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.     

Mechanical properties of actin filament networks depend on preparation, polymerization conditions, and storage of actin monomers.

This study investigates possible sources for the variance of more than two orders of magnitude in the published values for the shear moduli of purified actin filaments. Two types of forced oscillatory rheometers used in some of our previous work agree within a factor of three for identical samples. Polymers assembled in EGTA and Mg2+ from fresh, gel-filtered ATP-actin at 1 mg/ml typically have an elastic storage modulus (G') of approximately 1 Pa at a deformation frequency of 0.1-1 Hz. G' is slightly higher when actin is polymerized in KCl with Ca2+ and Mg2+. Gel filtration removes minor contaminants from actin but has little effect on G' for most preparations of actin from acetone powder. Storage of actin monomers without frequent changes of buffer containing fresh ATP and dithiothreitol can result in changes that increase the G' of filaments by more than a factor of 10. Frozen storage can preserve the properties of monomeric actin, but care is necessary to prevent protein denaturation or aggregation due to freezing or thawing.     

Quantifying the contribution of actin networks to the elastic strength of fibroblasts

The structural models created to understand the cytoskeletal mechanics of cells in suspension are described here. Suspended cells can be deformed by well-defined surface stresses in an Optical Stretcher [Guck, J., Ananthakrishnan, R., Mahmood, H., Moon, T.J., Cunningham, C.C., K?s, J., 2001. The optical stretcher: a novel laser tool to micromanipulate cells. Biophys. J. 81(2), 767-784], a two-beam optical trap designed for the contact-free deformation of cells. Suspended cells have a well-defined cytoskeleton, displaying a radially symmetric actin cortical network underlying the cell membrane with no actin stress fibers, and microtubules and intermediate filaments in the interior. Based on experimental data using suspended fibroblasts, we create two structural models: a thick shell actin cortex model that describes cell deformation for a localized stress distribution on these cells and a three-layered model that considers the entire cytoskeleton when a broad stress distribution is applied. Applying the models to data, we obtain a (actin) cortical shear moduli G of approximately 220 Pa for normal fibroblasts and approximately 185 Pa for malignantly transformed fibroblasts. Additionally, modeling the cortex as a transiently crosslinked isotropic actin network, we show that actin and its crosslinkers must be co-localized into a tight shell to achieve these cortical strengths. The similar moduli values and cortical actin and crosslinker densities but different deformabilities of the normal and cancerous cells suggest that a cell's structural strength is not solely determined by cytoskeletal composition but equally importantly by (actin) cytoskeletal architecture via differing cortical thicknesses. We also find that although the interior structural elements (microtubules, nucleus) contribute to the deformed cell's exact shape via their loose coupling to the cortex, it is the outer actin cortical shell (and its thickness) that mainly determines the cell's structural response.     

Stress relaxation of porcine gluteus muscle subjected to sudden transverse deformation as related to pressure sore modeling

Computational studies of deep pressure sores (DPS) in skeletal muscles require information on viscoelastic constitutive behavior of muscles, particularly when muscles are loaded transversally as during bone-muscle interaction in sitting and lying immobilized patients. In this study, we measured transient shear moduli G(t) of fresh porcine muscles in vitro using the indentation method. We employed a custom-made pneumatic device that allowed rapid (2000 mms) 4 mm indentations. We tested 8 gluteus muscles, harvested from 5 adult pigs. Each muscle was indented transversally (perpendicularly to the direction of fibers) at 3 different sites, 7 times per site, to obtain nonpreconditioned (NPC) and preconditioned (PC) G(t) data. Short-term (GS) and long-term (GL) shear moduli were obtained directly from experiments. We further fitted measured G(t) data to a biexponential equation G(t) = G1 x exp(-t/tau1)+ G2 x exp(-t/tau2) + Ginfinity, which provided good fit, visually and in terms of the correlation coefficients. Typically, plateau of the stress relaxation curves (defined as 10% difference from final GL) was evident approximately 20 s after indentation. Short-term shear moduli GS (mean NPC: 8509 Pa, PC: 5711 Pa) were greater than long-term moduli GL (NPC: 609 Pa, PC: 807 Pa) by about an order of magnitude. Statistical analysis of parameters showed that only G2 was affected by preconditioning, while GL, GS, Ginfinity, tau1, tau2, and G1 properties were unaffected. Since DPS develop over time scales of minutes to hours, but most stress relaxation occurs within approximately 20 s, the most relevant property for computational modeling is GL (mean approximately 700 Pa), which is, conveniently, unaffected by preconditioning.     

