Spire and Formin 2 Synergize and Antagonize in Regulating Actin Assembly in Meiosis by a Ping-Pong Mechanism

An in vitro study reveals how the three actin binding proteins profilin, formin 2, and Spire functionally cooperate by a ping-pong mechanism to regulate actin assembly during reproductive cell division.


Introduction
In mouse meiosis I, translocation of the spindle toward a cortical site that defines polar body extrusion is the first step in establishment of oocyte polarity [1,2]. This process is driven by assembly of cytoplasmic actin filaments in which formin 2 (Fmn2) plays a pivotal role [3][4][5][6][7][8]. Loss of Fmn2 prevents correct positioning of the metaphase spindle and causes pregnancy loss and infertility [9]. The mechanism of actin-based translocation of the spindle is an important issue in cell biology [7]. Fmn2 is required for assembly of an isotropic, dynamic cytoplasmic network, but the mechanism by which actin assembly drives asymmetric spindle positioning is not understood [3,7,10]. Local myosin-dependent pulling on the actin meshwork in the spindle pole region has been proposed [5,11]. Other studies suggest that the spindle is pushed by Fmn2-induced insertional assembly of filaments around the spindle [4]. Other actin-based mechanisms seem posssible considering the very slow rate of spindle translocation. A recent report indicates that in mouse oocytes, actin nucleators are clustered on Rab11a-positive vesicles associated with myosin Vb and that Rab11a and myosin Vb are also required for asymmetric positioning [12].
Fmn2 cooperates with two other actin binding proteins, Spire and profilin. Genetic interactions between Spire, formin Cappuccino (the ortholog of Fmn2 in Drosophila), and profilin were first revealed in polarity axis patterning of the Drosophila oocyte [13][14][15]. In the mouse oocyte, overexpression studies suggest that Spire and Fmn2 cooperate in a functional unit to achieve spindle translocation [6]. Fmn2 and Spire also display nearly identical expression patterns in developing and adult nervous tissues [16].
Fmn2 and Cappucccino are members of the Fmn family of Rho-GTPase-independent formins. The autoregulatory DAD domain of Diaphanous-related formins (DRFs) is replaced by a short FH2 tail sequence that makes an inhibitory contact with the N-terminal region in Cappuccino [17].
Spire is a modular protein. The N-terminal region (Nt-Spire) consists of a kinase-like noncatalytic domain (KIND) followed by four consecutive WH2 domains that bind actin. The C-terminal moiety contains a Spir box and a FYVE-related domain, potentially interacting with Rab GTPases and membranes [18]. Nt-Spire nucleates actin assembly in vitro in the absence of profilin [19]. Under physiological conditions where profilin-actin (PA) complex is the main form of polymerizable actin, the binding of Nt-Spire to filament barbed ends blocks assembly from PA [20,21].
The synergy observed in vivo between Spire and Fmn2 contrasts with in vitro evidence for opposite effects of Nt-Spire and Fmn2, taken individually, on filament barbed end assembly and for the inhibition of FH2 by KIND. To understand the molecular mechanism by which Spire and Fmn2 act in synergy to promote actin assembly and spindle translocation, here we perform bulk solution and single filament assays of the interplay between Nt-Spire, Fmn2, and profilin in actin assembly. We find that Nt-Spire binding to barbed ends facilitates the recruitment of Fmn2 via direct interaction between the KIND domain of Spire and the Cterminal region of Fmn2, called Formin-Spire Interacting (FSI) region, followed by release of Nt-Spire and fast processive filament growth. In the presence of Nt-Spire, Fmn2, and PA, filaments display rapid processive growth interrupted by pauses due to the alternating barbed end occupancy by Fmn2 and Nt-Spire, acting in an original ''ping-pong'' mechanism. In vitro data, validated by the effects of injected proteins in the mouse oocyte, lead to a comprehensive model of coupled dynamics of actin filaments and Rab11a vesicles.

Results
Fmn2-Induced Filament Assembly from PA Is Inhibited by the Isolated KIND Domain, but Stimulated by Nt-Spire We purified constructs of human Nt-Spire comprising the Nterminal KIND domain and the 4 WH2 domains, of the isolated KIND domain, of the FH2 and FH1-FH2 domains of mouse Fmn2, and the more soluble truncated FH1 t -FH2 and mDia1chimeric FH1 D -FH2 ( Figure 1A, Materials and Methods). The FH2 includes the C-terminal region of interaction with KIND, called ''tail'' or ''FSI.'' A FSI-deleted construct FH1 D -FH2DFSI was purified as well. The FSI peptide was chemically synthesized.
As demonstrated along the paper, FH1 t -FH2 and FH1 D -FH2 behaved quantitatively identical to the original FH1-FH2 domain of Fmn2. This result indicates that the original FH2 domain of Fmn2, but not the nature and proline content of the FH1 domain, is essential in the activity and regulation of formin 2 by Spire. Most quantitatively detailed data were collected with FH1 D -FH2. We further checked that all main properties resulting from interactions between Nt-Spire and FH1 D -FH2, were reproduced with FH1-FH2 of Fmn2. FH1 D -FH2 stimulates filament assembly from MgATP-G-actin (in the absence of profilin) more efficiently than the isolated FH2 domain ( Figure 1B). The FSI peptide did not affect assembly of actin alone, nor Nt-Spire-nucleated actin assembly, in contrast with a previous report [23]. The isolated KIND domain did not affect assembly of actin alone but inhibited FH2-or FH1 D -FH2stimulated polymerization. The FSI peptide abrogated the inhibitory effect of KIND, as reported with the mammalian proteins and their Drosophila orthologs Dm-Spir-KIND, Capu-CT, and Capu tail [24,25].
Profilin, the FH2 domain of formins, and Spire (via WH2 domains) all bind the barbed face of actin individually. The mutually exclusive binding of the three proteins to actin is at the heart of the puzzling mechanism by which they act in synergy. This issue was thus addressed in a straightforward fashion by monitoring spontaneous assembly of filaments from PA in the presence of either Fmn2, or Spire or both together. Profilin by itself strongly inhibits actin nucleation (Figure 2A, black line). FH1 D -FH2 (Figure 2A, blue line), but not FH2 (Figure 2A, red line), promoted filament assembly from PA, like other formins [27][28][29], albeit much less efficiently. The FH1-FH2 of mDia1 showed the same nucleation activity at a one order of magnitude lower concentration (unpublished data). Nt-Spire did not support assembly from PA ( Figure 2A, green line), consistent with the known capping of barbed ends by Nt-Spire [20]. In this experiment (2.5 mM actin, 6 mM profilin) the concentration of PA is 2.44 mM, and 0.06 mM actin is unliganded. Since no nucleation was observed, in the absence of FH1 D -FH2 or in presence of FH2 only, over at least 1 h, and since FH1 D -FH2 does not nucleate assembly of 0.06 mM actin, we conclude that FH1 D -FH2 most likely nucleates and assembles filaments from PA.
Remarkably, in this physiological situation, where PA is the polymerizing form of actin, Nt-Spire greatly enhanced FH1 D -FH2-induced nucleation ( Figure 2A, purple line) and promoted filament assembly by FH2 (Figure 2A, magenta line). Both FH1 D -FH2 and FH1t-FH2 nucleated assembly from PA and were stimulated by Spire quantitatively identically to the original FH1-FH2 of Fmn2 ( Figure S1A,B,C).
The KIND domain and the FSI peptide each abolished the synergistic effect of FH1 D -FH2 and Nt-Spire, indicating that enhanced promotion of actin assembly results from the direct interaction between Nt-Spire and Fmn2, as observed in vivo ( Figure 2B). The inhibition by KIND developed in a substoichiometric fashion, suggesting that only one KIND polypeptide bound per FH2 dimer greatly alters the activity of the dimer ( Figure S1D). To confirm that synergistic asssembly results from the direct interaction between Spire and FH2, we tested the ability of FH1 D -FH2DFSI to stimulate actin assembly in synergy with Nt-Spire. Although deletion of the FSI greatly diminished the stimulation of actin assembly, as observed with the Capu-CT construct [25], KIND did not inhibit the residual activity of FH1 D -FH2DFSI and Nt-Spire failed to stimulate it ( Figure S1E). The inhibition of assembly by Nt-Spire was attributed to its competitive displacement of FH1 D -FH2DFSI from barbed ends. We conclude that (1) the C-terminal region of Fmn2, like Cappuccino, plays a

