Tbeta 4 is not a simple G-actin sequestering protein and interacts with F-actin at high concentration.

Thymosin beta 4 is acknowledged as a major G-actin binding protein maintaining a pool of unassembled actin in motile vertebrate cells. We have examined the function of Tbeta 4 in actin assembly in the high range of concentrations (up to 300 micron) at which Tbeta 4 is found in highly motile blood cells. Tbeta 4 behaves as a simple G-actin sequestering protein only in a range of low concentrations (<20 micron). As the concentration of Tbeta 4 increases, its ability to depolymerize F-actin decreases, due to its interaction with F-actin. The Tbeta 4-actin can be incorporated, in low molar ratios, into F-actin, and can be cross-linked in F-actin using 1-ethyl-3-(3-dimethylaminopropyl)carbodiimide. As a result of the copolymerization of actin and Tbeta 4-actin complex, the critical concentration is the sum of free G-actin and Tbeta 4-G-actin concentrations at steady state, and the partial critical concentration of G-actin is decreased by Tbeta 4-G-actin complex. The incorporation of Tbeta 4-actin in F-actin is associated to a structural change of the filaments and eventually leads to their twisting around each other. In conclusion, Tbeta 4 is not a simple passive actin-sequestering agent, and at high concentrations the ability of Tbeta 4-actin to copolymerize with actin reduces the sequestering activity of G-actin-binding proteins. These results question the evaluation of the unassembled actin in motile cells. They account for observations made on living fibroblasts overexpressing beta-thymosins.

Thymosin ␤ 4 is acknowledged as a major G-actin binding protein maintaining a pool of unassembled actin in motile vertebrate cells. We have examined the function of T␤ 4 in actin assembly in the high range of concentrations (up to 300 M) at which T␤ 4 is found in highly motile blood cells. T␤ 4 behaves as a simple G-actin sequestering protein only in a range of low concentrations (<20 M). As the concentration of T␤ 4 4 is not a simple passive actin-sequestering agent, and at high concentrations the ability of T␤ 4 -actin to copolymerize with actin reduces the sequestering activity of G-actin-binding proteins. These results question the evaluation of the unassembled actin in motile cells. They account for observations made on living fibroblasts overexpressing ␤-thymosins.

increases, its ability to depolymerize F-actin decreases, due to its interaction with F-actin. The T␤ 4 -actin can be incorporated, in low molar ratios, into F-actin, and can be cross-linked in F-actin using 1-ethyl-3-(3-dimethylaminopropyl)carbodiimide. As a result of the copolymerization of actin and T␤ 4 -actin complex, the critical concentration is the sum of free G-actin and T␤ 4 -G-actin concentrations at steady state, and the partial critical concentration of G-actin is decreased by T␤ 4 -G-actin complex. The incorporation of T␤ 4 -actin in F-actin is associated to a structural change of the filaments and eventually leads to their twisting around each other. In conclusion, T␤
It is generally thought that to elicit a motile response to extracellular signals, living cells regulate their content in Factin, by spatially controlled changes in the steady state of filament assembly (1). Capping proteins and G-actin binding proteins are major players in this control. In the presence of ATP, capping proteins block the dynamics at the barbed ends of actin filaments and establish the high critical concentration of the pointed ends; when barbed ends are uncapped, the effective critical concentration is close to the critical concentration of the barbed end. The changes in critical concentration, however, represent a very small amount of actin in mass (less than 1 M), hence by themselves they cannot elicit any massive assembly of actin. These changes, however, are largely amplified by G-actin binding proteins which maintain a pool of unassembled (se-questered) actin, used for site-directed actin assembly. The concentration of actin in complex with sequestering proteins is indeed determined by the concentration of free G-actin, i.e. the critical concentration. The concentration of actin in complex with sequestering proteins is high when barbed ends are capped, and decreases locally to yield F-actin upon creation and maintenance of available barbed ends, which is thought to occur upon stimulation. A major G-actin binding protein is thymosin ␤ 4 (T␤ 4 ) discovered in 1991 (2) in platelets and later found to be ubiquitous in vertebrate cells (see for review, Refs. 3 and 4). The function of T␤ 4 as a simple passive sequestering protein was demonstrated in vitro (5)(6)(7) as well as in vivo (8 -11). The equilibrium dissociation constant for the G-actin-T␤ 4 1:1 complex lies in the 0.7-2.5 M range, from measurements of its sequestering activity (5-7) as well as from direct binding studies (12,13). However, in the above experiments, the concentrations of T␤ 4 used were lower than the physiological concentrations, especially those found in motile blood cells (200 -500 M in platelets and neutrophils (5,8)). In the present work, the function of T␤ 4 is explored in greater detail in the higher concentration range found in motile living cells. The role of T␤ 4 appears more complex than previously thought, because actin filaments fail to totally depolymerize in the presence of high concentrations (100 -200 M) of T␤ 4 , due to incorporation of very low amounts of T␤ 4 -actin in the filaments. The consequences of this property of T␤ 4 on the structure of filaments and on the regulation of actin assembly in living cells is examined.

