Polymerization of ADP-Actin and ATP-Actin under Sonication and Characteristics of the ATP- Actin Equilibrium Polymer*

Transcription

1 THE JOURNAL OF BIOLOGICAL CHEMISTRY Vol. 260, No. 11, Issue of June 10, pp ,1985 Printed in U.S.A. Polymerization of ADP-Actin and ATP-Actin under Sonication and Characteristics of the ATP- Actin Equilibrium Polymer* (Received for publication, November 24,1984) Marie-France CarlierS, Dominique Pantalonij, and Edward D. Korn From the Laboratory of Cell Biology, National Institutes of Health, National Heart, Lung, and Blood Institute, Bethesda, Maryland Polymerization under sonication has been developed as a new method to study the rapid polymerization of actin with a large number of elongating sites. The theory proposed assumes that filaments under sonication are maintained at a constant length by the constant input of energy. The data obtained or the reversible polymerization of ADP-actin under sonication have been successfully analyzed according to the proposed model and, therefore, validate the model. The results obtained for the polymerization of ATP-actin under sonication demonstrate the involvement of ATP hydrolysis in the polymerization process. At high actin concentration, polymerization was fast enough, as compared to ATP hydrolysis on the F-actin, to obtain completion of the reversible polymerization of ATPactin before significant hydrolysis of ATP occurred. A critical concentration of 3 I.~M was determined as the ratio of the dissociation and association rate constants for the interaction of ATP-actin with the ATP filament ends in 1 mm MgCIZ, 0.2 mm ATP. The plot of the rate of elongation of filaments versus actin monomer concentration exhibited an upward deviation at high actin concentration that is consistent with this result. The fact that F-actin at steady state is more stable than the ATP-F-actin polymer at equilibrium suggests that the interaction between ADP-actin and ATP-actin subunits at the end of the ATP-capped filament is much stronger than the interaction between two ATP-actin subunits. Considerable progress has been made recently in the understanding of actin polymerization in the presence of ATP and ADP and the involvement of ATP hydrolysis in the polymerization process of ATP-actin. It has been established that, in the polymerization of ATP-actin, ATP hydrolysis occurs on the polymer in a monomolecular reaction subsequent to polymerization (1-4). It is also known that ADPactin polymerizes (5-7). While the polymerization of ADPactin is a reversible reaction, since no nucleotide hydrolysis reaction is associated with it, F-actin polymerized in the presence of ATP is a steady-state polymer with a cap of ATP subunits at the ends of the filaments. At the steady-state * The costs of publication of this article were defrayed in part by the payment of page charges. This article must therefore be hereby marked aduertisernent in accordance with 18 U.S.C. Section 1734 solely to indicate this fact. $ Permanent address: Laboratoire d Enzymologie, Centre National de la Recherche Scientifique, Gif sur Yvette, France. J Supported in part by Centre National de la Recherche Scientifique and the Ligue Nationale Francaise Contre le Cancer. Permanent address: Laboratorie d Enzymologie, Centre National de la Recherche Scientifique, Gif sur Yvette, France critical Concentration, F-actin in ATP undergoes a transition between the uncapped (depolymerizing) conformation and the ATP-capped (growing) conformation similarly to microtubules (4, 8-11). Because ATP hydrolysis is not mechanistically coupled to polymerization, it should, however, be possible to observe the reversible polymerization of ATP-actin, at least transiently, under conditions in which polymerization is so fast that there is notime for ATP hydrolysis to occur on the F-actin before polymerization is complete. The equilibrium and kinetic parameters for the polymerization of ADP-actin (6, 7) are known, as are also the critical concentration of ATP-actin at steady state, the rate constant for ATP hydrolysis on F-actin (3,4), and the association and dissociation rate constants of ATP-actin for the steady-state polymer (3,4, 12). The issue which we deal with in this paper is the determination of the equilibrium and kinetic parameters for the reversible polymerization of ATP-actin in the absence of ATP hydrolysis. This can be accomplished provided that ATP-actin is polymerized at a concentration, C, high enough so that the rate of elongation of one filament, k+(c - Cc), greatly exceeds the rate of ATP hydrolysis on the filament of F-actin. The method chosen was to polymerize actin at high concentration under continuous sonication. Sonication has long been known to promote an explosive acceleration of the polymerization of actin due to the fragmentation of the few long filaments initially formed into short pieces which provide many ends for further growth (13). Recently, we confirmed that sonication increases the number of filaments without changing either the association or dissociation rate constants (12). Further use of this technique is described here. First, the theory of reversible polymerization under sonication is developed. Then, the data for polymerization under sonication of ADP-actin are shown to be well accounted for by the theory and to be consistent with previous results for spontaneous polymerization. The method, thus validated, has been used for the study of the rapid reversible polymerization of ATP-actin. The advantages of this novel way to study actin polymerization, i.e. polymerization under sonication, are discussed. MATERIALS AND METHODS Chemicab l1 reagents were analytical grade. ATP, ADP, and Ap,A were from Sigma. ADP was further purified by DEAE-cellulose chromatography (14). Actin-G-actin was purified from rabbit muscle according to the method of Spudich and Watt (15) as modified by Eisenberg and Kielley (16) and was further gel filtered through Sephadex G-200 equilibrated in buffer G, consisting of 5 mm Tris-C1-, ph 7.8,0.2 mm The abbreviations used are: Apd, diadenosyl pentaphosphate; NBD, 7-chloro-4-nitrobenzeno-2-oxa-1,3-diazole; D, ADP-actin; T, ATP-actin; EGTA, ethylene glycol bis(p-aminoethyl ether)-n,n,n, N -tetraacetic acid.