Author Summary
Mammalian reproduction requires successful meiosis, which consists of two strongly asymmetric cell divisions. In meiosis I, movement of the spindle (the subcellular structure that segregates chromosomes during division) toward the oocyte cortex (the outer layer of the egg) is essential for fertility. This process requires that actin filaments assemble in a dynamic mesh, driven by three actin binding proteins, profilin, formin 2, and Spire. To date the molecular mechanisms by which these three proteins cooperate are not known. We now explore this in vitro by a combination of bulk solution and single actin filament assembly assays in the presence of profilin, Spire, and formin 2. Individually, Spire binds to actin filament ends to block their growth, and by itself, formin 2 associates poorly with filament ends, promoting fast processive assembly from the profilin-actin complex. However, when present together, Spire and formin 2 interact with one another (the formin 2 C-terminal binds to the N terminal Spire KIND domain), forming transient complexes at filament ends from which each binds alternately to the filament ends to regulate actin assembly by a ping-pong mechanism. Our in vitro observations are validated by injection studies in mouse oocytes. In oocytes, the additional interaction of Spire and formin 2 with Rab11a-myosin Vb vesicles couples high actin dynamics to vesicle traffic.
functional role in actin assembly and (2) both the inhibition by KIND and the stimulation by Nt-Spire of the activity of FH1 D -FH2 are mediated by the direct interaction of the C-terminal region of Fmn2 with the KIND domain of Spire.
Puzzlingly, interaction of the FH2 domain of FH1 D -FH2 with the isolated KIND domain of Nt-Spire makes an abortive complex for nucleation, while this interaction, in the context of Nt-Spire comprising its four WH2 domains, is required for enhanced filament assembly from PA. The opposite behaviors of KIND and Nt-Spire thus reveal that the interaction of the WH2 domains of Nt-Spire with the barbed face of actin is involved in the synergy between Nt-Spire and FH1 D -FH2. Since in the polymerization assay G-actin is 97.5% saturated by profilin, the main candidate left for WH2 binding is an F-actin subunit at the filament barbed end. The FH1 domain of FH1 D -FH2 or FH1-FH2 is dispensable, but improves the synergy.
In the absence of profilin, FH1 D -FH2-or FH2-nucleated filament assembly is also stimulated by Nt-Spire, however since both formin and Nt-Spire individually nucleate actin, no clear evidence distinguishes synergistic from simple additive effects ( Figure S2).
We then measured the rate of assembly in the presence of profilin, FH1 D -FH2, and increasing concentrations of Nt-Spire ( Figure 2C). The assembly rate first increased with Nt-Spire up to a maximum of 5-fold. At higher Nt-Spire concentrations, the assembly rate and the amount of F-actin assembled at steady state both decreased. The increase in unassembled actin at steady state is consistent with increasing capping of the barbed ends Nt-Spire [20]. Indeed PA complex does not assemble at pointed ends; thus, profilin becomes a G-actin sequestering protein when all barbed ends are capped. The amount of PA at steady state, [PA SS ], then is expressed as follows [30,31]: where [P total ] represents the total concentration of profilin, A C P the critical concentration for actin assembly at pointed ends, and K P the dissociation constant of PA complex. The decreased amount of F-actin upon addition of Nt-Spire thus reflects the gradual saturation of barbed ends by Spire dominating over FH1-FH2.
The superimposed increases in the rate of assembly at a series of FH1 D -FH2 concentrations are suggestive of a titration of FH1 D -FH2 by Nt-Spire in an assembly-productive complex, whereas the competitive antagonism between Nt-Spire and FH1 D -FH2 at barbed ends appears when Nt-Spire dominates over FH1 D -FH2 ( Figure 2D). A similar behavior was displayed by FH2 and Nt-Spire ( Figure S3).
Spontaneous filament assembly from a large amount of monomeric actin is not a physiologically relevant process. In vivo, the steady state levels of assembled and unassembled actin vary via relaxation processes linked to regulatory signaling. To address the synergy between Nt-Spire, profilin, and FH1 D -FH2 under such cellular conditions, we monitored the amount of F-actin assembled at steady state in the presence of profilin, Nt-Spire, and increasing amounts of FH1 D -FH2. In the absence of FH1 D -FH2, Nt-Spire caused a decrease in the amount of F-actin at steady state, due to the accumulation of PA, subsequent to barbed end capping by Nt-Spire (see above). Addition of FH1 D -FH2 restored the amount of F-actin measured in absence of Nt-Spire ( Figure 2E). Thus, FH1 D -FH2 reversed the dominant barbed end capping effect of Nt-Spire by generating actively polymerizing barbed ends from PA. The relative amounts of unassembled and assembled actin at steady state are controlled by the Nt-Spire:FH1 D -FH2 molar ratio. In spontaneous assembly assays, both nucleation and barbed end growth contribute in the global polymerization rate. To understand whether only nucleation or also barbed end growth from PA is affected by FH1 D -FH2 and Nt-Spire, seeded barbed end growth assays were performed ( Figure 3A,B). Barbed end growth from PA was blocked by Nt-Spire alone ( Figure 3A, black line), in agreement with previous work [20], but not detectably affected by FH1 D -FH2 alone up to 200 nM (single filament studies described later in the text explain why). Strikingly, addition of FH1 D -FH2 in the range 0 to 30 nM to Nt-Spire-capped filaments (90 nM Nt-Spire) restored barbed end growth to a defined level. Note that in the absence of seeds, controls show a very low level of nucleation (dotted lines in Figure 3A, blue line in Figure 3B), demonstrating that the main effect measured in the presence of seeds is on seeded barbed end growth. The FH1 D -FH2 concentration dependence of the increase in initial rate displays a saturation behavior ( Figure 3B). The very low concentration at half-effect (Kd = 2 nM) of FH1 D -FH2 for Nt-Spire-bound barbed ends at largely saturating amounts of Nt-Spire is not consistent with the competitive displacement of Nt-Spire from barbed ends by FH1 D -FH2. A more plausible explanation is that enhanced barbed end growth results from high affinity direct binding of FH1 D -FH2 to barbed end-bound Nt-Spire, contrasting with its absence of effect on free barbed ends. In agreement with this interpretation, both KIND and FSI inhibited the stimulating effect of Nt-Spire on barbed end growth by FH1 D -FH2 ( Figure 3C). These bulk solution assays reveal the synergy between Nt-Spire and Fmn2 at barbed ends, but only provide an averaged measure of barbed end growth. They do not specify the number of regrowing filaments nor their individual growth rates and they do not provide information on Fmn2 processive parameters.
Fast Processive Assembly of Individual Filaments by Fmn2 Is Enhanced by the Transient Association of Nt-Spire and Fmn2 Together to an Individual Barbed End Bulk solution studies demonstrate that Nt-Spire and FH1 D -FH2 not only antagonize by competing with each other, but also bind together at barbed ends to enhance filament assembly from PA. These studies were essential in outlining the mechanistic issues and designing the appropriate conditions of assays conducted using TIRF microscopy of individual filaments, to understand how Nt-Spire and FH1 D -FH2, individually and together, affect barbed end nucleation and assembly dynamics.  Figure 4B, Movie S1), while 95% of filaments grew slowly at the rate characteristic of free barbed ends. Hence, by itself FH1 D -FH2 is processive, but rarely binds to free barbed ends. In the presence of PA, 10 nM Nt-Spire and 20 nM FH1 D -FH2, 47% of filaments displayed fast sustained growth with the same rate (63.666.3 subunits per second, N = 20) as with FH1 D -FH2 alone ( Figure 4C). Some of these filaments showed alternating periods of fast growth (63.8611.7 subunits per second, N = 7) and arrested growth (green traces, Figure 4C and Movie S2). Thus, Nt-Spire facilitates FH1 D -FH2-induced fast processive events.
The mutual interplay of the two proteins at individual barbed ends was quantified by kinetic experiments using microfluidicsassisted TIRF microscopy ( Figures 5 and 6). This method allows to monitor changes in filament growth rate within 1 s delay following a change in solution conditions [34,35].
The rate of association of Nt-Spire to barbed ends was revealed by the time taken for filaments to switch from slow growth in the presence of PA to arrested growth (growth rate = 0), following addition of Nt-Spire to the flowing PA solution ( Figure 5A, Movie S3). A kymograph of the capping of one filament by Spire (5 nM) is shown in central frame ( Figure 5A). The apparent first order rate constant for Spire binding to barbed ends was measured at different concentrations ( Figure 5A, right frame). The rate constant for Spire association to barbed ends was derived from the linear dependence of the pseudo-first order rate constant on Spire concentration. Conversely, dissociation of Nt-Spire from capped barbed ends was revealed by the switch from arrested growth to restored slow growth of free barbed ends from PA upon changing the flowing solution from PA+Nt-Spire to PA alone. Values of 2.7 mM 21 s 21 and 0.0101 s 21 were found for the association (k +S ) and dissociation (k 2S ) rate constants of Nt-Spire at free barbed ends ( Figure 5A) from which the equilibrium dissociation constant of Nt-Spire for barbed ends is K S = k 2S / k +S = 3.8 nM. This value is in reasonable agreement with our previous bulk solution measurements demonstrating capping of barbed ends by Spire [20], further documented here, (Figure 7).
The association of FH1 D -FH2 to free barbed ends, revealed by the switch from slow to fast growth, was addressed using the same protocol ( Figure 5B). The association of FH1 D -FH2 to free barbed ends was so slow that very few fast growing filaments were recorded over a period of 10 min, in contrast with mDia1 (our unpublished observations) and Capping Protein [36]. The measured association rate constant of FH1 D -FH2 to free barbed ends was k +F = 7.4 10 23 mM 21 s 21 ( Figure 5B). The off rate constant of FH1 D -FH2 derived from the duration of processive growth was k 2F = 3.17 10 23 s 21 , consistent with an average dwell time of FH1 D -FH2 at barbed ends of 3 to 4 min at 1 mM PA (corresponding to processive assembly of a 37 mm long filament). The rate of fast growth increased linearly with PA concentration, leading to a rate constant of 6364 mM 21 s 21 for processive assembly by FH1 D -FH2 from PA ( Figure 5B), compared with the value of 48 mM 21 s 21 for mDia1, so far the fastest known formin [37]. Quantitatively identical data were obtained with FH1-FH2 (Fmn2), indicating that the FH2 domain of formin 2, not the FH1 domain, is responsible for its intrinsic processive behavior (open symbol in Figure 5B, central panel, inset of Figure 6G, and table in Figure S5D).
In more complex assays, filaments first capped by Nt-Spire were switched to the same solution of PA containing FH1 D -FH2 either in absence or presence of Nt-Spire (kymographs in Figure 6A,B and Figure S5).
These assays revealed major striking features of the synergy between Nt-Spire and FH1 D -FH2. Remarkably, each of the two proteins associated with a barbed end occupied by the other. Binding of Nt-Spire to FH1 D -FH2-bound, rapidly growing barbed ends caused arrest of fast growth. Binding of FH1 D -FH2 to Nt-Spire-arrested barbed ends promoted fast growth. Nt-Spire associated to a FH1 D -FH2-bound barbed end more slowly than to a free barbed end, with a rate constant k9 +S = 0.396 mM 21 s 21 ( Figure 6C,D, red lines; Figure S5A), as might be anticipated from the partial occupancy of barbed end subunits by structural elements of FH1 D -FH2, hindering WH2 binding sites. In contrast, association of FH1 D -FH2 (as well as FH1-FH2) to Nt-Spireprecapped barbed ends was 30-fold faster than to free barbed ends, leading to k9 +F = 0.29 mM 21 s 21 , conspicuously similar to the association rate constant of Nt-Spire to FH1 D -FH2-bound barbed ends. Ninety percent of precapped filaments displayed fast processive growth within 2 min following addition of 40 nM FH1 D -FH2 ( Figure 6F,G, red lines; Figure S5B). Identical rates of fast growth were recorded when FH1 D -FH2 associated to a Nt-Spire-bound barbed end (57.666.1 subunits per second, N = 106) and to a free barbed end (55.565.9 subunits per second, N = 40) as in the absence of flow. Filament barbed ends were capped by Nt-Spire in the presence of FSI peptide at the same rate as without FSI ( Figure S5D). However, FH1 D -FH2 binding to barbed ends capped by Nt-Spire in the presence of FSI was strongly reduced ( Figure S5C). These results establish that direct interaction between barbed end-bound Nt-Spire and Fmn2, via the KIND-FSI contact, is required to facilitate binding of Fmn2 to barbed ends and resumed fast growth. The data rule out the possibility that the synergy results only from an indirect effect of Spire binding to barbed ends. However, they do not exclude the possibility that the structure/reactivity of barbed ends is affected  by the WH2 domains of Spire in a way that facilitates binding of Fmn2.
Filaments growing in the presence of both FH1 D -FH2 and Nt-Spire displayed alternating phases of fast growth and arrested growth, visualized by staircase-like kymographs ( Figure 6B). No slow growth periods were observed, suggesting that the barbed ends were never free. Arrests of growth and switches to fast growth were indicative of barbed end ocupancy by Nt-Spire and FH1 D -FH2, respectively.
Do Nt-Spire and FH1 D -FH2 remain bound to each other at the same barbed end, though in functionally different configurations, during the alternating periods of fast growth and arrested growth? The identical rates of FH1 D -FH2-catalyzed processive assembly in absence or presence of Nt-Spire already argue against this possibility. We also figured that Nt-Spire (respectively FH1 D -FH2) would dissociate from barbed ends at different rates whether it was or was not bound to FH1 D -FH2 (respectively, Nt-Spire). Measurements of the dwell times of FH1 D -FH2 at filaments precapped by Nt-Spire and of Nt-Spire at filaments previously in the fast growth phase before arrest unambiguously show that FH1 D -FH2 and Nt-Spire dissociate from these preoccupied ends at the exact same rates as from free barbed ends ( Figure 6E,H). Kinetic parameters are summarized in Figure S5D.
These results altogether convey the view that Nt-Spire associates directly to barbed end-bound FH1 D -FH2, and FH1 D -FH2 associates to barbed end-bound Nt-Spire, in transient ternary complexes. Thus, in the presence of Nt-Spire and FH1 D -FH2, filaments switch rapidly from a pausing, Nt-Spire-capped state to a fast-growing FH1 D -FH2-bound state, the two proteins kicking off each other to occupy their genuine binding sites at the barbed ends.

