The bimodal role of filamin in controlling the architecture and mechanics of F-actin networks

Reconstituted actin filament networks have been used extensively to understand the mechanics of the actin cortex and decipher the role of actin cross-linking proteins in the maintenance and deformation of cell shape. However, studies of the mechanical role of the F-actin cross-linking protein filamin have led to seemingly contradictory conclusions, in part due to the use of ill-defined mechanical assays. Using quantitative rheological methods that avoid the pitfalls of previous studies, we systematically tested the complex mechanical response of reconstituted actin filament networks containing a wide range of filamin concentrations and compared the mechanical function of filamin with that of the cross-linking/bundling proteins alpha-actinin and fascin. At steady state and within a well defined linear regime of small non-destructive deformations, F-actin solutions behave as highly dynamic networks (actin polymers are still sufficiently mobile to relax the stress) below the cross-linking-to-bundling threshold filamin concentration, and they behave as covalently cross-linked gels above that threshold. Under large deformations, F-actin networks soften at low filamin concentrations and strain-harden at high filamin concentrations. Filamin cross-links F-actin into networks that are more resilient, stiffer, more solid-like, and less dynamic than alpha-actinin and fascin. These results resolve the controversy by showing that F-actin/filamin networks can adopt diametrically opposed rheological behaviors depending on the concentration in cross-linking proteins.     

Micro- and macrorheological properties of isotropically cross-linked actin networks

Cells make use of semiflexible biopolymers such as actin or intermediate filaments to control their local viscoelastic response by dynamically adjusting the concentration and type of cross-linking molecules. The microstructure of the resulting networks mainly determines their mechanical properties. It remains an important challenge to relate structural transitions to both the molecular properties of the cross-linking molecules and the mechanical response of the network. This can be achieved best by well defined in vitro model systems in combination with microscopic techniques. Here, we show that with increasing concentrations of the cross-linker heavy meromyosin, a transition in the mechanical network response occurs. At low cross-linker densities the network elasticity is dominated by the entanglement length l_e of the polymer, whereas at high heavy meromyosin densities the cross-linker distance l_c determines the elastic behavior. Using microrheology the formation of heterogeneous networks is observed at low cross-linker concentrations. Micro- and macrorheology both report the same transition to a homogeneous cross-linked phase. This transition is set by a constant average cross-linker distance l_c ≈ 15 μm. Thus, the micro- and macromechanical properties of isotropically cross-linked in vitro actin networks are determined by only one intrinsic network parameter.     

A master relation defines the nonlinear viscoelasticity of single fibroblasts

Cell mechanical functions such as locomotion, contraction, and division are controlled by the cytoskeleton, a dynamic biopolymer network whose mechanical properties remain poorly understood. We perform single-cell uniaxial stretching experiments on 3T3 fibroblasts. By superimposing small amplitude oscillations on a mechanically prestressed cell, we find a transition from linear viscoelastic behavior to power law stress stiffening. Data from different cells over several stress decades can be uniquely scaled to obtain a master relation between the viscoelastic moduli and the average force. Remarkably, this relation holds independently of deformation history, adhesion biochemistry, and intensity of active contraction. In particular, it is irrelevant whether force is actively generated by the cell or externally imposed by stretching. We propose that the master relation reflects the mechanical behavior of the force-bearing actin cytoskeleton, in agreement with stress stiffening known from semiflexible filament networks.     

Viscoelastic properties of plasticized methylcellulose and chemically crosslinked methylcellulose

Films of methylcellulose (MC), poly(ethylene glycol)400 (PEG400) plasticized MC, and MC gels (MC crosslinked with glutaraldehyde (GA)) were prepared by casting from aqueous solutions. The swelling test has shown that the MC gels were insoluble in water and that their crosslinking density increased with increasing GA and HCl concentrations. The effect of the addition of PEG400 or GA to MC was investigated through dynamic mechanical analysis (DMA). The DMA analysis of PEG400/MC blends has shown that PEG400 was compatible with MC and was an effective plasticizer since the curves of tan δ against temperature exhibited single peaks (corresponding to a single glass transition temperature), which were displaced to lower values with increasing PEG400 content. The thermogravimetric analysis (TGA) indicated that the thermal stability of MC was not affected by the chemical crosslinking. The tensile strength was slightly increased through crosslinking while the elongation was slightly decreased. The presence of moisture in MC hydrogels decreased the tensile strength and enhanced the elongation while the addition of PEG400 decreased the tensile strength but sharply increased the elongation.     

