Cell Motility and the Cytoskeleton 42:73–81 (1999) Effect of Capping Protein, CapZ, on the Length of Actin Filaments and Mechanical Properties of Actin Filament Networks Jingyuan Xu,1 James F. Casella,2 and Thomas D. Pollard3,4* 1Department of Biophysics and Biophysical Chemistry, Johns Hopkins School of Medicine, Baltimore, Maryland 2Department of Pediatrics, Division of Pediatric Hematology, Johns Hopkins School of Medicine, Baltimore, Maryland 3Department of Cell Biology and Anatomy, Johns Hopkins School of Medicine, Baltimore, Maryland 4Salk Institute for Biological Studies, La Jolla, California We report on how physiological concentrations of capping protein shorten actin filaments and on the remarkably fluid nature of solutions of such short filaments even at the high concentrations that exist in cells. We measured the lengths of actin filaments formed by spontaneous polymerization of highly purified actin monomers by fluorescence microscopy after labeling with rhodamine-phalloidin. The length distributions are exponential with a mean of about 7 µm (2600 subunits). As observed previously with less quantitative assays, copolymerization with the actin capping protein, CapZ, reduces the length of the filaments. At cellular concentrations of capping protein, one filament forms for each molecule of capping protein and the population of filaments is uniformly short. Using CapZ to vary the length of actin filaments, we measured how their mechanical properties depend on length. The stiffness (elastic modulus) of actin filament networks depends steeply on the length, with long filaments contributing far out of proportion to their numbers to the stiffness. Even at physiological concentrations (300 µM), networks of filaments limited to lengths observed in cells with a 1 to 500 molar ratio of CapZ are more fluid and much less elastic than lower concentrations of longer actin filaments. Thus the high concentration of short actin filaments in cells must be crosslinked to produce the observed stiffness of the cortex. Cell Motil. Cytoskeleton 42:73–81, 1999. r 1999 Wiley-Liss, Inc. Key words: actin; capping protein; CapZ; filaments; mechanical properties; rheology INTRODUCTION Actin filaments are major components of the cytoskeleton, which provides the physical basis for the mechanical properties of cytoplasm. A key consideration is how actin filaments themselves, exclusive of any crosslinking proteins, contribute to mechanical properties. To relate physical measurements on purified actin filaments to conditions inside cells, one must consider the length of actin filaments. Polymer length is an important determinant of mechanical properties [Hvidt and Janmey, 1990; Janmey r 1999 Wiley-Liss, Inc. Contract grant sponsor: NIH; Contract grant number: GM-26338; Contract grant number: AR-40697. Jingyuan Xu is currently at Department of Chemical Engineering, Johns Hopkins University, Baltimore, Maryland. *Correspondence to: Thomas D. Pollard, Salk Institute for Biological Studies, 10010 N. Torrey Pines Road, La Jolla, CA 92037. E-mail: email@example.com Received 14 September 1998; accepted 10 October 1998 74 Xu et al. et al., 1994] and many [Cano et al., 1991; Podolski and Steck, 1990], but not all [Small et al., 1995; Svitkina et al., 1997] cellular actin filaments appear to be shorter, ⬍1 µm, than filaments polymerized in vitro from pure actin monomers. The most thorough study of this point used gelsolin to control polymer length and concluded ‘‘relatively isotropic F-actin networks are sufficiently strong to stabilize cells’’ [Janmey et al., 1994]. This hypothesis suggests that actin filaments at high concentration, estimated to be ⬎200 µM in the cell cortex [Niederman et al., 1983], might by themselves account for a major part of the stiffness of the cytoplasm exclusive of crosslinking by actin-binding proteins. Given the importance of this point for understanding the physical basis of cytoskeletal function, we reexamined the mechanical properties of actin filaments, using the muscle capping protein CapZ [Casella et al., 1986, 1987, 1995] to regulate polymer length. CapZ and its relatives in nonmuscle cells bind with high affinity and block the fast growing (barbed) end of actin filaments for both elongation and annealing [Isenberg et al., 1980; Cooper and Pollard, 1985; Casella et al., 1987; Casella and Torres, 1994; Caldwell et al., 1989]. Capping proteins are associated with the barbed ends of actin filaments in the Z-line of skeletal muscle [Casella et al., 1987] and