A master relation defines the nonlinear viscoelasticity of single fibroblasts

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.

Drag force as a tool to test the active mechanical response of PC12 neurites

We investigate the mechanical response of PC12 neurites subjected to a drag force imposed by a laminar flow perpendicular to the neurite axis. The curvature of the catenary shape acquired by an initially straight neurite under the action of the drag force provides information on both elongation and tension of the neurite. This method allows us to measure the rest tension and viscoelastic parameters of PC12 neurites and active behavior of neurites. Measurement of oscillations in the strain rate of neurites at constant flow rate provides insight on the response of molecular motors and additional support for the presence of a negative strain-rate sensitivity region in the global mechanical response of PC12 neurites.

Power-law rheology analysis of cells undergoing micropipette aspiration

Accurate quantification of the mechanical properties of living cells requires the combined use of experimental techniques and theoretical models. In this paper, we investigate the viscoelastic response of suspended NIH 3T3 fibroblasts undergoing micropipette aspiration using power-law rheology model. As an important first step, we examine the pipette size effect on cell deformation and find that pipettes larger than ~7 μm are more suitable for bulk rheological measurements than smaller ones and the cell can be treated as effectively continuum. When the large pipettes are used to apply a constant pressure to a cell, the creep deformation is better fitted with the power-law rheology model than with the liquid drop or spring-dashpot models; magnetic twisting cytometry measurement on the rounded cell confirms the power-law behavior. This finding is further extended to suspended cells treated with drugs targeting their cytoskeleton. As such, our results suggest that the application of relatively large pipettes can provide more effective assessment of the bulk material properties as well as support application of power-law rheology to cells in suspension.

Theoretical concepts and models of cellular mechanosensing

Recent discoveries have established that mechanical properties of the cellular environment such as its rigidity, geometry, and external stresses play an important role in determining the cellular function and fate. Mechanical properties have been shown to influence cell shape and orientation, regulate cell proliferation and differentiation, and even govern the development and organization of tissues. In recent years, many theoretical and experimental investigations have been carried out to elucidate the mechanisms and consequences of the mechanosensitivity of cells. In this review, we discuss recent theoretical concepts and approaches that explain and predict cell mechanosensitivity. We focus on the interplay of active and passive processes that govern cell-cell and cell-matrix interactions and discuss the role of this interplay in the processes of cell adhesion, regulation of cytoskeleton mechanics and the response of cells to applied mechanical stresses.

Tension dynamics and viscoelasticity of extensible wormlike chains

The dynamic response of prestressed semiflexible biopolymers is characterized by the propagation and relaxation of tension, which arises due to the near inextensibility of a stiff backbone. It is coupled to the dynamics of contour length stored in thermal undulations but also to the local relaxation of elongational strain. We present a systematic theory of tension dynamics for stiff yet extensible wormlike chains. Our results show that even moderate prestress gives rise to distinct Rouse-like extensibility signatures in the high-frequency viscoelastic response.

An active biopolymer network controlled by molecular motors

We describe an active polymer network in which processive molecular motors control network elasticity. This system consists of actin filaments cross-linked by filamin A (FLNa) and contracted by bipolar filaments of muscle myosin II. The myosin motors stiffen the network by more than two orders of magnitude by pulling on actin filaments anchored in the network by FLNa cross-links, thereby generating internal stress. The stiffening response closely mimics the effects of external stress applied by mechanical shear. Both internal and external stresses can drive the network into a highly nonlinear, stiffened regime. The active stress reaches values that are equivalent to an external stress of 14 Pa, consistent with a 1-pN force per myosin head. This active network mimics many mechanical properties of cells and suggests that adherent cells exert mechanical control by operating in a nonlinear regime where cell stiffness is sensitive to changes in motor activity. This design principle may be applicable to engineering novel biologically inspired, active materials that adjust their own stiffness by internal catalytic control.

