Reconstitution and Regulation of Actin Gel-Sol Transformation with Purified Filamin and Villin*

Gel-sol transformation of actin filaments, a process essential for cell motility, can be reconstituted in vitro and regulated in a predictable fashion by the combined action of villin and filamin. Measurements made in a low shear falling ball viscometer show that mixtures of actin, villin, and filamin exist either as a gel (yield point 2 140 dynes/cm2) or as a low viscosity liquid depending on the relative ratio of vil1in:actin. Filamin induces gelation of F-actin by forming stable cross-links be- tween actin filaments. Villin inhibits filamin-induced F-actin gelation, but the effect can be overcome by in- creasing the amount of filamin. Sedimentation assays show that villin does not inhibit gelation of actin by preventing filamin from binding to F-actin. Results from viscosity measurements and filament length de- terminations show that villin increases actin filament number by reducing the average filament length with- out altering the total amount of polymer. Because the gel point of a fixed amount of polymer is sharply de- pendent on the ratio of cross-links to number of poly-mers, the solation effect of villin might be explained by its effect on filament number. Based on the network theory of gel formation, calculations of the amount of additional cross-linker required to overcome the effect of a known increase in the number of actin filaments agree reasonably well with experimental findings. These results document the existence of cellular pro- teins which could regulate gel-sol transformation in vivo by their effect on actin polymer

The consistency of cytoplasm in intact cells transforms reversibly from that of a low viscosity liquid (sol) to that of a rigid gel. These consistency changes correlate with alterations in cell shape and motility, and convincing evidence shows that cytoplasmic sol-gel transformations form part of the structural basis for cell movements (recently reviewed by Taylor and Condeelis in Ref. 1).
The discovery that naked cytoplasm from various cell types can undergo consistency changes in vitro depending on envi-* This work was supported by Grant AI-13700 from the United States Public Health Service. Appreciation is extended to the Jane Coffin Childs Fund and the American Cancer Society, MD Division for pilot Grants 324 and 76-27, respectively. The costs of publication of this article were defrayed in part by the payment of page charges. This article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact. +Recipient of National Institutes of Health Medical Scientist Traineeship T32-  ronmental factors such as pH, Caz+, temperature, and ionic strength (2-5) has enabled identification of the molecular components responsible for production and control of gel-sol transformation. Fractionation and reconstitution studies showed that cytoplasmic gels are formed by F-actin and actin cross-linking proteins such as filamin (6,7), macrophage actinbinding protein (8, g), and the 58,000 plus 220,000 dalton proteins from sea urchin eggs (10).
Attention is now focused on identification of molecules which can regulate the development of cytoplasmic rigidity. The network theory of gel formation as put forth by Flory (11) predicts that the gel point of a fixed concentration of polymer will be sharply dependent on the ratio of the number of cross-links to the number of polymers. If cytoplasmic gels can be described by the network theory, as suggested by Hartwig and Stossel(12), then control of cytoplasmic gelation can be achieved by any mechanism which alters either the number of cross-links or the number of actin filaments. Already, two functionally distinct proteins which can regulate the gel point of F-actin have been described. Actinogelin (13) gels F-actin but only in the presence of 5 M Ca". Gelsolin, a protein from rabbit macrophage (14), does not gel F-actin, but confers Ca4+ sensitivity on gelation of F-actin by actinbinding protein or by filamin. At Caz+ ? 10"" M, gelsolin causes solation of actin/fiamin or actin/actin-binding protein gels. Yin and Stossel (14) suggest, on the basis of indirect evidence, that gelsolin acts by breaking F-actin filaments thereby altering the critical cross-linker to filament ratio.
Having recently found that villin, a 95,000-dalton protein isolated from chicken intestinal epithelial cell brush borders, shortens the length of F-actin without affecting the total amount of polymer (15), we predicted that villin would regulate the gel point of F-actin/filamin mixtures. In this paper, we show that this prediction is experimentally verified and that the effect of villin on the gel point is directly related to its effect on the number average (and weight average) actin filament length. Therefore, one mechanism for regulation of gel formation can be based on the demonstrated existence of cellular proteins which regulate the length and thus the number of actin filaments formed by a fixed amount of actin.

Preparation of Proteins
Rabbit skeletal muscle actin was prepared from an acetone powder by the procedure of Spudich and Watt (16). Monomeric actin was further purified by gel filtration on Sephadex G-150 to remove trace components which modify actin polymerization (17). Villin (98% homogeneous) was prepared from chicken intestinal epithelial brush borders as described by Craig and Powell (15). Filamin was isolated from chicken gizzard smooth muscle by the method of Shizuta et al.

