The cell as a material

Active actin gels

The self-organization of actin filaments is a topic that links cell biology with condensed matter physics. In vitro assays allow precise manipulation of component mechanical and chemical properties, needed for rigorous tests of theoretical models. We review recent work on in vitro motility assays that documented emergence of ordered actin filament microdomains powered by myosin motor proteins at high filament densities. Motor and filament surface density and mechanochemical cycle kinetics are additional parameters under current investigation. Individual filament collisions have been studied in order to elucidate the emergent population behavior. Apolar, weak  interactions evidenced by local filament deformations during crossover events are attenuated at high motor densities. Theoretical analysis requires refinement of rigid rod filament models. In intact cells, accessory proteins modulate actin filament length, bundling or sliding and this gives rise to complex emergent structures and behaviors such as cell motility and chemotaxis. The development of generic, mechanical and biochemical frameworks with predictive power that link molecular properties with micro- and macroscopic phenomena seen in living cells requires dialogue between theoreticians and experimentalists.

Elastic moduli of living epithelial pancreatic cancer cells and their skeletonized keratin intermediate filament network

In simple epithelia, such as living epithelial pancreatic cancer cells (Panc-1), unusual amounts of keratin filaments can be found, which makes these cells an ideal model system to study the role of keratin for cell mechanical properties. In this work, the elastic moduli of Panc-1 cells and their extracted in-situ subcellular keratin intermediate filament network are determined and compared with each other. For this, the living adherent cells and their extracted keratin network were probed with local quasistatic indentation testing during large deformations using the Atomic Force Microscope (AFM). We determined the elastic modulus of the skeletonized but structurally intact keratin network to be in the order of 10 Pa, while the living cell elastic modulus ranged from 100 to 500 Pa. By removing microfilaments, microtubules, membranes and soluble cytoplasmic components during keratin network extraction, we excluded effects caused by crosslinking with other filamentous fibers and from the viscosity of the cytoplasm. Thus, the determined elastic modulus equals the actual elastic modulus inherent to such a keratin filamentous network. In our assessment of the effective mechanical contribution of the architecturally intact, skeletonized keratin network to living cell mechanics, we come to the conclusion that it plays only a very limited role. Evidently, the quantitative dominance of keratin in these cells does not reflect a strong influence on determining the cell's elastic modulus. Instead, keratin like other filamentous structures in the cell's scaffolding, e.g., F-actin and microtubuli, is one part of a greater whole.

Nonlinear viscoelasticity of actin transiently cross-linked with mutant α-actinin-4

Filamentous actin and associated actin binding proteins play an essential role in governing the mechanical properties of eukaryotic cells. They can also play a critical role in disease; for example, mutations in α-actinin-4 (Actn4), a dynamic actin cross-linking protein, cause proteinuric disease in humans and mice. Amino acid substitutions strongly affect the binding affinity and protein structure of Actn4. To study the physical impact of such substitutions on the underlying cytoskeletal network, we examine the bulk mechanical behavior of in vitro actin networks cross-linked with wild-type and mutant Actn4. These networks exhibit a complex viscoelastic response and are characterized by fluid-like behavior at the longest timescales, a feature that can be quantitatively accounted for through a model governed by dynamic cross-linking. The elastic behavior of the network is highly nonlinear, becoming much stiffer with applied stress. This nonlinear elastic response is also highly sensitive to the mutations of Actn4. In particular, we observe that actin networks cross-linked with Actn4 bearing the disease-causing K255E mutation are more brittle, with a lower breaking stress in comparison to networks cross-linked with wild-type Actn4. Furthermore, a mutation that ablates the first actin binding site (ABS1) in Actn4 abrogates the network's ability to stress-stiffen is standard nomenclature. These changes in the mechanical properties of actin networks cross-linked with mutant Actn4 may represent physical determinants of the underlying disease mechanism in inherited focal segmental glomerulosclerosis.

Force estimation and prediction from time-varying density images

We present methods for estimating forces which drive motion observed in density image sequences. Using these forces, we also present methods for predicting velocity and density evolution. To do this, we formulate and apply a Minimum Energy Flow (MEF) method which is capable of estimating both incompressible and compressible flows from time-varying density images. Both the MEF and force-estimation techniques are applied to experimentally obtained density images, spanning spatial scales from micrometers to several kilometers. Using density image sequences describing cell splitting, for example, we show that cell division is driven by gradients in apparent pressure within a cell. Using density image sequences of fish shoals, we also quantify 1) intershoal dynamics such as coalescence of fish groups over tens of kilometers, 2) fish mass flow between different parts of a large shoal, and 3) the stresses acting on large fish shoals.