2 6566 Actin Polymerization under Sonication dithiothreitol, 0.1 mm CaC12, 0.2 mm ATP, and 0.01% sodium azide. G-actin was stored on ice at a concentration of p~ and used within 2 weeks. NBD-labeled actin was obtained as described by Detmers et al. (17); 0.9 k 0.1 mol of label was covalently bound to 1 mol of actin. The 1:l complex of ATP-G-actin was obtained free of unbound nucleotides by treating a solution of G-actin with Dowex 1 according to Mockrin and Korn (18). The 1:l complex of ADP-G-actin free of unbound nucleotides was obtained as previously described (4, 19). Polymerization under Sonication-Actin polymerization was monitored at 25 "C by the fluorescence increase of the NBD probe covalently attached to actin (20). Actin solutions containing 5-20% labeled actin were routinely used. Polymerization was usually started by addition of 1 mm MgClz to the actin solution in buffer G and simultaneously turning on the sonifier with the probe placed 2 mm deep into the fluorescence cell (Kontes Instruments, Inc. sonifier, lowest possible setting). The same results were obtained when experiments were done starting with M%+-G-actin instead of Ca2+-G-actin. Me-G-actin was obtained either by dialyzing Ca2+-G-actin against buffer G containing no CaCI2 and 50 p~ MgC12 for 24 h followed by centrifugation for 60 min at 100,000 X g at 4 "C or by preincubating Ca2+-G-actin with mm EGTA and 50 p~ MgC12 for 3 min before starting polymerization by addition of 0.95 mm MgCL This period of 3 min was found sufficient, and longer preincubation times did not affect the results. When polymerization was studied in the presence of ADP, 5-10 ptm Ap6A was always present in the buffer to inhibit the myokinase activity which contaminates actin preparations (7, 12). RESULTS Theory for Reversible Polymerization under Sonication- According to Oosawa and Asakura (21), the rate of filament elongation in the case of a reversible polymerization is: -d'c(t) - = k+m[c(t) - C,] dt where C(t) and C, are the concentrations of monomeric actin at time t and at equilibrium (critical concentration), respectively, k, is the association rate constant, and M is the number concentration of elongating filaments. It is unlikely that nucleation is affected by sonication because the size of the nucleus (probably a trimer (22)) is too small. We think, rather, that spontaneous nucleation takes place under sonication and that filaments then begin to elongate from the nuclei until they reach a limit size at which they have some probability to be fragmented. In experiments of sonication of DNA solutions, Freifelder and Davison (23) also found that sonication did not fragment polymers below a critical size. In addition, filaments have a higher probability to break in their middle (24). Polymerization under sonication thus takes place initially (assuming the monomer concentration is kept constant) as a geometric increase in the number of elongating filaments of a constant short length, according to the following scheme: Nuclei + monomer Fzrn F Fz, 7F,... frn \F, monomer I rf,,,... F-."-- "I -c Fa" \F, (1) concentration of polymerized subunits, C,. L, M = 7 m The length distribution of these short filaments under sonication is assumed to be narrow. Equation 1 can then be written: where Co is the total actin concentration. During the time course of polymerization the concentration of polymerized subunits, Co - C(t), and the concentration of polymerizable subunits, C(t) - C,, both vary between 0 and Co - C, with their sum being kept constant and equal to Co - C, (Fig. la, dashed line). Therefore, the evolution with time of the rate of polymerization, which is the product of these two terms (Equation 3), is a symmetrical function; the polymerization rate increases initially, reaches a maximum when Co - C(t) = C(t) - C, = (Co - C,)/2, i.e. at the time tlh when polymerization is half-completed, and then decreases to zero as the concentration of polymerizable monomers decreases to zero. The solid curue in Fig. la also shows the evolution of the rate of polymerization uersus the concentration of polymerized subunits, Co - C(t). The maximum rate of polymerization is the tangent at the point of the inflection of the polymerization curve, i.e. at the midpolymerization point. The theoretical time course of polymerization can be derived by integration of Equation 3, which gives: In - = -A(t - t d (AYJ 2 where y = Co - C(t) is the concentration of polymerized subunits at time t, A = Co - C, is the maximum