cell differentiation, and boosts immune cell activation and killing of tumor cells whereas lowering cytoskeletal prestress maintains embryonic stem cell pluripotency, promotes tumorigenesis and metastasis of stem cell-like malignant tumor-repopulating cells, and elevates drug delivery efficiency of soft-tumor-cell-derived microparticles. The overwhelming evidence suggests that the cytoskeletal prestress is the governing principle and the cellular hallmark in mechanobiology. The application of mechanobiology to medicine (mechanomedicine) is rapidly emerging and may help advance human health and improve diagnostics, treatment, and therapeutics of diseases.

Cell mechanical properties of human breast carcinoma cells depend on temperature

The knowledge of cell mechanics is required to understand cellular processes and functions, such as the movement of cells, and the development of tissue engineering in cancer therapy. Cell mechanical properties depend on a variety of factors, such as cellular environments, and may also rely on external factors, such as the ambient temperature. The impact of temperature on cell mechanics is not clearly understood. To explore the effect of temperature on cell mechanics, we employed magnetic tweezers to apply a force of 1 nN to 4.5 µm superparamagnetic beads. The beads were coated with fibronectin and coupled to human epithelial breast cancer cells, in particular MCF-7 and MDA-MB-231 cells. Cells were measured in a temperature range between 25 and 45 °C. The creep response of both cell types followed a weak power law. At all temperatures, the MDA-MB-231 cells were pronouncedly softer compared to the MCF-7 cells, whereas their fluidity was increased. However, with increasing temperature, the cells became significantly softer and more fluid. Since mechanical properties are manifested in the cell's cytoskeletal structure and the paramagnetic beads are coupled through cell surface receptors linked to cytoskeletal structures, such as actin and myosin filaments as well as microtubules, the cells were probed with pharmacological drugs impacting the actin filament polymerization, such as Latrunculin A, the myosin filaments, such as Blebbistatin, and the microtubules, such as Demecolcine, during the magnetic tweezer measurements in the specific temperature range. Irrespective of pharmacological interventions, the creep response of cells followed a weak power law at all temperatures. Inhibition of the actin polymerization resulted in increased softness in both cell types and decreased fluidity exclusively in MDA-MB-231 cells. Blebbistatin had an effect on the compliance of MDA-MB-231 cells at lower temperatures, which was minor on the compliance MCF-7 cells. Microtubule inhibition affected the fluidity of MCF-7 cells but did not have a significant effect on the compliance of MCF-7 and MDA-MB-231 cells. In summary, with increasing temperature, the cells became significant softer with specific differences between the investigated drugs and cell lines.

Keratins determine network stress responsiveness in reconstituted actin-keratin filament systems

The cytoskeleton is a major determinant of cell mechanics, and alterations in the central mechanical aspects of cells are observed during many pathological situations. Therefore, it is essential to investigate the interplay between the main filament systems of the cytoskeleton in the form of composite networks. Here, we investigate the role of keratin intermediate filaments (IFs) in network strength by studying in vitro reconstituted actin and keratin 8/18 composite filament networks via bulk shear rheology. We co-polymerized these structural proteins in varying ratios and recorded how their relative content affects the overall mechanical response of the various composites. For relatively small deformations, we found that all composites exhibited an intermediate linear viscoelastic behaviour compared to that of the pure networks. In stark contrast, when larger deformations were imposed the composites displayed increasing strain stiffening behaviour with increasing keratin content. The extent of strain stiffening is much more pronounced than in corresponding experiments performed with vimentin IF as a composite network partner for actin. Our results provide new insights into the mechanical interplay between actin and keratin filaments in which keratin provides reinforcement to actin. This interplay may contribute to the overall integrity of cells. Hence, the high keratin 8/18 content of mechanically stressed simple epithelial cell layers, as found in the lung and the intestine, provides an explanation for their exceptional stability.

Polymerization of Bacillus subtilis MreB on a lipid membrane reveals lateral co-polymerization of MreB paralogs and strong effects of cations on filament formation

BACKGROUND

MreB is a bacterial ortholog of actin and forms mobile filaments underneath the cell membrane, perpendicular to the long axis of the cell, which play a crucial role for cell shape maintenance. We wished to visualize Bacillus subtilis MreB in vitro and therefore established a protocol to obtain monomeric protein, which could be polymerized on a planar membrane system, or associated with large membrane vesicles.

RESULTS

Using a planar membrane system and electron microscopy, we show that Bacillus subtilis MreB forms bundles of filaments, which can branch and fuse, with an average width of 70 nm. Fluorescence microscopy of non-polymerized YFP-MreB, CFP-Mbl and mCherry-MreBH proteins showed uniform binding to the membrane, suggesting that 2D diffusion along the membrane could facilitate filament formation. After addition of divalent magnesium and calcium ions, all three proteins formed highly disordered sheets of filaments that could split up or merge, such that at high protein concentration, MreB and its paralogs generated a network of filaments extending away from the membrane. Filament formation was positively affected by divalent ions and negatively by monovalent ions. YFP-MreB or CFP-Mbl also formed filaments between two adjacent membranes, which frequently has a curved appearance. New MreB, Mbl or MreBH monomers could add to the lateral side of preexisting filaments, and MreB paralogs co-polymerized, indicating direct lateral interaction between MreB paralogs.

CONCLUSIONS

Our data show that B. subtilis MreB paralogs do not easily form ordered filaments in vitro, possibly due to extensive lateral contacts, but can co-polymerise. Monomeric MreB, Mbl and MreBH uniformly bind to a membrane, and form irregular and frequently split up filamentous structures, facilitated by the addition of divalent ions, and counteracted by monovalent ions, suggesting that intracellular potassium levels may be one important factor to counteract extensive filament formation and filament splitting in vivo.

