Some perspectives on the viscosity of actin filaments

Modelling the rheology of living cell cytoplasm: poroviscoelasticity and fluid-to-solid transition

Eukaryotic cell rheology has important consequences for vital processes such as adhesion, migration, and differentiation. Experiments indicate that cell cytoplasm can exhibit both elastic and viscous characteristics in different regimes, while the transport of fluid (cytosol) through the cross-linked filamentous scaffold (cytoskeleton) is reminiscent of mass transfer by diffusion through a porous medium. To gain insights into this complex rheological behaviour, we construct a computational model for the cell cytoplasm as a poroviscoelastic material formulated on the principles of nonlinear continuum mechanics, where we model the cytoplasm as a porous viscoelastic scaffold with an embedded viscous fluid flowing between the pores to model the cytosol. Baseline simulations (neglecting the viscosity of the cytosol) indicate that the system exhibits seven different regimes across the parameter space spanned by the viscoelastic relaxation timescale of the cytoskeleton and the poroelastic diffusion timescale; these regimes agree qualitatively with experimental measurements. Furthermore, the theoretical model also allows us to elucidate the additional role of pore fluid viscosity, which enters the system as a distinct viscous timescale. We show that increasing this viscous timescale hinders the passage of the pore fluid (reducing the poroelastic diffusion) and makes the cytoplasm rheology increasingly incompressible, shifting the phase boundaries between the regimes.

Gelsolin from mussel's catch muscle

Proteins of the gelsolin family are Ca2+-dependent, multifunctional, actin-binding proteins containing three (S1-S3, about 40 kDa) or six (S1-S6, about 80 kDa) highly conserved repeats in the amino acid sequence. The pattern of interaction of these proteins with actin is complex: they can sever actin filaments; promote polymer nucleation after binding to two actin monomers; and cap the growing barbed end of actin filaments. In the present study, an actin polymerizing factor (46 kDa) from the adductor muscle of a bivalve mollusc has been discovered and identified for the first time. This protein has turned out to belong to the gelsolin family of actin regulatory proteins. The expression of gelsolin-like proteins in the tissues of bivalves was predicted after analyzing their proteome, but this is the first study where an actually expressed protein has been found. A primary determination of its physicochemical properties such as molecular weight, charge, resistance to urea, influence on actin polymerization by viscosity, and light scattering is carried out and the molecular structure analyzed.

Symmetry breaking in hydrodynamic forces drives meiotic spindle rotation in mammalian oocytes

Patterned cell divisions require a precisely oriented spindle that segregates chromosomes and determines the cytokinetic plane. In this study, we investigated how the meiotic spindle orients through an obligatory rotation during meiotic division in mouse oocytes. We show that spindle rotation occurs at the completion of chromosome segregation, whereby the separated chromosome clusters each define a cortical actomyosin domain that produces cytoplasmic streaming, resulting in hydrodynamic forces on the spindle. These forces are initially balanced but become unbalanced to drive spindle rotation. This force imbalance is associated with spontaneous symmetry breaking in the distribution of the Arp2/3 complex and myosin-II on the cortex, brought about by feedback loops comprising Ran guanosine triphosphatase signaling, Arp2/3 complex activity, and myosin-II contractility. The torque produced by the unbalanced hydrodynamic forces, coupled with a pivot point at the spindle midzone cortical contract, constitutes a unique mechanical system for meiotic spindle rotation.

Dynamic organelle distribution initiates actin-based spindle migration in mouse oocytes

Migration of meiosis-I (MI) spindle from the cell center to a sub-cortical location is a critical step for mouse oocytes to undergo asymmetric meiotic cell division. In this study, we investigate the mechanism by which formin-2 (FMN2) orchestrates the initial movement of MI spindle. By defining protein domains responsible for targeting FMN2, we show that spindle-periphery localized FMN2 is required for spindle migration. The spindle-peripheral FMN2 nucleates short actin bundles from vesicles derived likely from the endoplasmic reticulum (ER) and concentrated in a layer outside the spindle. This layer is in turn surrounded by mitochondria. A model based on polymerizing actin filaments pushing against mitochondria, thus generating a counter force on the spindle, demonstrated an inherent ability of this system to break symmetry and evolve directional spindle motion. The model is further supported through experiments involving spatially biasing actin nucleation via optogenetics and disruption of mitochondrial distribution and dynamics.

Mammalian oocytes divide asymmetrically during meiotic maturation. Here, the authors show that spindle movement away from oocyte center depends on actin filaments nucleated from the spindle periphery pushing against surrounding mitochondria, which polarizes spontaneously to produce directional spindle motion.