High- and low-frequency mechanical properties of living starfish oocytes

We studied the mechanical properties of living starfish oocytes belonging to two species, Astropecten Auranciacus and Asterina pectinifera, over a wide range of timescales. We monitored the Brownian motion of microspheres injected in the cytoplasm using laser particle-tracking (LPT) and video multiple-particle-tracking (MPT) techniques, to explore high- and low-frequency response ranges, respectively. The analysis of the mean-square-displacements (MSD) allowed us to characterize the samples on different timescales. The MSD behavior is explained by three power-law exponents: for short times (τ < 1 ms) it reflects the semiflexible behavior of the actin network; for intermediate timescales (1 ms < τ < 1 s) it is similar to that of a soft-glass material; finally for long times (τ > 1 s) it behaves mainly like a viscous medium. We computed and compared the viscoelastic moduli using a recently proposed model describing the frequency response of the cell material. The large fluctuations found in the MSD over hundreds of trajectories indicate and confirm the significant cytoplasm heterogeneity.

Cooperative crosslink (un)binding in slowly driven bundles of semiflexible filaments

Combining simulations and theory I study the interplay between bundle elastic degrees of freedom and crosslink binding propensity. By slowly driving bundles into a deformed configuration, and depending on the mechanical stiffness of the crosslinking agent, the binding affinity is shown to display a sudden and discontinuous drop. This indicates a cooperative unbinding process that involves the crossing of a free-energy barrier. Choosing the proper crosslinker therefore not only allows us to change the composite elastic properties of the bundle but also the relevant time scales which can be tuned from the single crosslink binding rate to the much longer escape time over the free-energy barrier.

Imaging techniques for measuring the materials properties of cells

The “materials properties” of a biological material include its composition and microscopic structure and the relationship between its structure and its mechanical properties. For living cells, the motor-driven internal motion also significantly impacts the properties, even independently of any remodeling of the cell structure that can occur. These materials properties dictate the passive mechanical response of the material to an applied force. The mechanical properties of cells and tissues are essential for their function and health and affect how cells actively respond to mechanical force in important biological processes, ranging from motility to differentiation and morphogenesis. The mechanical properties of bulk tissues can be determined by traditional rheological techniques that measure the force required to stretch, compress, or shear macroscopic tissue. However, individual cells are too small to be measured by such methods and have highly heterogeneous structures; thus techniques are required that can probe soft materials at the micrometer scale. A variety of microrheological techniques, developed to determine the materials properties of cells, reveal that living cells have materials properties that are quite unusual compared with common inert materials. Cells are active, nonequilibrium materials with a highly nonlinear elasticity. This article presents a subset of microrheological techniques that involve optical imaging of micrometer-sized probes on or within individual cells, describes how to analyze probe motions, and discusses limitations of the techniques.

Highly nonlinear dynamics in a slowly sedimenting colloidal gel

We use a combination of original light scattering techniques and particles with unique optical properties to investigate the behavior of suspensions of attractive colloids under gravitational stress, following over time the concentration profile, the velocity profile, and the microscopic dynamics. During the compression regime, the sedimentation velocity grows nearly linearly with height, implying that the gel settling may be fully described by a (time-dependent) strain rate. We find that the microscopic dynamics exhibit remarkable scaling properties when time is normalized by the strain rate, showing that the gel microscopic restructuring is dominated by its macroscopic deformation.

Slow dynamics and internal stress relaxation in bundled cytoskeletal networks

Crosslinked and bundled actin filaments form networks that are essential for the mechanical properties of living cells. Reconstituted actin networks have been extensively studied not only as a model system for the cytoskeleton, but also to understand the interplay between microscopic structure and macroscopic viscoelastic properties of network-forming soft materials. These constitute a broad class of materials with countless applications in science and industry. So far, it has been widely assumed that reconstituted actin networks represent equilibrium structures. Here, we show that fully polymerized actin/fascin bundle networks exhibit surprising age-dependent changes in their viscoelastic properties and spontaneous dynamics, a feature strongly reminiscent of out-of-equilibrium, or glassy, soft materials. Using a combination of rheology, confocal microscopy and space-resolved dynamic light scattering, we demonstrate that actin networks build up stress during their formation and then slowly relax towards equilibrium owing to the unbinding dynamics of the crosslinking molecules.