The viscoelastic properties of actin solutions

The viscoelastic properties in actin solutions were investigated by measuring their elastic modulus and viscous modulus using a rheometer. The polymerization/gelation process of actin solutions was accompanied by an increase of both parameters, indicating the formation of a protein network. High shear rotational motion destroyed this network which, however, would reanneal if left undisturbed. At 25 °C under low ionic strength conditions, the viscoelastic moduli of a Spudich-Watt globular (G) actin preparation increased with time, while G-actin, purified by gel filtration maintained low viscoelastic moduli. The rigidity of the filamentous (F) actin network in a solution of Spudich-Watt actin, measured by the elastic modulus, was somewhat lower than that of gel-filtration-purified actin at the same protein concentration. The crosslink density of these F-actin networks was estimated, using models from rubber elasticity theory. The calculated density was 1 crosslink/50 actin monomers for the purified actin and 1 crosslink/120 actin monomers for Spudich-Watt actin. The results are consistent with the idea that a small amount of regulatory factor(s), which could be removed by the gel filtration step, modulates the structure of an actin network.     

Interconversion of structural and contractile actin gels by insertion of myosin during assembly

Extracts of the soluble cytoplasmic proteins of the sea urchin egg form gels of different composition and properties depending on the temperature used to induce actin polymerization. At temperatures that inactivate myosin, a gel composed of actin, fascin, and a 220,000-mol- wt protein is formed. Fascin binds actin into highly organized units with a characteristic banding pattern, and these actin-fascin units are the structural core of the sea urchin microvilli formed after fertilization and of the urchin coelomocyte filopods. Under milder conditions a more complex myosin-containing gel is formed, which contracts to a small fraction of its original volume within an hour after formation. What has been called "structural" gel can be assembled by combining actin, fascin, and the 220,000-mol-wt protein in 50-100 mM KCl; the aim of the experiments reported here was to determine whether myosin could be included during assembly, thereby interconverting structural and contractile gel. This approach is limited by the aggregation of sea urchin myosin at the low salt concentrations utilized in gel assembly. A method has been devised for the sequential combination of these components under controlled KCl and ATP concentrations that allows the formation of a gel containing dispersed myosin at a final concentration of 60-100 mM KCl. These gels are stable at low (approximately 10 micron) ATP concentrations, but contract to a small volume in the presence of higher (approximately 100 micron) ATP. Contraction can be controlled by forming a stable gel at low ATP and then overlaying it with a solution containing sufficient ATP to induce contraction. This system may provide a useful model for the study of the interrelations between cytoplasmic structure and motility.     

Characterization of structure and properties of bone by spectral measure method

Novel mathematical method called spectral measure method (SMM) is developed for characterization of bone structure and indirect estimation of bone properties. The spectral measure method is based on an inverse homogenization technique which allows to derive information about the structure of composite material from measured effective electric or viscoelastic properties. The mechanical properties and ability to withstand fracture depend on the structural organization of bone as a hierarchical composite. Information about the bone structural parameters is contained in the spectral measure in the Stieltjes integral representation of the effective properties. The method is based on constructing the spectral measure either by calculating it directly from micro-CT images or using measurements of electric or viscoelastic properties over a frequency range. In the present paper, we generalize the Stieltjes representation to the viscoelastic case and show how bone microstructure, in particular, bone volume or porosity, can be characterized by the spectral function calculated using measurements of complex permittivity or viscoelastic modulus. For validation purposes, we numerically simulated measured data using micro-CT images of cancellous bone. Recovered values of bone porosity are in excellent agreement with true porosity estimated from the micro-CT images. We also discuss another application of this method, which allows to estimate properties difficult to measure directly. The spectral measure method based on the derived Stieltjes representation for viscoelastic composites, has a potential for non-invasive characterization of bone structure using electric or mechanical measurements. The method is applicable to sea ice, porous rock, and other composite materials.     

