Physical basis of the rheologic properties of F-actin

Actin assembly produces sufficient forces for endocytosis in yeast

We formulated a spatially resolved model to estimate forces exerted by a polymerizing actin meshwork on an invagination of the plasma membrane during endocytosis in yeast cells. The model, which approximates the actin meshwork as a visco-active gel exerting forces on a rigid spherocylinder representing the endocytic invagination, is tightly constrained by experimental data. Simulations of the model produce forces that can overcome resistance of turgor pressure in yeast cells. Strong forces emerge due to the high density of polymerized actin in the vicinity of the invagination and because of entanglement of the meshwork due to its dendritic structure and cross-linking. The model predicts forces orthogonal to the invagination that are consistent with formation of a flask shape, which would diminish the net force due to turgor pressure. Simulations of the model with either two rings of nucleation-promoting factors (NPFs) as in fission yeast or a single ring of NPFs as in budding yeast produce enough force to elongate the invagination against the turgor pressure.

Actin dynamics, architecture, and mechanics in cell motility

Tight coupling between biochemical and mechanical properties of the actin cytoskeleton drives a large range of cellular processes including polarity establishment, morphogenesis, and motility. This is possible because actin filaments are semi-flexible polymers that, in conjunction with the molecular motor myosin, can act as biological active springs or "dashpots" (in laymen's terms, shock absorbers or fluidizers) able to exert or resist against force in a cellular environment. To modulate their mechanical properties, actin filaments can organize into a variety of architectures generating a diversity of cellular organizations including branched or crosslinked networks in the lamellipodium, parallel bundles in filopodia, and antiparallel structures in contractile fibers. In this review we describe the feedback loop between biochemical and mechanical properties of actin organization at the molecular level in vitro, then we integrate this knowledge into our current understanding of cellular actin organization and its physiological roles.

Viscoelastic properties of f-actin, microtubules, f-actin/alpha-actinin, and f-actin/hexokinase determined in microliter volumes with a novel nondestructive method

A nondestructive method to determine viscoelastic properties of gels and fluids involves an oscillating glass fiber serving as a sensor for the viscosity of the surrounding fluid. Extremely small displacements (typically 1-100 nm) are caused by the glass rod oscillating at its resonance frequency. These displacements are analyzed using a phase-sensitive acoustic microscope. Alterations of the elastic modulus of a fluid or gel change the propagation speed of a longitudinal acoustic wave. The system allows to study quantities as small as 10 microliters with temporal resolution >1 Hz. For 2-100 microM f-actin gels a final viscosity of 1.3-9.4 mPa s and a final elastic modulus of 2.229-2.254 GPa (corresponding to 1493-1501 m/s sound velocity) have been determined. For 10- to 100-microM microtubule gels (native, without stabilization by taxol), a final viscosity of 1.5-124 mPa s and a final elastic modulus of 2.288-2. 547 GPa (approximately 1513-1596 m/s) have been determined. During polymerization the sound velocity in low-concentration actin solutions increased up to +1.3 m/s (approximately 1.69 kPa) and decreased up to -7 m/s (approximately 49 kPa) at high actin concentrations. On polymerization of tubulin a concentration-dependent decrease of sound velocity was observed, too (+48 to -12 m/s approximately 2.3-0.1 MPa, for 10- to 100-microM tubulin). This decrease was interpreted by a nematic phase transition of the actin filaments and microtubules with increasing concentration. 2 mM ATP (when compared to 0.2 mM ATP) increased polymerization rate, final viscosity and elastic modulus of f-actin (17 microM). The actin-binding glycolytic enzyme hexokinase also accelerated the polymerization rate and final viscosity but elastic modulus (2.26 GPa) was less than for f-actin polymerized in presence of 0.2 mM ATP (2.28 GPa).

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.

Rheological measurements of the influence of 1,2-propanediol on actin/alpha-actinin gel structure: the effects of temperature and protein concentrations

In previous studies, we demonstrated that 1,2-propanediol induces shortening and bundling of actin filaments, both in vitro and in vivo, and that it enhances actin/alpha-actinin interaction, especially at low temperature. 1,2-Propanediol also promotes homogeneous microporous networks which can be vitrified by rapid cooling. In the present study, dynamical rheological measurements were performed under various sets of experimental conditions including temperature (4 or 20 degrees C), protein concentrations (actin and alpha-actinin), and 1,2-propanediol presence or absence. Gelation kinetics were monitored, and the resulting actin mechanical properties investigated, in order to untangle the respective effects of the experimental parameters. Whether in the presence or absence of solvent, low temperature brings about a rigidification of the sample, as does high protein concentration, as expected. However, 1,2-propanediol itself involves either softening of the sample (at high temperature and low protein concentration or at low temperature and high protein concentration) or rigidification in the case of low temperature and low protein concentration. These effects result from the competition between actin/alpha-actinin affinity (enhanced by both low temperature and 1,2-propanediol), bundling of filaments (fostered by alpha-actinin for alpha-actinin/actin ratios used), rate of actin polymerization (higher at high temperature), shortening effect of 1,2-propanediol on actin filaments, and chain mobility (lower at high protein concentration). As discussed, only the combination of low temperature and low protein concentration induces full crosslinking of the system into a viscoelastic solid under the influence of 1,2-propanediol.

