Competition for delivery of profilin–actin to barbed ends limits the rate of formin-mediated actin filament elongation

Formins direct the elongation of unbranched actin filaments by binding their barbed ends and processively stepping onto incoming actin monomers to incorporate them into the filament. Binding of profilin to actin monomers creates profilin–actin complexes, which then bind polyproline tracts located in formin homology 1 (FH1) domains. Diffusion of these natively disordered domains enables direct delivery of profilin–actin to the barbed end, speeding the rate of filament elongation. In this study, we investigated the mechanism of coordinated actin delivery from the multiple polyproline tracts in formin FH1 domains. We found that each polyproline tract can efficiently mediate polymerization, but that all tracts do not generate the same rate of elongation. In WT FH1 domains, the multiple polyproline tracts compete to deliver profilin–actin to the barbed end. This competition ultimately limits the rate of formin-mediated elongation. We propose that intrinsic properties of the filament-binding FH2 domain tune the efficiency of FH1-mediated elongation by directly regulating the rate of monomer incorporation at the barbed end. A strong correlation between competitive FH1-mediated profilin–actin delivery and FH2-regulated gating of the barbed end effectively limits the elongation rate, thereby obviating the need for evolutionary optimization of FH1 domain sequences.

Formins processively regulate actin polymerization by associating with filament barbed ends via their dimeric formin homology 2 (FH2) 2 domains and directly modulating the rate of subunit addition (6 -12). Barbed-end-bound FH2 dimers fluctuate between polymerization-competent "open" conformations and polymerization-incompetent "closed" conformations (8,13,14). When a formin is in an open conformation, an actin subunit can bind the barbed end. Subsequent stepping of one of the FH2 domains onto the newly-bound subunit incorporates it into the filament without necessitating full dissociation of the formin from the barbed end (13,(15)(16)(17). The probability of finding a particular formin in an open conformation is termed the "gating factor" and ranges from near 0 to 1. A formin with a small gating factor mediates very slow filament elongation, whereas a formin with a gating factor of 1 mediates polymerization at a rate that matches the elongation of filaments with free (i.e. not bound by formin) barbed ends.
Binding of the protein profilin to actin monomers enables formins to speed elongation beyond the basal rate mediated by their FH2 domains (8,13). Profilin-actin complexes bind to polyproline tracts located in the otherwise unstructured formin FH1 domain (18,19), which is positioned directly N-terminal to the FH2 domain ( Fig. 1). Diffusion of the flexible FH1 domain facilitates rapid delivery and transfer of bound profilin-actin complexes to the barbed end for incorporation via FH2 stepping ( Fig. 1) (13,20). Titration of profilin into polymerization reactions containing actin and formin FH1FH2 constructs increases the rate of FH1-mediated filament elongation in a profilin-dependent manner, such that maximal elongation rates are observed when the majority of actin monomers are bound by profilin (8,13,15,21). The elongation rate slows in the presence of a large molar excess of profilin, which competes with profilin-actin for binding to the polyproline tracts and reduces the efficiency of the FH1 domains (8,13).
The presence of multiple polyproline tracts in formin FH1 domains gives rise to an array of parallel pathways for forminmediated delivery of profilin-actin to the barbed end (Fig. 1). The number of polyproline tracts encoded in formin FH1 domain sequences varies widely, from as few as 1 to as many as 14 (18). It has been observed that formins whose FH1 domains contain a large number of polyproline tracts mediate faster elongation than do formins with fewer tracts (8). However, the mechanism of coordinated actin polymerization along the parallel routes presented by the FH1 domain remains poorly understood. As a result, it remains unknown why certain formins possess more polyproline tracts than do others.
In this study, we investigated the mechanism that governs the interactions of profilin-actin complexes with the multiple polyproline tracts in formin FH1 domains and their subsequent delivery to the barbed end. We found that although all polyproline tracts can efficiently mediate polymerization, competition among tracts to deliver profilin-actin to the barbed end imposes an upper limit on the rate of elongation that can be achieved by formins. We propose that intrinsic properties of the FH2 domain tune the efficiency of FH1-mediated elongation by directly regulating the rate of monomer addition at the barbed end. A strong correlation between competitive FH1mediated profilin-actin delivery and FH2-regulated gating thus obviates the need for evolutionary optimization of FH1 domain sequences.