In Silico Reconstitution of Actin-Based Symmetry Breaking and Motility

Eukaryotic cells assemble viscoelastic networks of crosslinked actin filaments to control their shape, mechanical properties, and motility. One important class of actin network is nucleated by the Arp2/3 complex and drives both membrane protrusion at the leading edge of motile cells and intracellular motility of pathogens such as Listeria monocytogenes. These networks can be reconstituted in vitro from purified components to drive the motility of spherical micron-sized beads. An Elastic Gel model has been successful in explaining how these networks break symmetry, but how they produce directed motile force has been less clear. We have combined numerical simulations with in vitro experiments to reconstitute the behavior of these motile actin networks in silico using an Accumulative Particle-Spring (APS) model that builds on the Elastic Gel model, and demonstrates simple intuitive mechanisms for both symmetry breaking and sustained motility. The APS model explains observed transitions between smooth and pulsatile motion as well as subtle variations in network architecture caused by differences in geometry and conditions. Our findings also explain sideways symmetry breaking and motility of elongated beads, and show that elastic recoil, though important for symmetry breaking and pulsatile motion, is not necessary for smooth directional motility. The APS model demonstrates how a small number of viscoelastic network parameters and construction rules suffice to recapture the complex behavior of motile actin networks. The fact that the model not only mirrors our in vitro observations, but also makes novel predictions that we confirm by experiment, suggests that the model captures much of the essence of actin-based motility in this system.     

Acanthamoeba profilin affects the mechanical properties of nonfilamentous actin

We investigated the mechanical properties of two abundant, cytoplasmic proteins from Acanthamoeba, profilin and actin, and found that while both profilin and nonfilamentous actin alone behaved as solids, mixtures of the two proteins were viscoelastic liquids. When allowed to equilibrate, profilin formed a viscoelastic solid with mechanical properties similar to filamentous and nonfilamentous actin. Consequently, profilin itself may contribute significantly to the elasticity and viscosity of cytoplasm. The addition of profilin to nonfilamentous actin caused a phase transition from gel (viscoelastic solid) to sol (viscoelastic liquid) when the concentration of free actin became too low to form a gel. In contrast, profilin had little effect on the rigidity and viscosity of actin filaments. We speculate that nonfilamentous actin and profilin, both of which form shear-sensitive structures, can be modeled as flocculant materials. We conclude that profilin may regulate the rigidity (elasticity) of the cytoplasm not only by inhibiting polymerization of actin, but also by modulating the mechanical properties of nonfilamentous actin.     

Viscoelasticity of F-actin measured with magnetic microparticles

Dispersed submicroscopic magnetic particles were used to probe viscoelasticity for cytoplasm and purified components of cytoplasm. An externally applied magnetic field exerted force on particles in cells, in filamentous actin (F-actin) solutions, or in F-actin gels formed by the addition of the actin gelation factor, actin-binding protein (ABP). The particle response to magnetic torque can be related to the viscoelastic properties of the fluids. We compared data obtained on F-actin by the magnetic particle method with data obtained on F-actin by means of a sliding plane viscoelastometer. F-actin solutions had a significant elasticity, which increased by 20-fold when gels were formed by ABP addition. Both methods gave consistent results, but the dispersed magnetic particles indicated quantitatively greater rigidity than the viscoelastometer (two and six times greater for F-actin solutions and for F-actin plus ABP gels, respectively). These differences may be due to the fact that, compared with traditional microrheometers, dispersed particle measurements are less affected by long-range heterogeneity or domain-like structure. The magnetometric method was used to examine the mechanical properties of cytoplasm within intact macrophages; the application of the same magnetometric technique to both cells and well-defined, purified protein systems is a first step toward interpreting the results obtained for living cells in molecular terms. The magnetic particle probe system is an effective nonoptical technique for determining the motile and mechanical properties of cells in vitro and in vivo.     