Filamin A is essential for active cell stiffening but not passive stiffening under external force

The material properties of a cell determine how mechanical forces are transmitted through and sensed by that cell. Some types of cells stiffen passively under large external forces, but they can also alter their own stiffness in response to the local mechanical environment or biochemical cues. Here we show that the actin-binding protein filamin A is essential for the active stiffening of cells plated on collagen-coated substrates. This appears to be due to a diminished capability to build up large internal contractile stresses in the absence of filamin A. To show this, we compare the material properties and contractility of two human melanoma cell lines that differ in filamin A expression. The filamin A-deficient M2 cells are softer than the filamin A-replete A7 cells, and exert much smaller contractile stresses on the substratum, even though the M2 cells have similar levels of phosphorylated myosin II light chain and only somewhat diminished adhesion strength. In contrast to A7 cells, the stiffness and contractility of M2 cells are insensitive to either myosin-inhibiting drugs or the stiffness of the substratum. Surprisingly, however, filamin A is not required for passive stiffening under large external forces.

The temperature dependence of cell mechanics measured by atomic force microscopy

The cytoskeleton is a complex polymer network that regulates the structural stability of living cells. Although the cytoskeleton plays a key role in many important cell functions, the mechanisms that regulate its mechanical behaviour are poorly understood. Potential mechanisms include the entropic elasticity of cytoskeletal filaments, glassy-like inelastic rearrangements of cross-linking proteins and the activity of contractile molecular motors that sets the tensional stress (prestress) borne by the cytoskeleton filaments. The contribution of these mechanisms can be assessed by studying how cell mechanics depends on temperature. The aim of this work was to elucidate the effect of temperature on cell mechanics using atomic force microscopy. We measured the complex shear modulus (G*) of human alveolar epithelial cells over a wide frequency range (0.1-25.6 Hz) at different temperatures (13-37 degrees C). In addition, we probed cell prestress by mapping the contractile forces that cells exert on the substrate by means of traction microscopy. To assess the role of actomyosin contraction in the temperature-induced changes in G* and cell prestress, we inhibited the Rho kinase pathway of the myosin light chain phosphorylation with Y-27632. Our results show that with increasing temperature, cells become stiffer and more solid-like. Cell prestress also increases with temperature. Inhibiting actomyosin contraction attenuated the temperature dependence of G* and prestress. We conclude that the dependence of cell mechanics with temperature is dominated by the contractile activity of molecular motors.

Universal behavior of the osmotically compressed cell and its analogy to the colloidal glass transition

Mechanical robustness of the cell under different modes of stress and deformation is essential to its survival and function. Under tension, mechanical rigidity is provided by the cytoskeletal network; with increasing stress, this network stiffens, providing increased resistance to deformation. However, a cell must also resist compression, which will inevitably occur whenever cell volume is decreased during such biologically important processes as anhydrobiosis and apoptosis. Under compression, individual filaments can buckle, thereby reducing the stiffness and weakening the cytoskeletal network. However, the intracellular space is crowded with macromolecules and organelles that can resist compression. A simple picture describing their behavior is that of colloidal particles; colloids exhibit a sharp increase in viscosity with increasing volume fraction, ultimately undergoing a glass transition and becoming a solid. We investigate the consequences of these 2 competing effects and show that as a cell is compressed by hyperosmotic stress it becomes progressively more rigid. Although this stiffening behavior depends somewhat on cell type, starting conditions, molecular motors, and cytoskeletal contributions, its dependence on solid volume fraction is exponential in every instance. This universal behavior suggests that compression-induced weakening of the network is overwhelmed by crowding-induced stiffening of the cytoplasm. We also show that compression dramatically slows intracellular relaxation processes. The increase in stiffness, combined with the slowing of relaxation processes, is reminiscent of a glass transition of colloidal suspensions, but only when comprised of deformable particles. Our work provides a means to probe the physical nature of the cytoplasm under compression, and leads to results that are universal across cell type.