Nt-Spire and Fmn2 Bind Tightly Together to Cap Depolymerizing ADP Barbed Ends
In filament growth assays in ATP, the nucleotide bound to barbed end subunits is ATP or ADP-Pi [32,38]. Dilution-induced filament disassembly assays were performed to know how FH1 D -FH2 and Nt-Spire interact with ADP-bound barbed end subunits in the absence ( Figure 7A,B) and presence ( Figure 7C,D) of profilin.
In the absence of profilin in the depolymerization buffer, FH2 and FH1 D -FH2 identically slowed down filament disassembly by 50%, corresponding to about 60% inhibition of barbed end disassembly ( Figure 7A). The inhibition of depolymerization occurred within 5 s mixing dead time. The formin concentration dependence of the depolymerization rate was consistent with high affinity binding of FH2 or FH1 D -FH2 to barbed ends (K D = 661 nM) causing a slow dissociation of ADP-actin. The rapid, high affinity binding of FH1 D -FH2 to ADP-bound barbed ends contrasts with its slow association with growing ATP-bound barbed ends ( Figure 7A). When barbed ends were saturated by FH1 D -FH2, KIND blocked barbed end disassembly, again indicating that it bound to FH1 D -FH2 barbed ends with a K D of 20 nM and the FH1 D -FH2-KIND complex acts as a barbed end capper ( Figure 7B, dashed blue curve). Strikingly, KIND had the opposite effect on disassembly of FH2-bound barbed ends and restored the fast rate of disassembly of free barbed ends ( Figure 7B, dashed red curve). Thus, binding of KIND to barbed end-bound FH2 weakens FH2 interaction with barbed end terminal subunits and promotes its dissociation from barbed ends in an inactive KIND-FH2 complex, allowing the free barbed ends to depolymerize ( Figure 7B, dashed lines). KIND in itself does not affect barbed end disassembly ( Figure 7B, grey curve).
The binding of Nt-Spire to barbed ends (with a K D of 9 nM) slows down barbed end disassembly by about 70% (Figure 7B, green curve, and [20]). In the presence of saturating amounts of FH1 D -FH2 or FH2 in depolymerizing buffer, which slow down disassembly by 60%, addition of Nt-Spire promoted complete blockage of barbed ends ( Figure 7B, solid blue and red curves, and expanded inset). The dependence of the decrease in depolymerization rate on Nt-Spire concentration reflects the binding of Nt-Spire to FH1 D -FH2-or FH2-bound barbed ends with 10-fold enhanced affinity (Kd = 0.5 to 1 nM) as compared to its binding to free barbed ends. Thus, Nt-Spire and FH1 D -FH2 bind together to ADP-bound barbed ends in a configuration in which filament disassembly is blocked.
Synergy Between Profilin, Fmn2, and Nt-Spire at Barbed Ends in a Regime of Disassembly When profilin was present in the depolymerization buffer, FH1 D -FH2 again slowed down filament disassembly. The dependence of the disassembly rate on FH1 D -FH2 concentration shows that FH1 D -FH2 binds to barbed ends with a higher affinity (Kd = 1 to 2 nM) in the presence than in the absence of profilin ( Figure 7C, Figure S6A). In contrast, the affinity of the FH2 domain for barbed ends was lowered by profilin (Kd = 20 nM, Figure 7C, Figure S6B). Thus profilin strengthens the binding of FH1 D -FH2 at barbed ends, presumably via the known interaction of profilin with the FH1 domain [39]. The effects of Nt-Spire and KIND observed in Figure 7B were conserved in the presence of profilin ( Figure 7D). In conclusion, the strong interaction of FH1 D -FH2 and Nt-Spire at ADP-bound barbed ends involves contacts between the WH2 domains of Nt-Spire and barbed end terminal subunits, in addition to the contacts between the KIND domain of Nt-Spire and the FH2 C-terminus.
Profilin enhanced the rate of disassembly from free, FH2bound, or FH1 D -FH2-bound barbed ends ( Figure S6C), as previously observed at free barbed ends [32,33,40]. At saturation by profilin, slower maximal rates of depolymerization were observed in the presence than in the absence of FH2 or FH1 D -FH2. Values of equilibrium dissociation constants of all proteins with barbed ends are summarized in the table in Figure 7E.