extent of polymerization, and tlh is the time at which half-polymeriza- tion is completed, i.e., when y(t%) = A/2. Equation 4 shows that y is symmetrical with respect to the point of halfpolymerization. The theoretical time course of polymerization is pictured in Fig. Ib. Equation 4 also indicates that, when normalized to the same final extent of polymerization, all the time courses obtained at different actin concentrations should be parallel curves differing only by their values of tlh, and, therefore, be identical to one another except for a translation TIME FE. 1. Theoretical analysis of the polymerization of an equilibrium polymer under sonication. a, theoretical evolution of the concentration of polymerizable free subunits, C(t) - C,, (dashed line), and of the rate of polymerization (solid curue) versus the where Fi represents a filament of i subunits. Since the input concentration of polymerized subunits, Co - C(t), according to Equaof fragmentation energy is constant, the same steady average tion 3. b, theoretical time course of polymerization under sonication short filament length of m subunits is maintained throughout according to Equation 4. Solid curve, evolution of the concentration of polymer, Co - C(t), versus time. Dashed line, tangent to the the polymerization process, independent of the actin concen- polymerization curve at the point of inflection, the slope of which is tration, as we previously observed (19). Therefore, the number the maximum rate of polymerization. t.,+ and T represent the times for concentration of elongating filaments is proportional to the 50 and 13.5% polymerization, respectively (see text).

3 Polymerization Actin under Sonication 6567 along the time axis. The difference in the values of th are related to the difference in the number of nuclei virtually present at time zero in the different actin solutions. The maximum rate of polymerization, VM, obtained at tth when Co - C(t) = C(t) - C, = (C, - C,)/2 is: I I I I I Equation 5 shows that the critical concentration can be derived from the plot of VM versus Co, which is a straight line intercepting the abscissa at the critical concentration: The tangent to the polymerization curve at the midpolymerization point has an interesting property; it intercepts the time axis at a time t such that t% - T = m/2k+a. Incidentally, m/k+a is the average time between two fragmentations in the initial part of the curve, at concentration CD. It can be calculated that at time T, the amount of polymer formed is Y(T) = ( ~(7) - A)e- = 0.135A. Consequently, drawing the tangent at the inflection of the polymerization curve provides an easy way to determine the time at which 13.5% of the polymer is formed and the average initial division time, td = (fib- T)/2. Reversible Polymerization of ADP-Actin under Sonicatwn- We have previously shown (4, 12) that ADP-actin polymerizes, in the presence of 1 mm MgC12 and 0.2 mm ADP, with a critical concentration of La1 et al. (7) confirmed this result and showed that, under conditions of spontaneous nucleation, polymerization of ADP-actin is extremely slow. Under continuous sonication, in contrast, the polymerization process can be conveniently observed within a reasonable period of time, which reduces the risk of actin denaturation. Fig. 2 shows typical polymerization data observed by monitoring the fluorescence of NBD-actin under continuous soni- cation. At all actin concentrations, the polymerization process followed a sigmoidal curve after a lag time, the duration of which depended on the actin concentration. A stable plateau was reached under sonication, and, when sonication was stopped, the fluorescence remained constant indicating that z TIME, s FIG. 2. Polymerization of ADP-actin under continuous sonication in the presence of 0.2 mm ADP and 1 mm MgCIZ. The ADP-G-actin complex, 10% NBD labeled, was prepared as described under Materials and Methods and polymerized under continous sonication at 17.3 pm (top curue) and 13.8s pm (bottom curue). Note the symmetry of the polymerization curves with respect to the midpolymerization points. The dashed curue represents the bottom curue normalized to the same amplitude as the top curue and appears to derive from it by translation along the time axis, in agreement with Equation 4. Inset, semilogarithmic plots of the data, according to Equation 4. O 0.4. I 0.3 t, Ca PM FIG. 3. Evolution of the maximum rate of polymerization under sonication versus ADP-actin concentration. ADP-actin at different