Elastic properties of cancellous bone: measurement by an ultrasonic technique

The high degree of porosity of cancellous bone makes elastic property measurement difficult by traditional mechanical testing methods. An ultrasonic technique is described with which mechanical properties of anisotropic, rigid, porous materials, such as cancellous bone, can be measured. The technique utilizes unique piezoelectric transducers operated in a continuous wave mode at a frequency of approximately 50 kHz. Both longitudinal and shear waves can be propagated and received with the transducers allowing both Young's moduli and shear moduli to be determined with the technique. A comparison between moduli measured with the ultrasonic technique and moduli measured with traditional mechanical testing shows the new method to be quite accurate in elastic property determination, (r2 = 0.935, Emech = 1.00E1dt + 23.3 MPa) (r2 = 0.656, Gmech = 1.08 Gult--3.3MPa).     

Rheological properties of cysteine-containing elastin-like polypeptide solutions and hydrogels

The rheological properties of cysteine-containing elastin-like polypeptide (Cys-ELP) solutions and Cys-ELP hydrogels are reported. The Cys-ELP solutions exhibit a surprisingly high apparent viscosity at low shear rate. The high viscosity is attributed to the formation of an interfacial cross-linked "skin" at the sample surface, rather than the bulk of the Cys-ELP solution. At higher shear rate, the interfacial cross-linked film breaks, and its influence on the viscosity of the Cys-ELP solution can be ignored. Cys-ELP hydrogels are formed by mixing Cys-ELP and hydrogen peroxide (H(2)O(2)). At fixed concentration of Cys-ELP, the gelation time can be tuned by the concentration of H(2)O(2). Cys-ELP hydrogels have the typical characteristics of covalent cross-linked networks, as the storage moduli are larger than the loss moduli and are independent of frequency in dynamic oscillatory frequency sweep experiments. The plateau moduli obtained from linear frequency sweep experiments are much lower than those estimated from the number of thiol groups along the Cys-ELP chain, indicating that only a small fraction of thiols form elastically active cross-links. From the small value of the fraction of elastically active cross-links, the Cys-ELP hydrogel is concluded to be an inhomogenous network. Under steady shear, a 2.5 wt % Cys-ELP hydrogel shear thickens at shear rates lower than that necessary for fracture.     

Viscoelasticity of biological materials - measurement and practical impact on biomedicine

Mechanical behavior of biological structures under dynamic loading generally depends on elastic as well as viscous properties of biological materials. The significance of "viscous" parameters in real situations remains to be elucidated. Behavior of rheological models consisting of a combination of inertial body and two Voigt's bodies were described mathematically with respect to inverse problem solution, and behavior in impulse and harmonic loadings was analyzed. Samples of walls of porcine and human aorta thoracica in transverse direction and samples of human bone (caput femoris, substantia compacta) were measured. Deformation responses of human skin in vivo were also measured. Values of elastic moduli of porcine aorta walls were in the interval from 10(2)kPa to 10(3) kPa, values of viscous coefficients were in the interval from 10(2) Pa.s to 10(3) Pa.s. The value of shear stress moduli of human caput femoris, substantia compacta range from 52.7 to 161.1 MPa, and viscous coefficients were in the interval from 27.3 to 98.9 kPa.s. The role of viscous coefficients is significant for relatively high loading frequencies - in our materials above 8 Hz in aorta walls and 5 Hz for bones. In bones, the viscosity reduced maximum deformation corresponding to short rectangular stress.     

Elastic contributions dominate the viscoelastic properties of sputum from cystic fibrosis patients

Sputum samples from cystic fibrosis (CF) patients were investigated by oscillatory, creep and steady shear rheological techniques over a range of time scales from 10(-3) to 10(6) s. The viscoelastic changes obtained by mixing sputa with the actin-filament-severing protein gelsolin and with the thiol-reducing agent dithiothreitol (DTT) were also investigated. At small strains sputum behaves like a viscoelastic solid rather than a liquid. A nearly constant steady shear viscosity at low shear rates is only observed after long shearing times which cause irreversible changes in the samples. Creep-recovery tests confirm that sputa exhibit viscoelastic properties, with a significant elastic recovery. The results suggest that measurements of elastic moduli, rather than viscosities are more closely related to the mechanical properties of sputum in situ. Severing of actin filaments lowers the elastic modulus by 30-40%, but maintains viscoelastic integrity, while reduction of thiols in the glycoproteins nearly completely fluidizes the samples.     

