How ATP Hydrolysis Controls Filament Assembly from Profilin-Actin

Formins catalyze rapid filament growth from profilin-actin, by remaining processively bound to the elongating barbed end. The sequence of elementary reactions that describe filament assembly from profilin-actin at either free or formin-bound barbed ends is not fully understood. Specifically, the identity of the transitory complexes between profilin and actin terminal subunits is not known; and whether ATP hydrolysis is directly or indirectly coupled to profilin-actin assembly is not clear. We have analyzed the effect of profilin on actin assembly at free and FH1-FH2-bound barbed ends in the presence of ADP and non-hydrolyzable CrATP. Profilin blocked filament growth by capping the barbed ends in ADP and CrATP/ADP-Pi states, with a higher affinity when formin is bound. We confirm that, in contrast, profilin accelerates depolymerization of ADP-F-actin, more efficiently when FH1-FH2 is bound to barbed ends. To reconcile these data with effective barbed end assembly from profilin-MgATP-actin, the nature of nucleotide bound to both terminal and subterminal subunits must be considered. All data are accounted for quantitatively by a model in which a barbed end whose two terminal subunits consist of profilin-ATP-actin cannot grow until ATP has been hydrolyzed and Pi released from the penultimate subunit, thus promoting the release of profilin and allowing further elongation. Formin does not change the activity of profilin but simply uses it for its processive walk at barbed ends. Finally, if profilin release from actin is prevented by a chemical cross-link, formin processivity is abolished.

The molecular mechanism that supports processive barbed end assembly of actin filaments by formins has been largely debated and remains controversial. The isolated dimeric FH2 domain was first proposed to act by itself as a processive assembly motor (10, 14, 18 -21). Later, measurements of barbed end growth of individual filaments initiated by immobilized formins showed that profilin was required for the processive assembly of actin filaments by the fission yeast Cdc12 (22), but was not required for and simply accelerated the processive assembly of actin by mDia1 and other formins (23). At variance with this view, profilin was shown to be required for processivity of FH1-FH2 but not FH2, of mDia1 (24). The crystal structure of TMRactin in complex with the FH2 domain of Bni1 shows that each FH2 protomer interacts with two consecutive actins connected by lateral contacts defining a pseudo-filament structure (25). In this structure, FH2 simply caps the exposed barbed end, and large structural rearrangements from the "closed" to an "open" state of actin-bound FH2 have to be postulated to account for the putative processive filament assembly by FH2. These proposed structural transitions would have to be extremely fast to account for the rapid processive filament assembly by formins.
The role of ATP hydrolysis in processivity of formins has also been debated. One work showed that the formin mDia1 used the direct coupling of ATP hydrolysis to assembly of profilinactin to support its processive walk at barbed ends (24), in an "actoclampin" type of mechanism (26), whereas a more recent study showed evidence for the processive assembly of ADPactin and profilin-ADP-actin by several formins including Cdc12 and mDia1 (23).
Understanding how profilin affects the function of formins requires a clear view of the molecular mechanism of profilin itself. However, this issue too is controversial (see Ref. 27 for a * This work was supported in part by European Commission for NoE "3D-EM" contract LSHG-CT-2004-502828 and Region Ile-de-France for convention SESAME 2000 E1435 supporting the JEOL 2100F installed at Institut de Miné ralogie et de Physique de la Matiè re Condensé e, UMR 7590 CNRS-UPMC. 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. □ S The on-line version of this article (available at http://www.jbc.org) contains supplemental Figs. S1-S4. 1 Supported by a fellowship from the Ligue Nationale contre le Cancer. 2  recent review). There is general agreement that the profilinactin complex does not assemble at pointed ends of actin filaments, but can productively associate at barbed ends (28 -30). Profilin thus enhances the efficiency of actin filaments treadmilling, in favoring steady-state barbed end growth events. This property is at the origin of the positive effect of profilin in actinbased motile processes, which are powered by treadmilling (31). Filament assembly from profilin-actin requires dissociation of profilin from the barbed end following association of profilin-actin, to allow further elongation. Several mechanisms have been proposed. In a first model, the dissociation of profilin from the barbed end is caused by ATP hydrolysis because profilin has a 20-fold lower affinity for ADP-actin than for ATP-actin (29,32). In this view, ATP hydrolysis is mechanistically coupled to filament assembly from profilin-actin, which is not the case for assembly from pure actin (33). Three independent facts are consistent with this view. First, the rate of barbed end growth increases linearly with the concentration of G-actin, but reaches a limit at high concentration of profilin-actin, which was attributed to the rate of ATP hydrolysis at the terminal subunit; second, profilin causes a decrease in the partial critical concentration of G-actin (33); third, filaments do not assemble from profilin-ADP-actin nor from profilin-CaATP-actin, which hydrolyzes ATP very slowly (29,32).