Time dependent stress relaxation and recovery in mechanically strained 3D microtissues

Characterizing the time-dependent mechanical properties of cells is not only necessary to determine how they deform but also to understand how external forces trigger biochemical-signaling cascades to govern their behavior. At present, mechanical properties are largely assessed by applying local shear or compressive forces on single cells grown in isolation on non-physiological 2D surfaces. In comparison, we developed the microfabricated vacuum actuated stretcher to measure tensile loading of 3D multicellular “microtissue” cultures. Using this approach, we here assessed the time-dependent stress relaxation and recovery responses of microtissues and quantified the spatial viscoelastic deformation following step length changes. Unlike previous results, stress relaxation and recovery in microtissues measured over a range of step amplitudes and pharmacological treatments followed an augmented stretched exponential behavior describing a broad distribution of inter-related timescales. Furthermore, despite the variety of experimental conditions, all responses led to a single linear relationship between the residual elastic stress and the degree of stress relaxation, suggesting that these mechanical properties are coupled through interactions between structural elements and the association of cells with their matrix. Finally, although stress relaxation could be quantitatively and spatially linked to recovery, they differed greatly in their dynamics; while stress recovery acted as a linear process, relaxation time constants changed with an inverse power law with the step size. This assessment of microtissues offers insights into how the collective behavior of cells in a 3D collagen matrix generates the dynamic mechanical properties of tissues, which is necessary to understand how cells deform and sense mechanical forces in vivo.

Structural and mechanical remodeling of the cytoskeleton maintains tensional homeostasis in 3D microtissues under acute dynamic stretch

When stretched, cells cultured on 2D substrates share a universal softening and fluidization response that arises from poorly understood remodeling of well-conserved cytoskeletal elements. It is known, however, that the structure and distribution of the cytoskeleton is profoundly influenced by the dimensionality of a cell’s environment. Therefore, in this study we aimed to determine whether cells cultured in a 3D matrix share this softening behavior and to link it to cytoskeletal remodeling. To achieve this, we developed a high-throughput approach to measure the dynamic mechanical properties of cells and allow for sub-cellular imaging within physiologically relevant 3D microtissues. We found that fibroblast, smooth muscle and skeletal muscle microtissues strain softened but did not fluidize, and upon loading cessation, they regained their initial mechanical properties. Furthermore, microtissue prestress decreased with the strain amplitude to maintain a constant mean tension. This adaptation under an auxotonic condition resulted in lengthening. A filamentous actin cytoskeleton was required, and responses were mirrored by changes to actin remodeling rates and visual evidence of stretch-induced actin depolymerization. Our new approach for assessing cell mechanics has linked behaviors seen in 2D cultures to a 3D matrix, and connected remodeling of the cytoskeleton to homeostatic mechanical regulation of tissues.

Complex modulus and compliance for airway smooth muscle cells

A cell can be described as a complex viscoelastic material with structural relaxations that is modulated by thermal and chemically nonequilibrium processes. Tissue morphology and function rely upon cells' physical responses to mechanical force. We measured the frequency-dependent mechanical relaxation response of adherent human airway smooth muscle cells under adenosine triphosphate (ATP) depletion and normal ATP conditions. The frequency dependence of the complex compliance J^{*} and modulus G^{*} was measured over the frequencies 10^{-1}<f<10^{3} Hz at selected temperatures between 4<T<54^{∘}C. Our results show characteristic relaxation features which can be interpreted by the mode-coupling theory (MCT) of viscoelastic liquids. We analyze the shape of the spectra in terms of a so-called A_{4} scenario with logarithmic scaling laws. Characteristic timescales τ_{β} and τ_{α} appear with corresponding energy barriers E_{β}≈(10-20)k_{B}T and E_{α}≈(20-30)k_{B}T. We demonstrate that cells are close to a glass transition. We find that the cell becomes softer around physiological temperatures, where its surface structure is more liquid-like with a plateau modulus around 0.1-0.8 kPa compared with the more solid-like interior cytoskeletal structures with a plateau modulus 1-15 kPa. Corresponding values for the viscosity are 10^{2}-10^{3} Pa s for the surface structures closer to the membrane and 10^{4}-10^{6} Pa s for the core cytoskeletal structures.

The role of stickiness in the rheology of semiflexible polymers

Semiflexible polymers form central structures in biological material. Modelling approaches usually neglect influences of polymer-specific molecular features aiming to describe semiflexible polymers universally. Here, we investigate the influence of molecular details on networks assembled from filamentous actin, intermediate filaments, and synthetic DNA nanotubes. In contrast to prevalent theoretical assumptions, we find that bulk properties are affected by various inter-filament interactions. We present evidence that these interactions can be merged into a single parameter in the frame of the glassy wormlike chain model. The interpretation of this parameter as a polymer specific stickiness is consistent with observations from macro-rheological measurements and reptation behaviour. Our findings demonstrate that stickiness should generally not be ignored in semiflexible polymer models.

Origin of Slow Stress Relaxation in the Cytoskeleton

Dynamically cross-linked semiflexible biopolymers such as the actin cytoskeleton govern the mechanical behavior of living cells. Semiflexible biopolymers nonlinearly stiffen in response to mechanical loads, whereas the cross-linker dynamics allow for stress relaxation over time. Here we show, through rheology and theoretical modeling, that the combined nonlinearity in time and stress leads to an unexpectedly slow stress relaxation, similar to the dynamics of disordered systems close to the glass transition. Our work suggests that transient cross-linking combined with internal stress can explain prior reports of soft glassy rheology of cells, in which the shear modulus increases weakly with frequency.