Injection of Nt-Spire, FH1 D -FH2, KIND, and FSI in Mouse Oocytes Affect Cytoplasmic Actin Asssembly Consistent with in Vitro Measurements
To investigate whether the direct interaction between Nt-Spire and FH1 D -FH2 also leads to synergistic actin assembly in vivo, the Nt-Spire or the isolated KIND domain, or FH1 D -FH2, or the FSI peptide, were injected into mouse oocytes (Figure 8). Injection of Nt-Spire or FH1 D -FH2 induced a large increase in the mass of cytoplasmic F-actin and 50% increase in intensity of fluorescent phalloidin staining as compared to the control, whereas injection of the KIND domain had the opposite effect and depressed by 2fold the intensity of phalloidin staining indicative of cytoplasmic Factin. Thus, constitutively active Nt-Spire and FH1 D -FH2 recapitulate the effects of overexpression of full-length Spire and Fmn2 [6].
In the oocyte, only a fraction of the Spire and Fmn2 molecules may be bound to each other; hence, addition of constitutively active Nt-Spire or FH1 D -FH2 may stimulate further actin assembly. In contrast, injection of KIND prevents the synergistic effect of Spire and Fmn2 on barbed end nucleation and growth. Thus, existing filaments disassemble. In agreement with our in vitro data showing that FH2 cannot promote processive filament assembly from PA, injection of FH2 depresses actin assembly. This result validates the concept that profilin is a player in the synergy between Spire and Fmn2.