Mechanical models for living cells--a review

As physical entities, living cells possess structural and physical properties that enable them to withstand the physiological environment as well as mechanical stimuli occurring within and outside the body. Any deviation from these properties will not only undermine the physical integrity of the cells, but also their biological functions. As such, a quantitative study in single cell mechanics needs to be conducted. In this review, we will examine some mechanical models that have been developed to characterize mechanical responses of living cells when subjected to both transient and dynamic loads. The mechanical models include the cortical shell-liquid core (or liquid drop) models which are widely applied to suspended cells; the solid model which is generally used for adherent cells; the power-law structural damping model which is more suited for studying the dynamic behavior of adherent cells; and finally, the biphasic model which has been widely used to study musculoskeletal cell mechanics. Based upon these models, future attempts can be made to develop even more detailed and accurate mechanical models of living cells once these three factors are adequately addressed: structural heterogeneity, appropriate constitutive relations for each of the distinct subcellular regions and components, and active forces acting within the cell. More realistic mechanical models of living cells can further contribute towards the study of mechanotransduction in cells.

Acto-myosin cytoskeleton dependent viscosity and shear-thinning behavior of the amoeba cytoplasm

The mechanical behavior of the human parasite Entamoeba histolytica plays a major role in the invasive process of host tissues and vessels. In this study, we set up an intracellular rheological technique derived from magnetic tweezers to measure the viscoelastic properties within living amoebae. The experimental setup combines two magnetic fields at 90 degrees from each other and is adapted to an inverted microscope, which allows monitoring of the rotation of pairs of magnetic phagosomes. We observe either the response of the phagosome pair to an instantaneous 45 degrees rotation of the magnetic field or the response to a permanent uniform rotation of the field at a given frequency. By the first method, we concluded that the phagosome pairs experience a soft viscoelastic medium, represented by the same mechanical model previously described for the cytoplasm of Dictyostelium discoideum [Feneberg et al. in Eur Biophys J 30(4):284-294 2001]. By the second method, the permanent rotation of a pair allowed us to apply a constant shear rate and to calculate the apparent viscosity of the cytoplasm. As found for entangled polymers, the viscosity decreases with the shear rate applied (shear-thinning behavior) and exhibits a power-law-type thinning, with a corresponding exponent of 0.65. Treatment of amoeba with drugs that affect the actin polymer content demonstrated that the shear-thinning behavior of the cytoplasm depends on the presence of an intact actin cytoskeleton. These data present a physiologic relevance for Entamoeba histolytica virulence. The shear-thinning behavior could facilitate cytoplasm streamings during cell movement and cell deformation, under important shear experienced by the amoeba during the invasion of human tissues. In this study, we also investigated the role of the actin-based motor myosin II and concluded that myosin II stiffens the F-actin gel in living parasites likely by its cross-linking activity.

Substrate compliance versus ligand density in cell on gel responses

Substrate stiffness is emerging as an important physical factor in the response of many cell types. In agreement with findings on other anchorage-dependent cell lineages, aortic smooth muscle cells are found to spread and organize their cytoskeleton and focal adhesions much more so on "rigid" glass or "stiff" gels than on "soft" gels. Whereas these cells generally show maximal spreading on intermediate collagen densities, the limited spreading on soft gels is surprisingly insensitive to adhesive ligand density. Bell-shaped cell spreading curves encompassing all substrates are modeled by simple functions that couple ligand density to substrate stiffness. Although smooth muscle cells spread minimally on soft gels regardless of collagen, GFP-actin gives a slight overexpression of total actin that can override the soft gel response and drive spreading; GFP and GFP-paxillin do not have the same effect. The GFP-actin cells invariably show an organized filamentous cytoskeleton and clearly indicate that the cytoskeleton is at least one structural node in a signaling network that can override spreading limits typically dictated by soft gels. Based on such results, we hypothesize a central structural role for the cytoskeleton in driving the membrane outward during spreading whereas adhesion reinforces the spreading.

Aspiration of human neutrophils: effects of shear thinning and cortical dissipation

It is generally accepted that the human neutrophil can be mechanically represented as a droplet of polymeric fluid enclosed by some sort of thin slippery viscoelastic cortex. Many questions remain however about the detailed rheology and chemistry of the interior fluid and the cortex. To address these quantitative issues, we have used a finite element method to simulate the dynamics of neutrophils during micropipet aspiration using various plausible assumptions. The results were then systematically compared with aspiration experiments conducted at eight different combinations of pipet size and pressure. Models in which the cytoplasm was represented by a simple Newtonian fluid (i.e., models without shear thinning) were grossly incapable of accounting for the effects of pressure on the general time scale of neutrophil aspiration. Likewise, models in which the cortex was purely elastic (i.e., models without surface viscosity) were unable to explain the effects of pipet size on the general aspiration rate. Such models also failed to explain the rapid acceleration of the aspiration rate during the final phase of aspiration nor could they account for the geometry of the neutrophil during various phases of aspiration. Thus, our results indicate that a minimal mechanical model of the neutrophil needs to incorporate both shear thinning and surface viscosity to remain valid over a reasonable range of conditions. At low shear rates, the surface dilatation viscosity of the neutrophil was found to be on the order of 100 poise-cm, whereas the viscosity of the interior cytoplasm was on the order of 1000 poise. Both the surface viscosity and the interior viscosity seem to decrease in a similar fashion when the shear rate exceeds approximately 0.05 s(-1). Unfortunately, even models with both surface viscosity and shear thinning studied are still not sufficient to fully explain all the features of neutrophil aspiration. In particular, the very high rate of aspiration during the initial moments after ramping of pressure remains mysterious.

