INTRODUCTION

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Cytoplasm is viscoelastic, so that it can either deform or rebound in response to force (1, 2). Deformation is essential for cellular movement, whereas elastic responses allow cells to maintain their shapes. Scientists have appreciated this duality of cytoplasm for more than 100 years (see Ref. 3 for a review of early work). To explain these complicated properties, Frey-Wyssling (4) proposed that cytoplasm consists of a network of long thin filaments held together by dynamic cross-links that can resist rapid deformation but allow slow deformation in response to sustained force. He did not know the molecular nature of the filaments or cross-links, because his suggestion, originally made in the late 1930s, predated the discovery of actin in muscle (5) and nonmuscle cells (6). Later Pollard and Ito (7) identified actin filaments as major contributors to the cytoplasmic gel, and Sato et al. (8) found that the mechanical properties of actin filament networks cross-linked with Acanthamoeba -actinin depend on the rate of deformation. At low rates of deformation, a network containing -actinin is no stiffer than the actin filaments alone, but at high rates of deformation, the network is far stiffer than actin alone. They postulated that amoeba -actinin forms dynamic cross-links between actin filaments and suggested that the Frey-Wyssling model might explain the ability of cells to resist rapid deformation but change shape in response to a slowly imposed force.

This hypothesis raised the question of whether dynamic cross-linkers are a general feature of actin filament networks. Janmey et al. (9) reported that actin-binding protein (ABP-280)¹ from a human smooth muscle tumor is not a dynamic cross-linker. ABP/actin gels have a higher elastic modulus than gels of actin filaments alone at all frequencies tested, similar to biotin-labeled actin filaments cross-linked irreversibly by avidin (10). Much lower concentrations of ABP than amoeba -actinin were needed to affect the modulus of actin gels. They argued that if cytoplasmic actin filaments were cross-linked by proteins like ABP-280, then rearrangement of cross-links could not account for the properties of cytoplasm. This work emphasized the need to explore the effects of cross-linkers with a range of affinities for actin. The affinity of macrophage and smooth muscle ABP-280 for actin is about 1 µM (11-13).

Wachsstock et al. (15) compared the mechanical properties of actin filaments cross-linked with biotin-avidin (K_d = 10¹⁵ M; Ref. 10), smooth muscle -actinin (K_d = 0.6 µM; Ref. 14 and 15), or Acanthamoeba -actinin (K_d = 5 µM; Ref. 16). Biotin-actin/avidin gels are a viscoelastic solid at all frequencies, and concentrations of avidin >0.03 µM do not increase the stiffness. At 0.03 µM smooth muscle -actinin increased the complex modulus 10-fold less than biotin/avidin. At higher concentrations, smooth muscle -actinin makes bundles of actin filaments that behave like a viscoelastic fluid (14, 16). High concentrations of amoeba -actinin are required to increase the stiffness, and the complex modulus depends dramatically on frequency.

The current work investigates actin filament cross-linking by -actinin in more detail to determine the effect of cross-linker dynamics on the mechanical properties in a system with only one variable, the temperature. We used chicken smooth muscle -actinin, because temperature affects its affinity for actin filaments (17, 18). Previous studies examined the effect of temperature of gels of actin and -actinin (19-21), but this is the first to correlate rheological measurements and binding rate constants on the same preparations of proteins. -Actinins consist of two identical polypeptides of 103 kDa with an N-terminal 30-kDa actin-binding domain, a tail with triple helical repeats, and two C-terminal EF hands (22). The rod-shaped tails associate to form an anti-parallel dimer with an actin filament-binding site on each end. The bivalent protein cross-links actin filament into three-dimensional gels or bundles depending upon the conditions (16).

We used the monovalent actin-binding domain (ABD) for our kinetic analysis to avoid complications arising from two binding sites. We assume that the properties of isolated ABD are the same as the heads of bivalent -actinin molecules. We initiated these experiments with ABD produced from chicken smooth muscle -actinin by proteolytic digestion (14) but found that this fragment differs in size and affinity for actin compared with full-length recombinant ABD, which also provides a convenient fluorescence change when it binds actin filaments (18).