In a second model, profilin dissociation is due to its lower affinity for filament barbed ends than for G-actin and is not dependent on ATP hydrolysis (34). In agreement with this view, ATP hydrolysis was found to lag slightly behind profilin-actin assembly, indicating that the release of profilin from barbed ends was not coupled to ATP hydrolysis (35).
To resolve the above discrepancies on profilin and formin mechanisms, we have analyzed the assembly of ADP-actin and CrATP-actin in the absence and presence of profilin, formin, or both profilin and formin. We demonstrate that the dissociation of profilin from barbed ends is directly coupled to ATP hydrolysis and phosphate release on actin. We confirm that profilin binds to ADP-actin at barbed ends and increases the rate of depolymerization (34,36). Profilin inhibits barbed end assembly from ADP-actin as well as from CrATP-actin by blocking the barbed ends.
These fundamental properties of profilin are conserved and enhanced when FH1-FH2 is bound to profilin-actin at barbed ends, and are used to promote the processive assembly by formins. The present results provide new insight into the correlation between mechanical and chemical steps in the processive cycle of formins.
ADP-Actin Polymerization Assays-ADP-actin was prepared by polymerizing the ATP-actin (1:1) complex (2% pyrenyl-labeled) in the presence of 100 M ADP and 15 units/ml hexokinase, 5 mM glucose. F-ADP-actin was sedimented by centrifu-gation at 400,000 ϫ g for 20 min. The pellet was resuspended in 5 mM Tris-Cl buffer, pH 7.8, containing 1 mM dithiothreitol, 100 M CaCl 2 , 100 M ADP, 10 M Ap 5 A (Sigma), 15 units/ml hexokinase, and 5 mM glucose, incubated on ice for 1 h and gel filtered on G25 in the same buffer. Polymerization was induced by addition of 0.1 M KCl, 0.2 mM EGTA, and 1 mM MgCl 2 to this solution. The increase in fluorescence of pyrenyl-labeled actin was monitored with a Safas spectrofluorimeter ( ex 366 nm, em 407 nm). Steady-state pyrene fluorescence measurements of F-actin assembly were carried out in a Spex spectrofluorimeter following a 3-h incubation at 20°C to avoid denaturation of ADP-actin.
Polymerization Assay of CrATP-Actin-Polymerization of CrATP-actin was performed (45). Briefly, ADP-actin was prepared as described above, except that the F-ADP-actin pellet was resuspended in G 0 buffer containing only 100 M ADP. 5% pyrenyl-labeled ADP-actin was polymerized in I-buffer (5 mM imidazole, pH 6.6, 0.2 mM dithiothreitol) with the indicated concentrations of CrATP. CrATP was added at time 0 to minimize dissociation of CrATP into chromiumion and ATP.
Electron Microscopy-Filaments of actin, polymerized at 7 M were negatively stained, using a 2% uranyl acetate solution, and observed at a magnification of ϫ50,000, under low electron dose conditions (less than 10 electrons per Å square) in a JEOL JEM 2100F electron microscope. Images were recorded on So163 Kodak films and treated for 12 min using pure D19 developer. Selected micrographs were digitized with a Nikon Coolscan 9000 microdensitometer, using a sampling distance and a scanning step of 2540 dots per inch, corresponding to a pixel size of 2 ϫ 2-Å square.
Modeling-The capping of barbed ends by profilin in ADP and CrATP and the growth of filaments from profilin and actin in MgATP was analyzed using Scheme 1.