A viscoelastic model of phagosome motion within cells based on cytomagnetometric measurements

Cytomagnetometry is a noninvasive method to investigate intracellular movements of organelles such as phagosomes by introducing magnetic particles into cells by phagocytosis, magnetizing them and measuring the field from the cells. To analyze the results of the cell-field measurement, we introduce a model for intracellular phagosome motion and investigate their behavior in terms of the cell field. The model includes an elastic body and two viscosity components which are ascribed to the filamentous structures surrounding the phagosomes. The magnetic relaxation phenomenon is assumed to derive from the rotationary Brownian motion as in our previous model. Although the model is simple, its behavior is not trivial because it contains a nonlinear term and the Brownian motion term. This model is the simplest one possible having a viscoelastic body and its behavior hence should be investigated thoroughly.

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.

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.

Measurement of elastic properties of Xenopus oocytes

Elastic properties of Xenopus oocytes were examined by measuring intracellular pressure (Pic) and cell volume (Vc) in cells undergoing osmotic swelling. Pic was measured by micropuncture, using the servo-null technique. Vc was obtained by analyzing images acquired from a microscope having a video camera attachment. During osmotic swelling, Pic increased from 61 +/- 17 to 500 +/- 59 Pa (mean +/- SE), but the relationship with volume was not linear. In cells that underwent sequential swelling and shrinking, Pic was always lower on shrinking and the cells showed hysteresis. Cells with vitelline envelope (VE) removed had Pic-Vc curves similar in shape to those of intact cells; however, Pic values were significantly lower. Specific elastance[delta Pic/(delta Vc/Vc)] was reduced by removal of the VE. The data indicate that oocytes are weakly elastic and that a large part of their resistance to expansion resides in the VE.

A computer-interfaced falling ball viscometer

We have developed a system that greatly facilitates viscosity measurement under low-shear conditions, based upon a falling ball viscometer interfaced to a personal computer. Three optical sensors indicate the rate of passage of a steel ball falling through a micro-capillary tube, and a potentiometer detects the angle of the tube. The resulting data are passed from a custom program with a graphical user interface to a spreadsheet. The spreadsheet then calculates and stores a value for the viscosity of the sample, using the data passed to it from the viscometer, and a look-up table of stored slope and intercept values calculated from precision viscosity standards. We used the viscometer to determine the kinetics of actin polymerization, and to measure the viscosity of F-actin-aldolase gels. This system provides significantly greater reproducibility and speed in data acquisition than does the traditional 'eyeball and stopwatch' method, and data reduction is virtually instantaneous.

Passive mechanical behavior of human neutrophils: power-law fluid

The mechanical behavior of the neutrophil plays an important role in both the microcirculation and the immune system. Several laboratories in the past have developed mechanical models to describe different aspects of neutrophil deformability. In this study, the passive mechanical properties of normal human neutrophils have been further characterized. The cellular mechanical properties were assessed by single cell micropipette aspiration at fixed aspiration pressures. A numerical simulation was developed to interpret the experiments in terms of cell mechanical properties based on the Newtonian liquid drop model (Yeung and Evans, Biophys. J., 56: 139-149, 1989). The cytoplasmic viscosity was determined as a function of the ratio of the initial cell size to the pipette radius, the cortical tension, aspiration pressure, and the whole cell aspiration time. The cortical tension of passive neutrophils was measured to be about 2.7 x 10(-5) N/m. The apparent viscosity of neutrophil cytoplasm was found to depend on aspiration pressure, and ranged from approximately 500 Pa.s at an aspiration pressure of 98 Pa (1.0 cm H2O) to approximately 50 Pa.s at 882 Pa (9.0 cm H2O) when tested with a 4.0-micron pipette. These data provide the first documentation that the neutrophil cytoplasm exhibits non-Newtonian behavior. To further characterize the non-Newtonian behavior of human neutrophils, a mean shear rate gamma m was estimated based on the numerical simulation. The apparent cytoplasmic viscosity appears to decrease as the mean shear rate increases. The dependence of cytoplasmic viscosity on the mean shear rate can be approximated as a power-law relationship described by mu = mu c(gamma m/gamma c)-b, where mu is the cytoplasmic viscosity, gamma m is the mean shear rate, mu c is the characteristic viscosity at characteristic shear rate gamma c, and b is a material coefficient. When gamma c was set to 1 s-1, the material coefficients for passive neutrophils were determined to be mu c = 130 +/- 23 Pa.s and b = 0.52 +/- 0.09 for normal neutrophils. The power-law approximation has a remarkable ability to reconcile discrepancies among published values of the cytoplasmic viscosity measured using different techniques, even though these values differ by nearly two orders of magnitude. Thus, the power-law fluid model is a promising candidate for describing the passive mechanical behavior of human neutrophils in large deformation. It can also account for some discrepancies between cellular behavior in single-cell micromechanical experiments and predictions based on the assumption that the cytoplasm is a simple Newtonian fluid.