Discussion
Spire and Fmn2 Regulate Processive Assembly from PA with a ''Ping-Pong'' Mechanism Bulk solution studies and single filament analysis of actin assembly provide mechanistic insight into the reported genetic interactions between Spire, Fmn2/Cappuccino, and profilin in oogenesis. The data reveal how Nt-Spire and FH1 D -FH2 both cooperate and antagonize in filament assembly from PA, and establish that replacing the FH1 of Fmn2 by FH1 D of mDia1 or deleting a few proline regions does not affect the function of Fmn2 nor its synergy with Nt-Spire. Thus, the conclusions of this work apply to FH1-FH2 (Fmn2). FH1-FH2 is highly processive in itself, but binds filament barbed ends inefficiently. Capping of barbed ends by Nt-Spire kinetically facilitates barbed end association of FH1-FH2. All data emphasize that the faster binding of FH1-FH2   is due to the direct interaction between the two proteins at barbed ends rather than to only an indirect effect of the WH2 domains of Nt-Spire on the conformation of the barbed end ( Figure 9A). Spire and FH1-FH2 control filament assembly using a ''ping-pong'' [41] (or ''tag-team'') mechanism that has no precedent in the regulation of formin-mediated actin assembly. Filaments display alternate phases of fast processive growth and arrested growth, in which barbed ends bind in turn FH1-FH2 or Nt-Spire, respectively. Each protein kicks off the other via formation of transient complexes in which they interact together at the barbed end. The dwell time in each phase, as well as the relative amounts of F-actin and G-actin at steady state, are governed by the relative concentrations of Nt-Spire and FH1-FH2. The control of actin assembly dynamics by the Nt-Spire:FH1-FH2 ratio may extend to the synergy between Nt-Spire and Cappuccino in Drosophila mid-oogenesis.
The following minimal scheme describes the data without making any mechanistic hypotheses.

