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J. Biol. Chem., Vol. 277, Issue 20, 18143-18150, May 17, 2002

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Microheterogeneity Controls the Rate of Gelation of Actin Filament Networks^*

Yiider Tseng^§, Kwang M. An, and Denis Wirtz^§¶

From the  Department of Chemical Engineering, ^§ Program in Molecular Biophysics, ^¶ Department of Materials Science and Engineering, The Johns Hopkins University, Baltimore, Maryland 21218

Received for publication, November 13, 2001, and in revised form, February 26, 2002

	ABSTRACT

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

Rapid sol-gel transitions of the actin cytoskeleton are required for many key cellular processes, including cell spreading and cell locomotion. Actin monomers assemble into semiflexible polymers that rapidly intertwine into a network, a process that in vitro takes ~1 min for an actin concentration of 1 mg/ml. The same actin filament network, however, takes ~1 h to exhibit a steady-state elasticity. We hypothesize that the slow gelation of F-actin is due to the slow establishment of a homogeneous meshwork. Using a novel method, time-resolved multiple particle tracking, which monitors the range of thermally excited displacements of microspheres imbedded in the network, we show that the increase in elasticity in a polymerizing solution of actin parallels the progressive decline of the network microheterogeneity. The rates of gelation and network homogenization slightly decrease with actin concentration and in the presence of the F-actin cross-linking proteins -actinin and fascin, whereas the rate of actin polymerization increases dramatically with actin concentration. Our measurements show that the slow spatial homogenization of the actin filament network, not actin polymerization or the formation of polymer overlaps, is the rate-limiting step in the establishment of an elastic actin network and suggest that a new activity of F-actin binding proteins may be required for the rapid formation of a homogeneous stiff gel.

	INTRODUCTION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

Many key cellular processes, including cell spreading and cell locomotion, require rapid sol-gel transitions of the actin cytoskeleton (1, 2). Under physiological conditions, G-actin¹ monomers assemble into semiflexible F-actin polymers, which rapidly overlap into a network, a process that in vitro takes ~1 min for an actin concentration of 1 mg/ml (3). The same actin filament network, however, takes ~1 h to exhibit a steady-state stiffness, a direct measure of the extent of gelation (see "Results" below). We also observe that increasing actin concentrations decelerate gelation but accelerate polymerization (see "Results"). Moreover, the gelation of F-actin in the presence of auxiliary proteins is much slower than required to produce morphological changes at the edge of adherent cells (4). Cellular protrusions, including filopodia and lamellipodia, typically appear and vanish in minutes even in slow-locomoting fibroblasts (1). We hypothesize that the large discrepancy in time scales between actin polymerization and actin network gelation in vitro is due to the slow establishment of a homogeneous network.

No existing method can quantitatively probe the evolution of the organization of a cytoskeletal network in real-time. Current methods either ensemble-average physical properties of the network yielding an average mesh size or average correlation length (e.g. neutron and light scattering) or have not been made quantitative (e.g. cryo-electron microscopy). We introduce a new method, time-resolved multiple particle tracking, which makes use of the distributions of Brownian displacements of microspheres imbedded in the network. This approach monitors the spatio-temporal organization of actin filaments in solution and quantifies the time-dependent degree of heterogeneity in F-actin solution undergoing gelation.

	MATERIALS AND METHODS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

Preparation of Actin and F-actin-binding Proteins-- Unless specified, all reagents were purchased from Sigma Chemical Co. (St. Louis, MO). Actin was prepared from chicken breast using Sephacryl S-300 for gel filtration (5, 6). Purified actin was stored as Ca²⁺-actin in continuous dialysis at 4 °C against buffer G (0.2 mM ATP, 0.5 mM dithiothreitol, 0.2 mM CaCl₂, 1 mM sodium azide, and 2 mM Tris-HCl, pH 8.0). Mg²⁺-actin filaments were generated by adding 0.1 volume of 10× KMEI (500 mM KCl, 10 mM MgCl₂, 10 mM EGTA, 100 mM imidazole, pH 7.0) polymerizing salt to 0.9 volume of G-actin in buffer G. -Actinin was purified from chicken gizzard (7, 8). Human fascin was expressed as a glutathione S-transferase fusion in Escherichia coli; the fusion protein was dialyzed against phosphate-buffered saline/dithiothreitol and liberated from glutathione S-transferase by cleavage with thrombin, followed by glutathione-Sepharose chromatography (6). Fascin and -actinin were used within 5 days of purification.