Nucleotide exchange and rheometric studies with F-actin prepared from ATP- or ADP-monomeric actin

It has recently been reported that polymer actin made from monomer containing ATP (ATP-actin) differed in EM appearance and rheological characteristics from polymer made from ADP-containing monomers (ADP-actin). Further, it was postulated that the ATP-actin polymer was more rigid due to storage of the energy released by ATP hydrolysis during polymerization (Janmey et al. 1990. Nature 347:95-99). Electron micrographs of our preparations of ADP-actin and ATP-actin polymers show no major differences in appearance of the filaments. Moreover, the dynamic viscosity parameters G' and G" measured for ATP-actin and ADP-actin polymers are very different from those reported by Janmey et al., in absolute value, in relative differences, and in frequency dependence. We suggest that the relatively small differences observed between ATP-actin and ADP-actin polymer rheological parameters could be due to small differences either in flexibility or, more probably, in filament lengths. We have measured nucleotide exchange on ATP-actin and ADP-actin polymers by incorporation of alpha-32P-ATP and found it to be very slow, in agreement with earlier literature reports, and in contradiction to the faster exchange rates reported by Janmey et al. This exchange rate is much too slow to cause "reversal" of ADP-actin polymer ATP-actin polymer as reported by Janmey et al. Thus our results do not support the notion that the energy of actin-bound ATP hydrolysis is trapped in and significantly modifies the actin polymer structure.

Quasielastic light scattering study of thermal excitations of F-actin solutions and of growth kinetics of actin filaments

In the first part of this work we report quasielastic light scattering (QELS) studies of the internal dynamics of transient actin networks over a time range of 10(-6)-10(-2) s, scattering angles between zeta = 20 degrees and 150 degrees, and a concentration range of 0.015 (0.3) to 0.7 mg/mL (15 microM). We confirm our previous result that (1) the dynamic structure factor g(q,t) is determined by the thermally excited undulations of the actin filaments and (2) that the initial decay of g(q, t) scales as g(q, t) varies; is directly proportional to exp(-q alpha t) while the long time decay scales as g(q, t) varies; is directly proportional to exp [-(Aq alpha t) 2/3] with alpha = 2.75. The deviation of alpha from the theoretical value of alpha = 3 predicted for Rouse-Zimm chains is similar to that found for high molecular weight macromolecular solutions by QELS. A refined analysis of the dynamic structure factor showed that it can be interpreted in terms of three relaxation processes (besides the contribution of the residual monomer diffusion): (1) the dominant Rouse-Zimm dynamics, which comprises between 65 (at high concentrations) and 85% of the signal; (2) a fast relaxation process with a decay constant of gamma = 9 x 10(3) s-1, which contributes at all concentrations with the same amplitude; and (3) a nonexponential ultraslow contribution of the form g(us) varies; is directly proportional to exp [(-gamma ust)]1/4. The third contribution appears only at high concentrations and increases strongly with decreasing scattering angles. It is thus attributed to fluctuations of the mesh size of the transient actin network. In the second part we show that high sensitivity QELS may be applied to follow the actin polymerization process at low temperatures (10 degrees C). The apparent diffusion coefficient and the static scattering intensity of the actin filaments were determined as functions of polymerization time tpol. We show that the process consists of the rapid growth of a few filaments that become very long (approximately 10 microns; even at actin concentrations of 0.04 micrograms/mL) near the critical growth concentration of 0.012 micrograms/mL, as is expected for a growth process determined by nucleation. Finally, we studied actin networks polymerized in the presence of complexes of gelsolin with actin. By application of the CONTIN program we could determine the length distribution of the filaments.(ABSTRACT TRUNCATED AT 400 WORDS)

Interaction of cardiac alpha-actinin and actin in the presence of doxorubicin

The therapeutic use of doxorubicin (an antitumoral antibiotic belonging to the anthracycline group) is limited by its cardiotoxicity. Adriamycin (DXR) causes myocardial subcellular damage, such as myocytolysis, disarray of actin filaments, and alterations in the Z-band with loss of sarcomeric organization. We studied the effect of stoichiometrical concentrations of DXR on the interaction between cardiac actin and alpha-actinin in solution. Doxorubicin inhibits the formation of alpha-actinin/actin tridimensional networks and bundles. The main effect of the drug seems to be on the size of the actin polymers.

Lithium increases actin polymerization rates by enhancing the nucleation step

Lithium affects the polymerization mechanism of some cytoskeletal proteins in vitro, so its biological activity could also reflect lithium influence on assembly processes. Our data demonstrate that lithium nucleates actin polymerization and, in parallel, is less effective in the elongation step. Furthermore, falling-ball and fluorimetric tests suggested that lithium-induced actin polymers at steady-state are shorter than K(+)-polymerized actin filamentous structures. The lithium-induced actin assembly seems to follow the "reversible polymerization model" and the critical concentration of Li(+)-assembled actin at steady-state is markedly lower than that of sister actin samples polymerized by potassium chloride. Finally, the stabilization of actin nuclei induced by lithium ions could be related to their effect of lowering the dissociation rate constant.