We show that actin filament networks cross-linked by -actinin differ fundamentally from biotin-actin/avidin gels. Biotin-actin/avidin gels are viscoelastic solid at all frequencies and temperatures tested. -Actinin/actin gels are less stiff, and the stiffness varies with temperature, because cross-linker dynamics depend on the temperature.

	MATERIALS AND METHODS

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Protein Purification-- Actin was prepared from rabbit skeletal muscle (23, 24) using Sephacryl S-300 instead of Sephadex G-150 for gel filtration. -Actinin was purified from chicken smooth muscle (25). Both actin and -actinin were stored by dialysis against daily changes of Buffer G (2 mM Tris, pH 8.0, at 25 °C, 0.2 mM ATP, 0.1 mM CaCl₂, 0.5 mM dithiothreitol, 0.3 mM NaN₃) and used within 5 days of purification. Lyophilized avidin (Pierce) was dissolved at 1 mg/ml in Buffer G. Actin was labeled with biotin as described by Wachsstock et al. (15) and Janmey et al. (9) by reacting polymerized actin with a 7-fold molar excess of iodoacetyl-N'-biotinhexenediamine (from a 40 mM stock in dimethylformamide). After purification by pelleting, depolymerization, and gel filtration, the extent of biotinylation was measured by the displacement of 2-[4'-hydroxyazobenzene] benzoic acid from avidin with a kit from Pierce. The actin was approximately 30% biotinylated. This actin was diluted to 2% biotinylated actin with unlabeled actin for the experiments.

Proteolytic Chicken Smooth Muscle -Actinin ABD-- The ABD of chicken smooth muscle -actinin was cleaved from the tails by digestion with thermolysin coupled to agarose beads (Sigma) and purified according to Wachsstock et al. (15), a modification of the method of Pavalko and Burridge (26). The thermolysin beads were filtered out and the soluble pABD was recovered in the void volume of a 5-ml Econo-Q column (Bio-Rad) equilibrated with Buffer G. The column retains the 53-kDa rod domain. Dr. Wolfgang Fischer of The Salk Institute for Biological Studies determined the N-terminal sequence of this pABD by automated Edman degradation and determined its mass by mass spectrometry.

Recombinant Chicken Smooth Muscle -Actinin ABD-- Dr. D. R. Critchley (University of Leicester, UK) kindly provided an NcoI-HincII restriction enzyme fragment encoding the ABD of chicken smooth muscle -actinin (residues 2-269, residue 1 = initiator met) cloned into expression vector pMW 172 (27). Recombinant ABD (rABD) was expressed in the BL21.de3 strain of Escherichia coli and purified by modifications of method Kuhlman et al. (18). Cells were sonicated in 16 mM Na₂HPO₄, 4 mM NaH₂PO₄, 200 mM NaCl, 1% Triton X-100, pH 8.0, at 25 °C) and clarified. The supernatant was dialyzed against Buffer T (10 mM Tris, pH 8.0, at 25 °C, 10 mM NaCl, 2 mM EDTA, 0.05% -mercaptoethanol) for 3 h. rABD was eluted with 60 mM NaCl from a 2 × 16-cm DE-52 fast flow anion exchange column (Whatman International Ltd., Maidstone, UK) equilibrated with Buffer T. After precipitation with 60% ammonium sulfate, rABD was resuspended in 5 ml of Buffer G and chromatographed on a 1 × 100-cm column of Sephadex G-75. The rABD peak was run on a MonoQ column (Bio-Rad) equilibrated with Buffer G and eluted with a linear gradient of 10-500 mM NaCl. The concentration of ABD was determined by absorbance using the extinction coefficient A₂₈₀ = 23.8 µM·cm¹ (27) or by the Bradford (28) method standardized with bovine serum albumin.