Time-dependent Microheterogeneity via Time-dependent Multiple Particle Tracking-- The trajectories of fluorescent carboxylated microspheres imbedded in actin solutions undergoing gelation were recorded using a silicon-intensified target camera (VE-1000, Dage-MTI, Michigan City, IN) mounted on an inverted epifluorescence microscope equipped with a 100× oil-immersion objective (numerical aperture 1.3) (Nikon, Inc., Melville, NY) (9). The centroid of each microsphere, defined as the intensity-weighted center of gravity of the microsphere, was tracked with a resolution of ~5 nm, as determined by immobilizing microspheres on a glass microslide using a strong adhesive and tracking their apparent displacements (10). MPT tracks the movements of the probe microspheres in the plane of focus of the microscope objective (i.e. two-dimensional tracking). Two-dimensional tracking assumes that the probed material is isotropic (11) but not necessarily homogenous. Microspheres that are slightly out of focus may appear larger than they are, but this is inconsequential, because we do not measure the (known) size of the particles only the displacements of their centroids. Fields of view were selected at random at each probed time during the course of gelation. Despite the fact that MPT can track hundreds of particles simultaneously, the number of tracked particles per field of view was chosen to be low (between 5 and 20) to avoid particle-particle interactions mediated by the filaments. For each tested actin concentration, the movements of a total of 110-140 microspheres were tracked, which necessitated 5-7 specimens per tested concentration and gelation time. Images of the microspheres were captured at a frequency of 30 Hz for 20 s, initially every 8 min for ~1.5 h followed by 15 min for ~2.5 h, using a custom routine incorporated to the software Metamorph (Universal Imaging Corp., West Chester, PA). Mean squared displacements of individual particles were computed from the microsphere trajectories (12) then transformed into local compliance as described previously (13) (see "Results"). Surface effects between the probe microsphere and the filaments may cause the local network moduli to be underestimated by particle tracking (14) without affecting measurements of the network heterogeneity. The compliance distributions were statistically analyzed by their moments and bin distributions as described previously (15, 16). We verified that our MPT measurements of network compliance distribution were independent of the size of the microspheres for diameters > 0.2 µm (data now shown). We observed little sedimentation of the 1-µm microspheres primarily used in our experiments. All MPT measurements were conducted at room temperature.

Gelation Kinetics via Time-resolved Mechanical Rheometry-- The rate and extent of gelation of F-actin networks were probed using a strain-controlled cone-and-plate rheometer (ARES-100, Rheometrics, Piscataway, NJ) as described (17, 18). The lower plate of the rheometer is coupled to a computer-controlled motor, which applies small oscillatory shear deformations of controlled frequency and amplitude. The upper cone is connected to a torque transducer, which measures the stress induced by shear deformations within the F-actin specimen, maintained here at room temperature. We report the time-dependent in-phase component of the stress divided by the amplitude of the applied oscillatory deformation of fixed frequency, i.e. the storage (or elastic) modulus, G'(t), where t is the elapsed time after initiation of actin polymerization. Each G-actin solution was mixed with a one-tenth volume of 10× KMEI and immediately loaded onto the lower plate of the rheometer using a micropipette with a cut-off tip to limit filament breakage. The dead time between the time of protein mixing and data collection was constant and equal to 30 s for all experiments. For each specimen, F-actin solution gelation was measured by recording G' by application of two cycles of (small) shear deformation of 1% amplitude and fixed frequency of 1 rad/s, every 30 s for 6 h. We verified that these repeated deformations did not affect the kinetics of gelation by applying 1%-amplitude shear deformations every 10 min for 6 h (data not shown). Evaporation of the specimen was avoided by using a vapor trap placed around the lower and upper tools; no apparent evaporation was observed compared with the control without the trap, for which about one-fourth of the sample had evaporated after 6 h. Using the strain-controlled rheometer, we also measured the frequency-dependent elastic modulus G'() over the frequency range of 0.5 rad/s-100 rad/s. The collection of each frequency spectrum took about 2 min, a time much shorter than characteristic times of gelation. Such a spectrum was collected every 10 min until a steady-state frequency profile was reached (see "Results").