The actin gelling activity of chicken gizzard alpha-actinin at physiological temperature is triggered by water sequestration

At 37 degrees C, in the presence of 6% (w/v) polyethylene glycol 6000, 30 nM alpha-actinin from chicken gizzard induces the gelation of 12 microM actin. Static measurement shows that the addition of 30 nM alpha-actinin increases the rigidity of the system from 23.5 to 54 dynes/cm2. According to the theory of osmoelastic coupling, also large additives, such as the proteins of the cell sap, are able to cause an osmotic stress equivalent to that caused by polyethylene glycol. We thus conclude that, in vivo, alpha-actinin acts as an actin gelling protein.

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.

Analysis of rhodamine and fluorescein-labeled F-actin diffusion in vitro by fluorescence photobleaching recovery

Properties of filamentous acetamidofluorescein-labeled actin and acetamidotetramethylrhodamine-labeled actin (AF and ATR-actin, respectively) were examined to resolve discrepancies in the reported translational diffusion coefficients of F-actin measured in vitro by FPR and other techniques. Using falling-ball viscometry and two independent versions of fluorescence photobleaching recovery (FPR), the present data indicate that several factors are responsible for these discrepancies. Gel filtration chromatography profoundly affects the viscosity of actin solutions and filament diffusion coefficients. ATR-actin and, to a lesser degree, AF-actin show a reduction in viscosity in proportion to the fraction labeled, presumably due to filament shortening. Actin filaments containing AF-actin or ATR-actin are susceptible to photoinduced damage, including a covalent cross-linking of actin protomers within filaments and an apparent cleavage of filaments detected by a decrease of the measured viscosity and an increase in the measured filament diffusion coefficients. Quantum yields of the two photoinduced effects are quite different. Multiple cross-links are produced relative to each photobleaching event, whereas less than 1% filament cleavage occurs. Substantial differences in the filament diffusion coefficients measured by FPR are also the result of differences in illumination geometry and sampling time. However, under controlled conditions, FPR can be used as a quantitative tool for measuring the hydrodynamic properties of actin filaments. Incremented filament shortening caused by photoinduced cleavage or incremental addition of filament capping proteins produces a continuous and approximately linear increase of filament diffusion coefficients, indicating that filaments are not associated in solution. Our results indicate that actin filaments exhibit low mobilities and it is inferred that actin filaments formed in vitro by column-purified actin, under standard conditions, are much longer than has conventionally been presumed.

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)

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.

On the elasticity of cytoskeletal networks

Models relating to the gelation and elasticity of complex cytoskeletal networks are formulated and investigated. Kinetic equations for reversible elongation of nucleated actin filaments are analyzed when the filaments are acted upon by capping proteins and cross-linking factors. Analytical expressions are obtained that relate the low frequency elastic shear modulus of a network, G, to chain growth kinetics, the number of nucleation sites, monomer concentration, and the amount of capping and cross-linking protein. Elasticity curves that relate G to such factors as the association constant for cross-linking are derived and then used to determine solation-gelation phase contours.

The molecular mobility of alpha-actinin and actin in a reconstituted model of gelation

Dictyostelium discoideum alpha-actinin (D.d. alpha-actinin) is a calcium and pH-regulated actin-binding protein that can cross-link F-actin into a gel at a submicromolar free calcium concentration and a pH less than 7 [Fechheimer, et al., 1982]. We examined mixtures of actin and D.d. alpha-actinin at four pH and calcium concentrations that exhibited various degrees of gelation or solation. The macroscopic viscosities of these mixtures were measured by falling ball viscometry (FBV) and compared to the translational diffusion coefficients measured by gaussian spot and periodic-pattern fluorescence photobleaching recovery (FPR) of both the actin filaments and D.d. alpha-actinin. A homogeneous, macroscopic gel was not composed of a static actin network. Instead, the filament diffusion coefficient decreased to approximately 65% of the control value. If the D.d. alpha-actinin concentration was increased, the solution became inhomogeneous, consisting of domains of higher actin concentration. These domains were often composed of a static actin network. The mobility of D.d. alpha-actinin consisted of a major fraction that freely diffused and a minor fraction that appeared immobile under the conditions employed. This suggested that D.d. alpha-actinin binding to the actin filaments was static over the time course of measurement (approximately 5 sec). Under solation conditions, there was no apparent interaction of actin with D.d. alpha-actinin. These results demonstrate that 1) actin filaments need not be cross-linked into an immobile, static array in order to have macroscopic properties of a gel; 2) interpretation of the rheological properties of actin:alpha-actinin gels are complicated by spatial heterogeneity of the filament concentration and mobility; and 3) a fraction of D.d. alpha-actinin binds statically to actin in undisturbed gels. The implications of these results are discussed in relation to cytoplasmic structure and contractility.