A torsion pendulum for measurement of the viscoelasticity of biopolymers and its application to actin networks

This report describes the design, construction, and method of operation of a torsion pendulum which is specifically designed for the measurement of soft and fragile biopolymer gels. The pendulum can be assembled and employed in a standard biological laboratory and provides data that currently require access to specialized equipment usually limited to physics or material science laboratories. This instrument measures the shear moduli of viscoelastic materials by applying either steady or oscillating shear forces to a disc-shaped sample and measuring the resulting angular displacement of a pendulum attached to one face of the sample. The device is easily constructed using commercially available materials and no specialized machinery. Shear stresses as low as 0.03 Pa and shear rates as low as 0.00003 s-1 can be measured in steady shear experiments, and dynamic shear moduli from 1 to 2500 Pa measured by oscillatory measurements with sample volumes as low as 0.5 ml. The use of the torsion pendulum is illustrated by measuring the effects of two different actin binding proteins on the viscoelasticity of actin filament networks.

Probe diffusion in cross-linked actin gels

The diffusion of monodisperse polystyrene latex spheres (PLS) in column-purified 0.65 mg/mL actin solutions, polymerized with 100 mM KCl in the absence and presence of a cross-linker, actin binding protein (ABP), has been studied using dynamic light scattering. Measurements over a wide range of scattering angles from 90 degrees to 8 degrees, corresponding to inverse scattering vector probing distances of about 40-400 nm, respectively, give a measure of both the fraction of PLS mobile over the probing distance (from the normalized time autocorrelation function amplitude) and the average diffusion coefficient of the mobile PLS. Both 100- and 500-nm diameter PLS are fully mobile in polymerized actin solutions over distances of less than 100 nm, as reported previously (Newman, J., Schick, K. S. & Gukelberger, G. Biophys. J. 53, 573a, and Newman, J., Mroczka, N. & Schick, K. L. Biopolymers, 28, 655-666). At increasing probing distances, or when ABP is added at molar ratios of 1:750 or 1:150, greater fractions of the PLS are immobilized, up to almost 99% at the conditions of a 400-nm probing distance with 500-nm probes and at a ratio of 1:150 added ABP to actin. The degree of immobilization correlated well with the amount of added ABP, the size of the PLS, and the probing distance. At increasing probe distances, as the degree of immobilization increases, the remaining mobile fraction of PLS has an increasing average diffusion coefficient. These results suggest a range of pore sizes in the actin gels with a mean size of a few hundred nanometers.

Dynamic light scattering measurements of the diffusion of probes in filamentous actin solutions

The diffusion coefficients of monodisperse polystyrene latex spheres in solutions of polymerized actin were measured using dynamic light scattering. Four different probes with radii R, ranging from 50 to 500 nm, were separately used in actin solutions with concentrations c, ranging from 1.5 to 21 microM, which had been polymerized with either 1 mM MgCl2, 1 mM CaCl2, or 100 mM KCl. Under all conditions, and at four different scattering angles in the range of 30 degrees-90 degrees, the measured average diffusion coefficients D of the probes were systematically smaller for samples of increased actin concentration or of increased probe radius. Control experiments indicated that the probes did not bind to the actin. These data for Mg2+- and Ca2+-polymerized actin agree and were found to be quite well summarized by the scaling relation D/D0 = exp[-alpha R delta c nu], where D0 is the measured diffusion coefficient of the probes in water (and, as also measured, in the starting actin solutions prior to polymerization with added salt), with values of delta = 0.73 +/- 0.05, nu = 1.08 +/- 0.09, and alpha = (1.1 +/- 0.6) x 10(-3) (with c in microM and R in nm). Data for KCl-polymerized actin show much more restricted diffusivities of the probes at comparable actin concentrations. Inhomogeneities in the solution are reflected in the "effective polydispersity" of the probe diffusion coefficients, which depend on local microviscosity differences.

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)

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.

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.

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.

A comparison of methods used to characterize gelation of actin in vitro

We have compared the meniscus depletion assay and falling ball viscometry, two means of assessing the extent of gelation in actin-based systems using mixtures of actin and the actin-binding protein filamin. We examined the effect of varying the concentrations of actin and filamin in both assays. The interaction of actin and filamin was detected only above a threshold concentration of filamin. This threshold concentration was lower for falling ball viscometry than for the meniscus depletion assay at equal actin concentrations. At constant concentrations of filamin, an increase in actin concentration caused an increase in apparent viscosity measured by the falling ball assay, but a decrease in sedimentability detected by the meniscus depletion assay. The rate of sedimentation of actin was dependent on the molar ratio of actin to filamin. At each molar ratio, the sedimentation of actin was not dependent on the specific concentrations of actin and filamin used. The apparent viscosity was dependent on both the molar ratio and the specific concentrations of actin and filamin. To relate the present results to earlier studies, we examined mixtures of actin and filamin using a macroscopic assay of gelation (tube tipping assay), and polarized light microscopy. The effect of increasing filamin concentration in the four assays was compared at three actin concentrations. Mixtures of actin and filamin whose apparent viscosities were low enough to be estimated by falling ball viscometry were optically isotropic fluids that flowed out of inverted test tubes. Mixtures of actin and filamin in the range of sensitivity of the meniscus depletion assay were either viscous fluids or gels, and were either optically isotropic or anisotropic. Thus, the four assays provide different estimates of gelation. Both the meniscus depletion assay and falling ball viscometry can be used to determine relative gelation activity, but neither can be used as a quantitative assay of gelation.