1)
A ϩ F n P 7 F n ϩ 1 P S 7) PA ϩ F n P 7 F n ϩ 1 PP S 8) P ϩ F n P 7 F n PP S 9) P ϩ F n P S 7 F n PP S 10) F n ϩ 1 P S 7 F n ϩ 1 ϩ P i ϩ P 11) F n ϩ 1 PP S 7 F n ϩ 1 P ϩ P i ϩ P SCHEME 1 In Scheme 1, line 1 describes the interaction between profilin and G-actin. Line 2 describes filament barbed end growth from G-actin. Line 3 represents binding of profilin-actin to the barbed end of a filament that has n subunits (called F n ), making a F nϩ1 P end with profilin bound to the terminal subunit. Line 4 represents binding of profilin to the terminal subunit of a filament that has n subunits, resulting in a F n P filament end. Line 5 represents binding of profilin to a F n barbed end, resulting in a F n P S end, corresponding to a filament that has n subunits but with a subterminal profilin-actin subunit, hence is structurally different from the F n P filament. Line 6 represents binding of G-actin to a F n P filament, resulting in a F nϩ1 P S filament. Line 7 represents binding of PA to a F n P filament, resulting in a filament F nϩ1 PP S that has nϩ1 subunits and profilin bound to the two terminal subunits. The same F nϩ1 PP S filament can be obtained by binding of profilin either to F nϩ1 P (line 8) or to F nϩ1 P S (line 9). Note that lines 4 and 5 are repeated on a F nϩ1 filament, giving F nϩ1 P and F nϩ1 P S , as well as lines 8 and 9, giving F nϩ1 PP S . Lines 10 and 11 describe irreversible hydrolysis of MgATP on the penultimate subunit of actin filaments assembling from profilin-actin, allowing cycles of assembly. The model is restricted to lines 1-9 in ADP and CrATP. In these cases, the profilin-bound filament ends are nonproductive, filament growth occurs only via line 2.
The rate of barbed end growth was modeled in ADP, CrATP, and MgATP, with and without formin, using the Madonna-Berkeley software, using the rate constants known for association dissociation of G-actin to free filament ends and using experimentally determined values of equilibrium dissociation constants for profilin binding to G-actin in ADP (K 1 ϭ 4 M in ADP, 0.1 M in ATP). Identical values were taken for K 2 and K 3 (1.5 M in ADP, 0.1 M in ATP), as well as for K 4 and K 9 and for K 5 and K 8 , for which best fit values to experimental curves were determined computationally.
In the absence of profilin, where [F 0 ], [A 0 ], and [P 0 ] represent the total concentrations of filament-barbed ends, G-actin, and profilin, respectively.
The Madonna-Berkeley software was used to model V/V 0 using the above equations. The parameters were adjusted to fit the experimental data in Figs. 2 and 4 in ADP and CrATP, with free and formin-bound barbed ends. Constraints were brought by using the known values of the equilibrium dissociation constant K 1 ϭ k Ϫ1 /k ϩ1 for binding of profilin to G-actin (K 1 ϭ 4 M in ADP and 0.2 M in MgATP or CrATP), and of the association and dissociation of G-actin to free barbed ends: k ϩ2 ϭ 10 M Ϫ1 s Ϫ1 in MgATP or CrATP and 2.5 M Ϫ1 s Ϫ1 in ADP; k Ϫ2 ϭ 1 s Ϫ1 in MgATP and 3.75 s Ϫ1 in ADP, giving Cc ϭ 0.1 M in ATP and 1.5 M in ADP. Other parameters were adjusted. The best fit values are given in Table 1. Whenever applicable, the range of values that equally well fitted experimental data were given.

Profilin Blocks the Growth and Increases the Rate of Depolymerization of ADP-bound Barbed Ends in an FH1-FH2-enhanced
Fashion-Under physiological conditions, ADP-G-actin polymerizes reversibly into ADP-F-actin with a critical concentration of 1.5 M. Previous work has shown that FH1-FH2 binds ADP-F-actin at barbed ends with a K F of 3 nM (10,19,24). Consistently, we now find that FH1-FH2 nucleates ADPactin, although less efficiently than ATP-actin (Fig. 1A).
Measurements of F-actin at equilibrium in ADP showed that profilin caused depolymerization of F-ADP-actin both in the absence and presence of FH1-FH2 (Fig. 1B). This result indicates that profilin-ADP-actin cannot participate in F-actin assembly, i.e. profilin sequesters ADP-actin, even if FH1-FH2 is bound to barbed ends. The derived binding constant (K d ) of profilin for ADP-G-actin is 4 M, in agreement with previous data (29).
In dilution-induced depolymerization assays ( Fig. 1C), profilin increased the rate of ADP-actin dissociation from free barbed ends, and even more from FH1-FH2-bound barbed ends, in agreement with previous reports (24,36). These observations indicate that profilin actually associates with ADPbound barbed ends, with equilibrium dissociation constants of 8 M in the absence of formin and 2 M in the presence of formin. These values are artifactually higher than the actual binding constant of profilin for ADP-bound barbed ends because for sensitivity purposes, the depolymerization assays had to be carried out using filaments containing 50% pyrenyllabeled actin to which profilin binds very poorly (37).