block many, if not most, barbed ends of actin filaments in nonmuscle cells [DiNubile et al., 1995] Capping proteins also nucleate actin polymerization by stabilizing small actin oligomers [Cooper and Pollard, 1985; Caldwell et al., 1989]. The physiological relevance of this nucleating activity is still in question, because growth is only in the slow direction. These activities allow capping proteins to reduce the length of actin filaments. This was shown by electron microscopy and by qualitative viscosity assays [Isenberg et al., 1980; Cooper et al., 1984], but the dependence of the polymer length on capping protein concentration has not been measured reliably. We use fluorescence microscopy of actin filaments labeled with rhodamine-phalloidin [Burlacu et al., 1992] to establish how copolymerization of highly purified actin with CapZ affects the length of the filaments. At physiological concentrations each CapZ molecule produces one filament. By varying the CapZ concentration we prepared filaments that ranged in mean length from 1.3 µm to 6.7 µm for rheological analysis. The elastic modulus depends strongly on the mean length. Similar experiments with gelsolin [Janmey et al., 1994] showed the same trend, but much higher values at all polymer lengths. Collaborative experiments with those investigators [Xu et al., 1998] showed that the lower values in the current paper are more reliable. For the first time, we also measured the mechanical properties of physiological concentrations (300 µM) of short (1.3 µm) actin filaments. They have a much lower elastic modulus and are much more fluid than low concentrations of long filaments formed by spontaneous assembly in vitro. We conclude, that without crosslinking, the short actin filaments observed in cells cannot account for the stiffness of the cell cortex. MATERIALS AND METHODS Solutions Buffer G contained 0.2 mM ATP, 0.5 mM dithiothreitol, 0.1 mM CaCl2, 1 mM sodium azide, 2 mM Tris-Cl, pH 8.0 at 25°C. Concentrated polymerizing buffer (10 ⫻ KME) contained 500 mM KCl, 10 mM MgCl2, 10 mM EGTA, and 20 mM Tris-Cl, pH 8.0 or 100 mM imidazole pH 7.0 at 25°C. The Kron et al.  fluorescence microscopy buffer contained 50 mM KCl, 1 mM MgCl2, 100 mM dithiothreitol, 20 µg/ml catalase, 0.1 mg/ml glucose oxidase, 3 mg/ml glucose, and 2 mM Tris-Cl, pH 8.0 or 10 mM imidazole pH 7.0 at 25°C. Protein Purification Actin was purified from rabbit skeletal muscle [MacLean-Fletcher and Pollard, 1980]. Each gram of acetone powder was extracted for 30 min on ice with 20 ml of Buffer G. Insoluble material was pelleted by centrifugation at 16,000 rpm at 2°C for 30 min and the pellet resuspended in same volume of Buffer G and immediately centrifuged. The supernatants were combined and the actin was polymerized by the addition of MgCl2 to 2 mM and KCl to 50 mM. After 1 h, KCl was added to 0.8 M and the actin filaments pelleted by centrifugation at 100,000 g for 2 h at 4°C. The filaments were depolymerized by dialysis against Buffer G changed daily for 2 days at 4°C and any remaining filaments were pelleted by ultracentrifugation. The top two thirds of the supernatant was gel filtered on a 2.5 ⫻ 110 cm column of Sephacryl S-300 equilibrated with Buffer G. The fractions at and following the peak were pooled, stored by dialysis vs. daily changes of fresh buffer G and used within 5 days. To remove traces of CapZ from this singly gel filtered actin, the fractions beginning at the midpoint of the leading edge of the actin peak were pooled, repolymerized with 50 mM KCl and 2 mM MgCl2, pelleted, depolymerized and gel filtered a second time [Casella et al., 1995]. We purified CapZ from chicken skeletal muscle acetone powder using a KI extraction, followed by DEAE chromatography, hydroxylapatite chromatography, gel filtration and sucrose density gradient centrifugation [Casella et al., 1986]. Measurement of Actin Filament Lengths We stabilized fully polymerized actin filaments with CapZ (to block the rapidly depolymerizing barbed end) and with rhodamine-phalloidin (to reduce subunit Actin Filament Lengths and Mechanical Properties dissociation at both ends to near zero [Collucio and Tilney, 1984; Sampath and Pollard, 1991]). Actin was polymerized by mixing one part of concentrated polymerizing buffer 10 ⫻ KME with nine parts of actin in Buffer G. After 3 h incubation, we added one CapZ per 500 actin subunits and one rhodamine-phalloidin (Molecular Probes, OR) per actin subunit and diluted the sample to 0.3 µM with fluorescence buffer [Burlacu et