Cell traction forces on soft biomaterials. I. Microrheology of type I collagen gels

A laser-trap microrheometry technique was used to determine the local shear moduli of Type I collagen gels. Embedded 2.1 microm polystyrene latex particles were displaced 10-100 nm using a near-infrared laser trap with a trap constant of 0.0001 N/m. The trap was oscillated transversely +/- 200 nm using a refractive glass plate mounted on a galvanometric scanner. The displacement of the microspheres was in phase with the movement of the laser trap at frequencies less than 1 rad/s, indicating that at least locally, the gels behaved as elastic media. The local shear modulus was measured at various positions throughout the gel, and, for gels at 2.3 mg/mL and 37 degrees C, values ranged from G = 3 to 80 Pa. The average shear modulus G = 55 Pa, which compares well with measurements from parallel plate rheometry.     

Couple-stress moduli of a trabecular bone idealized as a 3D periodic cellular network

Trabecular bone is modeled as a cellular material with an idealized periodic structure made of open cubic cells, which is effectively orthotropic. We evaluate apparent couple-stress moduli of such a periodic material; apparent moduli refer to the moduli obtained using a domain smaller than a Representative Volume Element and they depend on boundary conditions. We conduct this analysis computationally (using ANSYS) by subjecting a unit cell of this periodic cellular material to either displacement or traction boundary conditions. Cell walls, representing bone tissue, and void space, representing bone marrow, are both modeled and they are assumed to be linear elastic. The applied loadings include a uniaxial extension (or uniaxial stress), a hydrostatic deformation (or hydrostatic stress) and a shear deformation (or shear stress) to evaluate the first stiffness (or compliance) tensor, and an applied curvature (or bending moment), a uniaxial twist (or torsion), and a triaxial twist (or triaxial torsion) to evaluate the second couple-stress stiffness (or compliance) tensor. Apparent couple-stress moduli are computed by equating the total strain energy stored in the unit cell with the energy of an equivalent homogeneous orthotropic couple-stress material for each applied loading. The moduli computed using displacement boundary conditions give upper bound, while those obtained using traction boundary conditions give lower bound on effective couple-stress moduli. These bounds are very wide due to a large mismatch in elastic moduli of bone tissue and bone marrow. These results are in agreement with our studies on composite materials with very stiff or very compliant inclusions.     

Effect of steady and oscillatory shear stress on F-actin content and distribution in neutrophils

We investigated neutrophil activation, specifically F-actin content and distribution, in situations mimicking the in vivo environment using steady and oscillatory shear. Under low steady shear (<150 s(-1)) F-actin levels were decreased for both treated (n-formyl-L-methioryl-L-leucyl-L-phenylalanine (fMLP)) and untreated neutrophils. The F-actin content increased with a change to higher steady shear levels. Neutrophils show the same behavior of decreased F-actin content for oscillatory shear (26.7 s(-1)) as they did for steady shear. In both situations, the low shear levels caused a decrease in F-actin content. However, as the magnitude of the shear rate increased, cells showed a reversal to increasing F-actin content. Shear caused a decrease in F-actin in the cell cortex for both control and fMLP treated cells. Ctyochalasin B (CB), a common F-actin assembly blocker, significantly decreased F-actin content. The results indicate that neutrophils regulate their actin network based on the level and type of shear stress they encounter in the bloodstream.     

一种改进型体液表观粘度函数测量仪

本文介绍一种性能较好的体液表观粘度函数快测系统,它是在较严密的流变学理论基础上通过较精细的硬、软件设计而研究成功的.其前身为L-1型粘度计,但作了重要改进.它的最大特点是能在一次测量过程完后得到不同切变率下的表观粘度;同时能在通常认为困难却十分重要的“低剪切”段令人满意地工作.     