Glassy dynamics in composite biopolymer networks

The cytoskeleton is a highly interconnected meshwork of strongly coupled subsystems providing mechanical stability as well as dynamic functions to cells. To elucidate the underlying biophysical principles, it is central to investigate not only one distinct functional subsystem but rather their interplay as composite biopolymeric structures. Two of the key cytoskeletal elements are actin and vimentin filaments. Here, we show that composite networks reconstituted from actin and vimentin can be described by a superposition of two non-interacting scaffolds. Arising effects are demonstrated in a scale-spanning frame connecting single filament dynamics to macro-rheological network properties. The acquired results of the linear and non-linear bulk mechanics can be captured within an inelastic glassy wormlike chain model. In contrast to previous studies, we find no emergent effects in these composite networks. Thus, our study paves the way to predict the mechanics of the cytoskeleton based on the properties of its single structural components.

Broken detailed balance and non-equilibrium dynamics in living systems: a review

Living systems operate far from thermodynamic equilibrium. Enzymatic activity can induce broken detailed balance at the molecular scale. This molecular scale breaking of detailed balance is crucial to achieve biological functions such as high-fidelity transcription and translation, sensing, adaptation, biochemical patterning, and force generation. While biological systems such as motor enzymes violate detailed balance at the molecular scale, it remains unclear how non-equilibrium dynamics manifests at the mesoscale in systems that are driven through the collective activity of many motors. Indeed, in several cellular systems the presence of non-equilibrium dynamics is not always evident at large scales. For example, in the cytoskeleton or in chromosomes one can observe stationary stochastic processes that appear at first glance thermally driven. This raises the question how non-equilibrium fluctuations can be discerned from thermal noise. We discuss approaches that have recently been developed to address this question, including methods based on measuring the extent to which the system violates the fluctuation-dissipation theorem. We also review applications of this approach to reconstituted cytoskeletal networks, the cytoplasm of living cells, and cell membranes. Furthermore, we discuss a more recent approach to detect actively driven dynamics, which is based on inferring broken detailed balance. This constitutes a non-invasive method that uses time-lapse microscopy data, and can be applied to a broad range of systems in cells and tissue. We discuss the ideas underlying this method and its application to several examples including flagella, primary cilia, and cytoskeletal networks. Finally, we briefly discuss recent developments in stochastic thermodynamics and non-equilibrium statistical mechanics, which offer new perspectives to understand the physics of living systems.

Disentangling entanglements in biopolymer solutions

Reptation theory has been highly successful in explaining the unusual material properties of entangled polymer solutions. It reduces the complex many-body dynamics to a single-polymer description, where each polymer is envisaged to be confined to a tube through which it moves in a snake-like fashion. For flexible polymers, reptation theory has been amply confirmed by both experiments and simulations. In contrast, for semiflexible polymers, experimental and numerical tests are either limited to the onset of reptation, or were performed for tracer polymers in a fixed, static matrix. Here, we report Brownian dynamics simulations of entangled solutions of semiflexible polymers, which show that curvilinear motion along a tube (reptation) is no longer the dominant mode of dynamics. Instead, we find that polymers disentangle due to correlated constraint release, which leads to equilibration of internal bending modes before polymers diffuse the full tube length. The physical mechanism underlying terminal stress relaxation is rotational diffusion mediated by disentanglement rather than curvilinear motion along a tube.

Single Actin Bundle Rheology

Bundled actin structures play an essential role in the mechanical response of the actin cytoskeleton in eukaryotic cells. Although responsible for crucial cellular processes, they are rarely investigated in comparison to single filaments and isotropic networks. Presenting a highly anisotropic structure, the determination of the mechanical properties of individual bundles was previously achieved through passive approaches observing bending deformations induced by thermal fluctuations. We present a new method to determine the bending stiffness of individual bundles, by measuring the decay of an actively induced oscillation. This approach allows us to systematically test anisotropic, bundled structures. Our experiments revealed that thin, depletion force-induced bundles behave as semiflexible polymers and obey the theoretical predictions determined by the wormlike chain model. Thickening an individual bundle by merging it with other bundles enabled us to study effects that are solely based on the number of involved filaments. These thicker bundles showed a frequency-dependent bending stiffness, a behavior that is inconsistent with the predictions of the wormlike chain model. We attribute this effect to internal processes and give a possible explanation with regard to the wormlike bundle theory.

High-frequency microrheology reveals cytoskeleton dynamics in living cells

Living cells are viscoelastic materials, with the elastic response dominating at long timescales (≳1 ms)1. At shorter timescales, the dynamics of individual cytoskeleton filaments are expected to emerge, but active microrheology measurements on cells accessing this regime are scarce2. Here, we develop high-frequency microrheology (HF-MR) to probe the viscoelastic response of living cells from 1Hz to 100 kHz. We report the viscoelasticity of different cell types and upon cytoskeletal drug treatments. At previously inaccessible short timescales, cells exhibit rich viscoelastic responses that depend on the state of the cytoskeleton. Benign and malignant cancer cells revealed remarkably different scaling laws at high frequency, providing a univocal mechanical fingerprint. Microrheology over a wide dynamic range up to the frequency of action of the molecular components provides a mechanistic understanding of cell mechanics.

Implications and Assessment of the Elastic Behavior of Lamins in Laminopathies

Lamins are mechanosensitive and elastic components of the nuclear lamina that respond to external mechanical cues by altering gene regulation in a feedback mechanism. Numerous mutations in A-type lamins cause a plethora of diverse diseases collectively termed as laminopathies, the majority of which are characterized by irregularly shaped, fragile, and plastic nuclei. These nuclei are challenged to normal mechanotransduction and lead to disease phenotypes. Here, we review our current understanding of the nucleocytoskeleton coupling in mechanotransduction mediated by lamins. We also present an up-to-date understanding of the methods used to determine laminar elasticity both at the bulk and single molecule level.