Effective-medium approach for stiff polymer networks with flexible cross-links

Recent experiments have demonstrated that the nonlinear elasticity of in vitro networks of the biopolymer actin is dramatically altered in the presence of a flexible cross-linker such as the abundant cytoskeletal protein filamin. The basic principles of such networks remain poorly understood. Here we describe an effective-medium theory of flexibly cross-linked stiff polymer networks. We argue that the response of the cross-links can be fully attributed to entropic stiffening, while softening due to domain unfolding can be ignored. The network is modeled as a collection of randomly oriented rods connected by flexible cross-links to an elastic continuum. This effective medium is treated in a linear elastic limit as well as in a more general framework, in which the medium self-consistently represents the nonlinear network behavior. This model predicts that the nonlinear elastic response sets in at strains proportional to cross-linker length and inversely proportional to filament length. Furthermore, we find that the differential modulus scales linearly with the stress in the stiffening regime. These results are in excellent agreement with bulk rheology data.

The compaction of gels by cells: a case of collective mechanical activity

To understand mechanotransduction, purely mechanical phenomena resulting from the crosstalk between contractile cells and their elastic surroundings must be distinguished from adaptive responses to mechanical cues. Here, we revisit the compaction of freely suspended collagen gels by embedded cells, where a small volume fraction of cells (osteoblasts and fibroblasts) compacts the surrounding matrix by two orders of magnitude. Combining micropatterning with time-lapse strain mapping, we find gel compaction to be crucially determined by mechanical aspects of the surrounding matrix. First, it is a boundary effect: the compaction propagates from the edges of the matrix into the bulk. Second, the stress imposed by the cells irreversibly compacts the matrix and renders it anisotropic as a consequence of its nonlinear mechanics and the boundary conditions. Third, cell polarization and alignment follow in time and seem to be a consequence of gel compaction, at odds with current mechanosensing conceptions. Finally, our observation of a threshold cell density shows gel compaction to be a cooperative effect, revealing a mechanical interaction between cells through the matrix. The intricate interplay between cell contractility and surrounding matrix mechanics provides an important organizing principle with implications for many physiological processes such as tissue development.

Freely relaxing polymers remember how they were straightened

The relaxation of initially straight semiflexible polymers has been discussed mainly with respect to the longest relaxation time. The biologically relevant nonequilibrium dynamics on shorter times is comparatively poorly understood, partly because "initially straight" can be realized in manifold ways. Combining Brownian dynamics simulations and systematic theory, we demonstrate how different experimental preparations give rise to specific short-time and universal long-time dynamics. We also discuss boundary effects and the onset of the stretch-coil transition.

Fibronectin in aging extracellular matrix fibrils is progressively unfolded by cells and elicits an enhanced rigidity response

While the mechanical properties of a substrate or engineered scaffold can govern numerous aspects of cell behavior, cells quickly start to assemble their own matrix and will ultimately respond to their self-made extracellular matrix (ECM) microenvironments. Using fluorescence resonance energy transfer (FRET), we detected major changes in the conformation of a constituent ECM protein, fibronectin (Fn), as cells fabricated a thick three-dimensional (3D) matrix over the course of three days. These data provide the first evidence that matrix maturation occurs and that aging is associated with increased stretching of fibronectin fibrils, which leads to at least partial unfolding of the secondary structure of individual protein modules. A comparison of the conformations of Fn in these 3D matrices with those constructed by cells on rigid and flexible polyacrylamide surfaces suggests that cells in maturing matrices experience a microenviroment of gradually increasing rigidity. In addition, further matrix stiffening is caused by active Fn fiber alignment parallel to the contractile axis of the elongated fibroblasts, a cell-driven effect previously described for other fibrillar matrices. The fibroblasts, therefore, not only cause matrix unfolding, but reciprocally respond to the altered Fn matrix properties by up-regulating their own rigidity response. Consequently, our data demonstrate for the first time that a matured and aged matrix has distinctly different physical and biochemical properties compared to a newly assembled matrix. This might allow cells to specifically recognise the age of a matrix.