Results
To dissect the contributions of individual polyproline tracts to actin filament elongation mediated by formins, we made a series of variants of an FH1-FH2 construct of the Saccharomyces cerevisiae formin Bni1p. We selected Bni1p as a representative formin because its FH1 domain contains four polyproline tracts ( Fig. 2A), which corresponds to the average number of tracts present in the FH1 sequences of formins whose polymerization properties have been characterized (Table 1). These tracts mediate a robust filament elongation rate in the presence of profilin, making the FH1 domain of Bni1p an excellent candidate for dissection (8,15,20,21). Each of our designed variants contains the WT Bni1p FH2 domain preceded by the FH1 domain in which all but one of the polyproline tracts have been substituted with a repeated Gly-Gly-Gly-Ser sequence of the same length as the polyproline tract it replaces (Fig. 2B). Thus, the remaining tract in each construct is located at its native position within the FH1 domain, preserving its distance from the FH2 domain. We refer to each single-tract variant as Bni1p PX-FH2, where PX refers to the polyproline tract that is retained.

Individual polyproline tracts mediate actin polymerization
To evaluate the ability of each polyproline tract in Bni1p's FH1 domain to mediate filament elongation, we visualized actin polymerization in the presence of our single-tract constructs using total internal reflection fluorescence (TIRF) microscopy. Each polymerization reaction contained 0.75 M purified actin monomers, 33% of which were labeled with Oregon Green at cysteine 374, and a range of profilin concentrations (0 -17.5 M) selected to enable us to evaluate FH1 activity in the presence of sub-optimal (0 -1 M), optimal (2.5-10 M), and excess (17.5 M) amounts of profilin. Consistent with published observations of WT formins (8,21), our single-tract Bni1p variants preferentially incorporated unlabeled actin subunits in the presence of profilin due to 10-fold tighter binding of profilin to unlabeled monomers compared with fluorescently-labeled monomers (22). As a result, formin-bound filaments appeared more dimly fluorescent than filaments with free (i.e. not formin-bound) barbed ends, facilitating their distinction (Fig.  2C). In conditions that produced filaments with similar fluorescence intensities, we distinguished formin-bound from free filaments by comparing their elongation rates, which typically fell into two distributions.
In the absence of profilin, all single-tract formins mediated filament elongation rates of 5-7 subunits/s (Fig. 2D). In agreement with Bni1p's gating factor of 0.5, these rates are ϳ50% slower than the elongation rate of actin filaments with free barbed ends (8,15). Thus, deletion of multiple polyproline tracts in the FH1 domain does not significantly impact gating or subunit addition mediated by the FH2 domain. Inclusion of up to 5 M profilin increased the polymerization rate mediated by each single-tract formin, revealing that each polyproline tract is capable of binding and delivering profilin-actin to the barbed end. In the presence of profilin concentrations exceeding 5 M, the rates of filament elongation mediated by all single-tract formins decreased (Fig. 2D). Under these conditions, the concentration of profilin exceeds the concentration of actin monomers. Thus, like formins with WT FH1 domains, competition between profilin-actin and free profilin for binding polyproline decreases the efficiency of FH1-mediated transfer of profilinactin to the barbed end, ultimately slowing elongation (8,13).

Polyproline tract sequences are not optimized for rapid elongation
Whereas Bni1p PA-FH2, PC-FH2, and PD-FH2 mediated similar rates of filament elongation, Bni1p PB-FH2 polymerized actin ϳ50% faster at each profilin concentration than the other constructs (Fig. 2D). This suggests that individual polyproline tracts do not contribute equally to elongation and that some polyproline tract sequences may not be optimized for the most efficient delivery of profilin-actin to the barbed end. To test this hypothesis, we sought to determine whether it was possible to increase the rate at which a polyproline tract mediates elongation by systematically modifying its sequence.
Published work has established that the efficiency of profilinactin transfer from a polyproline tract in the FH1 domain to the barbed end depends both on the affinity of the tract for profilin and the position of the tract within the FH1 domain, which dictates the