Mechanical properties of actin

We used a cone and plate rheometer to evaluate the mechanical properties of actin over a wide range of oscillation frequencies and shear rates. Remarkably, both filamentous and nonfilamentous actin behaved as viscoelastic solids in both oscillatory and shear type experiments, providing that they were given ample time to equilibrate. Actin was purified by gel filtration from rabbit skeletal muscle and Acanthamoeba. Nonfilamentous actin in 2 different buffers had similar properties. In a low ionic strength buffer the absence of filaments was confirmed by electron microscopy, ultracentrifugation, and the fluorescence of pyrene-labeled actin. In 0.6 M KI, actin was monomeric by gel filtration. Filamentous actin had similar properties in 2 mM MgCl2 with either 50 mM KC1 or 500 mM KC1. Under all 4 of these conditions, actin required about 1000 min at 25 degrees C for the rheological properties to equilibrate. Under conditions where the oscillation of the rheometer did not affect the mechanical properties, all of the actin preparations had dynamic viscosities that were inverse functions of the frequency and dynamic elasticites that leveled off at low frequencies as expected for viscoelastic solids. For filamentous actin, the values of these parameters were about 2 times higher than for nonfilamentous actin. In shear experiments, both filamentous and nonfilamentous actin exhibited shear rate-dependent yield stresses. When filamentous and nonfilamentous actin structures were disrupted by transient shearing, the dynamic elasticity recovered to 90% in 30 min. Ovalbumin in the low ionic strength buffer also behaved as a viscoelastic material with elasticity and viscosity about 10 times lower than nonfilamentous actin, while cytochrome c behaved as a Newtonian fluid with a viscosity of 0.02 poise.     

Diffusing wave spectroscopy microrheology of actin filament networks.

Filamentous actin (F-actin), one of the constituents of the cytoskeleton, is believed to be the most important participant in the motion and mechanical integrity of eukaryotic cells. Traditionally, the viscoelastic moduli of F-actin networks have been measured by imposing a small mechanical strain and quantifying the resulting stress. The magnitude of the viscoelastic moduli, their concentration dependence and strain dependence, as well as the viscoelastic nature (solid-like or liquid-like) of networks of uncross-linked F-actin, have been the subjects of debate. Although this paper helps to resolve the debate and establishes the extent of the linear regime of F-actin networks' rheology, we report novel measurements of the high-frequency behavior of networks of F-actin, using a noninvasive light-scattering based technique, diffusing wave spectroscopy (DWS). Because no external strain is applied, our optical assay generates measurements of the mechanical properties of F-actin networks that avoid many ambiguities inherent in mechanical measurements. We observe that the elastic modulus has a small magnitude, no strain dependence, and a weak concentration dependence. Therefore, F-actin alone is not sufficient to generate the elastic modulus necessary to sustain the structural rigidity of most cells or support new cellular protrusions. Unlike previous studies, our measurements show that the mechanical properties of F-actin are highly dependent on the frequency content of the deformation. We show that the loss modulus unexpectedly dominates the elastic modulus at high frequencies, which are key for fast transitions. Finally, the measured mean square displacement of the optical probes, which is also generated by DWS measurements, offers new insight into the local bending fluctuations of the individual actin filaments and shows how they generate enhanced dissipation at short time scales.     

On the viscoelastic character of liver tissue: experiments and modelling of the linear behaviour

This paper presents the results of recent investigations into the viscoelastic character of liver tissue, especially the linear response. The linear domain of liver tissue has been determined by a strain sweep oscillation test. The fluid-like viscoelastic behaviour of liver tissue was confirmed by stress relaxation experiments. To demonstrate the consistency and quality of the experimental data, the relaxation spectrum was used to reconstruct the relaxation modulus, as well as the storage and loss moduli. The generalised Maxwell model was successfully employed to model the mechanical behaviour in the linear viscoelastic domain.     