We then examined how profilin affected the kinetics of filament growth from ADP-actin at pointed ends and at free or FH1-FH2-bound barbed ends. To avoid residual amounts of ATP on actin, assays were performed in the presence of 15 units/ml of hexokinase, 5 mM glucose, and 10 M Ap 5 A, to avoid ATP synthesis from ADP by myokinase, which often contaminates actin preparations (Ref. 38 and "Experimental Procedures").
Profilin inhibited pointed end growth from ADP-actin in a dose-dependent fashion ( Fig. 2A) consistent with formation of a non-polymerizable profilin-ADP-actin complex and a binding constant of profilin for ADP-actin of 4 M, identical to the value derived from measurements of F-actin at equilibrium (Fig. 1B). Altogether, kinetic and equilibrium measurements confirm that profilin has a 20-fold lower affinity for ADP-actin than for ATP-actin (29, 39 -41).
Profilin inhibited barbed end growth from ADP-actin, but the inhibition was not consistent with sequestration of ADPactin, because the inhibition curve at 9 M actin ( Fig. 2A, red curve) does not superimpose with the curve obtained at pointed ends at the same actin concentration ( Fig. 2A, green curve). Half-inhibition of barbed end growth was observed at a total  Table 1. B, barbed end growth initiated by spectrin-actin seeds (blue curves) or 200 nM FH1-FH2 (red curves) at 3 M ADP-actin in the absence (thin lines) and presence (thick lines) of 1.56 M profilin. C, the initial rate of barbed end growth from 3 M ADP-G-actin was measured at different concentrations of profilin using spectrin-actin seeds (blue) or 100 nM FH1-FH2 (red) and normalized to the value of 1 in the absence of profilin. Curves are calculated using the model with the values of dissociation constants given in Table 1. concentration of 3.5 M profilin, indicating that ADP-bound barbed ends are blocked, by binding either free profilin or profilin-ADP-actin complex. A satisfactory fit was obtained to all curves at both ends by the model described under "Experimental Procedures," using values of equilibrium and rate parameters summarized in Table 1.
In the presence of FH1-FH2, profilin inhibited assembly from ADP-actin much more efficiently at FH1-FH2-bound barbed ends than at free barbed ends (Fig. 2, B and C). Half-inhibition was observed at a total concentration of 0.21 M profilin. In fluorescence microscopy measurements (Fig. 3, A and B) of individual formin-bound filaments growing from ADP-actin, profilin again blocked barbed end growth with high affinity (K1 ⁄ 2 ϭ 0.15 M).
In conclusion, in binding to terminal ADP-actin subunits at barbed ends, profilin blocks barbed end growth while facilitating depolymerization by destabilizing barbed ends. Consistently, in measurements of F-actin at equilibrium, profilin simply sequesters ADP-actin.
Profilin Blocks Barbed End Growth from CrATP-Actin in an FH1-FH2-enhanced Fashion-Our previous studies indicated that filament assembly from profilin-ATP-actin requires the rapidly hydrolyzable MgATP to be bound to actin. No assembly occurred when the slowly hydrolyzable CaATP was bound to profilin-actin (32). Both the cleavage of the ␥-phosphate of ATP and the release of inorganic phosphate are slow on CaATP-actin, and occur at random on CaATP-F-actin (42,43), whereas the cleavage of the ␥-phosphate occurs vectorially on MgATP-F-actin (42). Finally, profilin prevents actin assembly at formin-bound barbed ends with the nonhydrolyzable ATP analog AMP-PNP (24).
Several experimental designs can be proposed to test whether the cleavage of the ␥-phosphate of ATP, or the release of P i are required for profilin function. The use of BeF 3 Ϫ , which binds to ADP-F-actin and reconstitutes the ADP-P*-F-actin transition state was precluded in this type of growth kinetic measurements because of its very slow rate of association to ADP-F-actin (44). Inorganic phosphate is known to bind ADP-F-actin and reconstitute the ADP-P i -Factin state in which the tetracoordinated phosphate ion geometry differs from the bipyramidal pentacoordinated geometry of the ADP-P*-F-actin transition state that precedes ADP-P i -Factin in the ATPase reaction. We challenged the ability of profilin to prevent barbed end growth from MgATP-actin when filaments are assembled in the presence of inorganic phosphate (supplemental Fig. S1). The slight inhibition caused by saturating amounts of inorganic phosphate was not greater than when sulfate was used as a control in place of phosphate. These data may indicate that the affinity of inorganic phosphate for terminal subunits at the barbed end is greatly decreased in the presence of profilin, or profilin does not cap barbed ends in the reconstituted ADP-P i -F-actin state.
