Steady State Length Distribution of F-actin under Controlled

VOl. 259, No., 16, , Issue of August 25, pp. 9987-9991,1984 Printed in U.S.A.

THEJOURNAL OF BIOLOGICAL CHEMISTRY 0 1984 by The American Society of Biological Chemists, Inc.

Steady State Length Distribution of F-actin under Controlled Fragmentation and Mechanism of Length Redistributionfollowing Fragmentation* (Received for publication, May 14, 1984)

Marie-France CarlierS, Dominique Pantalonig, and EdwardKorn D. From the Laboratory of Cell Biology, National Heart, Lung, and Blood Institute, National Institutes of Health, Bethesda, Maryland 20205

Under controlledlevels of fragmentation by sonica- Lung, and Blood Institute). N-Pyrenyl iodoacetamide was from Motion in the presence of ATP, actin filaments reached lecular Probes. Preparation and Labeling of Actin Solutions-F-actin was purified different length distributions corresponding todifferent steady states of polymerization. When the sonica- from rabbit muscle (2.3) and chromatographed through Sephadex Gtion was interrupted, a spontaneous decrease in the 200 equilibrated in buffer G, consisting of 5 mM Tris-C1-, pH 7.8, number of filaments and a corresponding increase in containing 0.1 mM CaCl2, 0.2 mM dithiothreitol, 0.2 mM ATP, and 0.01% azide. Pyrenyl actin was prepared according to Kouyama and length was observed. The kinetics of the process of (4) with the modification described (5) and converted to Glength redistribution subsequent to fragmentation was Mihashi actin. The procedure for obtaining F-actin at equilibrium in the studied for the simpler case of F-actin filaments at presence of ADP was derived from earlier observations (6). Briefly, equilibrium in the presence of ADP. Analysis of the the ATP.G-actin (pyrenyl-labeled) complex (20-30 p ~ )obtained , by data shows that a diffusion-like random walk mecha- removal of free ATP by Dowex l-CI- treatment (7) was polymerized nism of length redistribution quantitatively accounts in the presence of 1 mMMgC12 and 5 p~ diadenosylpentaphosphate. for the observations much better than the previously ATP was exhausted by repeated sonications (3 X 30 s ) until the proposed end-to-end reannealing of filaments. Thein- critical concentration of ADP-actin (8p ~was ) reached.0.2 mM ADP volvement ofthis process in the kinetics of actin polym- was then added and the solution was kept at 25 “C for at least 1 h erization and in establishing the length distribution at before use. steady state is discussed. Polymerization Measurements-Actin polymerization was started by addition of 1 mM MgClz to the G-actin solution in buffer G. Polymerization was monitored by the fluorescence enhancement of the pyrenyl probe covalently attached to actin (excitation 265 nm; emission 385 nm). Solutions containing 5% labeled actin were rouEarly experiments of Nakaoka and Kasai (1)showed that tinely used. Measurements were done at 25 “C in a thermostatted actin filaments could be fragmented by sonic vibration with SLM 4000 spectofluorimeter. Sonication was applied directly in the a decrease in the viscosity of the solution and an increase in assay cuvette as described (6), using a Kontes sonifier attached to a ATPase activity. Electron microscopy observations led to the homemade electronic timer. This timer allowed both the periods of view that these short filaments recombined in an end-to-end sonication and thetime intervals without sonication to be monitored fashion, once sonication was stopped, with a recovery of the and, therefore, a given periodic fragmentation force could be applied initial viscosity and steady state ATPase rate. The kinetics to the system.’ Measurement of the Concentration of Filament Ends-The relative of the recovery process have been investigated in more detail in the present work. Analysis of the data excludes a true number concentration of ends was assayed as described (6) by using the ability of filaments to act asseeds for polymerization of G-actin.