Rheological and microstructural investigation of oat β-glucan isolates varying in molecular weight

The rheological properties and microstructure of aqueous oat β-glucan solutions varying in molecular weight were investigated. The structural features and molecular weights (MW) were characterized by ¹³C NMR spectroscopy and high performance size-exclusion chromatography (HPSEC), respectively. The microstructure of the β-glucans dispersions was also examined by atomic force microscopy (AFM). The samples with β-glucan content between 78 and 86% on a dry weight basis had MW, intrinsic viscosity ([η]) and critical concentration (c*) in the range of 142-2800 × 10³ g/mol, 1.7-7.2 dl/g and 0.25-1.10 g/dl, respectively. The flow and viscoelastic behaviour was highly dependent on MW and on the concentration of the β-glucans dispersions. Pseudoplastic behaviour was exhibited at high concentrations and Newtonian behaviour was evident at low concentrations. At the same concentration, the viscosity was higher for higher MW samples. The Cox-Merz rule was applicable for the lower molecular weight samples at higher concentrations whereas the high molecular weight sample deviated at concentrations greater than 1.0%, w/v. The mechanical spectra with variation of both MW and concentration were typical of entangled biopolymer solutions. AFM images revealed the formation of clusters or aggregates linked via individual polymer chains scattered heterogeneously throughout the system. The aggregate size increased with the molecular weight of the samples investigated and has been linked to the rheological behaviour of the samples.     

Hyaluronan concentration within a 3D collagen matrix modulates matrix viscoelasticity, but not fibroblast response

The use of 3D extracellular matrix (ECM) microenvironments to deliver growth-inductive signals for tissue repair and regeneration requires an understanding of the mechanisms of cell–ECM signaling. Recently, hyaluronic acid (HA) has been incorporated in collagen matrices in an attempt to recreate tissue specific microenvironments. However, it is not clear how HA alters biophysical properties (e.g. fibril microstructure and mechanical behavior) of collagen matrices or what impact these properties have on cell behavior. The present study determined the effects of varying high molecular weight HA concentration on 1) the assembly kinetics, fibril microstructure, and viscoelastic properties of 3D type I collagen matrices and 2) the response of human dermal fibroblasts, in terms of morphology, F-actin organization, contraction, and proliferation within the matrices. Results showed increasing HA concentration up to 1 mg/ml (HA:collagen ratio of 1:2) did not significantly alter fibril microstructure, but did significantly alter viscoelastic properties, specifically decreasing shear storage modulus and increasing compressive resistance. Interestingly, varied HA concentration did not significantly affect any of the measured fibroblast behaviors. These results show that HA-induced effects on collagen matrix viscoelastic properties result primarily from modulation of the interstitial fluid with no significant change to the fibril microstructure. Furthermore, the resulting biophysical changes to the matrix are not sufficient to modulate the cell–ECM mechanical force balance or proliferation of resident fibroblasts. These results provide new insight into the mechanisms by which cells sense and respond to microenvironmental cues and the use of HA in collagen-based biomaterials for tissue engineering.     

Stress-induced alignment of actin filaments and the mechanics of cytogel

Experimental evidence suggests that anisotropic stress induces alignment of intracellular actin filaments. We develop a model for this phenomenon, which includes a parameter reflecting the sensitivity of the microfilament network to changes in the stress field. When applied to a uniform cell sheet at rest, the model predicts that for sufficiently large values of the sensitivity parameter, all the actin filaments will spontaneously align in a single direction. Stress alignment can also be caused by a change in external conditions, and as an example of this we apply our model to the initial response of embryonic epidermis to wounding. Our solutions in this case are able to reflect the actin cable that has been found at the wound edge in recent experiments; the cable consists of microfilaments aligned with stress at the wound boundary of the epithelium. These applications suggest that stress-induced alignment of actin filaments could play a key role in some biological systems. This is the first attempt to include the alignment phenomenon in a mechanical model of cytogel.     