BzSuBS, ð1Þ
BzFuBF, ð2Þ BFzSuBFS?BSzF: ð4Þ B, BS, and BF represent the barbed ends in free, Nt-Spire-bound, and FH1-FH2-bound states, respectively. BFS and BSF are transient states in which Nt-Spire and FH1-FH2 interact directly together as well as with terminal subunits at the barbed end. When Nt-Spire and FH1-FH2 coexist with PA in solution, because association of FH1-FH2 to barbed ends or prenuclei is extremely slow, a likely sequence of events ( Figure 9A) is the initial rapid capping of barbed ends or prenuclei by Nt-Spire, followed by rapid association of FH1-FH2 in a low affinity transient complex BSF, leading to dissociation of Nt-Spire and formation of BF. In other words, FH1-FH2 is firmly saddled on a barbed end nucleus or filament by Nt-Spire. Spire thus assists Fmn2, in agreement with genetic data [15]. Note that the origin of the synergistic action of Nt-Spire and FH1-FH2 derived from the present data contrasts with the anticipated mechanism within the alternate view that both Spire and Fmn2 are nucleators individually, and that their interaction leads to inhibition of actin assembly [23,25,42].
The mutual kick off of Nt-Spire and FH1-FH2 from barbed ends implies that the transient complexes BSF and BFS differ structurally/chemically, so as to lead to BF and BS, respectively. Thus, the present data, illustrated by this scheme, raise structural and mechanistic issues regarding the possible conformations of the FH2 domain of Fmn2 and the WH2 domains of Spire interacting with the terminal barbed ends subunits of the actin filament, individually and together.
A ''kick off'' process may imply that each protein interacts with the barbed end with at least two subsites, which in the present case may be facilitated by the fact that two actin subunits are exposed at the filament barbed end. For instance, uncapping of capping protein (CP) from barbed ends by VopF is possible because the ßtentacle of CP occupies the main WH2 binding site only on the terminal barbed end subunit, leaving the homologous site on the subterminal subunit available for one WH2 domain of the dimeric VopF [43]. Similarly, the crystal structure of the FH2 domain of Bni1 in complex with TMR-actin shows that the ''knob'' of FH2 occupies the WH2 binding site only on the subterminal subunit, leaving the barbed face of the terminal subunit exposed in the ''closed'' state [44][45][46]. Assuming that a large fraction of the FH2 of Fmn2 shares the actin binding mode of Bni1, it is tempting to suggest that one WH2 domain of Nt-Spire binds to the terminal subunit in the ''closed'' FH2-actin state, following association of the KIND domain with the C-terminal region of FH1-FH2. We find that the isolated KIND domain causes destabilization of FH2 from the barbed end, which implies that the C-terminus of FH2, which is specific to Fmn2, participates in the interaction of the FH2 domain with terminal subunits and processive walk, in agreement with Vizcarra et al. [25]. Therefore, when Nt-Spire binds to an FH1-FH2-bound barbed end, the structural change linked to FH2-KIND interaction may be involved in the kick off of FH1-FH2 coupled to tightening of Nt-Spire binding to terminal subunits. The proposed rapid equilibrium of FH2 between the ''closed'' and ''open'' states during processive assembly may be affected by Spire and may allow FH1-FH2 and Nt-Spire to adopt different conformations in BFS and BSF states as well.
The nature of the nucleotide bound to the two actin barbed end subunits may be important in the binding of FH1-FH2 and the kick off mechanism. The fact that FH1-FH2 associates very slowly to barbed ends in a regime of growth in ATP, while it binds rapidly and with high affinity to ADP-bound barbed ends, may suggest that FH1-FH2 has a higher affinity for ADP-actin, which is not frequently present at barbed ends growing from profilin-ATPactin. Alternatively, FH1-FH2 association to ATP-bound barbed ends may occur as a two step reaction, formation of a rapid equilibrium low affinity complex being followed by a structural change strengthening the binding of FH1-FH2 and allowing processive assembly. The observation that no stimulation of filament assembly by either FH1-FH2 or FH1-FH2+Nt-Spire takes place in AMPPNP nor ADP further suggests that ATP hydrolysis plays some role in Fmn2 function as well as in its cooperation with Spire. While evidence has been provided for processive tracking of barbed ends by formins mDia1 and Bni1 in a growth regime in ADP and in a depolymerization regime [36,46,47], thus demonstrating that ATP hydrolysis is not required for tracking of barbed ends by formin, the very fast processive assembly from PA is oberved only in ATP [29,33], and pauses in growth are observed upon addition of CrATP that does not release Pi following cleavage of ATP [32]. Moreover, processive assembly  can be modeled without involving ATP hydrolysis only if the affinity of profilin for ATP-actin is assumed to be 50-fold lower than its acknowledged value [48].
Two other formins, INF2 and FMNL3, use WH2 domains and FH2 domains in the same polypeptide chain, to regulate actin assembly. Remarkably, in this case, the WH2 domain affects nucleation using a different mechanism [49,50], in which interaction of the WH2 domain with G-actin relieves the autoinhibition [51].

Relevance of the Biochemical Interplay Between Nt-Spire and Fmn2 in Asymmetric Division
Most formins promote processive filament assembly in a Rho GTPase-mediated, site-directed fashion. In the mouse oocyte, Fmn2, which is not regulated by Rho GTPases, is recruited via Spire to Rab11a positive vesicles. Both the high dynamics of filament assembly and the action of myosin Vb, linked to Rab11a vesicles, are required for spindle translocation [12,52]. Myosin Vb, together with Nt-Spire and Fmn2, controls the global dynamics of this coupled vesicle-filament system leading to outward movement of vesicles and slow spindle translocation toward the cortex [52].
We tentatively propose that the ping-pong mechanism integrates this context as follows ( Figure 9B). Association of Nt-Spire to Rab11a vesicles leads to barbed end binding of filaments or prenuclei, triggering Fmn2 association to the Nt-Spire-attached barbed ends, displacement of Nt-Spire from the transient BSF state, and fast barbed end growth. The presumed presence of ADF/cofilin ensures rapid pointed end disassembly of the filaments, which creates a stationary large pool of PA, which feeds fast barbed end processive assembly and fosters rapid treadmilling at the scale of individual filaments [29]. The shortened filaments then either release Fmn2 spontaneously and again get capped by Nt-Spire at the surface of the vesicles, or directly bind Nt-Spire vesicles into the BFS state, then release Fmn2. For simplicity, the cycle of filament nucleation release at Rab11a vesicles organized by Spire and Fmn2 is illustrated at the level of an individual filament in Figure 9B. At the collective level, dynamic links between the filaments are imposed in part by the ping-pong mechanism and in part by the clustering of the players Nt-Spire, Fmn2, and myosin Vb at Rab11a-positive vesicles. These connections organize the formation and maintenance of a dynamic gel in a rapid renewal state that controls the plasticity of the oocyte cytoplasm and facilitates break of symmetry and the first slow step in directional migration of the spindle [53]. This process appears hampered in a gel in which filaments do not undergo rapid turnover, as demonstrated by the failure of spindle to translocate in jasplakinolide-treated oocytes [12]. The very slow migration rate of the spindle toward the cortex actually argues for a mechanism in which actin assembly in the oocyte is not directly applied to a surface to develop a pushing force. Microrheological studies of actin solutions in the presence of Nt-Spire, FH1-FH2, profilin, and ADF, mimicking cellular media, may reveal how the Nt-Spire:FH1-FH2 balance affects the properties of this gel. A confined environment may further affect rheological properties [54].
In Drosophila oocytes, massive actin assembly at midoogenesis, resulting from the synergy between formin Cappuccino and Spire, is required to avoid premature cytoplasmic streaming and failure in axis patterning. The rescue of Spir mutants by expression of SpirD [15], which is identical to the Nt-Spire protein studied here, further establishes the in vivo relevance of the present biochemical data. Completion of oogenesis requires the subsequent disappearance of the actin meshwork. Our work shows that an excess of Nt-Spire over FH1-FH2 causes capping of barbed ends by Nt-Spire that leads to depolymerization of F-actin by profilin. Monitoring the evolution of the Spire:Fmn2 ratio during oogenesis and manipulating it genetically may validate or rule out this potential regulatory mechanism.