MATERIALS AND METHODS
Proteins-Actin was purified from rabbit skeletal muscle (14) and isolated as calcium ATP-G-actin by Sephadex G-200 chromatography (15) in G buffer (5 mM Tris-Cl Ϫ , pH 7.8, 0.1 mM CaCl 2 , 0.2 mM ATP, 0.2 mM dithiothreitol, 0.01% NaN 3 ). Actin was pyrenyl-labeled as described (16). Thymosin ␤ 4 was purified from bovine spleen as follows. All operations were done at 4°C. 400 g of frozen spleen (cut into 2 ϫ 2 ϫ 2-cm cubes and frozen on dry ice at the slaughterhouse, then stored at Ϫ80°C) were homogenized with 4 volumes of cold 0.625 N HCl0 4 in a Waring blender for 2 min, then centrifuged at 20,000 ϫ g for 15 min. The supernatant was brought to pH 4 by dropwise addition of 5 N KOH, and filtered to remove KClO 4 . The solution was loaded onto a 6 ϫ 12-cm column of Lichroprep RP18 (40 -63 m, Merck). Following a 2000-ml H 2 O wash, elution was performed with 400 ml of 33% 1-propanol in water. The eluted material was concentrated to ϳ50 ml by rotary evaporation, brought to pH 7.8 with KOH, filtered over 0.22-m nitrocellulose filters, and submitted to anion exchange chromatography on Q-Sepharose (2.5 ϫ 25 cm) equilibrated in 40 mM ammonium acetate, pH 7.8. Elution was performed using a gradient from 40 mM ammonium acetate, pH 7.8, to 0.2 M ammonium acetate, 0.2 M acetic acid, pH 5.0 (400 ml ϫ 2). Elution was monitored by absorbance at 214 nm following 10-fold dilution of an aliquot of the fractions in H 2 O. The peak of T␤ 4 was identified by analytical HPLC 1 on RP18 Select B (Merck, 4 ϫ 125 mm) using a gradient from 5 to 50% acetonitrile. Fractions containing T␤ 4 were pooled, concentrated, and final purification was achieved by preparative HPLC on RP18 Select B as described (7). About 40 mg of pure T␤ 4 were obtained. The purity of T␤ 4 was checked by mass spectrometry. The concentration of T␤ 4 was determined by the bicinchoninic acid assay, using bovine serum albumin as a standard.
[ 14 C]Thymosin ␤ 4 was chemically synthesized on a model 431A peptide synthesizer (Applied Biosystems Inc., Foster City, CA) with an additional Gly-Cys at the extreme C terminus. Previous studies have indicated that the nature of the C terminus of T␤ 4 is not important for actin binding (17). The C-terminal cysteine residue was then labeled with iodo-[1-14 C]acetamide (Amersham) using a 1:1.5 molar ratio of thymosin ␤ 4 to label. The resulting [ 14 C]thymosin ␤ 4 had a specific activity of 20,000 cpm/nmol. T␤ 4 was oxidized into Met 6 -sulfoxide-T␤ 4 by incubation for 1 h at room temperature in the presence of 2 M H 2 O 2 (6% v/v), immediately followed by lyophilization. Profilin was purified from bovine spleen as described (18). Gelsolin was purified from pig plasma as described (19). Recombinant CapG was expressed and purified as described (20).
Steady State Measurements of F-actin-The amount of actin assembled at steady state in the presence of different amounts of T␤ 4 or profilin was monitored by pyrene fluorescence. Actin (1% pyrenyl labeled) was polymerized at the indicated concentration in G buffer supplemented with 2 mM MgCl 2 and 0.1 M KCl. Samples of 300 l containing T␤ 4 , profilin, gelsolin, or CapG at the indicated concentrations were incubated for 16 h at room temperature in the dark. Pyrenyl fluorescence was measured in a Spex Fluorolog 2 instrument. Excitation and emission wavelengths were 366 and 387 nm, respectively.
Barbed ends were capped by either gelsolin or CapG. Gelsolin was added at a gelsolin:actin ratio of 1:200 to 1:500. When CapG, which is a weaker capping protein, was used, it was added at a constant concentration of 120 nM in all samples, independently of actin concentration. Preliminary assays were run with each batch of CapG used in this work, to verify that the critical concentration of the pointed end was established as soon as at least 80 nM CapG was present in solution. The amount of F-actin and unassembled actin present at steady state was converted into molar concentrations by comparison of the fluorescence readings with a critical concentration curve carried out in parallel using the same actin solution, in the same concentration range as in the samples.