Actin Polymerization via Time-resolved Fluorescence Spectroscopy-- To monitor actin assembly, actin was labeled with N-(1-pyrenyl)iodoacetamide as described (19, 20), which produced 80 mol% pyrene-labeled actin. For each fluorometric measurement, a 0.7-ml mixture containing 90% unlabeled actin and 10% pyrene actin was used. The actin polymerization assay was conducted in an LS-50S luminance spectrophotometer (PerkinElmer Life Sciences, Shelton, CT). The excitation wavelength was set at 365 nm; the emission was monitored at 407 nm for 2 h at room temperature after initiation of actin polymerization.

	RESULTS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

Homogenization of F-actin Solutions as Measured by Time-resolved Multiple Particle Tracking-- We hypothesized that the slow increase in elasticity displayed by an F-actin solution undergoing gelation is due to the slow establishment of a homogeneous network (i.e. constant mesh size), not to the rate of monomer assembly into filaments. To test this model of actin gelation, we monitored the rate and extent of microheterogeneity in F-actin solutions using time-resolved multiple particle tracking. Fluorescently labeled, 1-µm diameter microspheres were suspended in 3 µM, 10 µM, and 24 µM G-actin solutions (Fig. 1A), where polymerization was initiated by addition of KMEI salt (see "Materials and Methods"). The Brownian trajectories of the centroids of a total ~130 particles per actin concentration were recorded with 5-nm spatial resolution and 30-Hz temporal resolution, for 20 s every 8 min for 1.5 h, then every 15 min for 2.5 h (Fig. 1). Typical trajectories of microspheres imbedded in actin solutions of increasing concentration and in an F-actin solution at different times during the gelation process are shown in Fig. 1. As expected, the range of the displacements was reduced by increasing actin concentration (Fig. 1C), i.e. the local compliance of the network decreased for increasing actin concentration. The extent of these movements decreased (slightly) with gelation time (Fig. 1D). As described next, these trajectories serve as raw data to analyze the degree of heterogeneity of actin filament networks undergoing gelation.

View larger version (17K): [in this window] [in a new window]   Fig. 1.   Principle of multiple particle tracking (MPT) measurements in F-actin solutions. A, randomly selected frame of a movie of fluorescently labeled carboxylated 1-µm diameter polystyrene microspheres dispersed in a 3 µM actin solution in the presence of the polymerizing salt KMEI (see "Materials and Methods"). The concentric squares around each microsphere allow the MPT software to continuously identify the particles during movie capture. Their sizes are initially set manually. The centroid of each microsphere is video-tracked with 5 nm of spatial resolution; a field of view of 120 µm × 120 µm is monitored for 20 s every 8 min for 1.5 h and then every 15 min for 2.5 h. B, 20-s trajectories of microspheres (shown in A) collected 30 min after initiation of polymerization. C, detail of a typical trajectory of a microsphere placed in a 3, 10, and 24 µM F-actin solution, 194 min after initiation of polymerization. D and E, detail of a 20-s displacement of a microsphere dispersed in a 10 µM F-actin solution collected 6 and 240 min after onset of polymerization.

To quantify the microheterogeneity of F-actin networks, individual mean squared displacements (MSD), r²(), of microspheres distributed throughout the solution were computed from the microspheres' time-dependent two-dimensional coordinates, which were then transformed into local time-dependent compliance values, (). We have indeed previously proved that the MSD is directly proportional to the (local) compliance of the network produced by the small random forces of order k_BT/a created by the thermally driven fluctuations of the particles (13). The time-dependent compliance, (), is related to the measured MSD by () = (a/k_BT)r²(), where k_BT is the thermal energy and a is the radius of the microsphere (13). A liquid of shear viscosity  subjected to a constant (small) stress displays a creep compliance that increases linearly with time, () = /; a Hookean solid of modulus G₀ under stress displays a time-independent compliance  = 1/G₀; the time-dependent compliance of a viscoelastic system such as an F-actin network shows an intermediate behavior (13). The magnitude and time dependence of the compliance traces (Fig. 2, A and B) show that the actin network at early times is softer (i.e. more compliant, more deformable) and more viscous-like (i.e. the slope of  is higher) than at later times during the gelation process.