Effect of filamin and controlled linear shear on the microheterogeneity of F-actin/gelsolin gels

We have previously established [Cortese and Frieden, J. Cell Biol. 107:1477-1487, 1988] that actin gels formed under shear are microheterogeneous. In this study, the effect of cross-linking (by chicken gizzard filamin), severing (by plasma gelsolin), and shear on actin microheterogeneity are investigated using fluorescence photobleaching recovery and video microscopy. We find that filamin and shear form microheterogeneous F-actin:gelsolin gels by different mechanisms. Bundling of actin:gelsolin filaments by filamin can be explained by an increase in the apparent length of the filaments due to interfilament binding, resulting in a decrease of the polymer number concentration at which filaments organize into anisotropic phases. Some intrafilament binding of filamin to actin filaments may also be present, and those filaments coated with filamin immobilize more slowly than actin under the same polymerization conditions. The length of F-actin/gelsolin filaments seems to be a major factor in controlling the extent of bundling relative to network formation. In contrast, the effect of shear on the microheterogeneity of actin:gelsolin filaments is consistent with our previous proposal that shear aligns actin filaments, allowing filament-filament interactions and phase formation to occur. Short filaments are unable to organize into branched actin networks, but they can create large aggregates under low shear. Longer actin filaments will exist as networks with variable levels of branching and are less sensitive to shear. The effect of the intensity of a shear field on the spatial distribution of actin may involve a progressively more random orientation of actin molecules and bundles. A regular pattern develops across the sample at low shear rates (0.04-1.39 s-1), and becomes very irregular at higher shear rates (greater than 10 s-1). We suggest here that actin-binding proteins and shear can control the transition between isotropic networks and anisotropic phases by their effect on apparent length and local filament concentration, and also that this transition can have substantial effects on the resistance of cells to mechanical stress.     

Thiol oxidation of actin produces dimers that enhance the elasticity of the F-actin network

Slow oxidation of sulfhydryls, forming covalently linked actin dimers and higher oligomers, accounts for increases in the shear elasticity of purified actin observed after aging. Disulfide-bonded actin dimers are incorporated into F-actin during polymerization and generate cross-links between actin filaments. The large gel strength of oxidized actin (>100 Pa for 1 mg/ml) in the absence of cross-linking proteins falls to within the theoretically predicted order of magnitude for uncross-linked actin filament networks (1 Pa) with the addition of sufficient concentrations of reducing agents such as 5 mM dithiothreitol or 10 mM beta-mercaptoethanol. As little as 1 gelsolin/1000 actin subunits also lowers the high storage modulus of oxidized actin. The effects of gelsolin may be both to increase filament number as it severs F-actin and to cover the barbed end of an actin filament, which otherwise might cross-link to the side of another filament via an actin dimer. These new findings may explain why previous studies of actin rheology report a wide range of values when purified actin is polymerized without added regulatory proteins.     

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.     

Rapid cell-deformability sensing system based on slit-flow laser diffractometry with decreasing pressure differential

A slit-flow apparatus with a laser-diffraction method has been developed with significant advances in ektacytometry design, operation and data analysis. In the slit-flow ektacytometry, the deformation of red blood cells subjected to continuously decreasing shear stress in slit-flow can be quickly measured with adopting a laser-diffraction technique. Both the laser-diffraction image and pressure were measured with respect to time, which enable to determine the elongation index (EI) and the shear stress. The range of shear stress is 0-35 Pa and the measuring time is < 2 min. The EI is determined from an isointensity curve in the diffraction pattern using an ellipse-fitting program. The present study proposed the deformability index (DI) as a new measure of the RBC deformability, which is defined as an integral area under the EI curve between 0 and tau10 (tau(w) = 0-10). The key advantage of this design is the incorporation of a disposable element that holds the blood sample, which enables the present system to be easily used in a clinical setting.     