Power-law creep behavior of a semiflexible chain

Rheological properties of adherent cells are essential for their physiological functions, and microrheological measurements on living cells have shown that their viscoelastic responses follow a weak power law over a wide range of time scales. This power law is also influenced by mechanical prestress borne by the cytoskeleton, suggesting that cytoskeletal prestress determines the cell's viscoelasticity, but the biophysical origins of this behavior are largely unknown. We have recently developed a stochastic two-dimensional model of an elastically joined chain that links the power-law rheology to the prestress. Here we use a similar approach to study the creep response of a prestressed three-dimensional elastically jointed chain as a viscoelastic model of semiflexible polymers that comprise the prestressed cytoskeletal lattice. Using a Monte Carlo based algorithm, we show that numerical simulations of the chain's creep behavior closely correspond to the behavior observed experimentally in living cells. The power-law creep behavior results from a finite-speed propagation of free energy from the chain's end points toward the center of the chain in response to an externally applied stretching force. The property that links the power law to the prestress is the chain's stiffening with increasing prestress, which originates from entropic and enthalpic contributions. These results indicate that the essential features of cellular rheology can be explained by the viscoelastic behaviors of individual semiflexible polymers of the cytoskeleton.

Mechanical properties of actin stress fibers in living cells

Actin stress fibers (SFs) play an important role in many cellular functions, including morphological stability, adhesion, and motility. Because of their central role in force transmission, it is important to characterize the mechanical properties of SFs. However, most of the existing studies focus on properties of whole cells or of actin filaments isolated outside cells. In this study, we explored the mechanical properties of individual SFs in living endothelial cells by nanoindentation using an atomic force microscope. Our results demonstrate the pivotal role of SF actomyosin contractile level on mechanical properties. In the same SF, decreasing contractile level with 10 microM blebbistatin decreased stiffness, whereas increasing contractile level with 2 nM calyculin A increased stiffness. Incrementally stretching and indenting SFs made it possible to determine stiffness as a function of strain level and demonstrated that SFs have nearly linear stress-stain properties in the baseline state but nonlinear properties at a lower contractile level. The stiffnesses of peripheral and central portions of the same SF, which were nearly the same in the baseline state, became markedly different after contractile level was increased with calyculin A. Because these results pertain to effects of interventions in the same SF in a living cell, they provide important new understanding about cell mechanics.

Nonlinear elasticity of composite networks of stiff biopolymers with flexible linkers

Motivated by recent experiments showing nonlinear elasticity of in vitro networks of the biopolymer actin cross-linked with filamin, we present an effective medium theory of flexibly cross-linked stiff polymer networks. We model such networks by randomly oriented elastic rods connected by flexible connectors to a surrounding elastic continuum, which self-consistently represents the behavior of the rest of the network. This model yields a crossover from a linear elastic regime to a highly nonlinear elastic regime that stiffens in a way quantitatively consistent with experiment.

Nonlinear mechanics of entangled F-actin solutions

Using a variety of different rheological approaches, we study the nonlinear shear response of purified entangled F-actin solutions. We show that the choice of the experimental protocol is crucial. Furthermore, a transition between stress hardening and weakening can be induced even in purely entangled solutions. This transition depends on various ambient and network parameters including temperature, buffer salt concentration, filament length and density.

Single cell mechanics: stress stiffening and kinematic hardening

Cell mechanical properties are fundamental to the organism but remain poorly understood. We report a comprehensive phenomenological framework for the complex rheology of single fibroblast cells: a superposition of elastic stiffening and viscoplastic kinematic hardening. Despite the complexity of the living cell, its mechanical properties can be cast into simple, well-defined rules. Our results reveal the key role of crosslink slippage in determining mechanical cell strength and robustness.