Microstructure of Sheared Entangled Solutions of Semiflexible Polymers

We study the influence of finite shear deformations on the microstructure and rheology of solutions of entangled semiflexible polymers theoretically and by numerical simulations and experiments with filamentous actin. Based on the tube model of semiflexible polymers, we predict that large finite shear deformations strongly affect the average tube width and curvature, thereby exciting considerable restoring stresses. In contrast, the associated shear alignment is moderate, with little impact on the average tube parameters, and thus expected to be long-lived and detectable after cessation of shear. Similarly, topologically preserved hairpin configurations are predicted to leave a long-lived fingerprint in the shape of the distributions of tube widths and curvatures. Our numerical and experimental data support the theory.

Viscoelasticity of reversibly crosslinked networks of semiflexible polymers

We present a theoretical framework for the linear and nonlinear viscoelastic properties of reversibly crosslinked networks of semiflexible polymers. In contrast to affine models where network strain couples to the polymer end-to-end distance, in our model strain rather serves to locally distort the network structure. This induces bending modes in the polymer filaments, the properties of which are slaved to the surrounding network structure. Specifically, we investigate the frequency-dependent linear rheology, in particular in combination with crosslink binding-unbinding processes. We also develop schematic extensions to describe the nonlinear response during creep measurements as well as during constant strain-rate ramps.

Strain-enhanced stress relaxation impacts nonlinear elasticity in collagen gels

The extracellular matrix (ECM) is a complex assembly of structural proteins that provides physical support and biochemical signaling to cells in tissues. The mechanical properties of the ECM have been found to play a key role in regulating cell behaviors such as differentiation and malignancy. Gels formed from ECM protein biopolymers such as collagen or fibrin are commonly used for 3D cell culture models of tissue. One of the most striking features of these gels is that they exhibit nonlinear elasticity, undergoing strain stiffening. However, these gels are also viscoelastic and exhibit stress relaxation, with the resistance of the gel to a deformation relaxing over time. Recent studies have suggested that cells sense and respond to both nonlinear elasticity and viscoelasticity of ECM, yet little is known about the connection between nonlinear elasticity and viscoelasticity. Here, we report that, as strain is increased, not only do biopolymer gels stiffen but they also exhibit faster stress relaxation, reducing the timescale over which elastic energy is dissipated. This effect is not universal to all biological gels and is mediated through weak cross-links. Mechanistically, computational modeling and atomic force microscopy (AFM) indicate that strain-enhanced stress relaxation of collagen gels arises from force-dependent unbinding of weak bonds between collagen fibers. The broader effect of strain-enhanced stress relaxation is to rapidly diminish strain stiffening over time. These results reveal the interplay between nonlinear elasticity and viscoelasticity in collagen gels, and highlight the complexity of the ECM mechanics that are likely sensed through cellular mechanotransduction.

On the embryonic cell division beyond the contractile ring mechanism: experimental and computational investigation of effects of vitelline confinement, temperature and egg size

Embryonic cell division is a mechanical process which is predominantly driven by contraction of the cleavage furrow and response of the remaining cellular matter. While most previous studies focused on contractile ring mechanisms of cytokinesis, effects of environmental factors such as pericellular vitelline membrane and temperature on the mechanics of dividing cells were rarely studied. Here, we apply a model-based analysis to the time-lapse imaging data of two species (Saccoglossus kowalevskii and Xenopus laevis) with relatively large eggs, with the goal of revealing the effects of temperature and vitelline envelope on the mechanics of the first embryonic cell division. We constructed a numerical model of cytokinesis to estimate the effects of vitelline confinement on cellular deformation and to predict deformation of cellular contours. We used the deviations of our computational predictions from experimentally observed cell elongation to adjust variable parameters of the contractile ring model and to quantify the contribution of other factors (constitutive cell properties, spindle polarization) that may influence the mechanics and shape of dividing cells. We find that temperature affects the size and rate of dilatation of the vitelline membrane surrounding fertilized eggs and show that in native (not artificially devitellinized) egg cells the effects of temperature and vitelline envelope on mechanics of cell division are tightly interlinked. In particular, our results support the view that vitelline membrane fulfills an important role of micromechanical environment around the early embryo the absence or improper function of which under moderately elevated temperature impairs normal development. Furthermore, our findings suggest the existence of scale-dependent mechanisms that contribute to cytokinesis in species with different egg size, and challenge the view of mechanics of embryonic cell division as a scale-independent phenomenon.

Molecular control of stress transmission in the microtubule cytoskeleton

In this article, we will summarize recent progress in understanding the mechanical origins of rigidity, strength, resiliency and stress transmission in the MT cytoskeleton using reconstituted networks formed from purified components. We focus on the role of network architecture, crosslinker compliance and dynamics, and molecular determinants of single filament elasticity, while highlighting open questions and future directions for this work.

Inelastic mechanics: A unifying principle in biomechanics

Many soft materials are classified as viscoelastic. They behave mechanically neither quite fluid-like nor quite solid-like - rather a bit of both. Biomaterials are often said to fall into this class. Here, we argue that this misses a crucial aspect, and that biomechanics is essentially damage mechanics, at heart. When deforming an animal cell or tissue, one can hardly avoid inducing the unfolding of protein domains, the unbinding of cytoskeletal crosslinkers, the breaking of weak sacrificial bonds, and the disruption of transient adhesions. We classify these activated structural changes as inelastic. They are often to a large degree reversible and are therefore not plastic in the proper sense, but they dissipate substantial amounts of elastic energy by structural damping. We review recent experiments involving biological materials on all scales, from single biopolymers over cells to model tissues, to illustrate the unifying power of this paradigm. A deliberately minimalistic yet phenomenologically very rich mathematical modeling framework for inelastic biomechanics is proposed. It transcends the conventional viscoelastic paradigm and suggests itself as a promising candidate for a unified description and interpretation of a wide range of experimental data. This article is part of a Special Issue entitled: Mechanobiology.