concentrations was polymerized under sonication. The maximum rate of polymerization V,. was measured as the tangent to the inflection point of the polymerization curves at the midpolymerization point. The square root of V,. is plotted uersus the total actin concentration Co. the same equilibrium was reached under sonication as in the absence of sonication. When normalized to the same final extent of polymerization, the polymerization curves obtained at different actin concentrations appeared to be parallel. Semilogarithmic plots of the time courses of polymerization, according to Equation 4 (Fig. 2, inset) are linear, as expected from the theory developed in the preceding section, which confirms that the polymerization curves were symmetrical with respect to the half-polymerization point. The maximum rate of polymerization, VM, was measured at different actin concentration and (V,) was plotted versus the total chain concentration, Co. Fig. 3 shows that a straight line was obtained, intercepting the abscissa at Co = 8.3 FM. This value is in good agreement with the critical concentration determined from measurements of the amount of polymer formed at equilibrium (7, 12) and from measurements of the dependence of the rate of growth of actin filaments on the concentration of monomeric actin (4). The good agreement between the data and theory validates the proposed model and the analysis of the reversible polymerization of actin under sonication. The fact that the experimental plot of VMH versus Co is linear confirms that filaments have a constar$ length under sonication. The slope of the plot is (2). Assuming that the sonicated filaments contain an average of subunits (19, 25), the data indicate that k+ is in the range of PM- s-. This value is in good agreement with previous independent measurements of the kinetics of polymerization in the absence of sonication (4, 7). It should be noted that the absolute absence of any ATP

4 6568 Polymerization Actin contamination of the ADP is a necessary condition to obtain the symmetrical polymerization curves shown in Fig. 2. This assay is extremely sensitive to the presence of trace amounts of ATP, which, if present, cause the following to occur. 1) The polymerization curves transiently exceed the equilibrium value. This transient polymerization can be attributed to the polymerization of contaminating ATP-actin, followed by ATP hydrolysis and depolymerization of the ADP-F-actin until the critical concentration of ADP-actin is reached. This polymerization overshoot is particularly notable at actin concentrations below 8.2 pm (where polymerization of ADP-actin should not occur because it is below the critical concentration) when the transient polymerization is followed by total depolymerization of the F-actin. This will be developed further in the following section. 2) When sonication is stopped before the contaminating ATP is hydrolyzed, a slight increase in fluorescence is observed which can be attributed to the polymerization of ATP-actin that accompanies the redistribution to fewer longer filaments that occurs. This phenomenon has been analyzed previously (12, 19). Reversible Polymerization of ATP-Actin under Sonicatwn- When actin was polymerized under sonication in the presence of ATP, the polymerization curves differed from the ones observed in ADP. In ATP, the shapes of the curves varied with the actin concentration. Examples are shown in Fig. 4. At high actin concentrations (above pm), the lag time was short, and polymerization was fast and completed within 5-15 s (Fig. 4, bottom). An apparent plateau was reached. Semilogarithmic plots of the polymerization curves in this range of actin concentrations gave parallel straight lines, in agreement with the reversible polymerization model (Fig. 4, bottom, inset). However, upon continued sonication, a very slow decrease in fluorescence was observed. The final steadystate fluorescence that was reached (not shown in figure) was identical to the fluorescence reached upon sonication of F- actin solutions that had been polymerized to steady state in ATP without sonication. These results can be interpreted as follows. At High Actin Concentrations-Under this condition ATPactin polymerizes fast enough to obtain long stretches of ATP- F-actin before the ATP is hydrolyzed on the filaments (4). Therefore, it is possible to reach, at least transiently, an equilibrium between ATP-G-actin and F-actin with ATP bound to the terminal subunits of the filaments. This