“reannealing” process, and indicates that a unidimensional random walk, or diffusion-like process, accounts for the deRESULTS crease in filament number after fragmentation. The simple case of F-actin at equilibrium in the presence of ADP is Establishment of Different Steady Statesof Fragmentation analyzed in detail. The difference in the steady state situation of F-actin in the Presence of A T P by Controlled Regimes of in the presence of ATP is also discussed. Sonication-When F-actin is at steady state, anequal number of on and off monomer-polymer reactions occurs at the filaMATERIALS ANDMETHODS ment ends. Due to theslow nucleotide exchange on the ADP. Chemicals-All chemicals used in buffers were analytical grade. G-actin, which dissociates from F-actin, a certain amount of ATP, diadenosylpentaphosphate,and dithiothreitol were from Sigma. ADP. G-actin exists in solution at steady state (6,8,9).Since ADP from P-L Biochemicals was further purified by DE--cellulose the rates of monomer-polymer reactions at steady state dechromatography and was a gift of Dr. A.A. La1 (National Heart, pend on the number of ends, the amount of ADP. G-actin at steady state increases with the number concentration of fila* The costs of publication of this article were defrayed in part by ments. A linear double reciprocalrelationship has been estabthe payment of page charges. This article must therefore be hereby marked “advertisement” in accordance with 18 U.S.C. Section 1734 lished between the number concentration of filaments [ F ] and the observed ADP-G-actin concentration GD at steady solely to indicate this fact. ’$ Permanent address, Laboratoire d’Enzymologie, Centre National de la Recherche Scientifique, 91190 Gif sur Yvette, France. 5 Supported in part by Centre National de la Recherche Scientifique and the Ligue Nationale Francaise Contre le Cancer. Permanent address, Laboratoire d’Enzymologie, Centre National de la Recherche Scientifique, 91190 Gif sur Yvette, France.

Theoretically, the steady state average length can be varied by varying the energy of sonication applied to the F-actin solution. The alternative procedure described was chosen because it is easier to quantify and yields more reproducible results than varying the energy of sonication.

9987

Distribution Length

9988

of Actin Filaments

state (6), as follows:

in which [ F ] represents the number concentration of filaments, [Gg] the critical concentration of ADP. G-actin, lz, the rate constant for ADP dissociation from ADP. G-actin, and k D the rate constant for ADP. actin dissociation from filaments. We reported previously (6) that F-actin reaches a steady state under sustained sonication, i.e. a constant number of filaments is formed for which there is a corresponding critical concentration. This steady state is established because the rate of decrease in filament number throughpolymer-polymer and/or polymer-monomer reactions equals the rate of filament formationby fragmentation. Hence, if different rates of fragmentation are imposed, different steadystates of polymer lengths should be established. To test this hypothesis, several samples of F-actin were polymerized in the presence of ATP and thensonication was applied for periods of 0.1 s with the interval between sonication periods varying between 0.1 and 99.9 s for different samples. The per cent of total time during which sonication was applied thus varied between 0.1 and 50%. The change in the mass concentrationof polymer during the experiment was monitored by the fluorescence of the pyrenyl probe covalently attached toactin. Fig. lA shows that each regime of sonication caused a limited depolymerization of F-actin and that the new steady states were reached faster at a higher per cent of time under sonication. Fig. 1B shows that thecritical concentration reached under steady state varied linearly with the logarithm of the per cent of time under sonication. The number concentration of filaments was measured when fluorescence had reached a stable plateau. The steady state number of ends increased with the per cent of time under sonication. A linear double reciprocal relationship was established between the number of filaments and thecorresponding ADP.G-actin concentration at steady state measured from the fluorescence change (Fig. 2B) with a value of 8 p M for the

A.