Constitutive modeling of the stress-strain behavior of F-actin filament networks

The central role of the cytoskeleton in both healthy and diseased cellular functions makes it a compelling subject for detailed three-dimensional (3D) micromechanical modeling. Microstructural features of the cytoskeleton govern the cell's mechanical behavior in many of the regulating cellular functions including cell division, adhesion, spreading, migration, contraction, and other mechanotransductive effects which influence biochemical processes. Actin microfilaments (AF) combine to form one of the predominant cytoskeletal networks important to these biological processes. Here, the AF cytoskeletal microstructure and stress-strain behavior is modeled via a microstructurally-informed continuum mechanics approach. The force-extension behavior of the individual filaments is captured using the MacKintosh derivation of the worm-like chain (WLC) constitutive relationship for short chains where a new and direct analytical expression for the filament force as a function of filament extension is developed in this paper. The filament force-extension behavior is then used in conjunction with the Arruda-Boyce eight-chain network model to capture the 3D multiaxial stress-strain behavior of the network. The resulting 3D cytoskeletal network constitutive model provides the ability to track microstructural stretch and orientation states during 3D macroscopic stretching conditions. The non-affine nature of the network model effectively accommodates the imposed macroscopic shear strain through filament rotation and a relatively small amount of filament stretch. These characteristics enable the network model, using physically realistic material properties, to capture the initial stiffness of the AF network as well as the nonlinear strain stiffening observed at large stresses. The network model predictions compare favorably with published microrheological data of in vitro AF networks.

Writhe distribution of stiff biopolymers

Motivated by the interest in the role of stiff polymers like actin in cellular processes and as components of biopolymer networks like the cytoskeleton, we present a statistical mechanical study of the twist elasticity of stiff polymers. We obtain simple, approximate analytical forms for the writhe distribution at zero applied force. We also derive simple analytical expressions for the torque-twist relation and discuss buckling of stiff polymers due to the applied torques. The theoretical predictions presented here can be tested against single-molecule experiments on neurofilaments and cytoskeletal filaments like actin and microtubules.

Mapping cell-matrix stresses during stretch reveals inelastic reorganization of the cytoskeleton

The mechanical properties of the living cell are intimately related to cell signaling biology through cytoskeletal tension. The tension borne by the cytoskeleton (CSK) is in part generated internally by the actomyosin machinery and externally by stretch. Here we studied how cytoskeletal tension is modified during stretch and the tensional changes undergone by the sites of cell-matrix interaction. To this end we developed a novel technique to map cell-matrix stresses during application of stretch. We found that cell-matrix stresses increased with imposition of stretch but dropped below baseline levels on stretch release. Inhibition of the actomyosin machinery resulted in a larger relative increase in CSK tension with stretch and in a smaller drop in tension after stretch release. Cell-matrix stress maps showed that the loci of cell adhesion initially bearing greater stress also exhibited larger drops in traction forces after stretch removal. Our results suggest that stretch partially disrupts the actin-myosin apparatus and the cytoskeletal structures that support the largest CSK tension. These findings indicate that cells use the mechanical energy injected by stretch to rapidly reorganize their structure and redistribute tension.

Computational analysis of adhesion force in the indentation of cells using atomic force microscopy

A mechanical model was developed to study the indentation of an atomic force microscopic (AFM) tip on a cell with adhesion mediated by receptor-ligand binding. The effects of indentation rate, indentation depth, indenter size, and the mechanical properties of cells on the adhesion force were investigated. It was found that the presence of adhesion between the cell and AFM tip may affect both the loading curve and unloading curve, which may in turn change the extracted elastic modulus values using the conventional indentation models. It was found that an increase in the receptor-ligand reaction rate may lead to a transition from a decrease of the maximum adhesion force with the indentation rate to an increase of the maximum adhesion force with the indentation rate. It was also found that factors such as indenter size, indentation depth, and cell mechanical properties influence the maximum adhesion force, and their corresponding underlying mechanisms were discussed.