Initial Rate of Filament Growth or Depolymerization-The rate of filament growth off preformed F-actin seeds (either capped or uncapped) was measured as described (21). A small aliquot (Ͻ5% of total volume) of a solution of pyrenyl-labeled F-actin (10 -20 M), preassembled at steady state at least 2 h prior to the assay, was added to a solution containing pyrenyl-labeled G-actin and T␤ 4 . The G-actin and the F-actin (seeds) solutions were identically pyrenyl-labeled. The increase or decrease in fluorescence indicating elongation or depolymerization of the seeds was measured. The rates of fluorescence increase were converted into micromolar actin assembled ϫ s Ϫ1 using a calibration critical concentration curve obtained with the same F-actin solutions, as described above. The initial rates of filament growth J were plotted versus the concentration of free G-actin, C. The concentration, C, of free G-actin in the presence of T␤ 4 was calculated as a function of the total concentrations of G-actin (C o ), and of T␤ 4 (T o ), and of the equilibrium dissociation complex K T for the T␤ 4 -actin complex, as follows: Measurements of the Equilibrium Dissociation Constant K T for the T␤ 4 -Actin Complex-The two following methods were used to determine the value of K T , at a low concentration of actin (Յ3 M). In the first method, samples of F-actin (3 M) were assembled at steady state in the presence of 10 nM gelsolin or 120 nM CapG and increasing amounts of T␤ 4 . The concentration of T␤ 4 -actin (TA) complex at steady state increased linearly with the total concentration of T␤ 4 (T o ) according to the following equation: where A c represents the critical concentration at the pointed end. The value of K T was derived from the slope Ϫ A c /(A c ϩ K T ) of the linear decrease in the fluorescence of pyrenyl-F-actin versus T o . In the second method, the rate of filament growth at a given concentration C o of G-actin was measured in the presence of different concentrations of T␤ 4 . Since only free G-actin can appreciably participate in assembly, filament growth was inhibited due to the formation of the T␤ 4 -actin complex (6). Gelsolin-capped filaments were used as seeds, and the value of C o was chosen low enough (C o Յ 3 M) for the free G-actin concentration dependence of the rate of growth at the pointed ends of actin filaments to vary linearly in the range (O to C o ) (22). Under these conditions, the fraction of T␤ 4 -bound actin, ␣, was directly proportional to the percent of inhibition of filament growth: where V(0), V(T o ), and V(ϱ) were the elongation rates measured in the absence or in the presence of a concentration T o of T␤ 4 , or at infinite concentration of T␤ 4 , respectively. (Note that V(ϱ) theoretically equals the rate of depolymerization of filaments upon dilution, which was experimentally verified.) Data were analyzed within the following equation which describes the hyperbolic binding of T␤ 4 to G-actin: The value of K T was derived from the slope of  (20,000 cpm/nmol) for 16 h, then supplemented with 4 mM 1-ethyl-3-(3-dimethylaminopropyl)carbodiimide (Pierce) and 4 mM sulfo-NHS at room temperature for 1 h. The reaction was stopped by addition of 20 mM Tris. The cross-linked sample was centrifuged at 400,000 ϫ g for 30 min in the ultracentrifuge (Beckman, TL 100). The supernatant, containing covalent and non-covalent Gactin-T␤ 4 complexes, and the pellet, containing F-actin and cross-linked F-actin-T␤ 4 complexes, were processed separately to identify the crosslinked T␤ 4 -actin polypeptides by SDS-polyacrylamide gel electrophoresis (23) and autoradiography. The cross-linked peptides were further characterized by cyanogen bromide cleavage for 24 h at room temperature in 70% formic acid using a 100 times molar excess of CNBr over methionine. The peptide profiles were analyzed on Tricine-SDS-polyacrylamide gels (24).
Incorporation of T␤ 4 into F-actin-The binding of T␤ 4 to F-actin was measured using a sedimentation assay. Samples of F-actin (20 M, 0.25 ml), containing different amounts of T␤ 4 in the range 0 -250 M, were sedimented at 400,000 ϫ g for 30 min, following 16 h incubation at room temperature. Pellets of F-actin were resuspended in a 2.5-fold smaller volume of G-buffer and assayed for T␤ 4 . Two methods were used to quantitate the amount of F-actin-bound T␤ 4 . In the first method, 14 C-T␤ 4 was used and the amount of bound T␤ 4 was derived from radioactivity measurements. To estimate the amount of T␤ 4 present in the interstitial volume of the pellets and not specifically bound to F-actin, control assays were run in parallel containing different amounts of F-actin in the range 5-20 M, and 5 M 14 C-T␤ 4 -ox prepared by H 2 O 2 oxidation of Met 6 in the 14 C-T␤ 4 material used in the experiments. Since T␤ 4 -ox is known not to bind significantly to actin at this concentration (12), it is present in the pellet as a marker of the interstitial volume. The percent of total oxidized T␤ 4 present as a contaminant in each pellet was measured at each concentration of F-actin, providing an estimation of the contamination per unit volume of the pellet. The amounts of F-actin and unassembled actin in the samples run at different concentrations of T␤ 4 are known ( Fig. 2A). Therefore the amount of 14 C-T␤ 4 actually bound to F-actin could be obtained after subtraction of the appropriate percent of the total 14 C-T␤ 4 as a contaminant.