To determine whether the release of inorganic phosphate is required for profilin to dissociate from free or formin-bound ends, we used CrATP, an exchange-inert analog of MgATP (45), which binds to the nucleotide-metal ion binding site on actin and allows polymerization into CrADP-P i -F-actin filaments in which cleavage of the ␥-phosphate has occurred but the phosphate remains strongly bound to the ␤and ␥-phos-

TABLE 1 Equilibrium and rate parameters for profilin interaction with G-actin and free or formin-bound filament barbed ends in ADP, MgATP, and CrATP
The values of parameters are the ones that are used in the calculated curves that represent the best fit to experimental data (Figs. 2 and 4), within the model described under "Experimental Procedures." The indicated range indicates the acceptable fit for a given parameter, keeping all other parameters at their indicated average value. ϩ and Ϫ refer to presence and absence of formin.

How ATP Hydrolysis Controls Filament Assembly
phates of ATP (45), in a ADP-P*-F-actin structural state. We first verified that profilin bound CrATP-actin with the same affinity as MgATP-actin, using the quenching of tryptophan fluorescence as a probe (Ref. 39, and supplementary Fig. S2). In the absence of profilin, the rate of filament growth was identical with MgATP-actin and CrATP-actin, as reported (45). FH1-FH2 nucleated assembly of CrATP-actin (Fig. 4A), as with MgATP-actin (45). On the other hand, nucleation of filaments by FH1-FH2 was allowed from profilin-MgATP-actin (10,15,24), but totally abolished from profilin-CrATP-actin (Fig. 4B). The effect of profilin on barbed end growth from CrATPactin was assayed with free or FH1-FH2-bound barbed ends (Fig. 4C). Profilin blocked barbed end growth in both cases, in a substoichiometric ratio with respect to G-actin, and in a range of even lower concentrations of profilin when FH1-FH2 was bound to barbed ends. The effect of profilin in CrATP therefore was strikingly different from the one observed in MgATP (dashed lines in Fig. 4C). We conclude that by capping CrATPor CrADP-P i -bound barbed ends, profilin prevents CrATP-actin or profilin-CrATP-actin assembly. The experimental data were accounted for using the model described under "Experimental Procedures" and parameter values in Table 1.
In conclusion, the release of P i appears indispensable for profilin dissociation from barbed ends and sustained barbed end growth from profilin-ATP-actin. Moreover, FH1-FH2 enhances this requirement. The higher affinity of profilin to cap formin-bound barbed ends is likely due to its interaction with the FH1 domain of formin.
CrATP Arrests Processive Growth from FH1-FH2 Beads in the Presence of Profilin-The above solution studies suggest that as long as P i is not released, FH1-FH2 remains strongly bound to profilin-actin at arrested barbed ends. To confirm that release of P i following ATP hydrolysis on actin is required for FH1-FH2-induced processive assembly of profilin-actin, beads coated with FH1-FH2 at low density were placed in a solution of profilin/F-actin at steady-state in physiological ionic conditions, in the presence of MgATP or CrATP. In the presence of MgATP, single filaments nucleated at the bead surface grew at a constant rate of 0.40 m/min, in agreement with previous results (24). In the presence of CrATP instead of MgATP, no filament processive assembly was recorded, all beads remained bare for at least 40 min (data not shown). In a medium containing 10% CrATP and 90% MgATP, single filaments grew at an average rate of 0.32 m/min for transient periods of time that were interrupted by pauses of several minutes during which the filament barbed end remained stably attached to formin at the surface of the bead (Fig. 5A). Pauses shorter than 40 s were not visually detectable. Typical pauses of up to 380 s (blue curve) between two periods of growth are shown in Fig. 5B. Consistent with the biochemical data described above, the arrest of growth is interpreted within the capping of barbed ends by formin-profilin-CrADP-P i -actin. The data provide visual evidence for the capping of filaments, confirming that in the in vitro polymerization assays, profilin inhibited filament growth and did not act by simply inhibiting CrATP-actin nucleation. The fact that growth resumes after 380 s indicates that either Cr-ADP-P i can be exchanged for ATP, or more likely that P i is eventually released from Cr-ADP-P i bound to actin because of the short life-time of the Cr-P i bonds at physiological pH (46). In conclusion, not only hydrolysis of ATP, but also release of inorganic phosphate is coupled to polymerization of profilin-actin, in the presence or absence of formin.