Competition limits elongation rates mediated by formins
frequency of collisions with the barbed end (20). A weak affinity for profilin-actin enables rapid delivery from tracts that collide frequently with the barbed end, whereas tracts that collide only infrequently with the barbed end must retain their bound profilinactin for a longer period of time to increase the likelihood of successful delivery.
Inspection of Bni1p's FH1 domain sequence revealed that polyproline tract PA contains 11 prolines, whereas PB contains 13 prolines. Based on published binding studies that were performed using poly-L-proline peptides, the sequences of polyproline tracts PA and PB bind profilin with estimated affinities of 36 and 25 M, respectively ( Fig. 2A) (23). Experimental and theoretical studies have demonstrated that the frequency of collisions between the two ends of a disordered polypeptide chain is proportional to n Ϫ3/2 , where n is the number of residues in the polypeptide (24). Thus, because of its closer proximity to the FH2 domain, the PB tract is predicted to collide 2.3 times more frequently with the barbed end than does the PA tract. Based on these calculations, we hypothesized that the PA tract interacts too weakly with profilin to promote maximally efficient rates of elongation given its position in the FH1 domain. We therefore sought to test the effect of increasing the affinity for profilin on the polymerization rate mediated by this tract. To do so, we designed two variants of Bni1p PA-FH2 in which the polyproline tract was increased in length. These variants, Bni1p PA 13 -FH2 and Bni1p PA 15 -FH2, encode modified PA tracts that contain 13 and 15 prolines, corresponding to increases of 31 and 53% in the affinity of PA for profilin (estimated K d values of 25 and 17 M, respectively) ( Fig. 3A) (23).
In the presence of 5 M profilin, Bni1p PA 13 -FH2 and Bni1p PA 15 -FH2 generated 15 and 30% faster filament elongation than did Bni1p PA-FH2, confirming that tighter binding promotes more efficient barbed-end delivery of profilin-actin from tracts that are distal to the FH2 domain (Fig. 3, B and C). Because Bni1p PA 15 -FH2 contains the most efficient polyproline tract, we analyzed this protein's elongation activity in the presence of 0 -17.5 M profilin. In all reactions containing profilin, Bni1p PA 15 -FH2 exhibited significantly faster rates of elongation than did Bni1p PA-FH2 (Fig. 3D). Thus, the WT sequence of polyproline tract PA is not optimized to mediate a maximal polymerization rate.

Competition limits elongation rates mediated by formins
We next sought to determine whether substituting polyproline tract PA with the PA 15 sequence in the context of the WT FH1 domain would produce a commensurate increase in the rate of elongation mediated by Bni1p FH1-FH2 (Fig. 3A, Bni1p FH1(PA 15 )-FH2). We found that Bni1p FH1(PA 15 )-FH2mediated filament elongation rates were nearly identical to those produced by Bni1p FH1-FH2 in the presence of low micromolar concentrations of profilin (Fig. 3E). Furthermore, Bni1p FH1(PA 15 )-FH2 polymerized actin less efficiently than the WT protein at profilin concentrations exceeding 2.5 M (Fig. 3E), indicating that tight binding of profilin by the most distal tract can inhibit FH1 domain activity. Thus, WT Bni1p mediates rapid polymerization despite the fact that its polyproline tract sequences are not individually optimized for efficient elongation. These results suggest that the rate of elongation mediated by Bni1p is restricted by a mechanistic "speed limit." This implies that optimization of individual polyproline tract sequences is unnecessary and, in some conditions, inefficient.

Competition among polyproline tracts limits the rate of filament elongation mediated by Bni1p
To establish the physical basis for the limit on the rate of filament elongation, we investigated the coordination of delivery of profilin-actin from all four polyproline tracts in Bni1p's FH1 domain. To do so, we separated the elongation rates mediated exclusively by the FH1 domains of the WT and single tract variants of Bni1p from the total elongation rate (which includes elongation arising from direct binding of actin monomers to FH2-bound barbed ends). We took advantage of the fact that conjugation of a fluorescent label to cysteine 374 of an actin