Internal stresses, normal modes, and nonaffinity in three-dimensional biopolymer networks

We numerically investigate deformations and modes of networks of semiflexible biopolymers as a function of crosslink coordination number z and strength of bending and stretching energies. In equilibrium filaments are under internal stress, and the networks exhibit shear rigidity below the Maxwell isostatic point. In contrast to two-dimensional networks, ours exhibit nonaffine bending-dominated response in all rigid states, including those near the maximum of z=4 when bending energies are less than stretching ones.

Hydrophobic nanopillars initiate mesenchymal stem cell aggregation and osteo-differentiation

Surface engineering approaches that alter the physical topography of a substrate could be used as an effective tool and as an alternative to biochemical means of directing stem cell interactions and their subsequent differentiation. In this paper we compare hydrophobic micro- vs. nanopillar type fabrication techniques for probing mesenchymal stem cell (MSC) interaction with the surface physical environment. The roles played by the topography of the nanopillar in particular influenced MSC growth and allowed for regulatory control of the stem cell fate. The nanopillar induced large 3-D cell aggregates to form on the surface which had up-regulated osteogenic specific matrix components. The ability to control MSC differentiation, using only the topographical factors, has a profound effect on both MSC biology and tissue engineering. This study aims to highlight the importance of the physical material carrier in stem cell based tissue engineering schemes.

Rupture of plasma membrane under tension

We present a study on the rupture behavior of single NIH 3T3 mouse fibroblasts under tension using micropipette aspiration. Membrane rupture was characterized by breaking and formation of an enclosed membrane linked to a tether at the cell apex. Three different rupture modes, namely: single break, initial multiple breaks, and continuous multiple breaks, were observed under similar loading condition. The measured mean tensile strengths of plasma membrane were 3.83 ± 1.94 and 3.98 ± 1.54mN/m for control cells and cells labeled with TubulinTracker, respectively. The tensile strength data was described by Weibull distribution. For the control cells, the Weibull modulus and characteristic strength were 1.86 and 4.40 mN/m, respectively; for cells labeled with TubulinTracker, the Weibull modulus and characteristic strength were 2.68 and 4.48 mN/m, respectively. Based on the experimental data, the estimated average transmembrane proteins-lipid cleavage strength was 2.64 ± 0.64 mN/m. From the random sampling of volume ratio of transmembrane proteins in cell membrane, we concluded that the Weibull characteristic of plasma membrane strength was likely to be originated from the variation in transmembrane proteins-lipid interactions.

Local rheology of human neutrophils investigated using atomic force microscopy

During the immune response, neutrophils display localized mechanical events by interacting with their environment through the micro-vascular transit, trans-endothelial, and trans-epithelial migration. Nano-mechanical studies of human neutrophils on localized nano-domains could provide the essential information for understanding their immune responsive functions. Using the Atomic Force Microscopy (AFM)-based micro-rheology, we have investigated rheological properties of the adherent human neutrophils on local nano-domains. We have applied the modified Hertz model to obtain the viscoelastic moduli from the relatively thick body regions of the neutrophils. In addition, by using more advanced models to account for the substrate effects, we have successfully characterized the rheological properties of the thin leading and tail regions as well. We found a regional difference in the mechanical compliances of the adherent neutrophils. The central regions of neutrophils were significantly stiffer (1,548 ± 871 Pa) than the regions closer to the leading edge (686 ± 801 Pa), while the leading edge and the tail (494 ± 537 Pa) regions were mechanically indistinguishable. The frequency-dependent elastic and viscous moduli also display a similar regional difference. Over the studied frequency range (100 to 300 Hz), the complex viscoelastic moduli display the partial rubber plateau behavior where the elastic moduli are greater than the viscous moduli for a given frequency. The non-disparaging viscous modulus indicates that the neutrophils display a viscoelastic dynamic behavior rather than a perfect elastic behavior like polymer gels. In addition, we found no regional difference in the structural damping coefficient between the leading edge and the cell body. Thus, we conclude that despite the lower loss and storage moduli, the leading edges of the human neutrophils display partially elastic properties similar to the cell body. These results suggest that the lower elastic moduli in the leading edges are more favorable for the elastic fluctuation of actin filaments, which supports the polymerization of the actin filaments leading to the active protrusion during the immune response.