Stopped Flow Fluorescence Measurements-- The rate constant (k_obs) for rABD binding to actin filaments was measured from the time course of the decrease in the intrinsic fluorescence after mixing equal volumes of the ABD and actin (18) in the stopped flow instrument described by Sinard and Pollard (29). Tryptophan fluorescence was excited at 289 nm with a short pass filter (Oriel, Stratford, CT), and emission was monitored using a 330-nm-long pass filter (Oriel, Stratford, CT). A thermocirculator controlled the temperature of the sample and the observation cell. Actin in Buffer G was polymerized for >2 h by adding one-tenth volume of 10× KME buffer (500 mM KCl, 10 mM MgCl₂, 10 mM EGTA, 100 mM imidazole, pH 7.0). ABD was made up in the same buffer. Prior to loading the stopped flow syringes, proteins were diluted to desired concentrations with Buffer F (2 mM Tris, 10 mM imidazole, pH 7.0, 50 mM KCl, 1 mM MgCl₂, 1 mM EGTA, 0.2 mM ATP, 0.5 mM dithiothreitol, 0.3 mM NaN₃). After rapid mixing (dead time, 3 ms), we collected 500 data points at a sampling interval of 0.1 or 1 ms. Transients were fitted to single exponentials. Association rate constants (k₊) were determined from the dependence of k_obs on rABD concentration. rABD concentrations were at least 4-fold higher than actin.

Rapid Dilution Fluorescence Measurements-- Rate constants for ABD dissociation from actin filaments were determined from the time course of the increase in intrinsic fluorescence after diluting the complex at least 20-fold with Buffer F. Measurements were made in a Photon Technology International Alphascan fluorescence spectrophotometer (Brunswick, NJ). The samples were diluted two ways: 1) syringe injection of 5 µl of complex into 3 ml of Buffer F in a 1 × 1-cm cuvette rapidly stirred with a magnetic stirring bar or 2) using a hand-driven model SFA-12 Rapid Kinetics Stopped Flow Accessory (Hi-Tech Scientific Ltd., Salisbury, UK) with a dead time of about 20 ms. The temperature of the sample handling system was maintained with circulating water. Actin and ABD were copolymerized by adding one-tenth volume of concentrated polymerized buffer 10× KME for at least 2 h. The time course was fitted with a single exponential.

Actin Filament Pelleting Experiments-- Various concentrations of actin with a fixed concentration of ABD were polymerized for 1 h at room temperature in 1× KME buffer and then centrifuged 200,000 × g for 40 min at 25 °C. The supernatants were concentrated by precipitation with chloroform/methanol, and the proteins were separated by polyacrylamide gel electrophoresis in SDS. After staining with Coomassie Blue, the gel was digitized using the program Adobe PhotoShop 3.0, and the integrated densities of the ABD bands were measured with the program NIH Image 1.6. These densities were converted to concentrations using ABD standards on the same gel, and the binding isotherm was determined by a nonlinear least squares fit of the data to a hyperbola.

Rheology-- The rheological measurements were made with a parallel plate Rheometrics RFS II rheometer (Rheometrics Inc., NJ) in the small amplitude (strain, 2%) forced oscillation mode (30). Monomeric actin was mixed with one-tenth volume of 10× KME polymerization buffer and immediately placed between the metal plates of the rheometer to polymerize at desired temperature. The plates were sealed with mineral oil (Sigma) to prevent sample dehydration. Measurements of G' and G" were made every 30 s using time sweep mode to observe the gel formation. After G' and G" reached a plateau, frequency sweep mode was used to measure the rheological parameters: the magnitude of complex modulus |G*|, where |G*| = (G'² + G"²)^1/2; and the phase shift , where  = ¹(G"/G') (31). A solid has a phase shift of 0. A viscous liquid has phase shift of 1.6 radians. Relaxation experiments measured stress relaxation ((t)) after a step input strain (_o) as a function of time. The relaxation modulus G(t) = (t)/_o. Unlike a dynamic mechanical assay, a stress relaxation assay does not require deformation of the actin network after the initial strain.

	RESULTS

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Comparison of Recombinant and Proteolytic Actin-binding Domain of Smooth Muscle -Actinin-- Both recombinant and proteolytic ABD preparations bind actin filaments in pelleting experiments (Fig. 1), but the affinities for actin filaments differ by an order of magnitude (Table I). At room temperature, the K_d values are 1.6 µM for rABD and 20 µM for pABD. This establishes that the wide range of affinities reported in the literature (Table I) are due to the methods of preparation and not differences in the assays.