Competition limits elongation rates mediated by formins
monomer decreases its binding affinity for profilin 10-fold. Thus, whereas the FH2 domain of Bni1p incorporates labeled and unlabeled monomers with equal probability, the FH1 domain preferentially polymerizes unlabeled actin because of the requirement for profilin-actin complex formation for FH1mediated elongation (8,21). We quantified the fluorescence intensities of formin-bound filaments, which provides a direct measurement of the fraction of polymerized, fluorescentlylabeled actin monomers (Fig. 4A). Consistent with measurements performed with WT Bni1p (21), we found that filaments polymerized by each single-tract variant were as bright as control filaments in the absence of profilin. In contrast, forminbound filaments were dimmer than control filaments in the presence of profilin, reflecting a bias for incorporation of unlabeled actin subunits via the FH1 domain (Fig. 4A). We used these fluorescence measurements and the published affinities of S. cerevisiae profilin for labeled and unlabeled actin monomers (22,25) to calculate the fraction of subunits incorporated by the FH1 domain of each Bni1p construct (see "Experimental procedures") (21). Multiplication of this fraction by the overall formin-mediated elongation rate then yielded the rate produced by the FH1 (Fig. 4B).
All four single-tract variants promoted robust FH1-mediated filament elongation rates that showed a similar dependence on the concentration of profilin (Fig. 4B). Consistent with our measurements of total (i.e. both FH1-and FH2-mediated) elongation rates (Fig. 2D), polyproline tract PB coordinated faster polymerization than did tracts PA, PC, and PD at most profilin concentrations (Fig. 4B). Notably, the rates generated by tracts PA and PB were more sensitive to excess profilin concentrations than subunit addition mediated by tracts PC and PD. This likely results from slower dissociation of profilin from longer polyproline tracts, which inhibits rapid exchange of profilin for profilin-actin.
To characterize the mechanism of coordinated profilinactin delivery from all four polyproline tracts, we compared the sum of the rates mediated by each individual tract in our singletract mutants to that produced by the WT FH1 domain of Bni1p. To guide our interpretation of these data, we considered three possible scenarios. First, if the sum of the rates generated by the individual tracts is equal to that produced by the WT FH1 domain, the four tracts coordinate polymerization in an additive manner (Fig. 4D, purple line). In this scenario, each tract contributes an elongation rate that is independent of the other tracts. Second, if the sum of the rates generated by the individual tracts is greater than the rate produced by the WT FH1 domain, the four tracts mediate polymerization in a competitive manner (Fig. 4D, blue region). In this scenario, individ-

Competition limits elongation rates mediated by formins
ual polyproline tracts mediate faster elongation in the absence of the other tracts. Third, if the sum of the rates generated by the individual tracts is smaller than the rate produced by the WT FH1 domain, the tracts coordinate polymerization in a cooperative manner (Fig. 4D, yellow region). In this case, individual polyproline tracts polymerize actin most efficiently in the presence of the other tracts.
We plotted the summed and WT elongation rates as a function of profilin concentration (Fig. 4E). At low profilin concentrations (i.e. 0.5-1 M profilin), the rate of polymerization mediated by Bni1p is enhanced via cooperative coordination among the polyproline tracts ( Fig. 4E and Fig. S1A). Thus, in these conditions, binding of profilin-actin or profilin to one polyproline tract speeds elongation mediated by another tract. In contrast, in the presence of profilin concentrations that promote the most rapid filament elongation (i.e. 2.5-17.5 M profilin), the polyproline tracts of Bni1p competitively deliver profilin-actin to the barbed end (Fig. 4E). Thus, the four tracts mediate slower filament elongation when they are found in the context of the WT FH1 domain than they do when only one tract is present.