Force propagation and force generation in cells

Determining how forces are produced by and propagated through the cytoskeleton (CSK) of the cell is of great interest as dynamic processes of the CSK are intimately correlated with many molecular signaling pathways. We are presenting a novel approach for integrating measurements on cell elasticity, transcellular force propagation, and cellular force generation to obtain a comprehensive description of dynamic and mechanical properties of the CSK under force loading. This approach uses a combination of scanning force microscopy (SFM) and Total Internal Reflection Fluorescence (TIRF) microscopy. We apply well-defined loading schemes onto the apical cell membrane of fibroblasts using the SFM and simultaneously use TIRF microscopy to image the topography of the basal cell membrane. The locally distinct changes of shape and depth of the cytoskeletal imprints onto the basal membrane are interpreted as results of force propagation through the cytoplasm. This observation provides evidence for the tensegrity model and demonstrates the usefulness of our approach that does not depend on potentially disturbing marker compounds. We confirm that the actin network greatly determines cell stiffness and represents the substrate that mediates force transduction through the cytoplasm of the cell. The latter is an essential feature of tensegrity. Most importantly, our new finding that, both intact actin and microtubule networks are required for enabling the cell to produce work, can only be understood within the framework of the tensegrity model. We also provide, for the first time, a direct measurement of the cell's mechanical power output under compression at two femtowatts.

Dynamics and regulation of contractile actin-myosin networks in morphogenesis

Contractile actin-myosin networks generate forces that drive cell shape changes and tissue remodeling during development. These forces can also actively regulate cell signaling and behavior. Novel features of actin-myosin network dynamics, such as pulsed contractile behaviors and the regulation of myosin localization by tension, have been uncovered in recent studies of Drosophila. In vitro studies of single molecules and reconstituted protein networks reveal intrinsic properties of motor proteins and actin-myosin networks, while in vivo studies have provided insight into the regulation of their dynamics and organization. Analysis of the complex behaviors of actin-myosin networks will be crucial for understanding force generation in actively remodeling cells and the coordination of cell shape and movement at the tissue level.

Frequency-dependent stiffening of semiflexible networks: a dynamical nonaffine to affine transition

By combining the force-extension relation of single semiflexible polymers with a Langevin equation to capture the dissipative dynamics of chains moving through a viscous medium we study the dynamical response of cross-linked biopolymer materials. We find that at low frequencies the network deformations are highly nonaffine, and show a low plateau in the modulus. At higher frequencies, this nonaffinity decreases while the elastic modulus increases. With increasing frequency, more and more nonaffine network relaxation modes are suppressed, resulting in a stiffening. This effect is fundamentally different from the high-frequency stiffening due to the single-filament relaxation modes [F. Gittes and F. C. MacKintosh, Phys. Rev. E 58, R1241 (1998)], not only in terms of its mechanism but also in its resultant scaling: G'(ω) ∼ ω(α) with α > 3/4. This may determine nonlinear material properties at low, physiologically relevant frequencies.

Energy distribution in disordered elastic networks

Disordered networks are found in many natural and artificial materials, from gels or cytoskeletal structures to metallic foams or bones. Here, the energy distribution in this type of networks is modeled, taking into account the orientation of the struts. A correlation between the orientation and the energy per unit volume is found and described as a function of the connectivity in the network and the relative bending stiffness of the struts. If one or both parameters have relatively large values, the struts aligned in the loading direction present the highest values of energy. On the contrary, if these have relatively small values, the highest values of energy can be reached in the struts oriented transversally. This result allows explaining in a simple way remodeling processes in biological materials, for example, the remodeling of trabecular bone and the reorganization in the cytoskeleton. Additionally, the correlation between the orientation, the affinity, and the bending-stretching ratio in the network is discussed.

Spatial organization acts on cell signaling: how physical force contributes to the development of cancer

Cells constantly encounter physical forces and respond to neighbors and circulating factors by triggering intracellular signaling cascades that in turn affect their behavior. The mechanisms by which cells transduce mechanical signals to downstream biochemical changes are not well understood. In their work, Salaita and coworkers show that the spatial organization of cell surface receptors is crucial for mechanotransduction. Consequently, force modulation that disrupts the mechanochemical coupling may represent a critical step in cancerogenesis.