al., 1992; Kaufmann et al., 1992; Käs et al., 1996]. After incubation at room temperature for 30 min to allow rhodamine-phalloidin binding [De La Cruz and Pollard, 1994], the labeled actin was diluted to 2–10 nM with fluorescence buffer, about 10 µL of solution was placed on a microscope slide and covered with a 20 mm square coverslip coated with nitrocellulose. To minimize shearing and artifactual fragmentation of filaments during manipulations, we trimmed the tip of the plastic pipette tip [Burlacu et al., 1992; Janmey et al., 1994]. We did not fix with aldehydes, because they damage actin filaments [Lehrer, 1972]. We observed filaments with a Leitz Orthoplan microscope equipped with a 3-mm BG-38, KP 560 (short wavelength pass interference filter), 2-mm BG-36 (excitation filter), TK-580 (dichroic mirror), two K-580 (colored glass barrier filters) and an Olympus 100⫻ (NA 1.25) objective. We recorded images on Kodak 3200 blackwhite professional film with an exposure of 30 to 60 s. Images of the filaments were clear enough to measure filament lengths ⱖ0.3 µm manually on prints at a final magnification of 3,150⫻. Two independent observers measured the same length distribution and number average length. In samples with predominantly short filaments ⬍2 µm long, many filaments appeared as fluorescent spots rather than asymmetrical rods, so we measured their lengths by densitometry. Negative films were digitized with Adobe Photo Shop 3.0. Taking a filament ⬎2 µm long as an internal standard for intensity per unit length, we used NIH Image 1.6 to measure the intensity of each fluorescent spot in the whole population on the same negative. The background was subtracted from the areas containing each fluorescent filament. The number average length (Ln ) is defined as Ln ⫽ (1/n)⌺li, where n is the number of filaments and li is the length of each filament. The length distributions were approximately exponential rather than Gaussian, so standard deviation could not be used to describe the variability. For an exponential distribution, the fraction of filaments (fi ) with length l is fi ⫽ exp (⫺li ), the mean length is l/ and the variance (li ) ⫽ (l/) 2. Rheometry Actin filaments networks are viscoelastic, having both solid (elastic) and fluid (viscous) properties. They both store and dissipate mechanical energy. Therefore, their mechanical properties can be described by rheologi- 75 cal parameters. For oscillatory deformations, the viscoelasticity is characterized by dynamic elasticity G8 (also called dynamic storage modulus) and loss shear modulus G9. G8 is the in-phase ratio of stress/strain and G9 is out of phase component. These relationships can also described by the complex modulus 0G*0 ⫽ (G82 ⫹ G92 ) 1/2 and phase shift ␦ ⫽ tan⫺1 (G9/G8) [Ferry, 1980]. Because G8 ⬎ G9 for actin filaments, 0G*0 mainly reflects the value of G8. A solid has a phase shift of 0. A viscous liquid has phase shift of 1.6 rad. The rheological measurements were made with a parallel plate Rheometrics RFS II rheometer (Rheometrics, NJ) in the small amplitude (strain ⱕ 2%), forced oscillation mode [Sato et al., 1985]. Monomeric actin in Buffer G was mixed with one-tenth volume of 10 ⫻ KME and immediately placed between the metal plates of the rheometer to polymerize at 25°C. The plates were sealed with mineral oil (Sigma, St. Louis, MO) to prevent sample dehydration. Measurements of G8 and G9 were made every 30 s using time sweep mode to observe the gel formation. After G8 and G9 reached a plateau, frequency sweep mode was used to measure the rheological parameters. RESULTS Actin Filament Lengths We assume that the population of fluorescent filaments attached to a coverslip is equivalent to the population in solution, because within several minutes all detectable fluorescent filaments in the 25 µm gap between slide and cover slip attached to the nitrocellulose-coated glass cover slip, leaving no filaments free in the solution (Fig. 1). However, the sample on the coverslip underestimates slightly the distribution of lengths in solution, because about 10% of longer filaments broke into two to four segments as they bound to the coverslip. The method may also miss some filaments less than 0.2 µm long due to their faint fluorescence. The polymers were stable, since the length distributions and average lengths did not change between 3 h and 2 days after polymerization. When rhodamine-phalloidin labeled actin filaments bound to coverslips coated with N-ethylmaleimide-inactivated rabbit skeletal muscle