In the second method, unlabeled bovine spleen T␤ 4 was used. T␤ 4 present in the pellets of F-actin was assayed by HPLC of the perchloric extract of the resuspended pellets, and comparison of the peak areas of the absorbance elution diagram at 220 nm with a calibration curve using standards in the range 0 -2 nmol of T␤ 4 . The proportion of contaminant T␤ 4 trapped in the pellet was estimated as in the first method.
Electron Microscopy-The structure of actin filaments at steady state in the presence of T␤ 4 at different concentrations was examined in the electron microscope. Samples of 3-10 M F-actin, 14 -50 nM gelsolin, and T␤ 4 in the range 0 -250 M were prepared 16 h in advance to make sure that steady state was established. Ten microliters of each sample were deposited on a carbon coated, air-glow discharged grid. Following 10 -20 s adsorption, the excess solution was blotted and the sample was negatively stained with several drops of a 2% uranyl acetate solution. Unidirectional shadowing of freeze-dried specimens was performed as described (25). Samples were prepared and adsorbed on the grid as for negative staining, rapidly rinsed with distilled water and immediately (within 2 s) frozen by immersion into liquid nitrogen. The grid was transferred into a Cryofract (Reichert-Jung) and maintained at Ϫ85°C for at least 2 h. The specimens were then shadowed with a 2-nm thick layer of carbon-platinum, evaporated at an angle of 45°, and coated with a 3-4-nm carbon film evaporated at 90°. Specimens were observed in a CM12 Philips electron microscope operated at 80 kV. Micrographs were recorded at a nominal magnification of 35,000.

RESULTS
T␤ 4 Binds G-actin Selectively at Low Concentration-In living cells, the physiological ionic conditions are such that Factin is assembled at steady state, i.e. filaments coexist with G-actin at the critical concentration. Hence in vitro measurements of F-actin at steady state lead to the closest description of the in vivo situation. The actin-sequestering activity of T␤ 4 was monitored by the linear decrease in the concentration of F-actin at steady state versus total concentration of T␤ 4 as described by Equation 2 (see "Materials and Methods"): When barbed ends are capped, A c is the critical concentration at the pointed ends of filaments, which is higher than at the barbed ends, hence T␤ 4 sequesters G-actin more efficiently. This situation is the most favorable, for economy of material, to measure the affinity of T␤ 4 for G-actin. Fig. 1 shows that upon addition of increasing amounts of T␤ 4 to a solution of 3 M F-actin capped by gelsolin, the concentration of unassembled actin (A ϩ TA) increased linearly with total ␤-thymosin until all actin was depolymerized. A value of 2 Ϯ 0.2 M was derived for T from the slope of the plot, in good agreement with previous data (5-7) obtained in the same range of actin and T␤ 4 concentrations.
T␤ 4 Does Not Behave as a Simple G-actin Sequestering Protein at High Concentration-The same experiment as above was repeated in a range of higher concentrations of F-actin. The data, displayed in Fig It was found appropriate to verify that the ATP had not been extensively hydrolyzed during the 16-h incubation period, due to the steady-state ATPase of F-actin, and that even the most concentrated F-actin samples could be truly considered as be- Thus far the conclusion that T␤ 4 fails to totally depolymerize F-actin at high concentration relies on fluorescence measurements of pyrenyl actin. To verify that the measurements truly reflect equilibrium values of F-actin, G-actin, and T␤ 4 -G-actin, the following controls were carried out. 1) Identical fluorescence readings were obtained 8 h later, indicating that measurements reflected a stable situation; 2) identical results were obtained with actin solutions containing different fractions of pyrene-labeled actin; 3) sedimentation of the samples of F-actin containing different concentrations of T␤ 4 and SDS-gel electrophoresis of the pellet and supernatant ( Fig. 2A, inset) established the validity of the interpretation of fluorescence measurements in terms of F-actin and unassembled actin; 4) sedimentation velocity of T␤ 4 at different concentrations up to 250 M showed that T␤ 4 was a monomeric 5-kDa protein in the whole range of concentrations investigated. Finally quantitatively identical results showing incomplete depolymerization of F-actin were obtained with chemically synthesized T␤ 4 , which eliminates the possibility that a minor contaminant present in the preparation of T␤ 4 from spleen would be responsible for the incomplete depolymerization of F-actin at high T␤ 4 .