The how, when, and why of the aging signals appearing on the human erythrocyte membrane: an atomic force microscopy study of surface roughness

We recently developed an atomic force microscopy-based protocol to use the roughness of the plasma membrane of erythrocytes (red blood cells, RBCs) as a morphological parameter, independently from the cell shape, to investigate the membrane-skeleton integrity in healthy and pathological cells. Here we apply the method to investigate a complex physiological phenomenon, the RBCs aging, that plays a major role in the regulation of the RBCs' turnover. The aging, monitored morphologically and biochemically, has been accelerated and modulated by preventing oxidative stresses as well as the effects of proteases and divalent cations, and by artificially consuming the intracellular adenosine triphosphate. The collected data evidence that the progression of aging causes a drastic decrease of the measured roughness that is diagnostic of a progressive, adenosine triphosphate-dependent alteration of the membrane-skeleton properties. Finally, the degree of reversibility of such effects has been investigated as a function of aging time, enabling the detection of irreversible transformation in the RBCs' structure and metabolism.

Tube width fluctuations in F-actin solutions

We determine the statistics of the local tube width in F-actin solutions, beyond the usually reported mean value. Our experimental observations are explained by a segment fluid theory based on the binary collision approximation. In this systematic generalization of the standard mean-field approach, effective polymer segments interact via a potential representing the topological constraints. The analytically predicted universal tube width distribution with a stretched tail is in good agreement with the data.

Bipedal locomotion in crawling cells

Many complex cellular processes from mitosis to cell motility depend on the ability of the cytoskeleton to generate force. Force-generating systems that act on elastic cytoskeletal elements are prone to oscillating instabilities. In this work, we have measured spontaneous shape and movement oscillations in motile fish epithelial keratocytes. In persistently polarized, fan-shaped cells, retraction of the trailing edge on one side of the cell body is out of phase with retraction on the other side, resulting in periodic lateral oscillation of the cell body. We present a physical description of keratocyte oscillation in which periodic retraction of the trailing edge is the result of elastic coupling with the leading edge. Consistent with the predictions of this model, the observed frequency of oscillation correlates with cell speed. In addition, decreasing the strength of adhesion to the substrate reduces the elastic force required for retraction, causing cells to oscillate with higher frequency at relatively lower speeds. These results demonstrate that simple elastic coupling between movement at the front of the cell and movement at the rear can generate large-scale mechanical integration of cell behavior.

Myosin VI: an innovative motor that challenged the swinging lever arm hypothesis

The swinging crossbridge hypothesis states that energy from ATP hydrolysis is transduced to mechanical movement of the myosin head while bound to actin. The light chain-binding region of myosin is thought to act as a lever arm that amplifies movements near the catalytic site. This model has been challenged by findings that myosin VI takes larger steps along actin filaments than early interpretations of its structure seem to allow. We now know that myosin VI does indeed operate by an unusual approximately 180 degrees lever arm swing and achieves its large step size using special structural features in its tail domain.

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.

Multiple-Particle-Tracking to investigate viscoelastic properties in living cells

Cell mechanical properties play an important role in determining many cellular activities. Passive microrheology techniques, such as Multiple-Particle-Tracking (MPT) give an insight into the structural rearrangements and viscoelastic response of a wide range of materials, in particular soft materials and complex fluids like cell cytoplasm in living cells. The technique finds an important field of application in large cells such as oocytes where, during their growth, several organelles and molecules are displaced in specific territories of the cell instrumental for later embryonic development. To measure cell mechanics, cells are usually deformed by many techniques that are slow and often invasive. To overcome these limits, the MPT technique is applied. Probe particles are embedded in the viscoelastic sample and their properties are extracted from the thermal fluctuation spectra measured using digital video-microscopy. The Brownian motion of a probe particle immersed in a network is directly related to the network's mechanical properties. Particles exhibit larger motions when their local environments are less rigid or less viscous. The mean-square-displacement (MSD) of the particle's trajectory is used to quantify its amplitude of motions over different time scales.