View larger version (41K): [in this window] [in a new window]   Fig. 2.   Time-resolved MPT measurements in actin filament networks undergoing gelation. Typical compliance traces () of the network in the vicinity of microspheres dispersed in a 10 µM F-actin solution. Compliance traces obtained (A) 6 min and (B) 240 min after addition of polymerizing salt to the G-actin solutions. The vertical lines in A and B show where distributions in C and D were collected. C and D, compliance distributions (n ~ 130) collected at a time lag of 0.1 s. Insets: associated  distributions at a time lag of 1.0 s.

Distributions of the local network compliance at different time scales were generated from measured MSDs (Fig. 2, C and D) and statistically analyzed in terms of bin distributions (see below). We found that the local compliance of a 10 µM actin solution showed a relatively wide distribution during a short time after initiation of actin polymerization (Fig. 2C). At long elapsed times, the distribution in compliance became progressively narrower and more symmetric (Fig. 2D), a qualitative effect that can be quantified using bin distributions (see below). This change of the compliance distribution was particularly pronounced at long time scales (Fig. 2, compare C and D with their respective insets), presumably due to the decrease in the extent of heterogeneity in F-actin gels after a long equilibration time (see more in "Discussion").

To determine the degree of heterogeneity in the physical properties of F-actin solutions undergoing gelation, compliance distributions were statistically analyzed by computing time-dependent means and bin distributions. As expected, the network stiffened during gelation, as detected by the decrease of the ensemble-averaged compliance, which is obtained by averaging all (~130) values of local compliance at a given gelation time for each tested actin solution (Fig. 3, A and B). Directly comparing statistical parameters of distributions (i.e. standard deviation, skewness, kurtosis) that encompass different values can be somewhat misleading, we therefore opted to report the "bin partition" of compliance values, which is insensitive to the actual values in the distribution. Bin partitions of the compliance distributions were obtained by comparing the contributions of the 10%, 25%, and 50% highest values of the local compliance to the mean compliance for each tested actin concentration and at different points in time during gelation. The fractional contributions of the highest 10%, 25%, and 50% local compliance to the mean compliance should be close to unity for a highly heterogeneous solution and close to 0.1, 0.25, and 0.50 for a perfectly homogeneous solution; these parameters therefore describe the degree of heterogeneity in compliance of the F-actin network. We verified that these parameters were indeed close to their homogenous values for perfectly homogenous glycerol solutions (Fig. 4A) and were close to unity for a highly heterogeneous solution (as qualitatively assessed by confocal microscopy) containing both fascin-mediated actin bundles and -actinin-cross-linked filaments (15). During gelation, contributions from the highest compliances to the ensemble-averaged compliance decreased toward values close to the theoretical values for homogeneous networks (Fig. 4, A-D). Higher actin concentrations typically produced values of these homogeneity parameters that were higher than obtained at low concentrations (compare Fig. 4, B and D), i.e. concentrated F-actin solutions were more heterogeneous than dilute solutions. Moreover, these parameters took longer to decrease toward their homogeneous values in concentrated actin solutions, i.e. the rate of network homogenization decreased with actin concentration. Therefore, the degree of heterogeneity decreases during gelation, a homogenization process that is slowed down by high actin concentrations.

View larger version (24K): [in this window] [in a new window]   Fig. 3.   Ensemble-averaged network compliance. A, time lag-dependent mean compliance (ensemble-averaged ) in 3 and 24 µM actin solutions measured 6 min (upper curve), 1 h (intermediate curve), and 4 h (lower curve) after initiation of actin polymerization. The last two curves are superimposed. B, evolution of the ensemble-averaged  evaluated at a time lag of 0.1 s during solution gelation.

View larger version (34K): [in this window] [in a new window]   Fig. 4.   Statistical analysis of network compliance () distributions. A, fractional contributions of the highest 10%, 25%, and 50% values of local compliance to the mean compliance in a glycerol solution measured at a time scale of 0.1 s (first columns) and 1.0 s (second columns). These contributions are close to the expected values for a perfectly homogeneous solution, i.e. 0.10, 0.25, and 0.50. B-D, time-dependent contributions (defined as fractions of unity) of the highest 10, 25, and 50% compliance values measured at a time scale of 1 s to the mean compliance in B, 3 µM; C, 10 µM; and D, 24 µM actin solutions.