occurs at high actin concentration because, under this condition, the rate of polymerization significantly exceeds the rate of ATP hydrolysis. In Fig. 5, the concentration of polymer formed at time transient plateau of fluorescence has been plotted uersw the total actin concentration. Above 15 pm actin the plot (open circles) is linear and parallel to the plot obtained at steady state in the absence of sonication (large filled circles). This linear plot extrapolates to a value of phi for the critical concentration of ATP-G-actin in equilibrium with ATP-F-actin, i.e. before ATP hydrolysis has occurred. The equilibrium can be written as follows. k+?t... TTT + T === TTTT. (7) k-"""" In this reversible reaction, the critical concentration is a true equilibrium dissociation constant equal to the ratio of the dissociation (k-m) and association (k+tt) rate constants for the interaction of ATP-G-actin (T) with an ATP-polymer (..... TTT). It should be noted that it was necessary to use NBD-labeled actin, and not pyrenyl-labeled actin, in this experiment because the fluorescence intensities of NBD-labeled ATP-F-actin and ADP-F-actin are the same while the under Sonication 9" I I I I I I r J k 01 I I I TIME, s FIG. 4. Time course of polymerization of NBD-labeled actin in the presence of ATP and under continuous sonication. Different dilutions of a stock solution of 50 p~ G-actin containing 9% NBD-labeled actin were made and polymerized under continuous sonication in the presence of0.2 mm ATP and 1 mmmgc12. The fluorescence of NBD is recorded. Top panel, the range of low actin concentrations. Bottom to top curves, 1.03 pm; 1.71 pm; 2.56 pm; 3.42 p ~ Bottom. panel, the range of high actin concentrations. Top to bottom curves, 41 pm; 30.8 pm; 25.7 pm; 20.5 pm; 17.1 pm; 13.7 pm; 10.3 pm; 6.8 pm; 5.1 pm; 3.42 pm (from toppanel); 1.71 pm (from top panel). Inset, semilogarithmic plots, according to Equation 4, of the curves. fluorescence intensities of pyrenyl-labeled ATP-F-actin and ADP-F-actin are different (4). Upon prolonged sonication, most of the ATP bound to the F-actin eventually gets hydrolyzed, and the size of the ATP cap becomesvery small and variable, thus allowing some dissociation of ADP-actin subunits from the filaments. F- actin is no longer at equilibrium, but at steady state. The critical concentration at steady state under sonication has been shown to approach the critical concentration of ADPactin, i.e. 8.2 p~ (12). This occurs, as explained in detail by Pantaloni et al. (12), because the rate of dissociation of ADP- G-actin from filaments under sonication is faster than the rate of conversion of ADP-G-actin to ATP-G-actin by nucleotide exchange. The increase in critical concentration from the 3 p~ value of the equilibrium polymer in ATP toward the 8.2 p~ value of the steady-state ATP polymer under sonication accounts for the slow decrease in fluorescence that follows the apparent plateau in Fig. 4 (bottom). Then, when sonica-

5 Polymerization Actin under Sonication 6569 I 1 I I I I 1 I 10 M P 4l ACTIN CONCENTRATION, pm FIG. 5. Critical concentration plot for ATP-G-actin in equilibrium with an ATP-F-actin end. The data obtained in the experiment shown in Fig. 4 are plotted as follows: 0, the fluorescence of G-actin at different concentrations. Note the deviation from the dashed straight line at high actin concentrations, due to a screen effect; 0, the transient fluorescence pseudo-plateau reached upon polymerization under sonication in the range of high actin concentrations (Fig. 4, bottom); A, the value of the overshoot observed in the range of low actin concentrations (Fig. 4, top). 0, the fluorescence reached at steady state and measured 2 h after sonication was stopped. Fluorescence measurements for F-actin were corrected for the screen effect at each actin concentration; the correction factor was the ratio of the corrected fluorescence for G-actin (from dashed line) and of the measured fluorescence for the same G-actin concentration. tion was stopped, a slow process of fluorescence recovery, ie. polymerization, accompanying the length redistribution to a lower number of filaments (12, 19) was observed (not shown in Fig. 4). After a few hours, the steady-state critical concentration of 0.35 phi characterization of actin polymerized in ATP without sonication was reached (Fig. 5, large filled circles). The same polymerization kinetics and the same equilibrium critical concentration of 3 p~ were obtained with Mg2+-Gactin as shown in