Biochemical Assays
Low Shear Viscometry-Low shear viscometry was performed with a falling ball viscometer as described by . This viscometer is useful for measuring the apparent gelsol transition of actin gels because the apparent viscosity of a solution increases sharply at the gel point (11). A gelled sample is defined as one through which the stainless steel ball does not fall when the capillary tube is held at an angle of 80"; such samples have a rigidity or yield strength 2 140 dynes/cm ' (19).
H i g h S h e a r Viscometry-These measurements were made in

Poly~c~ylamirle Gels
Sodium dodecyl sulfate-polyacrvlamide gels were run according to the procedure of Laemmli (21 ). The resolving gel was 7.51 acrylamide. 0.2'r hisacrylamide; the stacking gel contained 3.0qi acrylamide. 0.08"i bisacrylamide. Gel slices were stained with Coomassie blue and scanned in a Gilford spectrophotometer at 590 nm.
Protein was measured by the dye-binding assay of Bradford (22) using bovine serum albumin as a standard.

Electron Microscop-v of Number Average and Weight Alverage Length Measurements
Protein solutions were diluted to 0.05 mg/ml in polymerization buffer and applied (60 s) to carbon-shadowed grids which had been made hydrophilic by glow discharge or by pretreatment with 0.2 mg/ ml of cytochrome c in 0.17 isoamyl alcohol. Excess sample was removed: grids were floated three times in distilled water and then stained (30 s) with 0.75"; uranyl formate, pH 4.3. Samples were photographed at 10,000 magnification in a Zeiss EMIOA. Prints were made at a final magnification of 2fi.000. Collages were constructed to give an area large enough (23) for filament measurement (70 pm' for sample of short filaments to 220 pm' for control samples). An average of 950 filaments and no less than 400 filaments were measured for each sample. Number average length (xn,L,/xn,. where n, = number of filaments of length. L,) was calculated by dividing the total polymer mass in a given area (i.e. the total filament length. measured with a linear tracer) by one-half the number of ends present in that area (24). Weight average length was determined by recording lengths of individual filaments and calculating ~n , L , /~n , L , ' .
Filaments shorter than 0.04 pm cannot he detected on the prints: hence they are excluded from analysis.

RESULTS A N D DISCUSSION
As noted by others (9, 19). the transition of actin from a sol to a gel in the presence of an actin cross-linking protein such as fiiamin occurs sharply when the critical concentration of cross-linker is attained (Fig. 1A). At a molar ratio of 1 filamin dimer:450 actin monomers, the actin/filamin mixture exists as a liquid with an apparent viscosity only slightly higher than F-actin alone. In contrast, a t a molar ratio of 1 filamin dimer: 225 actin monomers, the mixture forms a gel with a static yield strength great enough to support the weight of a ball. In the presence of villin, the critical concentration of filamin required to gel the same amount of F-actin was found to increase (Fig. 1A). At a molar ratio of 1 villin monomer to 215 actin monomers, nearly a 5-fold increase in filamin concentration was required to gel the actin. Conversely, at fixed concentrations of filamin and actin (molar ratio filamin dimer:actin monomer 1:25 and 1:15) increasing amounts of villin are required to inhibit gelation (Fig. 1B). Thus, the transition from gel to sol state can be regulated by the relative amounts of F-actin, villin, and filamin.
How does villin inhibit gelation? Theoretically, villin could shift the gel point of actin/filamin mixtures by altering either the number of cross-links or the number of actin filaments. Measurement (by quantitative densitometry of Coomassie blue-stained gels) of the amount of filamin sedimented with F-actin in the presence and absence of villin showed that villin has no detectable effect on the binding of filamin to actin (Fig.  2) and, therefore, does not alter the number of cross-linkers. In contrast, a direct effect of villin on actin is detected by monitoring polymerization kinetics of villin/actin mixtures (15). Villin nucleates actin assembly (15) and reduces the steady state equilibrium viscosity of F-actin (Table I). At the two vil1in:actin ratios used in the experiment shown in Fig. lA, the final equilibrium high shear viscosity of F-actin was reduced by 14% (1 villin:360 actin monomers) and 40T (1 villin:215 actin monomers). We (15) have previously shown that the effect of villin on the equilibrium viscosity of F-actin is explained completely by its ability to shorten actin filaments since villin has no effect on the total amount of polymer as determined by the DNase 1 assay for actin monomer.
The effect of villin on F-actin length (and, therefore, filament number) was examined in detail by measuring the number average length ( [ L l n ) and the weight average length villin (0.3 p g ) , and filamin (4 p g ) in various combinations were polymerized and incubated under the same buffer and temperature conditions described in Fig. 1. After 1.5-h incubation, the samples were spun a t 130,OOO X g for 1.5 h in a Beckman Airfuge (room temperature). Supernatants were removed, pellets washed once, and wash combined with the supernatants. Pellets were solubilized directly into sodium dodecyl sulfate-polyacrylamide gel sample buffer. Supernatants were trichloroacetic acid-precipitated. then prepared for sodium ( [ L l w ) from electron micrographs such as those shown in Fig.  3. Table I summarizes the viscosity and filament length measurements obtained from three independent experiments in which different preparations of both actin and villin were used. The effect of a given amount of villin on F-actin length is not identical between experiments. However, if the percentage of reduction in F-actin viscosity is plotted as a function of the amount of villin (which normalizes for differences in polymerizability of the actin), the data from all three experiments fall on a common curve (Fig. 4A). Log-log plots of viscosity uersus ( [ L l n ) show that viscosity is linearly related to the square root of the number average filament length for ([Lln) 2 0.65 pm. For ([Lln) 5 0.65 pm, viscosity is a linear function of L'," (Fig. 4B). This linear relationship between viscosity and the number average filament length supports our assumption that calculation of changes in filament number based on electron microscopic measurement of changes in average filament length are relatively precise.
It should be noted that Staudinger's equation, 9 = KL", is generally true only when the viscosity measurements have been extrapolated to zero protein concentration (intrinsic viscosity) and to zero shear rate (20). The viscosity uersus shear rate profile of polymeric actin is pseudoplastic and, therefore, non-Newtonian (25); as the shear rate approaches zero, viscosity approaches infinity. Thus, extrapolation of viscosity to zero shear rate is impossible. Nevertheless, our experimental results show that the relationship between Factin viscosity measured in an Ostwald viscometer (which has a finite shear gradient across the radius of the capillary) and the measured number average filament length is described by 9 = KL", where 7 = q.,, rather than zero shear intrinsic viscosity. Whether the sharp break in the slope of the line (Fig. 4B) actually reflects a change in the flexibility of actin as predicted by theory (a = 0.5-1.0 for random coils; a = 2.0 for rigid rods) (20) will require independent analysis of flexibility. It has been recently suggested by Hartwig and Stossel (12), that the network theory of gel formation proposed by Flory  ( 1 1) can be used to calculate the predicted increase in crosslinks required to gel a known increase in the number of polymers. Because of the effect of villin on actin filament length and, therefore, on actin filament number, we decided to determine whether the increased amount of filamin required to gel actin in the presence of villin could be predicted by the gel theory. Gelation depends on the mass of material involved, therefore, weight average rather than the number average filament length was used to determine the change in filament number. The weight average filament length for actin alone was 5.6 pm and for actin plus villin (215:l) it was 1.5 pm. Histograms of the data used to obtain these average values are shown in Fig. 5. For actin alone, the ratio of weight average lengthhumber average length is 2.0, indicative of an exponential filament length distribution. In the presence of villin, this ratio is 1.5, which suggests that villin may shift the actin filaments to a more homogeneous length distribution. However, the inability to detect filaments shorter than 0.04 pm might also account for the apparent change in the length distribution profile.