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1500

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FIG. 1. Establishment of different steady states of polymerization of F-actin, corresponding to different number of filaments, under controlled regimes of fragmentation in ATP. Actin, in buffer G at aconcentration of 5.92 pM (7.8% pyrenyllabeled), was polymerized by addition of 1mM MgC1,. Polymerization was started 18 h before the experiment. Six identical samples were prepared in 3-ml cuvettes. A t time zero, different regimes of sonication were applied to each sample. Sonication periods of0.1 s were separated by intervals (in s) of 999 ( I ) , 49.9 ( 2 ) , 9.9 ( 3 ) ,4.9 ( 4 ) , 0.9 ( 5 ) , and 0.1 ( 6 ) . The upper horizontal line ( 0 ) corresponds to the nonsonicated sample. A, the fluorescence of the samples was monitored and converted to polymerized actin, pM. E , a semilog plot of the concentration of nonpolymerized actin reached at each steady state (dashed lines) uersus the per cent of time under sonication.

500 TIME, S

FIG. 2. Repolymerization of F-actin in ATP and accompanying decrease in the number of filaments following arrest of fragmentation. Once the steady states presented in Fig. 1 were reached, the relative number of filaments in each sample was measured as described under "Materials and Methods" (three measurements at 2-min intervals at steady state). Then sonication was stopped at time zero. A shows the repolymerization of F-actin. E shows the linear double reciprocal relationship between the number of filaments at steady state under each regime of sonication (average of three measurements) and the steady state ADP.G-actin concentration. C shows the decrease in filament number during the repolymerization. Note that after 1000 s, the number of filaments is still 3-3.5-fold greater than in the nonsonicated sample.

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ADP. actin cricital concentration. After measurement of the number of filaments,fragmentation was stopped and the fluorescence recovery accompanying the decrease in filament number wasfollowed (Fig. 2 4 ) . Equation 1 and the linear calibration curve shown in Fig. 2B allowed the conversion of the fluorescence data into filament concentration (Fig. 2C). The validity of this conversion has been established (6) and is due to the fact that the length redistribution is the kinetically limiting step in the fluorescence recovery process. The time courses of fluorescence (i.e.concentration of polymerized actin subunits) andnumber of filaments were similar curves of opposite directions. They were not exactly symmetric, however, since the steady state concentration of ADP. Gactin, GD,is not exactly proportional to the number of filaments (see Equation 1).Also, there was a lag preceding the change of fluorescence and number of ends which was greater when the filaments were longer. In the presence of ATP, the kinetics of the decrease in number of filaments, once fragmentation is stopped, are complicated by the interfering repolymerization of actin. Therefore, the kinetics of length redistribution were studied with the less complex system of F-actin at equilibrium in the presence of ADP, in which no change in amount of polymerized actin occurs during or after sonication. Evolution of the Number Concentration of Filaments Close to Equilibrium in ADP following Fragmentation-F-actin SOlutions polymerized at different concentrations in the presence of 0.2 mM ADP and 1 mM MgC12 were submitted to

Distribution Length

Filaments of Actin

9989

sustained sonication for 60 s. At t = 0, sonication was stopped and the number concentration of ends was assayed at different times. A time-dependent decrease of the number concentration of filaments was observedat all concentrations of F-actin (Fig. 3). The initial number concentration of filaments under sonication was directly proportional to the mass concentration of polymerized subunits verifying that, in ADP, the average length of the short filaments is independent of the concentration of polymer (Fig. 3, inset). If end-to-end association of these short filaments accounts for the observed decrease in number, the following equation should apply:

where m is the average length under sonication, and @ and a the reannealing and fragmentation rate constants for polymers of average length m and 2m, respectively. When sonication is stopped, fragmentation becomes negligible, and essentially only reannealing is expected to occur. According to Equation 2, the initial rate of decrease in the number of filaments should be proportional to the square of the initial number concentration of filaments [Fo].Fig. 4 shows that this is not the case. Rather, a linear relationship was established between the filament concentration under sonication [FO] and the initial rate of decrease in the number of filaments, ( ~ l [ F ] / d tonce ) ~ , fragmentation was stopped. In addition, the time dependence [ F ( t ) ]was the same at all actin concentrations, and the same value of 75 s was found for the half-time of the process in all samples. An alternative interpretation of the data of Fig. 3 is that the number of filaments decreases and the average length simultaneously increases, according to the following model. The probability exists that, while G-actin is maintained at the critical concentration, length fluctuations allow short 0.4