The regulation of stem cell differentiation by cell-cell contact on micropatterned material surfaces

Using the material technique recently developed by us, we prepared a micropattern on poly(ethylene glycol) (PEG) hydrogel to keep background resistant to cell adhesion for a long time, which made examination of differentiation of localized stem cells available. Our micropattern designed in this paper prevented or ensured contact between cells adhering in arginine-glycine-aspartic acid (RGD) microdomains, and thus afforded a unique way to study the effects of cell-cell contact on the lineage differentiation of stem cells while ruling out the interference of soluble factors or cell seeding concentration etc. As demonstration, mesenchymal stem cells derived from rats were examined in this study, and both osteogenic and adipogenic differentiations were found to be regulated by cell-cell contact. Isolated cells exhibited less significant differentiation than paired or aggregated cells. For those stem cells in contact, the extent of differentiation was fairly linearly related to the extent of contact characterized by coordination number. Additionally, we revealed the existence of some unknown cues besides gap junction responsible for such effects of cell-cell contact.

Mechanics of the F-actin cytoskeleton

Dynamic regulation of the filamentous actin (F-actin) cytoskeleton is critical to numerous physical cellular processes, including cell adhesion, migration and division. Each of these processes require precise regulation of cell shape and mechanical force generation which, to a large degree, is regulated by the dynamic mechanical behaviors of a diverse assortment of F-actin networks and bundles. In this review, we review the current understanding of the mechanics of F-actin networks and identify areas of further research needed to establish physical models. We first review our understanding of the mechanical behaviors of F-actin networks reconstituted in vitro, with a focus on the nonlinear mechanical response and behavior of "active" F-actin networks. We then explore the types of mechanical response measured of cytoskeletal F-actin networks and bundles formed in living cells and identify how these measurements correspond to those performed on reconstituted F-actin networks formed in vitro. Together, these approaches identify the challenges and opportunities in the study of living cytoskeletal matter.

Biomechanical and proteomic analysis of INF- beta-treated astrocytes

Astrocytes have a key role in the pathogenesis of several diseases including multiple sclerosis and were proposed as the designed target for immunotherapy. In this study we used atomic force microscopy (AFM) and proteomics methods to analyse and correlate the modifications induced in the viscoleastic properties of astrocytes to the changes induced in protein expression after interferon- beta (IFN-beta) treatment. Our results indicated that IFN-beta treatment resulted in a significant decrease in the Young's modulus, a measure of cell elasticity, in comparison with control cells. The molecular mechanisms that trigger these changes were investigated by 2DE (two-dimensional electrophoresis) and confocal analyses and confirmed by western blotting. Altered proteins were found to be involved in cytoskeleton organization and other important physiological processes.

Buckling, stiffening, and negative dissipation in the dynamics of a biopolymer in an active medium

We present a generic theory for the dynamics of a stiff filament under tension, in an active medium with orientational correlations, such as a microtubule in contractile actin. In sharp contrast to the case of a passive medium, we find the filament can stiffen, and possibly oscillate or buckle, depending on both the contractile or tensile nature of the activity and the filament-medium anchoring interaction. We also demonstrate a strong violation of the fluctuation-dissipation (FD) relation in the effective dynamics of the filament, including a negative FD ratio. Our approach is also of relevance to the dynamics of axons, and our model equations bear a remarkable formal similarity to those in recent work [Martin P, Hudspeth AJ, Juelicher F (2001) Proc Natl Acad Sci USA 98:14380-14385] on auditory hair cells. Detailed tests of our predictions can be made by using a single filament in actomyosin extracts or bacterial suspensions.

Cell mechanics: dissecting the physical responses of cells to force

It is now widely appreciated that normal tissue morphology and function rely upon cells' ability to sense and generate forces appropriate to their correct tissue context. Although the effects of forces on cells have been studied for decades, our understanding of how those forces propagate through and act on different cell substructures remains at an early stage. The past decade has seen a resurgence of interest, with a variety of different micromechanical methods in current use that probe cells' dynamic deformation in response to a time-varying force. The ability of researchers to carefully measure the mechanical properties of cells subjected to a variety of pharmacological and genetic interventions, however, currently outstrips our ability to quantitatively interpret the data in many cases. Despite these challenges, the stage is now set for the development of detailed models for cell deformability, motility, and mechanosensing that are rooted at the molecular level.