The fact that T␤ 4 fails to totally depolymerize F-actin in a range of high concentrations is a first indication that it can bind to F-actin as well as to G-actin, albeit with a lower affinity. Because other actin-binding proteins like ADF/cofilin (26,27) have been shown to bind preferentially either F-or G-actin depending on pH, the depolymerization of F-actin (20 M) by increasing amounts of T␤ 4 was measured at pH 6.5 and 7.  Fig. 1), consistent with a value of K T of 0.8 M, in agreement with previous determinations at low ionic strength (12).
The incomplete depolymerization of F-actin at high concentration of T␤ 4 was also observed when barbed ends were uncapped. Fig. 2B shows the amount of F-actin observed at steady-state upon addition of increasing amounts of T␤ 4 to 12 M F-actin, with barbed ends either capped by CapG, or un- capped, in two parallel series of samples. When 0.2 mM EGTA was added to the samples containing barbed end-capped Factin, the dissociation of CapG (28) led to the partial repolym-erization of actin filaments due to the shift in critical concentration caused by uncapping. The amount of F-actin reached at the end of this relaxation process was the same as the one measured in the uncapped samples, confirming that measurements shown in Fig. 2A reflect an equilibrium situation.
The data show that the extent of repolymerization upon uncapping of barbed ends, which is the difference between the two curves, first increases with the total concentration of T␤ 4 , and reaches a finite limit of ϳ3 M at high concentration of T␤ 4 . The time courses of actin desequestration/repolymerization upon uncapping by EGTA, displayed in Fig. 2C, show that the repolymerization process gets slower at higher concentrations of T␤ 4 . This result is very surprising for the following reason. Upon uncapping of barbed ends due to EGTA-induced dissociation of CapG, the initial rate of repolymerization is expected to be the following: where k ϩ B is the rate constant for addition of G-actin to the uncapped ends at concentration [F], C c P is the concentration of free G-actin at time of uncapping, which is equal to the critical concentration of the pointed ends, and C c B is the critical concentration for actin assembly at the barbed ends, which is reached upon completion of the uncapping-linked repolymerization process. According to Equation 2, the initial rate of repolymerization should be the same at all concentrations of T␤ 4 . Only the extent of repolymerization should vary in proportion with T␤ 4 , reflecting the difference in the amount of T␤ 4 -actin complex (TA), when barbed ends are capped or uncapped, as follows.
The Critical Concentration for Actin Assembly Decreases in the Presence of T␤4: Evidence for the Interaction of T␤4 with F-actin-The data shown in Fig. 2 suggest that the T␤ 4 -G-actin complex could be a weakly polymerizing actin species able to copolymerize with actin. If the T␤ 4 -actin complex can undergo the monomer-polymer exchange reactions which maintain filament stability at steady-state, the global critical concentration for actin assembly is the sum of the partial critical concentrations of G-actin and T␤ 4 -G-actin, respectively, and the contribution of T␤ 4 -G-actin to monomer-polymer exchange is expected to decrease the critical concentration of G-actin. The following simple experiment was designed to challenge this possibility. The sequestering efficiency of profilin was used as a probe for the concentration of free G-actin at steady-state in the presence or absence of T␤ 4 . When barbed ends are capped, profilin is known indeed to be a simple G-actin sequestering protein (4,18). The amount of profilin-actin complex formed at steady-state, [PA], therefore is controlled by the concentration of free G-actin, i.e. the critical concentration, as described by Fig. 3A shows that upon addition of increasing amounts of profilin to a solution of gelsolin-capped F-actin, the concentration of F actin at steadystate decreased linearly with a slope (negative) of 0.56, consistent with a value of 0.4 M for the equilibrium dissociation K p of the profilin-actin complex. 2 When the same experiment was done in the presence of 50 M T␤ 4 , the slope of the linear 2 We have checked that despite the fact that profilin does not bind pyrenyl-actin, the change in fluorescence of pyrenyl-F-actin capped by gelsolin upon increasing profilin is a valid measurement of the mass amount of F-actin at steady state over periods of several hours, as long as profilin is added to preassembled F-actin. This is no longer the case when actin has been assembled in the presence of profilin. A full study and justification of this assessment is provided elsewhere (I. Perelroi

which leads to a quadratic equation in [A]
, the solution which is:  Fig. 2A, that is a 3.3-fold decrease in critical concentration, in good agreement with the 3.8-fold decrease found in the experiment shown (Fig. 3A) carried out also at 50 M T␤ 4 , and in which profilin was used to derive the value of [A]. Hence two independent methods agree quantitatively to demonstrate that the partial critical concentration of G-actin decreases as larger amounts of TA complex are formed at steady-state. This result accounts for: 1) the limited extent of repolymerization upon uncapping and 2) the slowing down in the repolymerization process upon uncapping observed in Fig. 2C. Indeed, because c C P decreases from 0.5 M to less than 0. Incorporation of T␤ 4 in Actin Filaments-The binding of T␤ 4 to F-actin was quantitated using both the sedimentation assay and chemical cross-linking described under "Materials and Methods." The sedimentation assays (both using chemically synthesized 14 C-T␤ 4 and unlabeled spleen T␤ 4 ) showed evidence for a very weak, substoichiometric binding of T␤ 4 to F-actin. The binding also appeared cooperative, as can be seen on Fig. 4. Less than 0.01 T␤ 4 per F-actin subunit was bound at 100 M T␤ 4 , while about 0.04 T␤ 4 per F-actin was measured at 250 M T␤ 4 . Although these figures are very low and indicate that the binding constant lies in the 5-10 mM range, they were significantly above the level corresponding to simple trapping of T␤ 4 in the pellets. Typically, at 100 M T␤ 4 , the amount of T␤ 4 measured in the pellets was twice as high as the amount trapped in the interstitial volume.