myosin [Warshaw et al., 1990], their length distribution and number average length were the same as filaments on nitrocellulose. Filaments assembled by spontaneous polymerization from doubly gel filtered actin monomers at 24 µM varied in length from less than 0.3 µm to nearly 100 µm (Figs. 1A, 2A). The distribution of lengths was approximately exponential with a mean of 6.7 µm. The mean length was about 20% lower without a second cycle of purification to remove traces of capping protein [Casella et al., 1995], even though we used only the fractions from 76 Xu et al. Fig. 1. Fluorescence micrographs of filaments of doubly gel filtered actin labeled with rhodaminephalloidin. Conditions: 24 µM purified actin, 50 mM KCl, 1 mM MgCl2, 1 mM EGTA, 180 µM ATP, 0.45 mM DTT, 90 µM CaCl2, 0.9 mM azide, 4 mM Tris-Cl (pH 8.0), 22°C for 3 h. CapZ concentrations: zero (A); 48 nM (B). the top of the actin monomer peak from the first gel filtration column to avoid CapZ, which runs ahead of actin monomers. CapZ reduced the length (Fig. 1B) of filaments assembled from twice gel filtered actin and made their length distributions more uniform (Fig. 2B–D). Above 20 nM, one filament formed for each CapZ molecule (Fig. 3). Lower concentrations of CapZ increased the number of filaments over that produced by spontaneous polymerization, but the number concentration of filaments exceeded the concentration of capping protein, so some of the filaments were not capped. Very high concentrations of short actin filaments are found in vivo [Small, 1981; Podolski and Steck, 1990; Cano et al., 1991], so we examined the mechanical properties of high concentrations of mixtures of actin with a 1:500 ratio of CapZ (Fig. 6). These short, 1.3 µm filaments were more fluid-like than actin alone. The phase shift ␦ was in the range of 0.5 to 0.6 rad at 1 Hz compared with about 0.3 rad for pure actin. Even at 300 µM actin the complex modulus 0G*0 was less than 2 Pa. This is value of the complex modulus 0G*0 observed for 30–40 µM pure actin polymerized in the absence of CapZ. Mechanical Properties of Actin Filament Networks DISCUSSION Capping Protein Regulation of Polymer Length Actin filaments alone formed a weak gel with a complex modulus 0G*0 that depended on the frequency of oscillation (Fig. 4). Two preparations of doubly gel filtered actin had the same complex modulus as singly gel filtered actin filaments, while one preparation had a slightly higher complex modulus (Fig. 4A). The phase shift ␦ of all three preparations was around 0.3 rad (Fig. 4B). Thus, the low concentration of CapZ contaminating actin after one cycle of polymerization and gel filtration [Casella et al., 1994] had only a small effect on the mechanical properties of actin filament networks. Titration of pure actin with CapZ reduced 0G*0 (Fig. 4A) and increased ␦ (Fig. 4B). The complex modulus depended on the mean length of the filaments (Fig. 5). A fourfold difference in mean length (1.3 vs. 5.5 µm) resulted in a 30-fold difference in the complex modulus at a frequency of 0.01 Hz and 10-fold difference at 0.1–1.0 Hz. The uniform, short filaments behaved more like a viscoelastic liquid than the exponential distribution of longer pure actin filaments. The presence of CapZ also increased the variability in the rheological measurements. We confirm that copolymerization of actin monomers with capping protein, CapZ in this case, limits the length of the filaments at steady state. Earlier measurements by electron microscopy showed that actin filaments are shorter when polymerized in the presence of amoeba capping protein [Isenberg et al., 1980; Cooper et al., 1984] and muscle CapZ [Caldwell et al., 1989] but length distributions were not reported. Since negative staining underestimates the length of control actin filaments, our measurements by light microscopy are the only reliable quantitative assessment of the effect of CapZ on actin filament length. At CapZ concentrations above the Kd (0.5–1 nM or less [Casella et al., 1986, 1987; Caldwell et al., 1989]) and at ratios of actin to CapZ up to 1,000, one filament forms for every CapZ present during polymerization (Fig. 3). This is expected from the high affinity of CapZ for the barbed end of actin filaments and the ability of capping proteins to promote spontaneous polymerization of actin monomers by stabilizing transient oligomers Actin Filament Lengths and Mechanical Properties 77 Fig. 2. Length distributions of doubly gel filtered actin filaments as a function of CapZ concentration. Conditions