Glass transition and rheological redundancy in F-actin solutions

The unique mechanical performance of animal cells and tissues is attributed mostly to their internal biopolymer meshworks. Its perplexing universality and robustness against structural modifications by drugs and mutations is an enigma in cell biology and provides formidable challenges to materials science. Recent investigations could pinpoint highly universal patterns in the soft glassy rheology and nonlinear elasticity of cells and reconstituted networks. Here, we report observations of a glass transition in semidilute F-actin solutions, which could hold the key to a unified explanation of these phenomena. Combining suitable rheological protocols with high-precision dynamic light scattering, we can establish a remarkable rheological redundancy and trace it back to a highly universal exponential stretching of the single-polymer relaxation spectrum of a "glassy wormlike chain." By exploiting the ensuing generalized time-temperature superposition principle, the time domain accessible to microrheometry can be extended by several orders of magnitude, thus opening promising new metrological opportunities.

Fibroblast adaptation and stiffness matching to soft elastic substrates

Many cell types alter their morphology and gene expression profile when grown on chemically equivalent surfaces with different rigidities. One expectation of this change in morphology and composition is that the cell's internal stiffness, governed by cytoskeletal assembly and production of internal stresses, will change as a function of substrate stiffness. Atomic force microscopy was used to measure the stiffness of fibroblasts grown on fibronectin-coated polyacrylamide gels of shear moduli varying between 500 and 40,000 Pa. Indentation measurements show that the cells' elastic moduli were equal to, or slightly lower than, those of their substrates for a range of soft gels and reached a saturating value at a substrate rigidity of 20 kPa. The amount of cross-linked F-actin sedimenting at low centrifugal force also increased with substrate stiffness. Together with enhanced actin polymerization and cross-linking, active contraction of the cytoskeleton can also modulate stiffness by exploiting the nonlinear elasticity of semiflexible biopolymer networks. These results suggest that within a range of stiffness spanning that of soft tissues, fibroblasts tune their internal stiffness to match that of their substrate, and modulation of cellular stiffness by the rigidity of the environment may be a mechanism used to direct cell migration and wound repair.

Elasticity of stiff biopolymers

We present a statistical mechanical study of stiff polymers, motivated by experiments on actin filaments and the considerable current interest in polymer networks. We obtain simple, approximate analytical forms for the force-extension relations and compare these with numerical treatments. We note the important role of boundary conditions in determining force-extension relations. The theoretical predictions presented here can be tested against single molecule experiments on neurofilaments and cytoskeletal filaments like actin and microtubules. Our work is motivated by the buckling of the cytoskeleton of a cell under compression, a phenomenon of interest to biology.

Cell mechanics: integrating cell responses to mechanical stimuli

Forces are increasingly recognized as major regulators of cell structure and function, and the mechanical properties of cells are essential to the mechanisms by which cells sense forces, transmit them to the cell interior or to other cells, and transduce them into chemical signals that impact a spectrum of cellular responses. Comparison of the mechanical properties of intact cells with those of the purified cytoskeletal biopolymers that are thought to dominate their elasticity reveal the extent to which the studies of purified systems can account for the mechanical properties of the much more heterogeneous and complex cell. This review summarizes selected aspects of current work on cell mechanics with an emphasis on the structures that are activated in cell-cell contacts, that regulate ion flow across the plasma membrane, and that may sense fluid flow that produces low levels of shear stress.