Chemical cross-linking of T␤ 4 to F-actin displayed in Fig. 4, inset, confirmed that at high concentration T␤ 4 bound to Factin. Approximately 5-10% of F-actin could be covalently cross-linked to T␤ 4   sedimented together with F-actin. To test this possibility, Gactin (15 M) was supplemented with 200 MT␤ 4 , followed by 1 mM MgCl 2 and 0.1 M KCl, and the mixture was immediately submitted to cross-linking. No polymerization of G-actin could occur during cross-linking due to the high amount of T␤ 4 . The sample was centrifuged at 400,000 ϫ g. Although no pellet could be seen by the eye, any putative sedimented material was carefully resuspended. No covalent actin-T␤ 4 adduct was observed in gel electrophoresis of the resuspended material. Therefore the cross-linking experiments also demonstrate weak binding of T␤ 4 to F-actin. The Tricine-SDS gel patterns of the cyanogen bromide digests of the covalent 14 C-T␤ 4 -G-actin and 14 C-T␤ 4 -F-actin complexes were identical, which provided an indication that the contact points between T␤ 4 and either Gor F-actin were identical.
Morphology of Actin Filaments Assembled in the Presence of Increasing Amounts of T␤ 4 -Images of negatively stained specimens of F-actin at steady state in the presence of increasing amounts of T␤ 4 in the range 0 -250 M are displayed in Fig. 5. In the absence of T␤ 4 , filaments showed a distinct periodicity of the two-start long pitch helix (Fig. 5a). This periodic feature was already less apparent in filaments assembled in the presence of 22 M T␤ 4 (Fig. 5b). Unraveling of the two-start long pitch helix was more frequent in the presence than in the absence of T␤ 4 (Fig. 5d) the proportion of intertwining and twisting of filaments increased, and few isolated filaments could be seen. The intertwining of filaments in torsades was concentration-dependent, fewer torsades being observed at a lower concentration of F-actin in the presence of 250 M T␤ 4 . The destabilizing effect of T␤ 4 on the structure of the individual filament can best be seen in freeze-dried and shadowed specimens (Fig. 5, e and f). In the absence of T␤ 4 , actin filaments present clear transverse striations arising from the short pitch helix. The contrast of the transverse striations is reduced in the presence of 250 M T␤ 4 , and longitudinal depressions (arrows), which arise from the long pitch (2-start) helix, are longer and more frequent than in the absence of T␤ 4 . These observations suggest that incorporation of very few T␤ 4 molecules in the filament creates defects in the helical arrangement of subunits causing the local destabilization of the lateral actin-actin bonds in the filament. The resulting "opening" of the two strands of the long pitch helix allows lateral sidewise pairing of other filaments, which leads to the observed stiffer wider "ropes." As the number of defects is increased, the twisting of the torsades is increased. The T␤ 4 -induced structural changes of actin filaments were only observed at physiological ionic strength, which correlates with the thermodynamic data. In a first assay, the initial rate of filament depolymerization upon 20-fold dilution in F-buffer was measured in the presence of increasing amounts of T␤ 4 . With both capped and uncapped barbed ends, the rate of depolymerization was unaffected by T␤ 4 up to 200 M.