Bond breaking dynamics in semiflexible networks under load

We examine the bond-breaking dynamics of transiently cross-linked semiflexible networks using a single filament model in which that filament is peeled from an array of cross-linkers. We examine the effect of quenched disorder in the placement of the linkers along the filament and the effect of stochastic bond-breaking (assuming Bell model unbinding kinetics) on the dynamics of filament cross-linker dissociation and the statistics of ripping events. We find that bond forces decay exponentially away from the point of loading and that bond breaking proceeds sequentially down the linker array from the point of loading in a series of stochastic ripping events. We compare these theoretical predictions to the observed trajectories of large beads in a cross-linked microtubule network and identify the observed jumps of the bead with the linker rupture events predicted by the single filament model.

Characterization of anomalous movements of spherical living cells on a silicon dioxide glassy substrate

The random walk of spherical living cells on a silicon dioxide glassy substrate was studied experimentally and numerically. This random walk trajectory exhibited erratic dancing, which seemingly obeyed anomalous diffusion (i.e., Lévy-like walk) rather than normal diffusion. Moreover, the angular distribution (-π to π) of the cells' trajectory followed a "U-shaped pattern" in comparison to the uniform distribution seen in the movements of negatively charged polystyrene microspheres. These effects could be attributable to the homeostasis-driven structural resilient character of cells and physical interactions derived from temporarily retained nonspecific binding due to weak forces between the cells and substrates. Our results provide new insights into the stochastic behavior of mesoscopic biological particles with respect to structural properties and physical interactions.

Chemoenvironmental modulators of fluidity in the suspended biological cell

Biological cells can be characterized as "soft matter" with mechanical characteristics potentially modulated by external cues such as pharmaceutical dosage or fever temperature. Further, quantifying the effects of chemical and physical stimuli on a cell's mechanical response informs models of living cells as complex materials. Here, we investigate the mechanical behavior of single biological cells in terms of fluidity, or mechanical hysteresivity normalized to the extremes of an elastic solid or a viscous liquid. This parameter, which complements stiffness when describing whole-cell viscoelastic response, can be determined for a suspended cell within subsecond times. Questions remain, however, about the origin of fluidity as a conserved parameter across timescales, the physical interpretation of its magnitude, and its potential use for high-throughput sorting and separation of interesting cells by mechanical means. Therefore, we exposed suspended CH27 lymphoma cells to various chemoenvironmental conditions--temperature, pharmacological agents, pH, and osmolarity--and measured cell fluidity with a non-contact technique to extend familiarity with suspended-cell mechanics in the context of both soft-matter physics and mechanical flow cytometry development. The actin-cytoskeleton-disassembling drug latrunculin exacted a large effect on mechanical behavior, amenable to dose-dependence analysis of coupled changes in fluidity and stiffness. Fluidity was minimally affected by pH changes from 6.5 to 8.5, but strongly modulated by osmotic challenge to the cell, where the range spanned halfway from solid to liquid behavior. Together, these results support the interpretation of fluidity as a reciprocal friction within the actin cytoskeleton, with implications both for cytoskeletal models and for expectations when separating interesting cell subpopulations by mechanical means in the suspended state.

Direct visualization of flow-induced conformational transitions of single actin filaments in entangled solutions

While semi-flexible polymers and fibres are an important class of material due to their rich mechanical properties, it remains unclear how these properties relate to the microscopic conformation of the polymers. Actin filaments constitute an ideal model polymer system due to their micron-sized length and relatively high stiffness that allow imaging at the single filament level. Here we study the effect of entanglements on the conformational dynamics of actin filaments in shear flow. We directly measure the full three-dimensional conformation of single actin filaments, using confocal microscopy in combination with a counter-rotating cone-plate shear cell. We show that initially entangled filaments form disentangled orientationally ordered hairpins, confined in the flow-vorticity plane. In addition, shear flow causes stretching and shear alignment of the hairpin tails, while the filament length distribution remains unchanged. These observations explain the strain-softening and shear-thinning behaviour of entangled F-actin solutions, which aids the understanding of the flow behaviour of complex fluids containing semi-flexible polymers.

Advances in the mechanical modeling of filamentous actin and its cross-linked networks on multiple scales

The protein actin is a part of the cytoskeleton and, therefore, responsible for the mechanical properties of the cells. Starting with the single molecule up to the final structure, actin creates a hierarchical structure of several levels exhibiting a remarkable behavior. The hierarchy spans several length scales and limitations in computational power; therefore, there is a call for different mechanical modeling approaches for the different scales. On the molecular level, we may consider each atom in molecular dynamics simulations. Actin forms filaments by combining the molecules into a double helix. In a model, we replace molecular subdomains using coarse-graining methods, allowing the investigation of larger systems of several atoms. These models on the nanoscale inform continuum mechanical models of large filaments, which are based on worm-like chain models for polymers. Assemblies of actin filaments are connected with cross-linker proteins. Models with discrete filaments, so-called Mikado models, allow us to investigate the dependence of the properties of networks on the parameters of the constituents. Microstructurally motivated continuum models of the networks provide insights into larger systems containing cross-linked actin networks. Modeling of such systems helps to gain insight into the processes on such small scales. On the other hand, they call for verification and hence trigger the improvement of established experiments and the development of new methods.