0

0

0

200

400

600

800

loOD

TIME, S

FIG. 3. Decrease in the number of filaments followingsonication of solutions of F-actin at equilibrium in the presence of ADP. Actin was polymerized to equilibrium in the presence of 1 mM MgCl,, 0.2 mM ADP, and 5 p M diadenosylpentaphosphateas described under "Materials and Methods." Samples of different concentrations from 9 to 16 p M (corresponding to 1 to 8 p M polymerized actin) were maintained under continuoussonication for 60 s. At time zero, sonication was stopped and the number of filaments was measured a t different intervals of times. The plots correspond to the following total actin concentration(pM): 0,16; A,13; A, 11.5;a, 10.5; 0, 8.8. The curves are theoretical and are obtained by calculating at each time the value of Fap where Fo is the number of filaments under sonication and p is calculated (Equation 5 ) using the parameters m ,, = 22 subunits and a = 7 s". Assuming an average of 22 subunits/ filament under sonication, and knowing the mass concentration of ,, the molar concentration of filaments could be polymerized actin C calculated in each sample. The inset shows the linear relationship ., between Fo and C

0.2

0.3

[FoI, PM

FIG. 4. Evidence against end-to-end reannealing of actin filaments following fragmentation. Theinitial rate of decrease in filament number once sonication was stopped

is plotted

versus the initial number concentration of filaments under sonication, [Fo]. Thedata are fromFig. 3. Note that a [FO]' dependence of ($)o

would be expected in the case of reannealing of filaments, but

a linear dependence was observed.

filaments to disappear totally through successive subunit dissociation reactions, while other filaments lengthen. The result is a shift in the length distribution towards longer polymers, accompaniedby a decrease in the number of filaments. Within this model, the decrease in thenumber of filaments of a given length is independent of the initial number [Fo].The following scheme describes the reactions which take place: G t Fo

ACTIN POLWtRIZED. pM

0.1

a Fl

a f Fz

a

a

+ ::: + Fm-I 5Fm 5Fm+l

+

Fm+2

(3)

In this scheme, a represents the rate for ADP. G-actin association to or dissociation from filament ends. On and off rates are equal at equilibrium ( a = k+C, = k-); actually, the contribution of both ends is summedin a, k,, and k-. F,,, represents a filament containing m subunits more than the nucleus. Fo represents the nucleus, which is unstable by definition, so that assoon as one subunit dissociates from Fo, that filament disappears completely. The reverse reaction, i.e. nucleation, is assumed to be negligible within the period of time during which the process of length redistribution following fragmentation was observed. This process is in fact a random walk process with absorption at the boundary (10). The complete analysis as applied to microfilaments and microtubules has been developed by Hill (11). Briefly, the probability, P ( m ) , for a filament, F,,, to exist at time, t, obeys the diffusion-like law

The fraction of filaments, p , remaining present in solution at time, t, is

where x. = m/&t. The initial distribution is considered to be a very narrowgaussian centered at m = no(average length under sonication). As time goes by, this distribution spreads and filaments reaching the boundary, i.e. the size m = 0,