FH1-FH2, but Not FH2, Nucleates Polymerization of Covalently Cross-linked Profilin-Actin, Remains Bound to the Sides of Filaments, and Induces
Bundling-We have shown that profilin-actin processive assembly at formin-bound barbed ends requires ATP hydrolysis (24) and phosphate release. The fate of profilin in processive filament assembly by formin was addressed next using covalently cross-linked profilin-actin complex. The PAcov obtained by EDC coupling of a carboxylate of actin to a NH 2 from profilin has been shown to polymerize into filaments that display the helical structure of F-actin, profilin being tethered to actin and rejected at the outside of the filament at each association step (32). In contrast, another covalent EDC cross-linked complex, obtained by coupling a carboxylate of profilin to a NH 2 group of actin, acts as a capping protein and does not self-assemble (47).
Polymerization of PAcov was monitored by the increase in light scattering at 310 nm. At low PAcov concentrations, spontaneous polymerization was very slow, and was accelerated by addition of either spectrin-actin seeds or FH1-FH2. In contrast, FH2 did not induce PAcov polymerization (Fig. 6A). Thus, the covalent and noncovalent profilin-actin complexes react identically regarding the nucleating activity of formins (24).
The extent of change in light scattering upon assembly of noncovalent profilin-actin was not affected by FH1-FH2, but it strongly increased with the concentration of FH1-FH2 when the PAcov complex was assembled (Fig. 6B). These results suggest that FH1-FH2 binds to the sides of PAcov filaments while they are elongating. In contrast, FH1-FH2 does not bind to the sides of standard actin filaments, in agreement with previous studies (48). FH1-FH2 also bound filaments pre-assembled from the PAcov complex (Fig. 7A). Light scattering intensity increases with time upon addition of 300 nM FH1-FH2 to PAcov filaments, suggesting FH1-FH2 induced bundling. The change in light scattering increased in a saturating fashion with the FH1-FH2 concentration, indicating that FH1-FH2 interacts with defined sites of the PAcov filaments (Fig. 7B). These conclusions were validated by electron microscopy and low speed sedimentation assays. Examination of negatively stained filaments revealed that FH1-FH2 bundled PAcov filaments, but not filaments assembled from noncovalent profilin-actin (Fig. 7C). Low speed centrifugation assays showed that FH1-FH2 co-sedimented with PAcov filaments, not with filaments assembled from noncovalent profilin-actin, in agreement with light scattering data (Fig. 7D). This result confirms that FH1-FH2 interacts with the sides of PAcov filaments, inducing formation of bundles.

DISCUSSION
Models proposed so far for the function of profilin in actin polymerization rely on an energy square according to which filament growth occurs via either association of one profilinactin (PA) complex to a barbed end or association of free actin followed by profilin binding to the terminal subunit at barbed ends. Measurements of F-actin assembly at steady state in the presence of profilin showed that the energy square is not balanced in ATP, and profilin caused a decrease in the critical concentration of ATP-actin (29). These results led to the view that productive barbed end growth from profilin-actin occurred with direct coupling of ATP hydrolysis on the terminal subunit (29). In contrast, polymerization kinetic assays of filament growth from profilin-ATP-actin led to the opposite proposal that an isoenergetic square model could well account for the effect of profilin, and that profilin did not lower the critical concentration of ATP-actin (49). The controversy was clarified in a recent review (27) explaining that in the polymerization of ATP-actin, (i) the nature of barbed end-bound nucleotide, when filaments are either growing or in a dynamic steady-state in ATP, may be a mixture of ATP, ADP-P i , and ADP, which has to be considered in the energy square; (ii) the critical concentration of ATP-actin, meant as free ATP-G-actin concentration at steady-state, appears lowered by profilin both in steady-state (29) and in polymerization assays (49); and (iii) the possibility of an indirect coupling of ATP hydrolysis also existed (27).
The present work brings novel data supporting the direct coupling of ATP hydrolysis to profilin-actin assembly (27, 29,

32)
. We further demonstrate that the release of P i is required for profilin to dissociate from the barbed end and allow sustained growth. Because release of inorganic phosphate on F-actin is known to be slow (33), these results suggest, but do not demonstrate, that the rate of P i release is increased by profilin. Finally we find that the properties of profilin are enhanced by barbed end-bound formin and used for the processive walk of formin at barbed ends.