Optimization of an individual tract sequence increases the magnitude of competition among polyproline tracts
Competitive subunit addition mediated by the polyproline tracts of Bni1p's FH1 domain provides a possible mechanism for the establishment of an upper limit for Bni1p's elongation activity. This limit implies that optimization of individual polyproline tract sequences is unnecessary and explains why our optimized PA 15 polyproline tract does not increase the elongation rate mediated by Bni1p FH1-FH2. To test this hypothesis, we compared the sum of the rates mediated by tracts PA 15 , PB, PC, and PD to the rate generated by the FH1 domain of Bni1p FH1(PA 15 )-FH2. To do so, we first quantified the fluorescence intensities of filaments polymerized by Bni1p PA 15 -FH2 and used these measurements to determine the FH1-mediated filament elongation rates produced by the PA 15 tract within the context of this single-tract variant. Consistent with our measurements of total elongation rates (Fig. 3D), the PA 15 polyproline tract mediated faster elongation than the PA tract at all concentrations of profilin (Fig. 4C).
In the presence of 2.5 M and larger concentrations of profilin, the sum of the elongation rates mediated by the individual tracts in FH1(PA 15 )-FH2 (Fig. 4F, purple circles) is larger than both the rate produced by the FH1 domain of this construct (Fig. 4F, black circles) and the sum of the rates produced by the tracts comprising the WT FH1 domain (Fig. 4E, purple circles). Thus, an increase in the elongation rate mediated by an individual tract produces a corresponding increase in the magnitude of the competition among the tracts. This supports our hypothesis that competition among polyproline tracts obviates sequence optimization for each tract. At concentrations of profilin below 2.5 M, the contribution of each tract to the elongation rate is additive, rather than cooperative as in the case of the WT FH1 domain (Fig. 4F and Fig. S1B). This suggests that polyproline tracts mediate elongation in a cooperative manner only when interactions with profilin are weak and that tighter binding to profilin eliminates this enhancement in rate.

Competition among polyproline tracts is a general feature of formin FH1 domains
Our finding that filament elongation mediated by multiple polyproline tracts is competitive suggests that mechanistic redundancy is built into the FH1 domains of formins. To determine whether this property is a general feature of formins or whether it is unique to Bni1p, we designed single-tract variants of an FH1-FH2 construct of the Schizosaccharomyces pombe formin Cdc12p (Fig. 5, A and B). This formin's FH1 domain contains two polyproline tracts, enabling us to test whether competition takes place within the simplest context possible.
We measured elongation rates mediated by WT and the single-tract variants of Cdc12p FH1-FH2 in the absence and presence of profilin (Fig. 5, C and D). Similar to Bni1p, inclusion of profilin increased the elongation rates mediated by all Cdc12p constructs. In most polymerization conditions, elongation directed by Cdc12p PB-FH2 was faster than that generated by Cdc12p PA-FH2, consistent with our observations that individual polyproline tract sequences do not necessarily mediate identical rates of elongation (Fig. 2D).
Cdc12p has a gating factor that is near zero (8), and therefore, this formin mediates elongation exclusively via its FH1 domain in the presence of profilin (21). To evaluate the contributions made by both polyproline tracts to Cdc12p-directed polymerization, we summed the elongation rates produced by each single-tract variant and compared these rates to those generated by the WT protein (Fig. 5E). Consistent with our findings with Bni1p, this analysis revealed that the PA and PB tracts of Cdc12p mediate filament elongation competitively at profilin concentrations that promote maximal elongation rates ( Fig. 5E; 2.5-17.5 M profilin). At limiting concentrations of profilin (i.e. 0.5-1 M profilin), the polyproline tracts in Cdc12p's FH1 domain contribute to polymerization in an additive manner (Fig. 5E).