Microheterogeneity of actin gels formed under controlled linear shear

The diffusion coefficients and fluorescence polarization properties of actin subjected to a known shear have been determined both during and after polymerization, using a modification of a cone-plate Wells-Brookfield rheometer that allows monitoring of samples with an epifluorescence microscope. Fluorescence polarization and fluorescence photobleaching recovery experiments using rhodamine-labeled actin as a tracer showed that under conditions of low shear (shear rates of 0.05 s-1), a spatial heterogeneity of polymerized actin was observed with respect to fluorescence intensity and the diffusion coefficients with actin mobility becoming quite variable in different regions of the sample. In addition, complex changes in fluorescence polarization were noted after stopping the shear. Actin filaments of controlled length were obtained using plasma gelsolin (gelsolin/actin molar ratios of 1:50 to 1:300). At ratios of 1:50, neither spatial heterogeneity nor changes in polarization were observed on subjecting the polymerized actin to shear. At ratios of approximately 1:100, a decrease on the intensity of fluorescence polarization occurs on stopping the shear. Longer filaments exhibit spatial micro-heterogeneity and complex changes in fluorescence polarization. In addition, at ratios of 1:100 or 1:300, the diffusion coefficient decreases as the total applied shear increased. This behavior is interpreted as bundling of filaments aligned under shear. We also find that the F-actin translational diffusion coefficients decrease as the total applied shear increases (shear rates between 0.05 and 12.66 s-1), as expected for a cumulative process. When chicken gizzard filamin was added to gelsolin-actin filaments (at filamin/actin molar ratios of 1:300 to 1:10), a similar decrease in the diffusion coefficients was observed for unsheared samples. Spatial microheterogeneity might be related to the effects of the shear field in the alignment of filaments, and the balance between a three-dimensional network and a microheterogeneous system (containing bundles or anisotropic phases) appears related to both shear and the presence of actin-binding proteins.     

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.     

Viscoelasticity of F-actin and F-actin/gelsolin complexes

Actin is the major protein of eukaryote peripheral cytoplasm where its mechanical effects could determine cell shape and motility. The mechanical properties of purified F-actin, whether it is a viscoelastic fluid or an elastic solid, have been a subject of controversy. Mainstream polymer theory predicts that filaments as long as those found in purified F-actin are so interpenetrated as to appear immobile in measurements over a reasonable time with available instrumentation and that the fluidity of F-actin could only be manifest if the filaments were shortened. We show that the static and dynamic elastic moduli below a critical degree of shear strain are much higher than previously reported, consistent with extreme interpenetration, but that higher strain or treatment with very low concentrations of the F-actin severing protein gelsolin greatly diminish the moduli and cause F-actin to exhibit rheologic behavior expected for independent semidilute rods, and defined by the dimensions of the filaments, including shear rate independent viscosity below a critical shear rate. The findings show that shortening of actin filaments sufficiently to permit reasonable measurements brings out their viscoelastic fluid properties. Since gelsolin shortens F-actin, it is likely that the effect of high strain is also to fragment a population of long actin filaments. We confirmed recent findings that the viscosity of F-actin is inversely proportional to the shear rate, consistent with an indeterminate fluid, but found that gelsolin abolishes this unusual shear rate dependence, indicating that it results from filament disruption during the viscosity measurements.(ABSTRACT TRUNCATED AT 250 WORDS)     

Viscoelastic properties of vimentin compared with other filamentous biopolymer networks

The cytoplasm of vertebrate cells contains three distinct filamentous biopolymers, the microtubules, microfilaments, and intermediate filaments. The basic structural elements of these three filaments are linear polymers of the proteins tubulin, actin, and vimentin or another related intermediate filament protein, respectively. The viscoelastic properties of cytoplasmic filaments are likely to be relevant to their biologic function, because their extreme length and rodlike structure dominate the rheologic behavior of cytoplasm, and changes in their structure may cause gel-sol transitions observed when cells are activated or begin to move. This paper describes parallel measurements of the viscoelasticity of tubulin, actin, and vimentin polymers. The rheologic differences among the three types of cytoplasmic polymers suggest possible specialized roles for the different classes of filaments in vivo. Actin forms networks of highest rigidity that fluidize at high strains, consistent with a role in cell motility in which stable protrusions can deform rapidly in response to controlled filament rupture. Vimentin networks, which have not previously been studied by rheologic methods, exhibit some unusual viscoelastic properties not shared by actin or tubulin. They are less rigid (have lower shear moduli) at low strain but harden at high strains and resist breakage, suggesting they maintain cell integrity. The differences between F-actin and vimentin are optimal for the formation of a composite material with a range of properties that cannot be achieved by either polymer alone. Microtubules are unlikely to contribute significantly to interphase cell rheology alone, but may help stabilize the other networks.