The impact of environmental changes upon the microrheological response of adherent cells

The mechanical behaviour of adherent cells cultured in vitro is known to be dependent on the mechanical properties of the substrate. We show that this mechanical behaviour is also strongly affected by the cells' environment. We focus here on the impact of temperature and pH. Experiments carried out on individual cells in a tuneable environment reveal that the intra-cellular mechanical behaviour exhibits large and fast changes when the external cell environment is changed. Fast passive microrheometry measurements allow for the precise characterisation of the transient regime observed during a temperature drop. When maintained at a non-physiological temperature, the cells reach a stabilised state distinct from the state observed in physiological conditions. The perturbation can be reversed but exhibits hysteretic behaviour when physiological conditions are restored. The transient regime observed during the recovery process is found to be different from the transient regime observed when leaving physiological conditions. A modified generalized Stokes-Einstein equation taking into account the cell activity through an effective temperature is proposed here to fit the experimental results. Excellent agreement between the model and the measurements is obtained for time lags from 10⁻³ to 1 s considered in this study.

Continuum model of epithelial morphogenesis during Caenorhabditis elegans embryonic elongation

The purpose of this work is to provide a biomechanical model to investigate the interplay between cellular structures and the mechanical force distribution during the elongation process of Caenorhabditis elegans embryos. Epithelial morphogenesis drives the elongation process of an ovoid embryo to become a worm-shaped embryo about four times longer and three times thinner. The overall anatomy of the embryo is modelled in the continuum mechanics framework from the structural organization of the subcellular filaments within epithelial cells. The constitutive relationships consider embryonic cells as homogeneous materials with an active behaviour, determined by the non-muscle myosin II molecular motor, and a passive viscoelastic response, related to the directional properties of the filament network inside cells. The axisymmetric elastic solution at equilibrium is derived by means of the incompressibility conditions, the continuity conditions for the overall embryo deformation and the balance principles for the embryonic cells. A particular analytical solution is proposed from a simplified geometry, demonstrating the mechanical role of the microtubule network within epithelial cells in redistributing the stress from a differential contraction of circumferentially oriented actin filaments. The theoretical predictions of the biomechanical model are discussed within the biological scenario proposed through genetic analysis and pharmacological experiments.

On the nature of biomaterials

The situations in which biomaterials are currently used are vastly different to those of just a decade ago. Although implantable medical devices are still immensely important, medical technologies now encompass a range of drug and gene delivery systems, tissue engineering and cell therapies, organ printing and cell patterning, nanotechnology based imaging and diagnostic systems and microelectronic devices. These technologies still encompass metals, ceramics and synthetic polymers, but also biopolymers, self assembled systems, nanoparticles, carbon nanotubes and quantum dots. These changes imply that our original concepts of biomaterials and our expectations of their performance also have to change. This Leading Opinion Paper addresses these issues. It concludes that many substances which hitherto we may not have thought of as biomaterials should now be considered as such so that, alongside the traditional structural biomaterials, we have substances that have been engineered to perform functions within health care where their performance is directly controlled by interactions with tissues and tissue components. These include engineered tissues, cells, organs and even viruses. This essay develops the arguments for a radically different definition of a biomaterial.

Structural and viscoelastic properties of actin/filamin networks: cross-linked versus bundled networks

The high diversity of cytoskeletal actin structures is accomplished by myriads of actin binding proteins (ABPs). Depending on its concentration, even a single type of ABP can induce different actin microstructures. Thus, for an overall understanding of the cytoskeleton, a detailed characterization of the cross-linker's effect on structural and mechanical properties of actin networks is required for each ABP. Using confocal microscopy and macrorheology, we investigate both cross-linked and bundled actin/filamin networks and compare their microstructures as well as their viscoelastic properties in the linear and the nonlinear regime.

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.