Mechano-coupling and regulation of contractility by the vinculin tail domain

Vinculin binds to multiple focal adhesion and cytoskeletal proteins and has been implicated in transmitting mechanical forces between the actin cytoskeleton and integrins or cadherins. It remains unclear to what extent the mechano-coupling function of vinculin also involves signaling mechanisms. We report the effect of vinculin and its head and tail domains on force transfer across cell adhesions and the generation of contractile forces. The creep modulus and the adhesion forces of F9 mouse embryonic carcinoma cells (wild-type), vinculin knock-out cells (vinculin −/−), and vinculin −/− cells expressing either the vinculin head domain, tail domain, or full-length vinculin (rescue) were measured using magnetic tweezers on fibronectin-coated super-paramagnetic beads. Forces of up to 10 nN were applied to the beads. Vinculin −/− cells and tail cells showed a slightly higher incidence of bead detachment at large forces. Compared to wild-type, cell stiffness was reduced in vinculin −/− and head cells and was restored in tail and rescue cells. In all cell lines, the cell stiffness increased by a factor of 1.3 for each doubling in force. The power-law exponent of the creep modulus was force-independent and did not differ between cell lines. Importantly, cell tractions due to contractile forces were suppressed markedly in vinculin −/− and head cells, whereas tail cells generated tractions similar to the wild-type and rescue cells. These data demonstrate that vinculin contributes to the mechanical stability under large external forces by regulating contractile stress generation. Furthermore, the regulatory function resides in the tail domain of vinculin containing the paxillin-binding site.

Mechanical properties of axons

The mechanical response of PC12 neurites under tension is investigated using a microneedle technique. Elastic response, viscoelastic relaxation, and active contraction are observed. The mechanical model proposed by Dennerll et al. [J. Cell Biol. 109, 3073 (1989).10.1083/jcb.109.6.3073], which involves three mechanical devices--a stiff spring kappa coupled with a Voigt element that includes a less stiff spring k and a dashpot gamma--has been improved by adding a new element to describe the main features of the contraction of axons. This element, which represents the action of molecular motors, acts in parallel with viscous forces defining a global tension response of axons T against elongation rates delta(k). Under certain conditions, axons show a transition from a viscoelastic elongation to active contraction, suggesting the presence of a negative elongation rate sensitivity in the curve T vs delta(k).

3D finite element analysis of uniaxial cell stretching: from image to insight

Mechanical forces play an important role in many microbiological phenomena such as embryogenesis, regeneration, cell proliferation and differentiation. Micromanipulation of cells in a controlled environment is a widely used approach for understanding cellular responses with respect to external mechanical forces. While modern micromanipulation and imaging techniques provide useful optical information about the change of overall cell contours under the impact of external loads, the intrinsic mechanisms of energy and signal propagation throughout the cell structure are usually not accessible by direct observation. This work deals with the computational modelling and simulation of intracellular strain state of uniaxially stretched cells captured in a series of images. A nonlinear elastic finite element method on tetrahedral grids was applied for numerical analysis of inhomogeneous stretching of a rat embryonic fibroblast 52 (REF 52) using a simplified two-component model of a eukaryotic cell consisting of a stiffer nucleus surrounded by a softer cytoplasm. The difference between simulated and experimentally observed cell contours is used as a feedback criterion for iterative estimation of canonical material parameters of the two-component model such as stiffness and compressibility. Analysis of comparative simulations with varying material parameters shows that (i) the ratio between the stiffness of cell nucleus and cytoplasm determines intracellular strain distribution and (ii) large deformations result in increased stiffness and decreased compressibility of the cell cytoplasm. The proposed model is able to reproduce the evolution of the cellular shape over a sequence of observed deformations and provides complementary information for a better understanding of mechanical cell response.

Nonlinear mechanics of soft fibrous networks

Mechanical networks of fibres arise on a range of scales in nature and technology, from the cytoskeleton of a cell to blood clots, from textiles and felts to skin and collageneous tissues. Their collective response is dependent on the individual response of the constituent filaments as well as density, topology and order in the network. Here, we use the example of a low-density synthetic felt of athermal filaments to study the generic features of the mechanical response of such networks including strain stiffening and large effective Poisson ratios. A simple microscopic model allows us to explain these features of our observations, and provides us with a baseline framework to understand active biomechanical networks.