Profilin binds to barbed ends in ADP and CrATP, thus preventing barbed end growth. The capping of barbed ends by profilin is enhanced by FH1-FH2, consistent with the simultaneous binding of FH2 to actin and FH1 to profilin at barbed ends. The finding that profilin caps barbed ends when terminal subunits are in the intermediate states of ATP hydrolysis (ATP/ ADP-P* and ADP) contrasts with the established fact that pro-filin, even at a very high concentration, allows filament growth when regular ATP hydrolysis is associated with filament elongation. These results cannot be accounted for by the simple model used so far, in which profilin binds only to the barbed end terminal actin subunit on which ATP is hydrolyzed in ADP, resulting in profilin dissociation.
The simplest alternative model is fully described under "Experimental Procedures" and illustrated in supplemental Fig. S3. A simplified version is displayed in Fig. 8. The model considers that during barbed end assembly in the presence of actin and profilin, the two terminal subunits at barbed ends make an elongating site that can bind actin, profilin, and profilin-actin in different ways. Barbed end configurations can be F n , F n P, F n P S , and F n PP S representing a filament that has n subunits and either no profilin or profilin bound to the terminal subunit (P) or subterminal subunit (P S ) or both. ATP is hydrolyzed at the subterminal but not at the terminal position.
In the presence of ADP or a nonhydrolysable ATP, the square model describing interaction of profilin with actin filaments is truly isoenergetic, hence it does not allow effective polymerization from profilinactin, and barbed ends are capped by profilin, both with or without formin. In the presence of fully hydrolysable ATP, the square model is no longer isoenergetic, supporting polymerization from profilin-ATP-actin. In a regime of elongation, a barbed end constantly displays ATP and profilin bound to the terminal subunit. Association of a profilin-ATP-G-actin complex to this end triggers ATP hydrolysis on the penultimate actin subunit (F n P S and F n PP S ), leading to release of profilin from this subunit. Further growth occurs via recycling filaments F n and F n P. Interestingly, this model accounts for the fact (not accounted for so far) that profilin-MgATP-actin polymerizes with a barbed end critical concentration as low as unliganded MgATP-G-actin (32). The low value of the actin critical concentration at barbed ends is due to the persistent terminal ATPor ADP-P i -bound subunit at steady state, which the previous model (reviewed in Ref. 27) could not accommodate.
This model quantitatively accounts for all data globally (calculated curves in Figs. 2 and 4) using the values of equilibrium and rate parameters shown in Table 1. Although the model is formally simple, considering the role of two terminal subunits of the filament introduces 4 new equilibrium dissociation constants that could not be evaluated individually.
Several steric clashes occur, in particular between profilin bound to the penultimate subunit and the hydrophobic plug of the terminal subunit, if the two profilin-actins at the barbed end are assumed to adopt the same structure and orientation as all F-actin subunits in the body of the filament (50). A similar clash between the hydrophobic plug of the terminal subunit and the ␣-tentacle of Capping Protein has recently been observed (51). To resolve the conflict between biochemical and structural data, we propose that subunits at the barbed end may adopt a different structure, schematized by a tilted geometry in Fig. 8, which would allow the binding of profilin to the penultimate actin subunit. This possibility is supported by the fewer actinactin bonds made by these terminal subunits. The fact that formin enhances the affinity of profilin for barbed ends suggests that this different structure/orientation of the terminal subunits is stabilized by formin. In this respect, in the crystal structure of FH2-actin (25), subunits are arranged in a pseudo-filament that is structurally different from the regular F-ADP filament, and may represent the packed repeat of a filamentbarbed end. In support to our proposal, docking of profilin on the FH2-actin-barbed end structure (25) can be done with modest steric clashes. 4 The proposed modified interaction between the two terminal profilin-actin subunits is consistent with the profilin-induced increase in the depolymerization rate (36). It is also possible that the change in orientation of the hydrophobic plug is in relation with ATP hydrolysis on the penultimate subunit. Sterical constraints would be relaxed upon ATP hydrolysis and dissociation of profilin from the penultimate ADP-actin subunit, restoring the regular ADP-Factin orientation. The elementary steps of this model are formally unaffected by formin, except for an increased affinity of profilin for forminbound barbed end terminal subunits, allowing cycles of processive assembly (Fig. 8), in which ATP hydrolysis modulates the affinity of the transient complexes formed in the processive cycle (26,27,52). The FH1-FH2 makes a ternary complex with profilin and ATP-actin, stabilized by profilin-actin, FH1-profilin, and FH2-actin bonds. Hydrolysis of ATP and release of P i from the penultimate subunit weakens profilin-actin and FH2actin bonds, resulting in a global weakening of the ternary complex. Note that the structural change of the FH1-FH2-actin at barbed ends that allows processive growth is very similar to the postulated structural change that relieves the capped conformation of FH2-bound barbed ends in the crystal structure (25). In our model, this structural change is fostered by profilin. Profilin is the crucial coupling device in the formin machinery and is uniquely responsible for its processivity.