as in Figure 1. CapZ concentrations: zero (A); 4.8 nM (B); 12 nM (C); 48 nM (D). Smooth curves are the best exponential fits to the data. [Cooper and Pollard, 1985; Caldwell et al., 1989]. Since these filaments form rapidly, grow slowly only at their pointed ends and do not anneal, the steady state population of filaments is short and uniform in size. When the ratio of actin to CapZ exceeds 1,000, more filaments form than the concentration of CapZ. This is expected, because the rate of self-nucleation will exceed the rate of CapZ-mediated nucleation at low CapZ concentrations. At a ratio of 5,000 actins per CapZ about 30% of the filaments are capped and 70% are not. From comparison of length distributions of once and twice gel filtered actin, we estimate that our singly gel filtered actin is contaminated with about one part in 104 of capping protein, similar to that estimated by immunoassay [Casella et al., 1995]. Since the first gel filtration column removes most of the capping protein activity [MacLean-Fletcher and Pollard, 1980; Casella et al., 1987, 1995], actin that has not been gel filtered is more heavily contaminated. The dependence of polymer length on the concentration of other capping proteins shows that gelsolin, villin and scinderin all have a high capacity to nucleate actin filaments. At molar ratios up to 250 actins per gelsolin, the length distributions measured by negative staining 78 Xu et al. Fig. 3. Dependence of the number average length (Ln ) of actin filaments on concentration of CapZ. Conditions as in Figure 1. and electron microscopy show that exactly one filament forms per gelsolin [Janmey et al., 1986]. At higher ratios of actin to gelsolin, more than one filament forms per gelsolin. Spontaneous polymerization is one source of the excess filaments, but two other factors may contribute. First, CapZ contaminating once gel-filtered actin will be a significant fraction of the total nucleating activity at low concentrations of gelsolin. Second, any breakage during specimen preparation will over estimate of filament number. Mixing gelsolin with preformed actin filaments produced about one filament per gelsolin at ratios of 1,000 according to a light microscopic assay [Burlacu et al., 1992]. However, a ratio of 500 created many fewer filaments than gelsolin, so the relationship of gelsolin to polymer number needs further study. At molar ratios of actin to villin up to 250, fewer filaments form than the concentration of villin [Wang and Bonder, 1991], so villin may be somewhat less efficient at nucleating and capping than CapZ or gelsolin. At molar ratios up to 100, one filament formed for each molecule of a smooth muscle capping protein [Hinssen et al., 1984], but the limited range of the data precludes comparisons with the nucleating activity of other capping proteins. Polymer Length and the Mechanical Properties of Actin Filaments In agreement with theory [MacKintosh et al., 1995], pioneering work using semi-quantitative viscometric assays established the general principle that various capping and severing proteins lower the viscosity of actin filaments by reducing polymer length [Yin and Stossel, 1979; Isenberg et al., 1980; Hasegawa et al., 1980; Craig and Powell, 1980; Mooseker et al., 1980]. However, the low and high shear viscosities measured in these experiments are not interpretable physical parameters. The best quantitative measurements of rheological parameters used gelsolin to control the polymer length [Janmey et al., 1994], assuming that one filament forms per gelsolin, rather than measuring the polymer lengths. This assumption is valid at low, but not high ratios of actin to gelsolin [Janmey et al., 1986], so we recalculated the polymer lengths in the 1994 study from the data in the 1986 paper for comparison with our results where we measured polymer lengths by light microscopy under the conditions used in the rheometer. While agreeing with on basic trends, our measurements of rheological constants as a function of actin filament length are much lower than in the previous work [Janmey et al., 1994]. For example, we find 0G*0 is 0.04 Pa for 24 µM actin filaments with a mean length of 2.8 µm. For an assumed mean polymer length of 2.7 µm (adjusted value 2.2 µm) and a concentration of 48 µM, Janmey et al. reported a range of values for the elastic modulus, G8: 0.4 to 1.3 Pa in Figure 1 and 200 Pa in Figure 2. For filaments 5–6 µm long, we measured 0G*0 ⫽ 0.3 Pa for 24 µM actin, similar to Goldmann et al.  who