Length Distribution of Actin Filaments

9990

disappear. Consequently, the number concentration of filaments, [ F ] ,decreases while the amount of polymerized subunits which is equal to [Fo]E m Pdm, remains constant and equal to [ F o ] ~[FO] , being the number concentration of filaments at time zero. The validity of this model was tested by adjusting the theoretical curves of [ F o b versus time, for each sample, to the corresponding experimental plots [ F ( t ) ] shown in Fig. 3. Asshown in thefigure, a good fit was obtained to all five plots using the same set of parameters, m = 22 subunits and a = 7 s-', in the theoretical curves. The value of 7 s-' was chosen because it is the value found experimentally for the rate constant of ADP .actin dissociation from filaments under these ionic conditions (12, 13): Since filaments have been fragmented 20-30-fold upon sustained sonication, the value of 22 subunits for their average length under sonication indicates that they would have 440-660 subunits in the nonfragmented equilibrium state, Le. would be 1-2-pm long, a value in good agreement with the reported electron microscopy data (14, 15). Incidentally, a peculiar feature of the curves in Fig. 3 is that thelog of the decrease in filament concentration is linear with the square root of time, for more than 80%of the decrease. This linearity is a simple qualitative indication of the diffusion-like character of this process. DISCUSSION

The aim of this paper has been to document the nature and the importance of the reactions which change the number and/or the length distribution of actin filaments. The reactions of filament dissociation (fragmentation) and association (reannealing) have often been invoked in analyzing the polymerization of actin (12, 17, 18).In addition to their role in the interpretation of the kinetics of polymerization, the extent to which these reactions take place once the polymer is formed may be important in the determination of the steady state distribution of filaments in the presence of ATP (18), and also in the quantitative analysis of the data on monomerpolymer exchange at steady state. It was convenient to impose aperturbation to F-actin solutions by controlled sonication regimes, and thenstudy the establishment of a new steady state and therelaxation to the unperturbed state following fragmentation. The fact that a steady state average length could be obtained under a given input of fragmentation energy indicates that a reverse reaction exists which tends to re-establish a longer averagelength. The nature of this reverse reaction has been investigated by analyzing the kinetics of the decrease in the number of filaments once mechanical fragmentation was stopped. The data show that trueend-to-end reannealing of filaments is not the mainprocess through which the number of filaments decreases. Rather,a random walk fluctuation process, with absorption at the boundary, accounts for the data. In the simple case of F-actin at equilibrium in ADP solutions, it was found that the time for 50% decrease in the number of filaments containing 22 subunits was 75 s under our conditions. Due to the diffusion-like nature of this process, this time is proportional to the square of the average number of subunits/filament. Specifically, it wouldbe 26 min for a filament of 100 subunits and 5.6 h for a 1-pm long filament (-360 subunits). It, therefore, appears that this process may actually take place during the time required for spontaneous polymerization, and that the number of filaments may thus be lower in the last stages of the polymerization time course than just after completion of the nucleation. Further experi-

* A. A. Lal, E. D. Korn, and S. L. Brenner, manuscript in preparation.