Plasmid Constructs
The following constructs of human Spire 1 (accession number NP_001122098), mouse Formin 2 (accession number NP_062318.2), and mDia1 (accession number NP_031884) were designed as follows. FH1 D -FH2 (P854-T1578) and truncated FH1t-FH2 (P854-T1578D(912-967)) constructs, FH2 (F1128-T1578) and KIND (G35-S257) cDNA were cloned between BamH1 and Xho1 cloning sites of a modified pGEX-6P1 expression vector containing a N-terminal histidine thioredoxine tag in place of the GST tag and a C-terminal Streptag II. The cDNA of the chimeric FH1(mDia1)-FH2(Fmn2), called FH1 D -FH2, was chemically synthetized from the amino acid sequence obtained by juxtaposing the FH1 amino acid sequence of mDia1 (S568-P747) to the FH2 amino acid sequence of Fmn2 (F1128-T1578) and back-translating it to a nucleotide sequence optimized for expression in E. coli. The FH1 D -FH2DFSI construct was subcloned from the FH1 D -FH2 cDNA sequence down to S1558 (thus deleting the last 20 residues of the FH2 domain) into the modified pGEX-6P1 expression vector. The Nt-Spire cDNA sequence corresponding to (M1-S443) was cloned in an unmodified pGEX-6P1 vector between the BamH1 and Xho1 cloning sites.

Expression and Purification of Fmn2 Constructs
All constructs were expressed in E. coli Rosetta (DE3) (Novagen), in LB medium. Cultures were induced by 1 mM IPTG at 16uC overnight. Bacteria pellet were resuspended in lysis buffer (20 mM potassium phosphate buffer pH 7.4, 900 mM NaCl, 15 mM imidazole, 3 mM DTT, 5% sucrose, 0.1 mM EDTA, 1 mM PMSF, 5 mM benzamidine, protease inhibitor cocktail, 1% Triton X100, and lyzozyme) and sonicated on ice. Ultracentrifuged cell lysates were loaded on HisTrap FF crude column (GE Healthcare). The HisTrap resin was equilibrated with binding buffer 1 (20 mM phosphate buffer pH 7.4, 900 mM NaCl, 15 mM imidazole, 3 mM DTT, 5% sucrose, 0.1 mM EDTA), then washed with 4% of elution buffer 1 (binding buffer 1 except for 250 mM imidazole). Proteins were eluted with a 60% elution buffer gradient step. The Fmn2-enriched fraction was then diluted with a suitable volume of 100 mM Tris pH 7.5 to decrease NaCl concentration to 300 mM and loaded to a Strep Trap HP (GE Healthcare). The resin was then washed with binding buffer 2 (100 mM Tris pH 7.5, 300 mM NaCl, 1 mM EDTA, 3 mM DTT, 5% sucrose), and bound proteins were eluted with elution buffer 2 (binding buffer 2 supplemented with 4 mM desthiobiotin). Eluted fractions were pooled and concentrated with a Vivaspin

Purification of FH2 and KIND
FH2 and KIND were expressed and purified similarly to FH1 D -FH2 constructs up to the HisTrap purification step. Prior to the Strep Trap purification step, the histidine thioredoxine tag was cleaved using Prescission Protease (5 U/mg fusion protein) overnight at 4uC. Digested protein was then loaded to a Strep Trap HP (GE Healthcare). The resin was then washed with binding buffer 2, and bound proteins were eluted with elution buffer 2. Eluted fractions were pooled, concentrated, and loaded on a Superdex 200 16/60 (GE Healthcare) pre-equilibrated with 20 mM Tris pH 7.5, 75 mM KCl, 1 mM DTT for FH2, or 20 mM Tris pH 7.5, 100 mM KCl, 1 mM DTT for KIND. Fractions corresponding to pure FH2 or KIND were pooled and concentrated. FH2 was stored at 4uC. KIND was flash frozen in liquid nitrogen and stored at 280uC.

Purification of Nt-Spire
Nt-Spire was expressed and purified similarly to FH1 D -FH2 constructs up to the HisTrap purification step. The concentrated His Trap eluted material was loaded onto a desalting Hiprep 10-26 column pre-equilibrated with a desalting buffer (50 mM Tris pH 7.5, 400 mM NaCl, 1 mM DTT, 1 mM EDTA). The GST tag was cleaved by overnight incubation at 4uC of the concentrated fusion protein solution with Prescission Protease (5 U/mg fusion protein). Nt-Spire was eventually purified by gel filtration in 15 mM Tris pH 7.5, 250 mM KCl, 1 mM DTT, 1% sucrose buffer, and was kept frozen at 280uC.

TIRF Measurements of Single Filaments
Standard TIRF assays were performed using a flow chamber assembled by placing two parallel strips of double-sided tape (2661060.1 mm) spaced by 8 mm onto a cleaned glass slide (76626 mm), surmounted with a PLL-PEG passivated coverslip. Chambers were sequentially washed with G buffer, 5% BSA, Fluo F buffer (5 mM Tris-Cl2 pH 7.8, 150 mM NaCl, 1 mM MgCl 2 , 0.2 mM EGTA, 0.2 mM ATP, 10 mM DTT, 1 mM DABCO, 0.01% NaN 3 ). Assays were performed in Fluo F buffer supplemented with 0.3% methylcellulose (Sigma Cat. No. M-0262, 400 cP for a 2% aqueous solution at 20uC) and with actin, profilin, Nt-Spire, and FH1 D -FH2 or FH1-FH2 at indicated concentrations. Microfluidics-assisted TIRF microscopy assays were performed using PDMS flow cells, with three inlets [34]. Prior to flowcell assembly, coverslips are first extensively cleaned by sequential sonication in pure water, ethanol, and 1 M KOH for 20 min each, then dried with air and exposed to a plasma discharge for 2 min. The microchambers were placed on the microscope stage and connected to the microfluidic system (MFCS and Flowell, from Fluigent). The coverslip is then functionalyzed by absorption of PLL-PEG/PLL-PEG-biotin (20%) (from SuSoS) to minimize nonspecific protein binding and achieve specific anchoring of biotinylated spectrin-actin seeds via a streptavidin sandwich. Actin was labeled with Alexa488 succimidyl ester [34]. The fraction of labeled actin was 10%. Assays were performed in FluoF buffer without methylcellulose.
TIRF observations were carried out on an Olympus IX71 inverted microscope, with a 606 TIRF objective, and a 473 nm laser (Cobolt). The experiment was controlled using the Metamorph software. Images were acquired using a cascade II EMCCD camera (Photometrics), with a frame interval of 10 s for all experiments. Images are further analyzed by ImageJ to obtain kymographs and to determine the times at which filaments experience transitions from one to another of the three possible states: slow elongation (''free barbed-end''), rapid elongation (''FH1 D -FH2-bound barbed end''), or capped (''Nt-Spire-bound barbed end''). Single exponential curve fitting of the data points is done using Gnuplot. On the kymographs, slopes of elongation phases give us the elongation rates in presence or absence of FH1 D -FH2. We considered that each actin subunit contributes to 2.7 nm of the filament length.