Polarization and Movement of Keratocytes: A Multiscale Modelling Approach

Eukariotic cell motility is a complex phenomenon, in which the cytoskeleton and its major constituent, actin, play an essential role. Actin forms polymers of long, stiff filaments that are cross-linked into an anisotropic network inside a thin sheet-like cellular protrusion, the lamellipod. At the leading edge of this structure, polymerization of actin filaments creates the force that pushes out the membrane and leads to translocation of a motile cell. Dynamics of the actin network account for changes in cell shape, crawling motion and turning of the cell in response to external cues. Regulating the dynamics of the cytoskeleton, and playing a central role in signal transduction in the cell, are Cdc42, Rac and Rho (GTPases of the rho family, collectively known as the small G-proteins) and the actin nucleating complex, Arp2/3.In this paper, we use a multiscale modelling approach in a 2D model of a motile cell. We describe the mutual interactions of the small G-proteins, and their effects on capping and side-branching of actin filaments. We incorporate the pushing exerted by oriented actin filament ends on the cell edge, and a Rho-dependent contraction force. Combining these biochemical and mechanical aspects, we investigate the dynamics of a model epidermal fish keratocyte through in silico experiments. Our model gives insight into how, in response to some cue, a cell can polarize, form a leading edge, and move; concomitantly it explains how a keratocyte cell can maintain its shape and polarity, even after removal of the initial stimulus, and how it can change direction quickly in response to changes in its environment. We show that establishment of polarity stems from interactions of Cdc42, Rac and Rho, while maintenance and robustness of polarity is due to the rapid cytosolic diffusion of the inactive (GDI-bound) forms of the small G-proteins. Our model produces a cell shape that closely resembles the keratocytes and correct speeds for biologically reasonable parameter values. Movies of the simulations can be obtained from http://theory.bio.uu.nl/stan/keratocyte.     

In situ chondrocyte viscoelasticity

It has been proposed, based on theoretical considerations, that the strain rate-dependent viscoelastic response of cartilage reduces local tissue and cell deformations during cyclic compressions. However, experimental studies have not addressed the in situ viscoelastic response of chondrocytes under static and dynamic loading conditions. In particular, results obtained from experimental studies using isolated chondrocytes embedded in gel constructs cannot be used to predict the intrinsic viscoelastic responses of chondrocytes in situ or in vivo. Therefore, the purpose of this study was to investigate the viscoelastic response of chondrocytes in their native environment under static and cyclic mechanical compression using a novel in situ experimental approach. Cartilage matrix and chondrocyte recovery in situ following mechanical compressions was highly viscoelastic. The observed in situ behavior was consistent with a previous study on in vivo chondrocyte mechanics which showed that it took 5-7min for chondrocytes to recover shape and volume following virtually instantaneous cell deformations during muscular loading of the knee in live mice. We conclude from these results that the viscoelastic properties of cartilage minimize chondrocyte deformations during cyclic dynamic loading as occurs, for example, in the lower limb joints during locomotion, thereby allowing the cells to reach mechanical and metabolic homeostasis even under highly dynamic loading conditions.     

Nonlinear viscoelastic characterization of bovine trabecular bone

The time-independent elastic properties of trabecular bone have been extensively investigated, and several stiffness–density relations have been proposed. Although it is recognized that trabecular bone exhibits time-dependent mechanical behaviour, a property of viscoelastic materials, the characterization of this behaviour has received limited attention. The objective of the present study was to investigate the time-dependent behaviour of bovine trabecular bone through a series of compressive creep–recovery experiments and to identify its nonlinear constitutive viscoelastic material parameters. Uniaxial compressive creep and recovery experiments at multiple loads were performed on cylindrical bovine trabecular bone samples (\(n = 19\)). Creep response was found to be significant and always comprised of recoverable and irrecoverable strains, even at low stress/strain levels. This response was also found to vary nonlinearly with applied stress. A systematic methodology was developed to separate recoverable (nonlinear viscoelastic) and irrecoverable (permanent) strains from the total experimental strain response. We found that Schapery’s nonlinear viscoelastic constitutive model describes the viscoelastic response of the trabecular bone, and parameters associated with this model were estimated from the multiple load creep–recovery (MLCR) experiments. Nonlinear viscoelastic recovery compliance was found to have a decreasing and then increasing trend with increasing stress level, indicating possible stiffening and softening behaviour of trabecular bone due to creep. The obtained parameters from MLCR tests, expressed as second-order polynomial functions of stress, showed a similar trend for all the samples, and also demonstrate stiffening–softening behaviour with increasing stress.     

A solid-liquid composite model of the red cell membrane

Summary Direct mechanical experiments and analyses support the view that the red cell membrane is a composite with a solid structural matrix, which can behave as either a viscoelastic or viscoplastic material.