Actin Polymerization and Gelation Kinetics: Effect of Actin Polymerization and F-actin Cross-linking Proteins -Actinin and Fascin-- Time-resolved multiple particle tracking measurements were complemented by traditional fluorescence and rheological measurements to directly compare the rates of homogenization of actin solution to the rates of actin polymerization and rates of gelation. Gelation kinetics, as detected by the time-dependent elasticity G'(t), where t is the elapsed time after initiation of actin polymerization and which is measured at a fixed frequency of 1 rad/s, did not follow a simple exponential behavior (Fig. 5A). Therefore, the rate of gelation was conveniently defined as the inverse of the time necessary to reach 90% of the steady-state value of G' (averaged here over 10 min). The rate of gelation measured by rheology slightly decreased with actin concentration (Fig. 5B). We monitored the propensity of actin filaments to diffuse in solutions during gelation by probing the frequency dependence of the elastic modulus, G'() every 10 min for 6 h. Each frequency sweep took ~2 min, a time much shorter than characteristic times of gelation (as shown in Fig. 5B). Moreover, we verified that the gelation process (i.e. extent and rate of gelation) were independent of the rate of data acquisition, i.e. subjecting the network to (small) deformations did not affect its gelation process (see "Materials and Methods"). At the beginning of gelation, G'() values were low at low frequencies and elevated at high frequencies, which reflects a relatively high degree of mobility of the filaments in the network (Fig. 5C), presumably due to the presence of large heterogeneities at early times. This steep dependence on frequency declined progressively before reaching a steady-state frequency-dependent profile (Fig. 5C). The elastic modulus remained relatively unchanged at high frequencies, but greatly increased at low frequencies (Fig. 5C). These measurements therefore corroborate the MPT measurements, which showed that compliance profiles displayed a steep time scale dependence at early times during gelation and less time scale dependence at later times (Fig. 2, A and B).

View larger version (52K): [in this window] [in a new window]   Fig. 5.   F-actin polymerization and solution gelation: Effect of F-actin cross-linking proteins. A, time-dependent elasticity G'(t) measured at a fixed frequency of 1 rad/s and deformation amplitude of 1%. Closed arrows indicate when actin polymerization has reached a steady state (times taken from E); open arrows indicate when G' has reached 90% of its steady-state value. Note the increasing time distance between gelation times and polymerization times for increasing actin concentration. B, concentration-dependent gelation rate of F-actin solution as probed by rheometry. These rates correspond to the inverse of the time required to reach 90% of the steady-state elasticity (see "Materials and Methods"). Error bars correspond to variations around the mean time required to reach steady-state values. C, gelation time-dependent, frequency-dependent elasticity, G'(), of a 24 µM actin solution undergoing gelation. G'() was measured at a fixed deformation amplitude of 1% at the gelation times indicated in the figure. D, rate of gelation of 24 µM actin solutions in the presence of the F-actin bundling protein fascin and the F-actin cross-linking/bundling protein -actinin divided by the rate of gelation of a 24 µM F-actin solution (= 7.7 × 102 min1). E, fluorescence intensity increase due to F-actin assembly using the pyrene assay (see "Materials and Methods"). F, concentration dependence of the rate of fluorescence intensity increase.

It is often assumed that the rate of gelation, which describes the kinetics at which a steady-state elasticity is reached, can be enhanced by the presence of filament cross-linkers. We tested this hypothesis by polymerizing actin in the presence of the prototypical F-actin cross-linker chicken -actinin (15, 21, 22) and the F-actin bundling protein human fascin (6, 10). We found that the rate of gelation as probed by rheology changed little or slightly decreased in the presence of fascin and -actinin (Fig. 5D). In contrast, the pyrene assay showed that the rate of actin assembly was relatively insensitive to the presence of -actinin (data not shown), but greatly increased with actin concentration (Fig. 5, E and F). We observed that the polymerization rates were much higher than the rates of gelation (Fig. 5B) and the rates of network homogenization (Fig. 4). The difference between the rate of gelation and the rate of network homogenization was enhanced at high actin concentrations as indicated by the increasing time distance between arrows in Fig. 5a, which show the times at which actin polymerization and actin gelation have reached 90% of their steady-state values.