reported G8 ⫽ 0.2 Pa for 10 µM actin, while Janmey et al.  measured 500 Pa for filaments 4 µm long at a concentration of 48 µM. Two factors are likely to contribute to these large differences: the actin preparations and the capping protein used to control the length of the filaments. In a recent collaboration with the laboratory of P.A. Janmey, we found that the methods used to prepare and store actin appear to account for most of the differences reported previously [Xu et al., 1998]. We now agree that 24 µM solutions of filaments prepared from fresh, purified actin have an elastic modulus of about 1 Pa in low amplitude oscillation experiments at 0.1 to 1.0 Hz. These filaments have a mean length of about 6 µm, as reported here. The different capping proteins used to control polymer length may also contribute to the differences. We used capping protein copolymerization as a convenient method to control the length of actin filaments without altering their conformation [De La Cruz and Pollard, 1996]. Previous studies [Hvidt et al., 1990; Janmey et al., 1994] used gelsolin to control polymer length. Gelsolin severs and caps actin filaments, so it is very effective in regulating filament length, but in addition, gelsolin causes a conformational change that appears to propagate far along the filament from the binding site at the barbed end [Prochniewicz et al., 1996]. This change alters the shape of the subunits [Orlova et al., 1995] and the binding of rhodamine-phalloidin [Allen and Janmey, 1994], so it could conceivably alter their mechanical properties as well. Actin Filament Lengths and Mechanical Properties 79 Fig. 4. Effect of CapZ on the mechanical properties of actin filament networks. Conditions as in Figure 1. A: The value of the complex modulus 0 G* 0. B: Phase shift ␦. Open square: Singly gel filtered actin. Filled triangle: Doubly gel filtered actin alone. Filled square: Doubly gel filtered actin polymerized with 4.8 nM CapZ. Open circle: Doubly gel filtered actin polymerized with 12 nM CapZ. Filled circle: Double gel filtered actin polymerized with 48 nM CapZ. oped by MacKintosh et al.  for semi-flexible polymers like actin. Long filaments, far above the persistence lengths, contribute to the moduli not only from stiffness and rotational motion but also from bending movement. Therefore, longer filaments are major contributors of actin networks. Implications for Actin Filaments in Cells Fig. 5. Dependence of the mechanical properties of actin filament networks on polymer length. Conditions as in Figure 1. The length of filaments of 24 µM doubly gel filtered actin was varied by copolymerization with various concentrations of CapZ as in Figure 3. The complex modulus 0 G* 0 was measured at a frequency of 0.01 Hz. The steep dependence of the elastic modulus on polymer length (Fig. 5) means that long filaments contribute to the mechanical properties far out of proportion to their length, in general agreement with concepts (but not with the absolute values of the predicted moduli) devel- Biochemical and morphological estimates of actin filament lengths in cells differ [Small, 1981; Podolski and Steck, 1990; Cano et al., 1991; Small et al., 1995; Svitkina et al., 1997], but many filaments are shorter than 1 µm. We examined solutions of short actin filaments at physiological concentrations for the first time, finding that they have a low elastic modulus and behave more like a fluid than networks of long actin filaments (Fig. 6). Below 100 µM actin, the complex modulus depends on the actin concentration. Above 100 µM, the actin concentration has less effect on the properties of the networks in three different experiments. Thus, short actin filaments alone cannot account for the high elastic modulus of cytoplasm [Evans et al., 1993; Oliver et al., 1994]. This result emphasizes the importance of actin filament crosslinking proteins in establishing the mechanical properties of the cell and provides an opportunity for future research. No studies are available on actin filament crosslinking at physiological concentrations of short filaments. 80 Xu et al. Fig. 6. Mechanical properties of high concentrations of short actin filaments. Singly gel filtered actin was copolymerized with a 1:500 molar ration of CapZ to actin. Conditions as in Figure 1. A: The value of the complex modulus 0 G* 0. B: Phase shift ␦. Filled circle: 25 µM actin. Open circle: 50 µM actin. Filled square: 100 µM actin. Open square: 300 µM actin. 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