View larger version (13K): [in this window] [in a new window]   Fig. 1.   Pelleting assay for pABD and rABD binding to skeletal muscle actin filaments. The conditions were 50 mM KCl, 1 mM MgCl2, 1 mM EGTA, 10 mM imidazole, pH 7.0, in Buffer G, 22 °C. A, 1 µM pABD pelleted with various concentrations of actin filaments. The fitted curve corresponds to a dissociation equilibrium constant (Kd) of 20.2 µM. B, 0.4 µM rABD pelleted with various concentrations of actin filaments. The Kd is 1.6 µM.

View this table: [in this window] [in a new window]   Table I Rate and equilibrium constants for chicken smooth muscle -actinin binding skeletal muscle actin filaments The errors cited for k are standard deviations. SF, stopped flow; ND, not determined.

Kinetics of -Actinin ABD Binding to Actin Filaments-- We followed the binding of rABD to actin filaments under pseudo-first order conditions with a molar excess of rABD over polymerized actin subunits. Following rapid mixing in the stopped flow instrument, rABD binds to actin filaments accompanied by a quench in tryptophan fluorescence that follows an exponential time course (Fig. 2A), as first reported by Kuhlman et al. (18). The pseudo-first order rate constant of the fluorescence change depends linearly on rABD concentration up to a rate of at least 80 s¹ (Fig. 2B). A simple model for the reaction is a bimolecular binding event followed by a first order change in fluorescence. The absence of curvature in the plots of k_obs versus rABD shows that the fluorescence change is much faster than binding under our conditions (>80 s¹). The slopes of these plots at three temperatures give the apparent second order association rate constants (k₊) (Table I).

View larger version (15K): [in this window] [in a new window]   Fig. 2.   Kinetics of the association of rABD with skeletal muscle actin filaments. The conditions were 50 mM KCl, 1 mM MgCl2, 1 mM EGTA, 10 mM imidazole, pH 7.0, in Buffer G. A, time course of the change in tryptophan fluorescence during the reaction of 10 µM actin-binding domain with 2 µM actin at 25 °C. The data fit a single exponential, giving a pseudo-first order rate constant of 25 s1. B, dependence of the pseudo-first order rate constant for ABD binding to actin filaments on ABD concentration and temperature. (The points are the average of at least four runs.) Slopes are the association rate constants summarized in Table I.

View larger version (30K): [in this window] [in a new window]   Fig. 3.   Time course of dissociation of rABD from skeletal muscle actin filaments. The conditions were 50 mM KCl, 1 mM MgCl2, 1 mM EGTA, 10 mM imidazole, pH 7.0, in Buffer G. Shown is the time course of increase in tryptophan fluorescence after diluting the sample from 10 µM -actinin and 2 µM actin to 0.03 µM -actinin and 0.006 µM actin at 25 °C. The data were fitted to a single exponential with a rate constant of 2.5 s1. The dissociation rate constants in Table I are the average of at least four runs.

Mechanical Properties-- Actin filament networks are viscoelastic materials with mechanical properties that are strongly influenced by cross-linking proteins. This study addresses the hypothesis (8, 16) that the rate of cross-linker dissociation is a major determinant of the mechanical properties of actin gels. The particular test was to use temperature to vary the dissociation rate constant of the well characterized cross-linker smooth muscle -actinin and to measure how this single parameter influences the mechanical properties of a cross-linked actin gel, under conditions where network is isotropic and the actin concentration is high enough that most -actinin is bound at all temperatures.

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View larger version (15K): [in this window] [in a new window]   Fig. 4.   The dependence of the mechanical properties of biotin-actin filaments and biotin-actin filaments cross-linked with avidin on temperature and the frequency of deformation. The conditions were 15 µM 2% biotinylated actin ± 0.03 µM avidin polymerized in the rheometer in Buffer F. , 15 µM 2% biotinylated actin at 25 °C; , 15 µM 2% biotinylated actin at 8 °C; , 15 µM 2% biotinylated actin with 0.03 µM avidin at 25 °C; , 15 µM 2% biotinylated actin with 0.03 µM avidin at 8 °C. A, complex modulus |G*|. B, phase shift ().