Attractive interactions among intermediate filaments determine network mechanics in vitro

Mechanical and structural properties of K8/K18 and vimentin intermediate filament (IF) networks have been investigated using bulk mechanical rheometry and optical microrheology including diffusing wave spectroscopy and multiple particle tracking. A high elastic modulus G₀ at low protein concentration c, a weak concentration dependency of G₀ (G₀∼c^0.5±0.1) and pronounced strain stiffening are found for these systems even without external crossbridgers. Strong attractive interactions among filaments are required to maintain these characteristic mechanical features, which have also been reported for various other IF networks. Filament assembly, the persistence length of the filaments and the network mesh size remain essentially unaffected when a nonionic surfactant is added, but strain stiffening is completely suppressed, G₀ drops by orders of magnitude and exhibits a scaling G₀∼c^1.9±0.2 in agreement with microrheological measurements and as expected for entangled networks of semi-flexible polymers. Tailless K8Δ/K18ΔT and various other tailless filament networks do not exhibit strain stiffening, but still show high G₀ values. Therefore, two binding sites are proposed to exist in IF networks. A weaker one mediated by hydrophobic amino acid clusters in the central rod prevents stretched filaments between adjacent cross-links from thermal equilibration and thus provides the high G₀ values. Another strong one facilitating strain stiffening is located in the tail domain with its high fraction of hydrophobic amino acid sequences. Strain stiffening is less pronounced for vimentin than for K8/K18 due to electrostatic repulsion forces partly compensating the strong attraction at filament contact points.

Mechanics of biological networks: from the cell cytoskeleton to connective tissue

From the cell cytoskeleton to connective tissues, fibrous networks are ubiquitous in metazoan life as the key promoters of mechanical strength, support and integrity. In recent decades, the application of physics to biological systems has made substantial strides in elucidating the striking mechanical phenomena observed in such networks, explaining strain stiffening, power law rheology and cytoskeletal fluidisation - all key to the biological function of individual cells and tissues. In this review we focus on the current progress in the field, with a primer into the basic physics of individual filaments and the networks they form. This is followed by a discussion of biological networks in the context of a broad spread of recent in vitro and in vivo experiments.

An inverse power-law distribution of molecular bond lifetimes predicts fractional derivative viscoelasticity in biological tissue

Viscoelastic characteristics of many materials falling under the category of soft glassy substances, including biological tissue, often exhibit a mechanical complex modulus Y(ω) well described by a fractional derivative model: Y(ω) = E(iω/ϕ)k, where E = a generalized viscoelastic stiffness; i = (-1)1/2; ω = angular frequency; ϕ = scaling factor; and k = an exponent valued between 0 and 1. The term "fractional derivative" refers to the value of k: when k = 0 the viscoelastic response is purely elastic, and when k = 1 the response is purely viscous. We provide an analytical derivation of the fractional derivative complex modulus based on the hypothesis that the viscoelastic response arises from many intermittent molecular crosslinks, whose lifetimes longer than a critical threshold lifetime, tcrit, are distributed with an inverse power law proportional to t-(k+2). We demonstrate that E is proportional to the number and stiffness of crosslinks formed at any moment; the scaling factor ϕ is equivalent to reciprocal of tcrit; and the relative mean lifetime of the attached crosslinks is inversely proportional to the parameter k. To test whether electrostatic molecular bonds could be responsible for the fractional derivative viscoelasticity, we used chemically skinned human skeletal muscle as a one-dimensional model of a soft glassy substance. A reduction in ionic strength from 175 to 110 mEq resulted in a larger E with no change in k, consistent with a higher probability of interfilament molecular interactions. Thick to thin filament spacing was reduced by applying 4% w/v of the osmolyte Dextran T500, which also resulted in a larger E, indicating a greater probability of crosslink formation in proportion to proximity. A 10°C increase in temperature resulted in an increase in k, which corresponded to a decrease in cross-bridge attachment lifetime expected with higher temperatures. These theoretical and experimental results suggest that the fractional derivative viscoelasticity observed in some biological tissue arises as a mechanical consequence of electrostatic interactions, whose longest lifetimes are distributed with an inverse power law.

Viscoelastic behavior of human lamin A proteins in the context of dilated cardiomyopathy

Lamins are intermediate filament proteins of type V constituting a nuclear lamina or filamentous meshwork which lines the nucleoplasmic side of the inner nuclear membrane. This protein mesh provides a supporting scaffold for the nuclear envelope and tethers interphase chromosome to the nuclear periphery. Mutations of mainly A-type lamins are found to be causative for at least 11 human diseases collectively termed as laminopathies majority of which are characterised by aberrant nuclei with altered structural rigidity, deformability and poor mechanotransduction behaviour. But the investigation of viscoelastic behavior of lamin A continues to elude the field. In order to address this problem, we hereby present the very first report on viscoelastic properties of wild type human lamin A and some of its mutants linked with Dilated cardiomyopathy (DCM) using quantitative rheological measurements. We observed a dramatic strain-softening effect on lamin A network as an outcome of the strain amplitude sweep measurements which could arise from the large compliance of the quasi-cross-links in the network or that of the lamin A rods. In addition, the drastic stiffening of the differential elastic moduli on superposition of rotational and oscillatory shear stress reflect the increase in the stiffness of the laterally associated lamin A rods. These findings present a preliminary insight into distinct biomechanical properties of wild type lamin A protein and its mutants which in turn revealed interesting differences.