In a second experiment, the initial rate of filament growth was measured in the presence of 3 M G-actin and increasing concentrations of T␤ 4 . The inhibition of filament growth was complete at saturation by T␤ 4 , i.e. eventually filaments depolymerized when the concentration of free G-actin fell below the critical concentration. The data (Fig. 6A) Equation 1). Since the incorporation of TA in filaments is extremely low, the process of filament growth was fed essentially by addition of free G-actin to filament pointed ends. Accordingly, the rate of elongation J varied linearly with the concentration of free G-actin, but the plots obtained at 10.5 M and 14 M total G-actin did not superimpose, in the region 0 -3 M free G-actin, with the regular J(c) plot obtained in the absence of T␤ 4 (Fig.  6B). The linear J(c) plots obtained at about 90% saturation of G-actin by T␤ 4 , i.e. in a range of concentrations of free G-actin of 0 -2 M (i.e. in the presence of 20 -100 M T␤ 4 ), were characterized by a higher slope than the control J(c) curve carried out in the absence of T␤ 4 , a lower critical concentration (defined as the concentration of free G-actin at which the rate of filament growth is zero), and the same value of the ordinate intercept. At the somewhat lower value of C o of 6.5 M, data clearly showed a gradual shift from the coincidence with the standard J(c) at concentrations of TA Յ 3 M, toward coincidence with the plots obtained at A o ϭ 10.5 M and 14 M and high T␤ 4 concentrations, as the saturation of G-actin by T␤ 4 increased. In other words, at high concentrations T␤ 4 is less efficient to inhibit filament growth than expected from the extent of inhibition at low concentration of T␤ 4 , a result essentially in agreement with previous observations (6). These data demonstrate that in the presence of large concentrations of TA complex, the partial critical concentration of actin is lower, and this decrease in critical concentration is mediated by an increase in the rate constant k ϩ for association of G-actin to filament ends, while the dissociation rate constant k Ϫ seems practically unchanged. This kinetic piece of data agrees with and further expands upon the data of incomplete depolymerization of actin filaments in the presence of high concentrations of TA reported in Fig. 2, A and B, the slow rate of repolymerization upon uncapping shown in Fig. 2C, and the steady state measurements of the decrease in critical concentration shown in Fig. 3.

DISCUSSION
The present results demonstrate that the function of T␤ 4 in the regulation of actin assembly is more complex than previously thought. We confirm that in a range of low concentrations (Ͻ20 M), typical of the physiological concentration of ␤ thymosins in many cells, T␤ 4 acts as a simple G-actin binding protein. The 1:1 thymosin-actin complex, which may accumulate at steady state up to ϳ4 M when barbed ends are capped, does not participate in actin assembly and does not affect the kinetic parameters of filament growth. On the other hand, in a range of higher concentrations (20 -250 M), T␤ 4 appears to also interact with F-actin with a very low affinity (K D ϳ 5-10 mM). The weak incorporation of T␤ 4 into filaments creates defects in the structure of the polymer. These defects can be described in terms of local points of destabilization of actinactin contacts perpendicular to the filament axis, which results in local separation of the two strands of the long-pitch helix, thus enhancing the incidental "lateral slipping" feature noticed by U. Aebi on standard filaments (29). Therefore our results indicate that T␤ 4 binding to G-actin inhibits polymerization by interfering with the formation of lateral actin-actin bonds along the short pitch helix, rather than with the formation of longitudinal bonds. At high filament concentration, the destabilized, partially unravelled filaments tend to self-associate and twist around each other to yield thick rope-like structures. The effect of T␤ 4 on the F-actin structure may be compared to The curve obtained at 6.5 M total G-actin (Ⅺ) exhibits a change in regime between 3 and 5.5 M TA during which the kinetic parameters change from those of the control curve to those operating at high TA. the effect of intercalating drugs on DNA structure.
The main consequence of the incorporation of T␤ 4 in F-actin is the decrease in the partial critical concentration of G-actin. The T␤ 4 -G-actin complex cannot be considered as a good polymerizing actin monomer since filaments containing on average 5% or less T␤ 4 -actin subunits exhibit a destabilized structure. These unstable filaments therefore are maintained at steady state by exchanging subunits at their ends with a pool of monomers at a high critical concentration. The total critical concentration of monomeric actin is the sum of free G-actin and T␤ 4 -G-actin at steady state. The partial critical concentration of T␤ 4 -actin monomer is 2 orders of magnitude higher than the partial critical concentration of G-actin itself under these conditions, while the copolymer consists of less than 5% T␤ 4 -actin subunits. These figures illustrate the fact that although T␤ 4actin is a weak polymerizing species, its contribution to filament assembly, via a high partial critical concentration, helps to diminish the partial critical concentration of G-actin. Therefore, in addition to its G-actin sequestering function, T␤ 4 also possesses the power to control the steady state of actin assembly, like capping proteins and profilin do (18), but in contrast to profilin, it can do it at both ends. The decrease in partial critical concentration of G-actin occurs smoothly over a range of high concentrations of T␤ 4 (only a 3-4-fold decrease was observed at 50 M T␤ 4 ).