View larger version (15K): [in this window] [in a new window]   Fig. 5.   The dependence of the mechanical properties of actin filaments cross-linked with smooth muscle -actinin on temperature and the frequency of deformation. The conditions were 15 µM actin ± 0.03 µM -actinin polymerized in the rheometer in Buffer F. , 15 µM actin at 25 °C; , 15 µM actin at 8 °C. , 15 µM actin with 0.03 µM -actinin at 25 °C; , 15 µM actin with 0.03 µM -actinin at 15 °C; , 15 µM actin with 0.03 µM -actinin at 8 °C. A, complex modulus |G*|. B, phase shift ().

View larger version (20K): [in this window] [in a new window]   Fig. 6.   A, dependence of dynamic rate constants and mechanical properties from Fig. 5 on temperature. B, relaxation experiment. The conditions were 15 µM actin ± 0.03 µM -actinin polymerized in the rheometer in Buffer F at 25, 15, or 8 °C. At time 0, the samples were subjected to a step input strain of 1%, and G was followed as a function of time.

	DISCUSSION

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Comparison of Proteolytic and Recombinant ABD-- This and previous work (14, 18) employed the isolated actin-binding domain of chicken smooth muscle -actinin rather than the bivalent native molecule to evaluate the rates of actin filament binding and dissociation. In previous work on pABD of smooth muscle -actinin, it was assumed that thermolysin simply cleaves the ABD from the -helical tail (14, 26), because Baron et al. (32) found that isolated pABD did not yield any product upon Edman degradation, as expected for a fragment with an intact, blocked N terminus (33). However, Davison et al. (34) presented evidence that thermolysin actually cleaves between Leu²⁴ and Leu²⁵. We confirm this observation. By mass spectroscopy we show that thermolysin also cleaves after Glu²⁵⁷, suggesting that this is the end of the compactly folded head, rather than Phe²⁴⁶, which begins the spectrin-like repeats of the tail or Glu²⁶⁹, which seems to have been chosen as the end of rABD simply because of a convenient restriction site (27). The last 12 residues of pABD were not included in the crystallized fimbrin ABD, but presumably link the -actinin ABD to its tail.

Temperature Dependence of -Actinin Binding to Actin Filaments-- Both the association and dissociation rate constants for ABD-binding actin filaments depend on temperature (Table I). Our dissociation rate constants are smaller than those of Kuhlman et al. (18) using exactly the same proteins. Their values were based on extrapolation to zero rABD concentration of plots of k_obs versus rABD concentration in association experiments, a procedure with some error. In a confirmatory experiment they observed a rate constant of 15 s¹ in a 1:10 dilution of 5 µM complex but did not investigate the dissociation reaction in a much detail as we have. As expected for a larger molecule, Goldman and Isenberg (13) found that intact smooth muscle -actinin binds and dissociates somewhat more slowly at 20 °C than ABD (Table I).

Cross-linker Dynamics Determine the Mechanical Properties of Actin Filament Gels-- We assume that the two heads of -actinin bind actin filaments with the same rate constants as rABD, with a small correction for slower diffusion of the larger native protein (14), but several factors complicate the situation. First, actin filaments are immobile on the time scale of the association reaction (39). Second, at the concentrations employed most univalent reactions of -actinin with an actin filament will not position the second head appropriately to interact with a neighboring (immobile) actin filament. Third, prolonged dissociation of an -actinin bound between two immobile actin filaments will be slower than two independent heads, because rebinding of a single dissociated head will be favored by being anchored to the neighboring filament. This may not complicate interpretation of mechanical properties, because dissociation of a single head breaks cross-links between filaments. Finally, force applied to a cross-link is likely to increase the rate of dissociation.

Implications for the Cell-- The physical structure of the cytoplasm must adapt as a moving cell changes shape. There is little doubt that the actin cytoskeleton uses both filament assembly and disassembly as well as filament severing (and possibly annealing) to reconfigure. Because actin filaments themselves are quite stable kinetically (41), actin filament dynamics in the cell depend upon numerous actin-binding proteins that can sever, cap, nucleate, and cross-link the filaments.