Magnetic particle motions within living cells. Measurement of cytoplasmic viscosity and motile activity

Submicrometer magnetic particles, ingested by cells and monitored via the magnetic fields they generate, provide an alternative to optical microscopy for probing movement and viscosity of living cytoplasm, and can be used for cells both in vitro and in vivo. We present methods for preparing lung macrophages tagged with magnetic particles for magnetometric study. Interpretation of the data involves fitting experimental remanent-field decay curves to nonlinear mechanistic models of intracellular particle motion. The model parameters are sensitive to mobility and apparent cytoplasmic viscosity experienced by particle-containing organelles. We present results of parameter estimation for intracellular particle behavior both within control cells and after (a) variable magnetization duration, (b) incubation with cytochalasin D, and (c) particle twisting by external fields. Magnetometric analysis showed cytoplasmic elasticity, dose-dependent motion inhibition by cytochalasin D, and a shear-thinning apparent viscosity.

Nonideality of volume flows and phase transitions of F-actin solutions in response to osmotic stress

Ovalbumin and G-actin solutions decreased their volume in a concentration-dependent manner in response to an osmotic stress, arising from an osmotic pressure gradient of 5-20 cm H2O at 25 degrees C, at protein concentrations as high as 20 mg/ml. In contrast, solutions of F-actin exhibited a concentration-dependent decrease in their rate of volume change in response to the osmotic stress. Shortening of F-actin by gelsolin did not affect this decrease, suggesting that the elastic response of the filaments underlies the osmotically nonideal behavior. However, above a critical actin concentration of approximately 7 mg/ml, no volume change occurred in response to osmotic gradients as high as 20 cm H2O. The concentration at which this critical phenomenon occurred and its abolition by shortening of F-actin by gelsolin suggest that a transition of diffusible rods to a glassy state is the cause of this critical phenomenon. Above the critical concentration, an increase in the osmotic pressure applied to an F-actin solution to greater than 20 cm H2O produced a transient increase in flow rate to that expected for a solution containing no polymer. This finding may represent a transition from an isotropic glassy state to an anisotropic and heterogeneous one wherein regions of pure solvent coexist with domains of pure polymer.

F-actin and microtubule suspensions as indeterminate fluids

The viscosity of F-actin and microtubule suspensions has been measured as a function of shear rate with a Weissenberg rheogoniometer. At shear rates of less than 1.0 per second the viscosity of suspensions of these two structural proteins is inversely proportional to shear rate. These results are consistent with previous in vivo measurements of the viscosity of cytoplasm. This power law implies that shear stress is independent of shear rate; that is, shear stress is a constant at all shear rates less than 1.0 per second. Thus the flow profile of these fluids is indeterminate, or nearly so. This flow property may explain several aspects of intracellular motility in living cells. Possible explanations for this flow property are based on a recent model for semidilute suspensions of rigid rods or a classical friction model for liquid crystals.

Dependence of the mechanical properties of actin/alpha-actinin gels on deformation rate

The cortical cytoplasm, including the cleavage furrow, is largely composed of a network of actin filaments that is rigid even as it is extensively deformed during cytokinesis. Here we address the question of how actin-filament networks such as those in the cortex can be simultaneously rigid (solid-like) and fluid-like. Conventional explanations are that actin filaments rearrange by some combination of depolymerization and repolymerization; fragmentation and annealing of filaments; and inactivation and reestablishment of crosslinks between filaments. We describe the mechanical properties of a model system consisting of actin filaments and Acanthamoeba alpha-actinin, one of several actin crosslinking proteins found in amoeba and other cells. The results suggest another molecular mechanism that may account for the paradoxical mechanical properties of the cortex. When deformed rapidly, these mixtures are 40 times more rigid than actin filaments without alpha-actinin, but when deformed slowly these mixtures were indistinguishable from filaments alone. These time-dependent mechanical properties can be explained by multiple, rapidly rearranging alpha-actinin crosslinks between the actin filaments, a mechanism proposed by Frey-Wyssling to account for the behaviour of cytoplasm long before the discovery of cytoplasmic actin or alpha-actinin. If other actin-filament crosslinking proteins behave like Acanthamoeba alpha-actinin, this mechanism may explain how the cortex recoils elastically from small rapid insults but deforms extensively when minute forces are applied over long periods of time.

A novel 40,000 Da Ca2+-dependent actin modulator from bovine brain

A monomeric protein of Mr 40,000 that modulates the polymer state of actin has been isolated from bovine brain. When added either to preformed actin filaments or to monomeric actin, prior to polymerization, the modulator reduces the low-shear viscosity of F-actin provided that Ca2+ is present. The 40 kDa protein also inhibits the rate of actin polymerization. The inhibition is fully suppressed by removal of Ca2+ and restored by subsequent readdition of Ca2+, suggesting that the Ca2+-controlled interaction of actin with the 40 kDa modulator is freely reversible.