Polyproline tracts compete to deliver, but not to bind, profilin-actin
Our finding that competitive subunit addition occurs even within an FH1 domain that contains only two polyproline tracts suggests that this mechanism is likely a conserved feature among formins. FH1-mediated elongation involves two sequential binding reactions (Fig. 1). Therefore, competition among polyproline tracts might arise from either competitive binding of profilin-actin to neighboring tracts or competitive delivery of multiple, FH1-bound profilin-actin complexes to a single barbed-end binding site. To identify the origins of the competition among polyproline tracts, we designed three variants of Bni1p FH1-FH2 that contained combinations of two polyproline tracts. Each of these double-tract variants retained the PD tract and one other tract (Fig. 6A). We predicted that if profilin-actin binds competitively to neighboring polyproline tracts, Bni1p PCPD-FH2, which retains the two tracts located closest to one another, would exhibit the most competitive polymerization, whereas Bni1p PAPD-FH2, which retains the two most distal tracts, would exhibit little or no competition. In contrast, if polyproline tracts compete at the delivery step, Bni1p PBPD-FH2, which contains the tract that delivers actin Competition limits elongation rates mediated by formins most efficiently to the barbed end (i.e. PB), would exhibit the greatest amount of competition.
We measured elongation rates mediated by our double-tract Bni1p variants in a range of profilin concentrations (Fig. 6, B and C). Profilin stimulated filament elongation by all three doubletract variants. Each variant generated slower rates of filament elongation than did WT Bni1p (Fig. 2D). Consistent with the difference in the binding affinity of profilin for short and long polyproline tracts, the elongation rates produced by Bni1p PAPD-FH2 and Bni1p PBPD-FH2, which each contain a long polyproline tract, reached a peak at 2.5-5 M profilin, whereas those mediated by Bni1p PCPD-FH2, which contains only short polyproline tracts, were fastest in the presence of 10 M profilin (Fig. 6C).
We quantified the elongation rates mediated by the FH1 domains of each double-tract variant and compared these rates to the sum of the rates individually produced by their component tracts (Fig. 6, D-F). In the presence of limiting profilin, the polyproline tracts in all three variants cooperatively coordinate filament elongation, indicating that cooperative polymerization can occur when only two polyproline tracts are present in a formin's FH1 domain.
At profilin concentrations exceeding 1 M, the polyproline tracts comprising the FH1 domains of Bni1p PAPD-FH2 and Bni1p PCPD-FH2 coordinate elongation in an additive manner, whereas Bni1p PBPD-FH2 exhibits competitive polymerization (Fig. 6, D-G). Thus, the tracts in PAPD-FH2 and PCPD-FH2 bind and deliver profilin-actin to the barbed end independently of one another, suggesting that neither neighboring nor distal polyproline tracts compete to bind profilin. In contrast, the competition exhibited by Bni1p PBPD-FH2 suggests the existence of a kinetic threshold for competitive profilin-actin delivery. If the individual polyproline tracts that comprise a formin's FH1 domain mediate filament elongation at a combined rate that falls below this threshold, each tract will deliver profilin-actin in an additive manner. If the combined rate of polymerization exceeds this threshold, the polyproline tracts will compete to deliver their bound profilin-actin complexes to the barbed end. We tested this model by increasing the sum of the rates mediated by the individual polyproline tracts in Bni1p PAPD-FH2 by substituting the PA tract with our optimized PA 15 sequence (Fig. 6, Bni1p PA 15 PD-FH2). We found that this construct also exhibits competitive profilin-actin delivery (Fig. 6G), supporting our hypothesis for a kinetic threshold for competition.

Discussion
Formin FH1 domains direct actin polymerization by binding profilin-actin complexes and delivering them to growing FH2bound barbed ends for incorporation into filaments (8,13,16,17). The existence of multiple binding sites for profilin in most FH1 domains creates a series of parallel pathways for polymerization. We dissected the contributions of each polyproline tract in the FH1 domains of the formins Bni1p and Cdc12p to determine how subunit addition along these parallel routes is coordinated. We found that each polyproline tract is capable of

Competition limits elongation rates mediated by formins
mediating actin polymerization when it is the only tract in the FH1 domain and that some tracts mediate significantly faster polymerization rates than others (Figs. 2D and 5D).