	DISCUSSION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

Network Homogenization Controls the Rate of Gelation of F-actin Networks-- The sol-gel transition of the actin cytoskeleton is believed to be one of the necessary steps in cell locomotion (1, 2, 23). Yet the fundamental mechanism of F-actin network gelation is not well understood because rates of gelation and actin polymerization occur at completely different time scales. This large time scale discrepancy means that the rate at which the elasticity increases in an F-actin network undergoing gelation is not governed by the onset of topological overlaps between filaments, which occurs as soon as actin filaments have polymerized, at least at the tested actin concentrations. Indeed, as soon as filaments are formed, they will overlap even at concentrations as low as 3 µM, due to the fact that F-actin is a semiflexible polymer (24). To the best of our knowledge, the concentration dependence of the rate of gelation has not been previously reported. We note, however, that the rate of gelation measured at 24 µM was slightly lower than that measured by Janmey et al. (25), but the actin used in those experiments is now known to display thiol oxidation, which artificially enhances the elasticity of the F-actin network. Our measured rates of actin polymerization were in quantitative agreement with results obtained by many groups (20, 26). We also note that precautions were taken to eliminate possible artifacts due to presence of capping proteins (which would accelerate actin polymerization) (27) and enhanced interactions between filaments due to thiol oxidation (25). In particular, the actin used in our experiments was doubly gel-filtered, was continuously dialyzed against buffer G for storage, was used within 2 days of purification, and was never frozen (28). Therefore, gelation kinetics does not seem to correspond to the onset of topological overlaps in the network during actin polymerization and after actin polymerization has occurred.

Based on our results, our working model to explain the slow rate of F-actin network gelation (despite rapid actin polymerization) is that filaments take a long time to form a homogeneous network. The large pores initially formed at random in the network greatly reduce the overall elasticity of the network during the early phase of gelation. We speculate that actin filaments progressively move into those large network pores to gain conformational entropy, a process that is slow because actin filaments are long and semiflexible. Note that the commonly used falling-ball assay, which measures the viscous friction generated by a heavy bead moving down a tube of polymerizing actin, cannot be used to monitor actin polymerization, because it effectively probes F-actin network gelation. To investigate the degree of network heterogeneity during F-actin gelation, we introduced a novel method, time-resolved multiple particle tracking, that monitors the dispersion of displacements of microspheres imbedded in the network. These new measurements, which were complemented with traditional rheological and fluorescence measurements, suggest that the rate of network homogenization, not the extent of polymerization, controls the kinetics of F-actin network gelation. In support of this model of gelation, we found that the rate of network homogenization and the rate of gelation decrease both with actin concentration while the rate of polymerization increases with concentration and the degree of heterogeneity increases with actin concentration. We also found that the rate of gelation and rate of homogenization are comparable.

We suggest that the rate of homogenization decreases with actin concentration, because filaments, which are quickly formed, take an increasing time to diffuse toward large pores. That time increases partly because the mesh size of the network is smaller at high actin concentration (29) and because polymer transport becomes slow and sub-diffusive in a progressively more congested network (30, 31). We note that the characteristic time for network homogenization to set in (Fig. 4C) is of the same magnitude as the relaxation time of filaments in an entangled solution (32). This relaxation time is the diffusion time required for a filament to move approximately its own length (33). We shall test our hypothesis that polymer diffusion is a mechanism of network homogenization in future studies. Can other slow processes, including filament annealing and fragmentation and ATP hydrolysis, be responsible for the slow homogenization of F-actin networks (34, 35)? We think that filament fragmentation and annealing are unlikely to play a major role in setting the pace for F-actin gelation, because polymer length has no effect on the overall elasticity of a semidilute solution of semiflexible polymers according to well-accepted models of polymer physics (36, 37). This is due to the fact that polymer length does not affect the mesh size and, therefore, the modulus of polymer networks (30, 33). Moreover, the rate of filament annealing increases with actin concentration, whereas the rate of gelation decreases with actin concentration. Finally, ATP hydrolysis of F-actin has been shown not to affect the mechanical properties and ultrastructure of actin filaments (38).