Fig. 4 for Ca2+-G-actin except that the lag time was shorter when M$+-G-actin was polymerized, in agreement with previous observations (22, 26,27). At Low Actin Concentration (below 5 pm)-under this condition ATP-actin under sonication polymerized more slowly and with a long lag (Fig. 4, top). The polymerization curves exhibited a pronounced "overshoot." This overshoot is consistent with the polymerization model proposed previously (12). At the beginning of polymerization, all the actin has bound ATP and the polymerization rate increases with the increase in the number of ends generated by fragmentation. In this range of actin concentration, the rate of polymerization is not much greater than the rate of ATP hydrolysis on the F-actin. Therefore, polymerization proceeds toward the critical concentration of actin at steady state in ATP, i.e pm. But, as the monomer concentration decreases, the rate of dissociation of subunits from the filaments begins to contribute significantly to the polymerization kinetics. Then, mostly ADP-actin subunits dissociate, due to ATP hydrolysis following more closely the incorporation of actin subunits in the filaments and to the continual conversion of internal subunits to filament-end subunits by sonication. Because of the large concentration of filaments and the slow exchange of nucleotide on G-actin (28, 29), the concentration of ADP-G-actin increases. Therefore, the critical concentration begins to approach that of ADP-actin (8.2 phi), which is much higher than for ATP-actin (0.35 p ~), and a partial depolymerization is observed. The present results thus indicate (Fig. 5) that the critical concentration of the ATP-actin equilibrium polymer, when ATP hydrolysis is not involved in the polymerization process, is 8-9-fold higher than the critical concentration of the ATPactin steady-state polymer (3 phi versus 0.35 p ~). It has been shown previously (4) that the critical concentration of 0.35 phi for the steady-state polymer is a transition point between two regimes and that filaments depolymerize faster when added to G-actin below the critical concentration than expected from their rate of growth as a function of G-actin concentration above the critical concentration, This was accounted for by postulating the presence of an ATP cap at the end of the filaments; the ATP cap maintains dynamically the stability of the filaments and prevents the fast depolymerization of the ADP-F-actin metastable core. Within that context, the present results can be understood with the simple hypothesis that DT-filament ends, at steady state in the presence of T monomers, are more stable (ie. have a lower critical concentration) than TT-filament ends at equilibrium with T monomers (and absence of ATP hydrolysis). Upon increasing the actin concentration, the number of T subunits in the cap of a growing filament increases because the rate of polymerization exceeds the rate of ATP hydrolysis. Therefore, it is expected that, at high enough actin concentrations, most of the growing filament ends will have the TT conformation. In this region, the plot of the rate of filament growth versus actin concentration should, therefore, be a straight line extrapolating on the abscissa to the value of 3 p~ found above for the critical concentration of the ATPactin equilibrium polymer. The slope of this straight line will be proportional to the association rate constant of ATP-actin for TT ends and the ordinate intercept will be proportional to the dissociation rate constant of ATP-actin from a TT polymer. This experiment has been done, and the data are shown in Fig. 6. Above 10 p~ actin, the rate of addition of actin subunits onto sonicated seeds deviated slightly upward from the straight line, extrapolating to a critical concentration of 0.35 phi, that was previously observed below 5 p~ actin (4). The increase in slope above 10 phi actin was no more than 20%, however. Although this increase is too small to provide unequivocal evidence for the existence of the kinetic pathway of T monomers binding to TT-filament ends, the plot obtained, when extrapolated to the abscissa, does yield a critical concentration consistent with the value of 3 p~ found in Fig. 5 for the reversible equilibrium polymer. In addition, the ordinate intercept in Fig. 6 indicates that the rate of dissociation of ATP-actin from TT ends is about 5-fold higher than from DT ends and is, therefore, comparable to the rate of dissociation of ADP-actin from the all ADP polymer (4, 7).