Competition for delivery of multiple polyproline-bound profilin-actin complexes to the barbed end establishes a speed limit for polymerization
To assess the coordination of actin polymerization along the multiple pathways presented by formin FH1 domains, we compared the elongation rates mediated by the WT FH1 domains of Bni1p and Cdc12p to the sum of the rates mediated by each of their polyproline tracts when it is the only tract present (Figs. 4D and 5E). In the presence of profilin concentrations that promote maximal polymerization rates, the sum of the elongation rates mediated by the individual polyproline tracts exceeds the rate mediated by the WT FH1 domains of both formins (Figs. 4D and 5E). Thus, in optimal polymerization conditions, subunit addition mediated by the multiple polyproline tracts in a formin's FH1 domain is competitive.
Our experiments with double-tract variants of Bni1p indicated that neighboring polyproline tracts do not compete to bind profilin-actin (Fig. 6D). This is consistent with published crystallographic and molecular modeling studies, which demonstrated that FH1 domains can accommodate simultaneous binding of multiple profilin-actin complexes to neighboring tracts (18,19). Instead, competition arises when multiple tracts compete to deliver profilin-actin to the barbed end (Fig. 6E).
FH1-mediated delivery of a profilin-actin complex is successful only when the FH2-bound barbed end is in a polymerization-competent, open conformation. Following delivery, stepping of the FH2 dimer incorporates the newly-associated actin subunit into the filament. The FH2 domain then returns to its open conformation, making the barbed end available once again for monomer binding (15,17). This mechanism can only accommodate binding of a single actin monomer to the barbed end during each cycle of subunit addition. It therefore follows that, if multiple profilin-actin complexes are bound simultaneously to polyproline tracts in an FH1 domain, all but one of the tracts will be less efficient at transferring their bound profilinactin to the barbed end than they would be if they were the only tract present in the FH1 domain (Fig. 7A).
Competition among polyproline tracts establishes a limit on the rate of formin-mediated filament elongation. Consistent with this model, substitution of Bni1p's polyproline tract PA with a sequence that binds profilin more tightly yielded nearly identical rates of elongation as WT Bni1p in the presence of up to 2.5 M profilin (Fig. 3E). This optimized formin mediated slower polymerization than did WT Bni1p in the presence of 5 M and higher concentrations of profilin. Thus, an increase in the binding affinity of the terminal polyproline tract for profilin interferes with barbed-end delivery of profilin-actin from the other tracts. These results suggest that binding of profilin-actin at a distal position may disrupt FH1 diffusion in a way that slows the overall rate of collisions of all polyproline tracts with the barbed end. This provides a second possible mechanism for competition among polyproline tracts. Thus, individual polyproline tract sequences might be optimized not only for their profilin-binding properties but also to minimize position-spe-cific effects on the diffusional properties of the FH1 domain when the site is bound by profilin.

Role of gating in regulating the competition among polyproline tracts
Kinetic competition for delivery limits the maximal rate at which profilin-actin can be transferred to the barbed end. In addition to obviating polyproline tract sequence optimization, this limit likely also restricts the number of polyproline tracts a formin's FH1 domain can accommodate. Consistent with this hypothesis, doubling the number of polyproline . Proposed mechanism for kinetic regulation of FH1 activity by FH2 gating. A, reaction schemes depicting the delivery and incorporation of profilin-actin (purple and yellow circles) at the barbed end of a filament by formins whose FH1 domains encode a single polyproline tract (top row: green ovals) or two polyproline tracts (bottom row: green and blue ovals). When the FH1 domain contains two or more polyproline tracts, competition for delivery of profilin-actin to the barbed end binding site decreases the relative polymerization efficiency of the individual tracts. For simplicity, binding of profilin-actin to only one of the FH1 domains is depicted. B, number of polyproline tracts encoded by FH1 domains, plotted as a function of the reported FH2 gating factor for each formin. The formins represented in this graph are listed in Table 1 along with references to the publications in which their gating factors were reported. For studies that did not explicitly report a gating factor, this number was calculated by dividing the formin-mediated elongation rate measured in the absence of profilin by the elongation rate of filaments with free barbed ends. A linear fit (red line) was applied to the data to obtain the equation: y ϭ 9.15x ϩ 1.4. The data point for Cappuccino was omitted from the fit.

Competition limits elongation rates mediated by formins
tracts in Bni1p's FH1 domain does not significantly increase the rate of filament elongation mediated by this formin (15). Some FH1 domain sequences may also possess more polyproline tracts than are strictly required to achieve a particular elongation rate. For example, an FH1-FH2 construct of the mammalian formin mDia1 that encodes five polyproline tracts elongates actin filaments at rates that are similar to those produced by the WT protein, which contains 12 tracts (8).
What determines the number of polyproline tracts encoded by a formin's FH1 domain? This number ranges among formin isoforms from as few as 1 to as many as 14 (18). Because the probability of simultaneous binding of multiple profilin-actin complexes increases with the number of polyproline tracts, competition for delivery should strongly attenuate the elongation rates mediated by formins with large numbers of tracts. However, rates of filament elongation mediated by different formin isoforms have been demonstrated to be directly proportional to the number of polyproline tracts in their FH1 domains (8). This suggests that the kinetic threshold for competitive profilin-actin delivery to the barbed end differs among formin isoforms.
The FH2 domain must adopt an open conformation to enable actin binding, so the likelihood of incorporating a new subunit following a collision with the barbed end is proportional to the formin's gating factor. Consistent with this relationship, computational studies of formin-mediated actin polymerization have revealed that collisions between profilin-actin and the barbed end are more frequently productive when the barbed end is bound by a formin with a large gating factor than a formin with a small gating factor (13,26). The frequency of collisions between profilin-actin complexes and the barbed end is proportional to the number of binding sites for profilinactin in each formin's FH1 domain. Therefore, the number of polyproline tracts encoded by a formin's FH1 domain might also scale with its gating factor.
Analysis of the FH1 domain sequences of 12 formins with published gating factors reveals that, in general, as a formin's gating factor increases, so does the number of polyproline tracts encoded in its FH1 domain (Table 1; Fig. 7B). Every additional polyproline tract is matched by an increase of ϳ0.1 in gating, corresponding to an increase of 10% in the likelihood that the FH2-bound barbed end will be found in an open conformation. Binding affinities of individual polyproline tract sequences likely also play a role in determining the number of polyproline tracts that can be accommodated in a formin's FH1 domain. For example, the mammalian formin mDia1 and the Drosophila formin Cappuccino both possess gating factors of 1 (8,27), but mDia1 has 12 relatively short polyproline tracts, and Cappuccino has five long tracts. Because of these particular combinations of tract numbers and lengths, it is possible that both formins are bound by similar numbers of profilin-actin complexes at any given time, and thus the tracts in each FH1 domain likely compete to the same extent for delivery of profilin-actin to the barbed end.