Due to permanent tethering of the actin filament, the formin-profilin machinery differs from the N-WASP/Arp2/3 machinery that promotes movement via insertional actin association to fluctuating free ends, transiently tethered during branching (see Ref. 53 for a review). The formin-profilin motor thus allows faster polymerization, and we expect it should also produce a higher force per growing filament than the few piconewtons produced by the growth of a free fluctuating end.
Our conclusion and model are at variance with other works on three points, discussed below. First, Kinosian et al. (34) concluded that filaments could be assembled from profilin-ADP-actin. However, the discrepancy is only apparent, because the data (Fig. 5 in Ref. 33) actually show that profilin inhibits assembly of ADP-actin. To reach the conclusion that profilin-ADP-actin polymerizes, data were modeled assuming that profilin bound ADP-actin with a high affinity. The same data would be fully consistent with our conclusions if they were modeled using a value of the K d of profilin for ADP-actin in the micromolar range, as derived from the two independent methods presented here.
Second, filament assembly from profilin-ATP-actin was proposed not to require ATP hydrolysis (35), because a slight delay was recorded between polymerization of profilin-actin and release of P i (Fig. 4B in Ref. 35); however, in that experiment, the initiation of rapid polymerization of [␥-32 P]ATP-actin by ADP-F-actin seeds at equilibrium with ADP-G-actin resulted in 20% of the polymerizing actin that was not bound to [␥-32 P]ATP, thus biasing the analysis of the coupling of actin assembly and ATP hydrolysis by generating an artifactual delay.
Third, Kovar and co-workers (23) reported processive growth of HMM-attached filaments from immobilized formin in ADP. The striking discrepancy with our results may have diverse origins, among which the production of ATP by myokinase that contaminates actin preparations (38) and may contaminate the HMM as well. In addition, due to the high surface: volume ratio in microscopy assays, myokinase may be concentrated by adsorption to the glass surfaces of the flow chamber. To test the possible effect of myokinase, we repeated all the experiments performed in ADP (Figs. 1 and 2) but omitting the myokinase inhibitor Ap 5 A. A transient overshoot polymerization was observed, indicating that ATP is present under these conditions and that after hydrolysis of residual ATP, profilin blocks ADP-actin polymerization (supplemental Fig. S4). The possible presence of ATP may explain the internal difficulties of the model proposed by Vavylonis et al. (54) to accommodate processive growth independent of ATP hydrolysis reported by Kovar et al. (54). The data were accounted for only if a value of 5 M was used for the K d of the profilin-ATPactin complex, incompatible with the consensus values of K d ranging from 0.05 to 0.2 M. The model of coupled hydrolysis was considered as a valid alternative by Vavylonis et al. (54) who stated that they "tested the approximate effects of a coupled hydrolysis mechanism by violating detailed balance and were able to obtain a good fit to the elongation rate by using K d ϭ 0.1 M (supplemental Fig. S2)." The FH1-FH2 domain of mDia1 does not bind to the sides of actin filaments assembled from either actin or profilin-actin, in contrast to other formins like FRL, mDia2, and AFH1 (10,48,55,56). On the other hand, FH1-FH2 remains bound to F-actin assembled from the covalently cross-linked profilin-actin complex, indicating that the flexibility of FH1-FH2 is sufficient to maintain the FH2-actin and FH1-profilin contacts even though the profilin-actin interface is disrupted following ATP hydrolysis. In regular processive assembly of noncovalent profilin-actin  Table  1. The two strands of a growing filament barbed end are represented. ADPactin subunits are in gray, ATP-and ADP-P i actin are in yellow. Profilin is a red circle. The barbed end is capped in the intermediate state with two profilins bound to the terminal and penultimate subunits. A, self-assembly of actin alone is not coupled to ATP hydrolysis. B, filament assembly from profilinactin occurs with coupled ATP hydrolysis and P i release from the penultimate subunit. C, processive barbed end assembly of profilin-actin by formin occurs with coupled ATP hydrolysis and P i release.
by FH1-FH2, profilin dissociation from actin following ATP hydrolysis causes translocation of a protomer of FH1-FH2 from the filament end, a step that is required for processivity. Within this view, formins like FRL, which bundle filaments by remaining bound to the sides of filaments may need an additional regulatory element to retain a processive function.