Why F-actin Cross-linking/Bundling Proteins Do Not Enhance the Rate of Gelation of F-actin Solutions-- One may speculate that the rate of gelation could be enhanced by gelation factors such as F-actin cross-linking and bundling proteins. Using mechanical rheometry, we measured the rate of gelation of F-actin solutions in the presence of different types of ubiquitous F-actin binding proteins. In the presence of the prototypical F-actin cross-linking protein -actinin, we found that the rate of gelation was, somewhat surprisingly, decreased at low molar ratios of -actinin to actin and became constant at high molar ratios (see also Refs. 6, 15). Although -actinin greatly increased the final steady-state values of the elasticity of F-actin, it did not enhance the rate to reach that steady-state value (39). A similar effect was observed in the presence of the prototypical F-actin bundling protein fascin (6), which promotes the parallel arrangement of actin filaments: The rate of gelation of F-actin slightly decreased at low fascin concentrations and became constant at high concentrations. These results suggest that actin cross-linking/bundling proteins are not necessarily good candidates for gelation factors. This result is readily explained by recent steady-state multiple particle tracking measurements. Both fascin and -actinin were shown to greatly enhance the degree of heterogeneity of F-actin networks (10, 15) even a long time (~6 h) after initiation of actin polymerization. We think that two conflicting effects are therefore at work when F-actin cross-linking/bundling proteins are present. Actin cross-linking/bundling proteins decrease the propensity for actin filaments to move in solution, which increases the overall network stiffness, but also slows down network homogenization.

Implications for the Cell-- The physical state of the actin network is clearly more complex in vivo than that of reconstituted actin network systems. Nevertheless, insight into possible mechanisms of actin gelation in vivo can be derived from our results in vitro. The observed slow rate of actin gelation in the presence/absence of actin cross-linking proteins implies that either the cell requires levels of elasticity that are lower than those obtained at steady state with cross-linking/bundling proteins or that F-actin networks are homogenized by another activity of F-actin binding proteins. A good candidate to rapidly form homogeneous and stiff F-actin structures, when and where needed (for instance, during cell migration at the leading edge), is the protein complex Arp2/3. The complex Arp2/3 nucleates dendritic actin structures at the leading edge of migratory cells (40). Cryo-electron microscopy of detergent-extracted lamella shows that the Arp2/3-rich cytoskeleton at the leading edge of locomotive keratocytes is indeed remarkably uniform (41, 42). The cytoskeleton becomes, however, more heterogeneous in the perinuclear region and in the myosin/-actinin-rich lamella. Our recent local micromechanical measurements in situ also show that the elasticity at the edge of the cell is much higher than in the perinuclear region (43). Arp2/3 would therefore not only help provide the cell with some of the propulsive forces for its locomotion as suggested by earlier work (3) but also structurally support new protrusions more effectively and more rapidly than conventional F-actin cross-linkers such as -actinin.

Our rheological measurements show that increasing concentrations of actin slightly slow down gelation kinetics. This results suggests that passive entropy-driven diffusion of filaments into the large pores of the meshwork or other passive effects such as annealing and breaking of filaments that may influence the rate of homogenization are too slow to sustain fast morphological changes of the cell. The homogenization of the actin cytoskeleton by passive filament diffusion could to be complemented by an activated process. This process could be initiated by motor proteins such as myosin, which would bias and enhance the transport of filaments into large meshwork pores (44). Large pores could also be "filled in" by localized polymerization of actin via nucleators such as the Arp2/3 complex and/or by the activation of F-actin severing/nucleating proteins such as gelsolin. Using the method of time-resolved multiple particle tracking introduced in this report, we are currently measuring the rate of gelation and ultrastructural homogenization of F-actin networks in the presence of myosin, the Arp2/3 complex, and gelsolin.

We believe that the versatility of the novel method presented in this report, time-resolved multiple particle tracking, will help shed new light on multiple problems in the biological sciences, including the determination of the local micromechanical properties of cells during cell locomotion and chemotactic migration, and materials science, including the local microstructure of complex fluids undergoing a glass transition or gelation.

	ACKNOWLEDGEMENT

We thank David Sept for helpful discussions.

	FOOTNOTES

^* This work was supported by National Science Foundation Grant CTS007227.The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

To whom correspondence should be addressed. Tel.: 410-516-7006; Fax: 410-516-5510; E-mail: wirtz@jhu.edu.

Published, JBC Papers in Press, March 11, 2002, DOI 10.1074/jbc.M110868200

	ABBREVIATIONS

The abbreviations used are: G-actin, globular actin; F-actin, filamentous actin; MPT, multiple particle tracking; MSD, mean-squared displacement.

	REFERENCES

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

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