6 6570 Actin Polymerization under Sonication ACTIN CONCENTRATION, )rm FIG. 6. Dependence of the rate of filament elongation on actin concentration. A solution of 20 p~ F-actin in polymerization buffer containing ATP was maintained under sonication (Kontes instrument, lower setting) and used as seeds. After 30-s sonication, 50 pl of the sonication solution were immediately added to 750 pl of a solution of G-actin at a given concentration in ATP, to which 1 mm MgC& had been added 5 s before the seeds. Polymerization was monitored by the fluorescence increase of the NBD probe. Both F- actin and G-actin solutions contained the same relative proportion of labeled actin. The initial rate of growth onto seeds was measured (0) as the initial slope of fluorescence increase, according to Pantaloni et al. (12). Controls were run in the absence of seeds to estimate the rate of spontaneous polymerization. Due to the large amount of seeds added (estimated seeds concentration in the assay = 30 nm), essentially all the fluorescence increase can be attributed to the elongation onto the seeds. The rate of fluorescence increase in the control samples was less than 10% of the seeded rates at G-actin concentrations above 20 p~ and negligible at concentrations below 20 pm actin. The dashed curues represent the plots previously obtained (4) in the presence of ADP (straight line intercepting the abscissa at C, = 8 pm) and in the presence of ATP at concentrations of actin in the range 0-5 pm (abscissa intercept at c, = 0.35 pm). DISCUSSION The classical kinetic analysis of actin polymerization consists in computer fitting of theoretical models to experimental time courses of either spontaneous polymerization or seeded elongation (22, 27, 30, 31). These methods are powerful because, in addition to the accurate determination of kinetic parameters, they allow a rapid elimination of oversimplified models as insufficient to account for the data and suggest the involvement of supplementary steps. However, in such experiments the concentration of one of the active species, the elongating filaments, is generally extremely small, i.e. at least 3 orders of magnitude lower than the concentration of monomeric actin. This situation is similar to the case of classical steady-state studies of enzyme kinetics, in which the concentration of the enzyme is extremely small as compared to the concentration of substrates and products. The complementary approach to the study of enzyme mechanisms is provided by experiments in which enzyme and substrates are reacted at comparable concentrations, leading to the pre-steady-state observation of the formation and evolution of various transient complexes. In analogy with enzyme kinetics, in order to study the nature of the reactions between monomeric actin and the filament ends, it is most interesting to increase the number of ends sufficiently to observe the complexes and all possible intermediates formed. Polymerization under sonication has proved a successful and reliable method to investigate the various steps involved in the polymerization process, and most especially the role of ATP hydrolysis. The experimental data for the polymeriza- tion of ADP-actin under sonication are consistent with the model proposed for the reversible polymerization under sonication. According to this model, nucleation per se is not affected by sonication, and nuclei form and filaments begin to elongate as in the absence of sonication. As soon as the first filaments reach a critical size of about 60 subunits they are fragmented and continue to grow and fragment, keeping this average, constant, small size throughout the polymerization process. This constant short length during polymerization under continuous sonication is in direct contrast to the constant number of filaments that occurs in seeded polymerization without sonication. Also, as soon as fragmentation begins under sonication, the concentration of polymerized actin increases in an explosive manner; therefore, in this type of polymerization the nucleation phase does not overlap the elongation phase as it does in the case of unseeded spontaneous polymerization without sonication (22). The kinetics of nucleation, then, are not part of the model for polymerization under sonication. However, the virtual value of the concentration of actin polymerized in small polymers of size m present in the reaction solution at time zero can be calculated from Equation 4 and is equal to: y t* Y(O) =A e (8) y t* l+e That is to say, the observed polymerization curve is identical to the one which would be obtained if a concentration (y(o))/ m of short filaments were present initially in solution. The variation of the maximum rate of polymerization under sonication with total actin concentration provides a kinetic method for determining the critical concentration of ADPactin. The value of 8.3 MM that was found is in perfect agreement with the value determined by measurement of the polymer concentration at equilibrium, with or without sonication. The involvement of ATP hydrolysis in the polymerization of ATP-actin is revealed by the results of polymerization under sonication. The kinetic curves in ATP, in contrast to the results in ADP, appear to vary in shape with the actin concentration. Analysis of the polymerization curves obtained at high actin concentrations demonstrates the existence of a transient reversible polymerization. We have shown (41, in agreement with Pardee and Spudich (2) and Pollard and Weeds (3), that ATP hydrolysis takes place on F-actin as a monomolecular reaction independent of the actin concentration, while the rate of polymerization increases with actin concentration. Therefore, the size