Cellular chemomechanics at interfaces: sensing, integration and response

Living cells are complex entities whose remarkable, emergent capacity to sense, integrate, and respond to environmental cues relies on an intricate series of interactions among the cell's macromolecular components. Defects in mechanosensing, transduction,or responses underlie many diseases such as cancers, immune disorders, cardiac hypertrophy, genetic malformations, and neuropathies. Here, we highlight micro- and nanotechnology-based tools that have been used to study how chemical and mechanical cues modulate the responses of single cells in contact with the extracellular environment. Understanding the physical aspects of these complex processes at the micro- and nanometer scale could produce profound and fundamental new insights into how the processes of cell migration, metastasis, immune function and other areas which are regulated by mechanical forces.

Soft biological materials and their impact on cell function

Most organs and biological tissues are soft viscoelastic materials with elastic moduli ranging from on the order of 100 Pa for the brain to 100 000 Pa for soft cartilage. Biocompatible synthetic materials already have many applications, but combining chemical compatibility with physiologically appropriate mechanical properties will increase their potential for use both as implants and as substrates for tissue engineering. Understanding and controlling mechanical properties, specifically softness, is important for appropriate physiological function in numerous contexts. The mechanical properties of the substrate on which, or within which, cells are placed can have as large an impact as chemical stimuli on cell morphology, differentiation, motility, and commitment to live or die.

Soft matters in cell adhesion: rigidity sensing on soft elastic substrates

This contribution highlights recent advances in our understanding of the relation between soft matter and biological systems. We first discuss the physical scales of living cells which follow from simple scaling arguments developed in soft matter physics. Then we discuss the way cells sense and react to extracellular stiffness as revealed by recent experiments with soft elastic substrates. Theoretical modelling allows addressing of the physical basis of the underlying mechanotransduction processes and its consequences for the organization of single cells and cell communities in soft environments. In the future, these efforts will also lead to an improved understanding of physiological and artificial tissue.

The cell as a material

To elucidate the dynamic and functional role of a cell within the tissue it belongs to, it is essential to understand its material properties. The cell is a viscoelastic material with highly unusual properties. Measurements of the mechanical behavior of cells are beginning to probe the contribution of constituent components to cell mechanics. Reconstituted cytoskeletal protein networks have been shown to mimic many aspects of the mechanical properties of cells, providing new insight into the origin of cellular behavior. These networks are highly nonlinear, with an elastic modulus that depends sensitively on applied stress. Theories can account for some of the measured properties, but a complete model remains elusive.

Cell dynamic adhesion and elastic properties probed with cylindrical atomic force microscopy cantilever tips

Cell adhesion is required for essential biological functions such as migration, tissue formation and wound healing, and it is mediated by individual molecules that bind specifically to ligands on other cells or on the extracellular matrix. Atomic force microscopy (AFM) has been successfully used to measure cell adhesion at both single molecule and whole cell levels. However, the measurement of inherent cell adhesion properties requires a constant cell-probe contact area during indentation, a requirement which is not fulfilled in common pyramidal or spherical AFM tips. We developed a procedure using focused ion beam (FIB) technology by which we modified silicon pyramidal AFM cantilever tips to obtain flat-ended cylindrical tips with a constant and known area of contact. The tips were validated on elastic gels and living cells. Cylindrical tips showed a fairly linear force-indentation behaviour on both gels and cells for indentations >200 nm. Cylindrical tips coated with ligands were used to quantify inherent dynamic cell adhesion and elastic properties. Force, work of adhesion and elasticity showed a marked dynamic response. In contrast, the deformation applied to the cells before rupture was fairly constant within the probed dynamic range. Taken together, these results suggest that the dynamic adhesion strength is counterbalanced by the dynamic elastic response to keep a constant cell deformation regardless of the applied pulling rate.