Cytoskeletal organization affects cellular responses to cytochalasins: comparison of a normal line and its transformant

The relationships between cytoskeletal network organization and cellular response to cytochalasin D (CD) in a normal rat fibroblast cell line (Hmf-n) and its spontaneous transformant (tHmf-e), with markedly different cytoskeletal phenotypes, were compared (using immunofluorescence, electron microscopy, and DNAse I assay for actin content). Hmf-n have prominent, polar stress fiber (SF) arrays terminating in vinculin adhesion plaques whereas tHmf-e, which are apolar, epithelioid cells with dense plasma membrane-associated actin networks, lack SF and adhesion plaques. Hmf-n exposed to CD become markedly retracted and dendritic, SF-derived actin aggregates form large endoplasmic masses, and discrete tabular aggregates at the distal ends of retraction processes. Prolonged exposure leads to recession of process, cellular rounding, and development of large cystic vacuoles. tHmf-e cells exposed to similar doses of CD display a diagnostically different response; retraction is less drastic, cells retain broad processes containing scattered actin aggregates in discrete foci often associated with plasma membrane, large tabular aggregates are never found and processes persist throughout long exposure, vacuolation is uncommon. The CD-induced microfilamentous aggregates in Hmf-n are composed of short, kinky filament fragments forming a felt-like skein, often aggregates contain a more ordered array of roughly parallel fragments, while those of tHmf-e are very short, kinky, randomly orientated filaments imparting a distinctly granular nature to the mass. Total actin content and the amount of actin associated with detergent-resistant cytoskeletons increase following CD exposure in both cell types. Throughout exposure to CD, the actin-associated contractile proteins tropomyosin, myosin, and alpha-actinin co-localize within the actin aggregates in both cell types. Fodrin, the protein linking cortical actin to membrane, co-localizes with actin aggregates in tHmf-e cells and most, but not all, such aggregates in Hmf-n cells, consistent with their stress fiber derivation. Vinculin is lost from the tabular aggregates at the distal ends of retraction processes in Hmf-n cells concomitant with the fragmentation and contraction of SF. The aborized processes in both cells types contain strikingly similar axial cores of bundled vimentin filaments associated with passively compressed microtubules. The characteristic CD-induced distribution of actin filament aggregates and redistribution of vimentin in these cell types also occur when cells are allowed to respread from the rounded state in the presence of CD.

A computerized low-shear pendulum viscoelastometer, stress-relaxation, shear creep, and dynamic elastic moduli measurements of soft biogels

A computerized low-shear pendulum viscoelastometer that is well suited for measurements of the viscoelastic properties of soft biogels is described. The instrument has three modes of operation: (i) measurement of dynamic elastic moduli, (ii) stress relaxation, and (iii) shear creep-creep recovery. The main mechanical parts of the instrument include a specimen cuvette and a pendulum with a thin metal plate extending into the specimen cuvette. The cuvette and pendulum can undergo independent angular movements relative to a horizontal axis located about 12 cm above the specimen cuvette. The absolute angular position of the cuvette is under on-line computer control through a stepping motor driven micrometer. The angular position of the pendulum relative to the cuvette is measured using an inductive position detector. The necessary software for automatic operation, data acquisition and processing has been developed for all the three modes of operation. The instrument is well suited for measurements of dynamic elastic moduli in the range 0.02-150 dyn/cm2. Calibration data obtained using 100% ethanol are presented. The instrument suitability for measurements of stress relaxation and shear creep-creep recovery is illustrated by presenting the results of such measurements on a 5.5-mg/ml erythrocyte spectrin gel in isotonic solution.

Cytoplasmic motions, rheology, and structure probed by a novel magnetic particle method

The motions of magnetic particles contained within organelles of living cells were followed by measuring magnetic fields generated by the particles. The alignment of particles was sensed magnetometrically and was manipulated by external fields, allowing non-invasive detection of particle motion as well as examination of cytoplasmic viscoelasticity. Motility and rheology data are presented for pulmonary macrophages isolated from lungs of hamsters 1 d after the animals had breathed airborne gamma-Fe2O3 particles. The magnetic directions of particles within phagosomes and secondary lysosomes were aligned, and the weak magnetic field produced by the particles was recorded. For dead cells, this remanent field was constant, but for viable macrophages, the remanent field decreased rapidly so that only 42% of its initial magnitude remained 5 min after alignment. A twisting field was applied perpendicular to the direction of alignment and the rate at which particles reoriented to this new direction was followed. The same twisting was repeated for particles suspended in a series of viscosity standards. Based on this approach, the low-shear apparent intracellular viscosity was estimated to be 1.2-2.7 X 10(3) Pa.s (1.2-2.7 X 10(4) poise). Time-lapse video microscopy confirmed the alignment of ingested particles upon magnetization and showed persistent cellular motility during randomization of alignment. Cytochalasin D and low temperature both reduced cytoplasmic activity and remanent-field decay, but affected rheology differently. Magnetic particles were observed in association with the microtubule organizing center by immunofluorescence microscopy; magnetization did not affect microtubule distribution. However, both vimentin intermediate filaments and f-actin reorganized after magnetization. These data demonstrate that magnetometry of isolated phagocytic cells can probe organelle movements, rheology, and physical properties of the cytoskeleton in living cells.

Functionality of muscle proteins in gelation mechanisms of structured meat products

Recent advances in muscle biology concerning the discoveries of a large variety of proteins have been described in this review. The existence of polymorphism in several muscle proteins is now well established. Various isoforms of myosin not only account for the difference in physiological functions and biochemical activity of different fiber types or muscles, but also seem to differ in functional properties in food systems. The functionality of various muscle proteins, especially myosin and actin in the gelation process in modal systems which simulate structured meat products, is discussed at length. Besides, the role of different subunits and subfragments of myosin molecule in the gelation mechanism, and the various factors affecting heat-induced gelation of actomyosin in modal systems are also highlighted. Finally, the areas which need further investigation in this discipline have been suggested.