Computational analysis of viscoelastic properties of crosslinked actin networks

Mechanical force plays an important role in the physiology of eukaryotic cells whose dominant structural constituent is the actin cytoskeleton composed mainly of actin and actin crosslinking proteins (ACPs). Thus, knowledge of rheological properties of actin networks is crucial for understanding the mechanics and processes of cells. We used Brownian dynamics simulations to study the viscoelasticity of crosslinked actin networks. Two methods were employed, bulk rheology and segment-tracking rheology, where the former measures the stress in response to an applied shear strain, and the latter analyzes thermal fluctuations of individual actin segments of the network. It was demonstrated that the storage shear modulus (G') increases more by the addition of ACPs that form orthogonal crosslinks than by those that form parallel bundles. In networks with orthogonal crosslinks, as crosslink density increases, the power law exponent of G' as a function of the oscillation frequency decreases from 0.75, which reflects the transverse thermal motion of actin filaments, to near zero at low frequency. Under increasing prestrain, the network becomes more elastic, and three regimes of behavior are observed, each dominated by different mechanisms: bending of actin filaments, bending of ACPs, and at the highest prestrain tested (55%), stretching of actin filaments and ACPs. In the last case, only a small portion of actin filaments connected via highly stressed ACPs support the strain. We thus introduce the concept of a 'supportive framework,' as a subset of the full network, which is responsible for high elasticity. Notably, entropic effects due to thermal fluctuations appear to be important only at relatively low prestrains and when the average crosslinking distance is comparable to or greater than the persistence length of the filament. Taken together, our results suggest that viscoelasticity of the actin network is attributable to different mechanisms depending on the amount of prestrain.

Active biological materials

Cells make use of dynamic internal structures to control shape and create movement. By consuming energy to assemble into highly organized systems of interacting parts, these structures can generate force and resist compression, as well as adaptively change in response to their environment. Recent progress in reconstituting cytoskeletal structures in vitro has provided an opportunity to characterize the mechanics and dynamics of filament networks formed from purified proteins. Results indicate that a complex interplay between length scales and timescales underlies the mechanical responses of these systems and that energy consumption, as manifested in molecular motor activity and cytoskeletal filament growth, can drive transitions between distinct material states. This review discusses the basic characteristics of these active biological materials that set them apart from conventional materials and that create a rich array of unique behaviors.

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.

Germline P granules are liquid droplets that localize by controlled dissolution/condensation

In sexually reproducing organisms, embryos specify germ cells, which ultimately generate sperm and eggs. In Caenorhabditis elegans, the first germ cell is established when RNA and protein-rich P granules localize to the posterior of the one-cell embryo. Localization of P granules and their physical nature remain poorly understood. Here we show that P granules exhibit liquid-like behaviors, including fusion, dripping, and wetting, which we used to estimate their viscosity and surface tension. As with other liquids, P granules rapidly dissolved and condensed. Localization occurred by a biased increase in P granule condensation at the posterior. This process reflects a classic phase transition, in which polarity proteins vary the condensation point across the cell. Such phase transitions may represent a fundamental physicochemical mechanism for structuring the cytoplasm.

Desmin and vimentin intermediate filament networks: their viscoelastic properties investigated by mechanical rheometry

We have investigated the viscoelastic properties of the cytoplasmic intermediate filament (IF) proteins desmin and vimentin. Mechanical measurements were supported by time-dependent electron microscopy studies of the assembly process under similar conditions. Network formation starts within 2 min, but it takes more than 30 min until equilibrium mechanical network strength is reached. Filament bundling is more pronounced for desmin than for vimentin. Desmin filaments (persistence length l(p) approximately 900 nm) are stiffer than vimentin filaments (l(p) approximately 400 nm), but both IFs are much more flexible than microfilaments. The concentration dependence of the plateau modulus G(0) approximately c(alpha) is much weaker than predicted theoretically for networks of semiflexible filaments. This is more pronounced for vimentin (alpha=0.47) than for desmin (alpha=0.70). Both networks exhibit strain stiffening at large shear deformations. At the transition from linear to nonlinear viscoelastic response, only desmin shows characteristics of nonaffine network deformation. Strain stiffening and the maximum modulus occur at strain amplitudes about an order of magnitude larger than those for microfilaments. This is probably attributable to axial slippage within the tetramer building blocks of the IFs. Network deformation beyond a critical strain gamma(max) results in irreversible damage. Strain stiffening sets in at lower concentrations, is more pronounced, and is less sensitive to ionic strength for desmin than for vimentin. Hence, desmin exhibits strain stiffening even at low-salt concentrations, which is not observed for vimentin, and we conclude that the strength of electrostatic repulsion compared to the strength of attractive interactions forming the network junctions is significantly weaker for desmin than for vimentin filaments. These findings indicate that both IFs exhibit distinct mechanical properties that are adapted to their respective cellular surroundings [i.e., myocytes (desmin) and fibroblasts (vimentin)].