ments wouldbenecessary to check this possibility. Once equilibrium is reached, this diffusion-like process would tend to make the average length increase indefinitely, unless it were counterbalanced by spontaneous fragmentation. If the average length measured at equilibrium is between 1 and 2 pm, it can be calculated that a plausible value for the fragmentation rateconstant of a filament 2-pmlongis kf = 0.69/tIl2, where tllzwould be the time needed for a filament of 1 pm to double its length by diffusion, i.e. 20,366 s. Then, kf = 3.4 s-'. This value is in reasonable agreement with the one proposed by Wegner (16) and Cooper et al. (12). The fact that, in the range of filament concentrations we studied, no true reannealing occurred does not eliminate the possibility of this reaction but does allow estimation of the maximum value possible for the rate constant k, for end-toend association of two filaments of22 subunits, in ADP solutions. For example, ifwe assume that 10% of the initial decrease in filament number is accounted for by reannealing, a maximum value of 3 M" 8" can be calculated for k, for filaments of 22 subunits' average length. The reannealing rate constant is expected to decrease with the 4th-5th power of subunits (18);it would then be 104-106-fold lowerfor a 1-pm long filament, and reannealing is, therefore, very improbable under the usual conditions of actin polymerization in vitro. Thus, the tentative value of 2-106 M" s" given by Frieden and Goddette (17) in modeling the polymerization curves appears tobe greatly overestimated. The change in distribution following fragmentation of Factin at steady state in the presence of ATP is theoretically more complicated to analyze than thecase of the equilibrium polymer in the presence of ADP. In thepresence of ATP, two difficulties complicate the quantitative analysis of the data. First, as observed (Ref. 6 and Fig. 2), repolymerization of actin takesplace simultaneously with the decrease in number of ends, so that Equation 5 cannot be applied. Second, at steady state, anATP cap exists at theends of actin filaments (13). Due to the presence of this cap, there is no longer a single dissociation rate constant ( a in Equation 3) involved in the length redistribution process, but rather a complex combination of the dissociation rate constants of ATP. actin and ADP.actin from filaments. In addition, the size of the cap and itsinterference with the length redistribution process are likely to varybecause the critical concentration also changes with the number of filaments. These complications prevent a simple analysis of the data obtained in thepresence of ATP. Nevertheless, the same diffusion-like process analyzed above for the equilibrium polymer is very likely to take place for the steady state polymer too and account for the observed increase in average length that occurs after polymerization is complete. In agreement with this proposal, a significant lag time was observed preceding the decrease in the number of filaments, when the initial average length under moderate, controlled fragmentation was large enough (Fig. 2). This behavior is theoretically expected within the described diffusion process, since some time is needed for the shorter polymers to disappear completely. The lag time is also expected to increase with the average length, as observed. The lag time is, however, too small (3-4 s) to be easily observed experimentally starting with the very short filaments obtained under sustained sonication. It is interesting to note that microtubules too can undergo changes of length distribution. The very short microtubules, formed in the presence of taxol, slowly transform into longer less numerous microtubules by the same diffusion-likeprocess (19).

Distribution Length Acknowledgment-We gratefully acknowledge the generous contribution of Dr. Terrell Hill in providing the mathematical description of the random walk model for filament length redistribution.

of Actin Filaments

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8. Neidl, C., and Engel, J. (1979)Eur. J. Biochem. 101,163-169 9. Hill, T.L. (1981)Bioph~s.J. 33,353-372 10. Chandrasekar. S. (1943)Rev. Mod. Phvsics 15.1-89 11. Hill, T. L. (1984)Proc. Natl. Acad. Sci U.S. A., in press REFERENCES 12. Cooper, J. A., Buhle, E., Jr., Walker, S. B., Tsong, T. Y.,and 1. Nakaoka, Y., and Kasai, M. (1969)J. Mol. Biol. 44,319-332 Pollard, T. D. (1983)Biochemistry 22, 2193-2202 2. Spudich, J. A., and Watt, S. (1971)J. Biol. Chem. 246,4866- 13. Carlier, M.-F., Pantaloni, D., and Korn, E. D. (1984)J . Biol. 4871 Chem. 259,9983-9986 3. Eisenberg, E., and Kielley, W. W. (1974)J. Biol. Chem. 249, 14. Wegner, A., and Engel, J. (1975)Biophys. Chem. 3,215-225 4742-4748 15. Kawamura, M., and Maruyarna, K. (1970)J. Biochem. (Tokyo) 4. Kouyama, T., and Mihashi, K. (1981)Eur. J. Biochem. 114,337,437-457 48 5. Brenner, S. L., and Korn, E. D. (1983)J. Biol. Chem. 258,5013- 16. Wegner, A., and Savko, P. (1982)Biochemistry 21, 1909-1913 17. Frieden, C., and Goddette, D. W. (1983)Biochemistry 22,58365020 5843 6. Pantaloni, D., Carlier, M. F., Coue, M., Lal, A., Brenner, S. L., 18. Hill, T. L. (1983)Biophys. J. 44, 285-288 and Korn, E. D. (1984)J. Biol. Chem., 259,6274-6283 7. Mockrin, S. C., and Korn, E. D. (1980)Biochemistry 19, 5359- 19. Carlier, M. F., and Pantaloni, D. (1983)Biochemistry 22, 47145362 4721