Isolation and some properties of macrophage alpha-actinin: evidence that it is not an actin gelling protein

We have isolated an actin-binding protein from rabbit alveolar macrophages which by virtue of its physical properties we classify as a nonmuscle alpha-actinin. The protein consists of two subunits of Mr 103 000 and has a Stokes' radius of 7.26 nm and a sedimentation coefficient of 6.83 X 10(-13) s-1. Under the electron microscope, rotary-shadowed molecules appeared as short rods with an average length of 39.9 nm. We have examined the nature of the interaction of macrophage alpha-actinin with F-actin. The binding of radioiodinated macrophage alpha-actinin to F-actin is calcium sensitive. At a low concentration of free calcium (less than 10(-9) M), the binding affinity is 4.2 X 10(6) M-1 and is relatively unaffected by changes in temperature, while in the presence of 0.1 mM Ca2+, binding is reduced more than 5-fold. The stoichiometry of binding suggests that alpha-actinin binds all along the length of the actin filaments. The affinity of 45Ca2+ for macrophage alpha-actinin is 4 X 10(6) M-1 with a capacity of four calcium ions per molecule. Although macrophage alpha-actinin has calcium-inhibitable actin gelation activity at 7 degrees C, its effect on the apparent viscosity of F-actin decreases with increasing temperature, and at 37 degrees C, no gel point is observed. Therefore, at the temperature at which macrophages function in vivo, alpha-actinin probably does not promote the isotropic gelation of actin.

Interaction of rat liver lysosomal membranes with actin

Membranes were prepared from lysosomes purified 80-fold by centrifugation in a discontinuous metrizamide gradient. When salt-washed membranes were combined with rabbit muscle actin, an increase in viscosity could be measured using a falling ball viscometer. The lysosomal membrane-actin interaction was actin- and membrane-concentration dependent and appeared to be optimal under presumed physiological conditions (2 mM MgCl2, 1 mM MgATP, neutral pH, and free calcium concentration less than 10(-8) M). The actin cross-linking activity of the membrane was optimal at pH 6.4. The interaction was maximal between 10(-7) and 10(-9) M free calcium ions and inhibited by approximately 50% at concentrations of calcium greater than 0.5 x 10(-7) M. The actin-lysosomal membrane interaction was destroyed if the membranes were pretreated with Pronase, or if the membranes were purified in the absence of protease inhibitors. The interaction was not destroyed if membranes were washed with high salt or extracted with KCl and urea. In addition, a sedimentation assay for the actin-lysosomal membrane interaction was also performed to corroborate the viscometry data. The results suggest the existence of an integral lysosomal membrane actin-binding protein.

Abundance, relative gelation activity, and distribution of the 95,000-dalton actin-binding protein from Dictyostelium discoideum

We have studied the abundance, relative gelation activity, and distribution of the 95,000-dalton actin-binding protein in Dictyostelium discoideum amoebae. The 95,000-dalton protein was a prominent polypeptide as assessed using quantitative densitometry and radioimmunoassay. We estimated that this protein comprised approximately 1.2% of the protein in a soluble extract of amoebae. The molar ratio of the dimeric 95,000-dalton protein to actin in the soluble extract was 1:30. The apparent viscosities of actin mixtures with either the purified 95,000-dalton protein or the soluble extract were measured by falling ball viscometry in an attempt to assess the contribution of the 95,000-dalton protein to gelation of the soluble extract. The gelation of the soluble extract was significantly less than that expected from the contribution of the 95,000-dalton protein alone. Consequently, we questioned the validity of quantitative analyses of the contributions of specific actin-binding proteins to the gelation of cell extracts. The apparent distribution of the 95,000-dalton protein was observed in chemically fixed and extracted cells by immunofluorescence microscopy and compared with the distribution of cytoplasm and organelles visible using light microscopy. The 95,000-dalton protein was dispersed throughout the cytoplasm of fixed cells, was apparently excluded from prominent organelles, and displayed brightest fluorescence in regions of hyaline cytoplasm. These regions of hyaline cytoplasm that exhibited the brightest fluorescence were observed in the cortical region of rounded cells and in pseudopods of polarized cells. Thus, cell shape and polarity may also have influenced the apparent distribution of the 95,000-dalton protein observed by immunofluorescence microscopy. Study of the distribution of fluorescein-labeled ovalbumin injected into living cells supported the interpretation that the thickness of the cell and the distribution of organelles contributed to the apparent distribution of the 95,000-dalton protein observed in fixed cells using immunofluorescence microscopy. We suggest that the 95,000-dalton protein contributes to modulation of the consistency and contractility of the cytoplasm of D. discoideum amoebae, since it could cross-link actin filaments in vitro in a reversible process that was regulated by changes in the concentration of calcium and of protons, and since it was present in large quantity in the cytoplasm of these cells.