Preparation and Microinjection of Mouse Oocytes
All mice were maintained in a specific pathogen-free environment according to UK Home Office regulations. Oocytes were isolated from ovaries of 8-wk-old FVB mice, cultured, and microinjected as described in detail [53]. BSA (Sigma) or recombinant Nt-Spire, KIND, FH2, and FH1 D -FH2 protein fragments were microinjected into oocytes in buffer supplemented with 0.05% NP-40 Alternative (Calbiochem). Final protein concentrations were calculated by dividing the total amount of injected protein by the total volume of the oocyte. These were 1 to 3 mM for each protein, 8 mM for KIND, and 163 mM for FSI.
Single optical sections in the equatorial region of oocytes were acquired with a Zeiss LSM710 confocal microscope equipped with a 663 C-Apochromat 1.2 NA water-immersion objective as described previously [56]. Images in control and perturbed situations were acquired with identical imaging conditions. Care was taken that images were not saturated during acquisition. To quantify the density of the cytoplasmic actin network, the mean intensity of Alexa Fluor-488 phalloidin was measured in the cytoplasm and in a region outside the oocyte for background subtraction using ImageJ. Average (mean), standard deviation, and statistical significance based on Student's t test (always two-tailed) were calculated in OriginPro (OriginLab).  . Sketch for the synergy between Nt-Spire and Fmn2 in processive barbed end filament assembly and blockage of disassembly. (A) The ping-pong mechanism. A filament barbed end (B) in the presence of Spire (S) and Fmn2 (F) associates faster to Nt-Spire than to Fmn2, leading to BS state. BS interacts much faster than B with Fmn2. Displacement of S leads to processive fast growth from BF. Binding of Spire to BF leads to dissociation of Fmn2 and establishment of the capped, nongrowing BS state. Filaments transit between the BS and BF states at frequencies governed by the amounts of Spire and Fmn2. (B) Model for organisation of a dynamic nonpolarized actin meshwork from Spire-bound vesicles in the presence of Fmn2. The following reactions are drawn. (1) attachment of a filament or nucleus barbed end to a Spire-vesicle; (2) Fmn2 is recruited by Spire at vesicle-attached barbed ends (BSF transient state); (3) Fmn2-catalyzed fast processive growth of the filament from PA; (4) ADFpromoted shortening of filaments enhances treadmilling; (5) dissociation of Fmn2 leads to recycling of barbed ends to Spire-vesicle; and (6) recycling of Fmn2-bound barbed ends to a Spire-vesicle (BFS transient state). Myosin Vb-driven translocation of Rab11a vesicles along Fmn2-assembled filaments implicitly contributes in coordinating the vesicle-filaments network dynamics, however Rab11a-activated myosin Vb is not represented for simplicity. doi:10.1371/journal.pbio.1001795.g009 prepared in ADP-(A) or AMPPNP-(B) bound form (Materials and Methods) and assembled in the presence of profilin without (black lines) and with 200 nM FH1 D -FH2, in absence (blue lines) or presence of Nt-Spire (red lines). ATP was then added (arrow). (TIF) Figure S5 Measurement of the association rates of Spire (resp. Fmn2) to Fmn2-(resp. Spire-) bound barbed ends. (A) Fmn2-bound filament barbed ends (BF) are exposed to a flow of PA+Spire (without Fmn2). Arrest of rapid growth of Fmn2-bound barbed ends by Spire results from the combination of Fmn2 dissociation followed by association of Spire to a free barbed end and direct association of Spire to Fmn2-bound barbed ends, possibly followed by dissociation of Fmn2. The free barbed ends produced by the very slow reaction BFRB (rate constant k 2F ) grow slowly or are capped (transition from BF to BS). The reaction BRBS is rapid, and thus, the transition from state BF to BS includes the route BFRBRBS in addition to reaction BFRBS (with apparent rate constant k9 app +S for a given concentration of Spire). Based on the resolution of our experiment and on the rate constants k +S and k 2S , most filaments reaching state B are capped and convert to state BS very rapidly, while the vast majority (more than 90%) of the capped states BS last long enough to be identified unambiguously. Consistently, as shown at 40 nM Nt-Spire (graph), we observe almost only transitions from state BF to BS. The observed rate constant can be written k obs = k +S [S](k9 app +S +k 2F )/ (k +S [S]+k 2F ). The data are fitted with k9 app +S as a free parameter. The resulting k9 app +S varies linearly with [Spire] ( Figure 6D). (B) Spire-capped filaments (BS) are exposed to a flow of PA+Fmn2 (without Spire). Resumed fast growth at Spire precapped barbed ends results from two combined kinetic routes, dissociation of Spire followed by association of Fmn2 to a free barbed end, and direct association of Fmn2 to a Spire-capped barbed end possibly followed by rapid dissociation of Spire. Free barbed ends enter a state of slow growth (reaction BSRB, with rate constant k 2s ). Filaments that undergo reaction BSRBF, with the apparent rate constant k9 app +F (for a given concentration of Fmn2), grow fast. The reactions BRBF and BFRB are slow, and states B and BF last long enough to be identified unambiguously in our experiment. Overall loss of capping occurs at an observed rate k 2s +k9 app +F , with a fraction k 2s /(k 2s +k9 app +F ) of the filaments undergoing reaction BSRB, and a fraction k9 app +F /(k 2s +k9 app +F ) of the filaments undergoing reaction BSRBF. The graph shows the measured transitions occurring over time for each class and the sum of the two, for [FH1 D -FH2] = 10 nM (full symbols, solid lines) and 20 nM (open symbols, dashed lines), fitted using k9 app +F as a free parameter. The resulting k9 app +F is found to vary linearly with [Fmn2] (as reported in Figure 6G). (C) Filaments capped by Nt-Spire in the presence of FSI fail to associate with FH1 D -FH2 (10 nM) and resume fast growth. The values of k obs are measured as under Figure 6G. (D) Table summarizing the rate constants for FH1 D -FH2, FH1-FH2 (italics), and Nt-Spire association and dissociation at free or FH1 D -FH2-(resp. Nt-Spire-) bound barbed ends, and the asssociation rate constant k+ of PA to FH1 D -FH2bound barbed ends in fast processive assembly. The dissociation of Nt-Spire from barbed ends is not affected by FSI.