Mechanical and structural plasticity

Excessive narrowing of the airways due to airway smooth muscle (ASM) contraction is a major cause of asthma exacerbation. ASM is therefore a direct target for many drugs used in asthma therapy. The contractile mechanism of smooth muscle is not entirely clear. A major advance in the field in the last decade was the recognition and appreciation of the unique properties of smooth muscle--mechanical and structural plasticity, characterized by the muscle's ability to rapidly alter the structure of its contractile apparatus and cytoskeleton and adapt to the mechanically dynamic environment of the lung. This article describes a possible mechanism for smooth muscle to adapt and function over a large length range by adding or subtracting contractile units in series spanning the cell length; it also describes a mechanism by which actin-myosin-actin connectivity might be influenced by thin and thick filament lengths, thus altering the muscle response to mechanical perturbation. The new knowledge is extremely useful for our understanding of ASM behavior in the lung and could provide new and more effective targets for drugs aimed at relaxing the muscle or keeping the muscle from excessive shortening in the asthmatic airways.

Multicellular aggregates: a model system for tissue rheology

Morphogenetic processes involve cell flows. The mechanical response of a tissue to active forces is linked to its effective viscosity. In order to decouple this mechanical response from the complex genetic changes occurring in a developing organism, we perform rheometry experiments on multicellular aggregates, which are good models for tissues. We observe a cell softening behavior when submitting to stresses. As our technique is very sensitive, we were able to get access to the measurement of a yield point above which a creep regime is observed obtained for strains above 12%. To explain our rheological curves we propose a model for the cytoskeleton that we represent as a dynamic network of parallel springs, which will break under stress and reattach at null strain. Such a simple model is able to reproduce most of the important behavior of cells under strain. We highlight here the importance of considering cells as complex fluids whose properties will vary with time according to the history of applied stress.

Emergent complexity of the cytoskeleton: from single filaments to tissue

Despite their overwhelming complexity, living cells display a high degree of internal mechanical and functional organization which can largely be attributed to the intracellular biopolymer scaffold, the cytoskeleton. Being a very complex system far from thermodynamic equilibrium, the cytoskeleton's ability to organize is at the same time challenging and fascinating. The extensive amounts of frequently interacting cellular building blocks and their inherent multifunctionality permits highly adaptive behavior and obstructs a purely reductionist approach. Nevertheless (and despite the field's relative novelty), the physics approach has already proved to be extremely successful in revealing very fundamental concepts of cytoskeleton organization and behavior. This review aims at introducing the physics of the cytoskeleton ranging from single biopolymer filaments to multicellular organisms. Throughout this wide range of phenomena, the focus is set on the intertwined nature of the different physical scales (levels of complexity) that give rise to numerous emergent properties by means of self-organization or self-assembly.

Minimal model for the inelastic mechanics of biopolymer networks and cells

We explore the mechanism behind the ambiguous nonlinear mechanical response of biopolymer networks and cells. Our theoretical analysis is based on the inelastic glassy wormlike chain model (iGWLC), which accounts for simultaneous softening and stiffening in terms of two antagonistic mechanisms: viscoelastic stress stiffening caused by polymer stretching, and inelastic fluidization caused by bond breaking. On this basis, we derive a set of simple schematic constitutive equations that faithfully reproduce the rich inelastic phenomenology of biopolymer networks and cells.

Resolving the stiffening-softening paradox in cell mechanics

BACKGROUND

Despite their notorious diversity, biological cells are mechanically well characterized by only a few robust and universal laws. Intriguingly, the law characterizing the nonlinear response to stretch appears self-contradictory. Various cell types have been reported to both stiffen and soften, or "fluidize" upon stretch. Within the classical paradigm of cells as viscoelastic bodies, this constitutes a paradox.

PRINCIPAL FINDINGS

Our measurements reveal that minimalistic reconstituted cytoskeletal networks (F-actin/HMM) exhibit a similarly peculiar response. A mathematical model of transiently crosslinked polymer networks, the so-called inelastic glassy wormlike chain (iGwlc) model, can simulate the data and resolve the apparent contradiction. It explains the observations in terms of two antagonistic physical mechanisms, the nonlinear viscoelastic resistance of biopolymers to stretch, and the breaking of weak transient bonds between them.

CONCLUSIONS

Our results imply that the classical paradigm of cells as viscoelastic bodies has to be replaced by such an inelastic mechanical model.

Squeezing and detachment of living cells

The interaction of living cells with their environment is linked to their adhesive and elastic properties. Even if the mechanics of simple lipid membranes is fairly well understood, the analysis of single cell experiments remains challenging in part because of the mechanosensory response of cells to their environment. To study the mechanical properties of living cells we have developed a tool that borrows from micropipette aspiration techniques, atomic force microscopy, and the classical Johnson-Kendall-Roberts test. We show results from a study of the adhesion properties of living cells, as well as the elastic response and relaxation. We present models that are applied throughout the different stages of an experiment, which indicate that the contribution of the different components of the cell are active at various stages of compression, retraction, and detachment. Finally, we present a model that attempts to elucidate the surprising logarithmic relaxation observed when the cell is subjected to a given deformation.

Longitudinal response of confined semiflexible polymers

The longitudinal response of single semiflexible polymers to sudden changes in externally applied forces is known to be controlled by the propagation and relaxation of backbone tension. Under many experimental circumstances, realized, for example, in nanofluidic devices or in polymeric networks or solutions, these polymers are effectively confined in a channel- or tubelike geometry. By means of heuristic scaling laws and rigorous analytical theory, we analyze the tension dynamics of confined semiflexible polymers for various generic experimental setups. It turns out that in contrast to the well-known linear response, the influence of confinement on the nonlinear dynamics can largely be described as that of an effective prestress. We also study the free relaxation of an initially confined chain, finding a surprising superlinear ~t(9/8) growth law for the change in end-to-end distance at short times.