The following consequences can be derived from our results: the property of T␤ 4 to decrease the concentration of G-actin at steady state causes a self-limitation of the G-actin sequestering function of T␤ 4 , but also promotes a decrease in the amount of G-actin sequestered by other G-actin binding proteins like ADF/cofilin and, when barbed ends are capped, of profilin (as illustrated in Fig. 3A). The present in vitro results and their analysis provide an explanation of in vivo observations of actin dynamics in cells overexpressing T␤ 10 (a variant of T␤ 4 ), which show evidence for a paradoxical decrease in the amount of unassembled actin in overexpressing cells as compared to control cells (see accompanying article, Ref. 33). Examination of the measured cellular amounts of T␤ 10 and other G-actin binding proteins leads to the conclusion that a putative 2-fold decrease in critical concentration linked to the 3-fold overexpression of T␤ 10 is enough to account for the observed lower amount of unassembled actin. Under these conditions, the moderate increase in T␤ 10 4 and varied with T␤ 4 as described in the legend to Fig. 3. The values of the equilibrium dissociation constants for TA and GBP-A complexes were assumed to be 1.6 M and 0.5 M, respectively. The concentration of unassembled actin was calculated as follows. assume that a living cell contains T␤ 4 and other "bona fide" G-actin binding proteins that do not affect the critical concentration. For simplicity, all these non-T␤ 4 G-actin binding proteins will be collectively considered as a single species called "GBP." The pool of unassembled actin consists of T␤ 4 -actin and GBP-actin complexes. The concentration of unpolymerized actin in cells at different total concentrations of T␤ 4 and GBP is described in a three-dimensional plot shown in Fig. 7. Iso-GBP lines outline the effect of overexpression of T␤ 4 at different concentrations of GBP. At low concentration of GBP, the increase in T␤ 4 -actin concentration predominates over the decrease in GBP-actin concentration, and a net increase in unassembled actin is linked to overexpression of T␤ 4 . In the intermediate range of GBP concentration, the two effects roughly compensate each other, and very little change in unassembled actin is observed upon overexpression of T␤ 4 . At high concentration of GBP, the decrease in GBP-actin complex predominates over the increase in T␤ 4 -actin, resulting in a net decrease in unassembled actin upon overexpression of T␤ 4 . Our in vitro results therefore allow understanding of the discrepancies reported by different groups concerning the effects of T␤ 4 overexpression on the level of actin assembly, in terms of differences in concentrations of GBPs in different cell types. It will be interesting to challenge this interpretation by detailed measurements of the amounts of GBPs in different cell types. The present in vitro data also provide an explanation for the unexplained slower rate of propulsion of Listeria in Xenopus egg extracts supplemented with F-actin together with high amounts of T␤ 4 (Fig. 6 in Ref. 30). According to the proposed model for actin-based Listeria movement, the rate of actin assembly is controlled by the difference in critical concentrations between the bulk cytoplasm (where capping proteins acts to establish the high critical concentration of pointed ends) and the bacterium surface (where anchored uncapped barbed ends, characterized by a low critical concentration, are actively growing). If the critical concentration in the bulk cytoplasm is decreased by large amounts of T␤ 4 , then the rate of assembly at the bacterium surface is expected to decrease (such as observed here in Fig. 2C).
Our work raises questions concerning the actual amount of actin sequestered by T␤ 4 in resting platelets and neutrophils and the physiological significance of the "in vitro physiological ionic conditions." Clearly according to the present in vitro data, very little actin (ϳ10 M) would be sequestered by T␤ 4 in resting platelets or neutrophils, while in vivo data clearly indicate that at least 100 M actin would be unpolymerized in these cells, profilin (estimated at 50 M in platelets) and T␤ 4 (estimated at 400 M in platelets) being the major actin sequestering agents. Therefore some cytoplasm component, or macromolecular crowding, has to be thought of, which would limit the effects of T␤ 4 at the high concentration that we observed in vitro. This component could either stabilize F-actin (as tropomyosin would do) and consequently prevent the incorporation of T␤ 4 -actin in filaments, or it could screen the effects of ionic strength, thereby favoring the sequestering activity of T␤ 4 over its interaction with F-actin. Nonetheless, the intrinsic properties of T␤ 4 illustrated here have to be considered to some extent in the in vivo situation. It may be worth noting that complete agreement has not been reached among different groups concerning the actual value of the T␤ 4 content of motile blood cells (5,11). In addition, the dilution of cytoplasm that takes place in the preparation of cellular extracts without fixation causes depolymerization of a part of the F-actin pool (31,32), which may lead to a somewhat overestimated concentration of unassembled actin.
From a structural point of view, the fact that T␤ 4 -actin is able, although weakly, to copolymerize with actin, accounts for the difficulties encountered in the crystallization of the T␤ 4actin monomer in salt-containing solutions. The observation that T␤ 4 -actin incorporates into filaments only in high ionic strength (0.1 M KCl) assembly buffers indicates that either electrostatic bonds in the actin-T␤ 4 interface have to be weakened, or hydrophobic bonds have to be strengthened, to allow incorporation of T␤ 4 -actin in the filament. More detailed studies of the structure of T␤ 4 -actin complex will challenge these expectations.