Effect of rillin on specific viscosity and number average length of F-actin
The number density of cross-links ( P C ) required for incipient network formation in a population of arbitrary length distribution (11) is equal to l/%, where Rw = weight average degree of polymerization. This latter value is obtained by multiplying the weight average length ([Llw) times the known value of 370 actin monomers/pm of F-actin (26). For F-actin alone the value of PC is 4.8 X IO"' . This number times the molar concentration of actin monomer in filaments (7.8 PM), corrected for the critical concentration, yields the theoretical amount of cross-linker (filamin) necessary for gelation, which is 3.76 X lo-" M. The experimentally determined amount of filamin dimer necessary to gel 7.8 p~ actin is 4 X IO-" M. In the presence of villin (villin:actin, 1:215), PC is 1.8 X 10"' and the theoretically calculated amount of cross-linker required is 14 X lo-" M. The actual amount of cross-linker necessary to FIG. 3. Electron micrographs of negatively-stained actin filaments in the presence and absence of villin. A, actin at 9.0 p~ polymerized under the conditions described in Fig. 1. B, 9.0 Figs. 1 and 3) were polymerized as described in Fig. 1 and applied to EM grids. The length of individual filaments was measured on micrographs as described under "Experimental Procedures"; 453 filaments were measured in the control experiment; 351 filaments were measured in the actin plus villin experiment. overcome the effect of villin is 1.9 X M. Although the absolute difference between the theoretical concentration of filamin and the actual concentration of filamin is 10-13-fold, the relative increase (4.7-fold) in filamin concentration necessary to gel 7.8 IJ.M actin in the presence of villin is close to the theoretical fold-increase (i.e. 3.7-fold). That the absolute concentration of filamin required for gelation is higher than theoretically predicted might be explained by the probable formation of cyclic structures that do not contribute to network formation (ll), and by aggregation of filamin dimer (27).

Regulation of Actin Gel-Sol Transformation by Filamin and Villin
In conclusion, these preliminary data indicate that the effect of villin on the gel point of actin/filamin mixtures can be partially accounted for by its effect on actin filament number. However, a more precise method for measuring the point of incipient gelation will be needed to rigorously test the conformity of this gel system to the network theory. Recently, two other proteins have been described which are functionally similar to villin. Gelsolin (14) confers Ca2' sensitivity on gelation of actin by filamin or by macrophage actin-binding protein. Indirect evidence suggests that gelsolin acts by restricting the length of actin filaments (14). Fragmin, a 50,000dalton protein isolated from Physarum (28), exerts Ca2+-sensitive control over the length of actin filaments. It is to be expected that fragmin will have the same effect on in vitro actin gelation systems as do villin and gelsolin. Thus, a class of regulatory proteins has been defined which may well be important in the control of cytoplasmic rigidity and, therefore, of cell shape and motility.