of the ATP cap, i.e. the number of actin terminal subunits a in filament having bound ATP, increases with the actin concentration. Consequently, ATP hydrolysis has no effect on the polymerization at high actin concentration, because the size of the ATP cap is big enough to avoid any dissociation events involving ADP subunits. Under these conditions, the equilibrium state between ATP-G-actin and an ATP-F-actin filament can be reached transiently. The critical concentration for this reversible polymerization of ATP-actin is, in the presence of l mm MgClz, almost one order of magnitude larger than the critical concentration reached at the usual steady state, when the ATP cap is smaller and the probability for some ADP-actin dissociation is not negligible. On the other hand, ATP hydrolysis is clearly involved in the polymerization process under sonication when the ATP cap is small, which happens when actin is polymerized at low concentration. Then, the liberation of ADP-actin, followed

7 by the slow nucleotide exchange on monomeric actin, creates the overshoot shape of the polymerization curves. In conclusion, as expected, the additional involvement of ATP hydrolysis affects the course of polymerization under sonication in a manner dependent on the actin concentration. The implication of these results for spontaneous polymerization in the absence of sonication is that the polymerization curve cannot be analyzed as a single monophasic process at actin concentrations above 10 p ~ Under. these conditions of high actin concentration, polymerization will initially take place as the reversible polymerization of ATP-actin with a critical concentration of 3 p ~ As. more and more polymer is Sonication Actin Polymerization under 6571 terminal ATP-actin subunits can stabilize the F-actin polymer means that the interaction between ADP-actin and ATPactin in the filament at the interface of the ATP cap is very strong, much stronger than the interaction between two ATPactin subunits. Further experiments to investigate the existformed and the monomer concentration approaches 3 p ~, ence of a very strong heterologous interaction between ATPpolymerization will not stop but, instead, will continue under actin and ADP-actin are described in the accompanying paper a different regime, a steady-state polymerization with a criti- (33). cal concentration of 0.35 phi. Therefore, the course of polym- REFERENCES erization of ATP-actin is expected to be complex at the end 1. Cooke, R. (1975) Biochemistry 14, of the reaction as it approaches the steady state. Actually, 2. Pardee, J., and Spudich, J. (1982) J. Cell Biol. 98, deviations from the expected simple polymerization time 3. Pollard, T. D., and Weeds, A. G. (1984) FEBS Lett. 170,94-98 course have been reported, but they were accounted for on 4. Carlier, M.-F., Pantaloni, D., and Korn, E. D. (1984) J. Bwl. the basis of possible filament fragmentation (27, 32). Such Chem. 259, complexity, of course, is not expected in the polymerization 5. Cooke, R., and Murdoch, L. (1973) Biochemistry 12, Pollard, T. D. (1984) J. Cell Biol. 99, of ADP-actin, which is a simple reversible polymerization 7. Lal, A. A., Brenner, S. L., and Korn, E. D. (1984) J. Biol. Chem. throughout. 259, Although all the data presented in this paper concern polymerization in the presence of 1 mm M&12, preliminary experiments showed that qualitatively the same phenomena can be observed when actin is polymerized in the presence of 0.1 M KC1 and no M2'. Under these conditions, however, the critical concentration for the reversible polymerization of ATP-actin was only about twice the critical concentration found at steady state. Obviously the relation between the two critical concentrations depends on the combination of rate constants for association and dissociation of ATP-actin and ADP-actin, and for the rate of ATP hydrolysis under the two conditions. A complete quantitative model should account for all these results and is now underway. The plot of the monomer concentration dependence of the rate of growth of actin filaments at higher monomer actin concentration is consistent with a critical concentration of 3 p~ for the ATP-actin equilibrium polymer. These data also indicate that the dissociation rate of ATP-actin from the ATP polymer in the absence of ATP hydrolysis is about &fold larger than the dissociation rate constant extrapolated from the plot in the region of low actin concentration, where ATP hydrolysis is involved in the polymerization. A reasonable interpretation of these data is that ATP-actin is not dissociating from the same type of filament end at high and low concentrations of G-actin. Similarly, the fact that the steady- state critical concentration in ATP (0.35 p ~ is ) lower than the transient equilibrium critical concentration (3 p ~ in ) ATP is surprising since an ATP cap stabilizes an ADP filament in the steady-state polymer. This indicates, therefore, that the highest stability of the filament is reached when the ATP cap has a discrete minimum size greater than zero (totally uncapped filament) but much less than the extensive stretch of ATP subunits in the ATP equilibrium polymer. Incidentally, the hypothesis of a small ATP cap at steady state is in agreement with the very low rate of ATP hydrolysis that is observed at steady state. Typically, ATP is hydrolyzed at a rate of 0.7 nm/s in a solution of 15 pm F-actin. Assuming an intrinsic rate of ATP hydrolysis of s-' under these conditions (4) and an average of 1000 actin subunits/filament, there would be a maximum of only one active site for ATP hydrolysis/filament at steady state. The fact that one or two 8. 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