Stress transmission within the cell

An outstanding problem in cell biology is how cells sense mechanical forces and how those forces affect cellular functions. During past decades, it has become evident that the deformable cytoskeleton (CSK), an intracellular network of various filamentous biopolymers, provides a physical basis for transducing mechanical signals into biochemical responses. To understand how mechanical forces regulate cellular functions, it is necessary to first understand how the CSK develops mechanical stresses in response to applied forces, and how those stresses are propagated through the CSK where various signaling molecules are immobilized. New experimental techniques have been developed to quantify cytoskeletal mechanics, which together with new computational approaches have given rise to new theories and models for describing mechanics of living cells. In this article, we discuss current understanding of cell biomechanics by focusing on the biophysical mechanisms that are responsible for the development and transmission of mechanical stresses in the cell and their effect on cellular functions. We compare and contrast various theories and models of cytoskeletal mechanics, emphasizing common mechanisms that those theories are built upon, while not ignoring irreconcilable differences. We highlight most recent advances in the understanding of mechanotransduction in the cytoplasm of living cells and the central role of the cytoskeletal prestress in propagating mechanical forces along the cytoskeletal filaments to activate cytoplasmic enzymes. It is anticipated that advances in cell mechanics will help developing novel therapeutics to treat pulmonary diseases like asthma, pulmonary fibrosis, and chronic obstructive pulmonary disease.

Single molecule fluorescence microscopy investigations on heterogeneity of translational diffusion in thin polymer films

Translational diffusion of single perylene diimide molecules in 25 nm thin polymer films was investigated by single molecule widefield fluorescence microscopy. Spatial heterogeneities in single molecule motion were detected and analyzed by a new, quantitative method which draws a comparison of log-Gaussian fits of experimentally determined diffusion coefficient-distributions and diffusion coefficient-distributions from Monte Carlo random walk simulations. Heterogeneities could be observed close to the glass transition temperature, but disappear at ca. 1.1 × T(g). At higher temperatures, heterogeneities do not exist or they average out on the time and length scales of observation. The observed heterogeneities also explain why the dependency of diffusion coefficients on temperature does not follow Vogel-Fulcher-Tammann behavior.

Emergence of airway smooth muscle functions related to structural malleability

The function of a complex system such as a smooth muscle cell is the result of the active interaction among molecules and molecular aggregates. Emergent macroscopic manifestations of these molecular interactions, such as the length-force relationship and its associated length adaptation, are well documented, but the molecular constituents and organization that give rise to these emergent muscle behaviors remain largely unknown. In this minireview, we describe emergent properties of airway smooth muscle that seem to have originated from inherent fragility of the cellular structures, which has been increasingly recognized as a unique and important smooth muscle attribute. We also describe molecular interactions (based on direct and indirect evidence) that may confer malleability on fragile structural elements that in turn may allow the muscle to adapt to large and frequent changes in cell dimensions. Understanding how smooth muscle works may hinge on how well we can relate molecular events to its emergent macroscopic functions.

A continuous-binding cross-linker model for passive airway smooth muscle

Although the active properties of airway smooth muscle (ASM) have garnered much modeling attention, the passive mechanical properties are not as well studied. In particular, there are important dynamic effects observed in passive ASM, particularly strain-induced fluidization, which have been observed both experimentally and in models; however, to date these models have left an incomplete picture of the biophysical, mechanistic basis for these behaviors. The well-known Huxley cross-bridge model has for many years successfully described many of the active behaviors of smooth muscle using sliding filament theory; here, we propose to extend this theory to passive biological soft tissue, particularly ASM, using as a basis the attachment and detachment of cross-linker proteins at a continuum of cross-linker binding sites. The resulting mathematical model exhibits strain-induced fluidization, as well as several types of force recovery, at the same time suggesting a new mechanistic basis for the behavior. The model is validated by comparison to new data from experimental preparations of rat tracheal airway smooth muscle. Furthermore, experiments in noncontractile tissue show qualitatively similar behavior, suggesting support for the protein-filament theory as a biomechanical basis for the behavior.

Remodeling of integrated contractile tissues and its dependence on strain-rate amplitude

Here we investigate the origin of relaxation times governing the mechanical response of an integrated contractile tissue to imposed cyclic changes of length. When strain-rate amplitude is held constant as frequency is varied, fast events are accounted for by actomyosin cross-bridge cycling, but slow events reveal relaxation processes associated with ongoing cytoskeletal length adaptation. Although both relaxation regimes are innately nonlinear, these regimes are unified and their positions along the frequency axis are set by the imposed strain-rate amplitude.

Dense-body aggregates as plastic structures supporting tension in smooth muscle cells

The wall of hollow organs of vertebrates is a unique structure able to generate active tension and maintain a nearly constant passive stiffness over a large volume range. These properties are predominantly attributable to the smooth muscle cells that line the organ wall. Although smooth muscle is known to possess plasticity (i.e., the ability to adapt to large changes in cell length through structural remodeling of contractile apparatus and cytoskeleton), the detailed structural basis for the plasticity is largely unknown. Dense bodies, one of the most prominent structures in smooth muscle cells, have been regarded as the anchoring sites for actin filaments, similar to the Z-disks in striated muscle. Here, we show that the dense bodies and intermediate filaments formed cable-like structures inside airway smooth muscle cells and were able to adjust the cable length according to cell length and tension. Stretching the muscle cell bundle in the relaxed state caused the cables to straighten, indicating that these intracellular structures were connected to the extracellular matrix and could support passive tension. These plastic structures may be responsible for the ability of smooth muscle to maintain a nearly constant tensile stiffness over a large length range. The finding suggests that the structural plasticity of hollow organs may originate from the dense-body cables within the smooth muscle cells.