In suboptimal polymerization conditions, the polyproline tracts in the FH1 domain of Bni1p cooperatively mediate actin polymerization
In reactions where the concentration of profilin-actin is limiting (i.e. at 1 M profilin and below), the rate of filament elongation mediated by the FH1 domain of Bni1p exceeds the sum of the rates mediated by its individual polyproline tracts, indicating that each polyproline tract is more efficient at polymerizing actin in the presence of the other tracts. We also observed cooperative coordination of the polyproline tracts in our double-tract Bni1p constructs, which contained only two polyproline tracts (Fig. 6, D-F).
Recent molecular dynamics simulations have demonstrated that polyproline tracts in FH1 domains adopt PPII conformations with high propensity, whereas the sequences separating the tracts are largely disordered (18). Binding of profilin to a polyproline tract causes conformational extension of the FH1 domain, which expands by ϳ5-8% to sterically accommodate the volume occupied by the profilin (18,28,29). Profilin binding to internal polyproline tracts (e.g. tracts PB and PC in the case of Bni1p) produces a larger expansion than does binding to the most distal tract (e.g. tract PA) (18). As such, profilin binding events "untangle" the otherwise collapsed FH1 domain. This expansion may facilitate access to other polyproline tracts for successive binding events or reduce the conformational space sampled by the FH1 domain, ultimately speeding diffusion-limited delivery of profilin-actin to the barbed end. Thus, the cooperativity we observe may arise from local effects on chain flexibility and diffusion that occur upon profilin binding. The magnitude of the cooperativity likely depends on the specific sequence and intrinsic flexibility of the FH1 domain, because the polyproline tracts in Cdc12p's FH1 domain do not exhibit cooperativity under these conditions (Fig. 5E).
Optimization of Bni1p's PA tract for tighter profilin binding eliminated the cooperativity observed at low profilin concentrations and promoted additive contributions to elongation by the polyproline tracts ( Fig. 4F and Fig. S1). This suggests that conformational expansion of the FH1 domain enhances its polymerization activity only when profilin-polyproline interactions are very weak. Increasing the affinity of a polyproline tract for profilin, which increases the lifetime of its profilin-bound state, might thus negate the effects an increase in tract accessibility would otherwise produce on binding and delivery of profilin-actin.

Mechanistic comparisons with other nucleation-promoting factors with multiple subunit-binding sites
Formins are unique among actin nucleation-promoting factors in their dual abilities to processively regulate the availability of actin filament barbed ends via their FH2 domains and to speed the rate of elongation by delivering subunits directly to the barbed end via multiple profilin-binding sites in their FH1 domains. However, a number of other cytoskeletal proteins promote filament assembly by binding and bringing together multiple actin or tubulin subunits. Ena/Vasp, Spire, Cobl, Junction-mediating and regulatory protein (JMY), and leiomodin all use tandem sequences to bind and promote stable interactions Competition limits elongation rates mediated by formins among multiple actin monomers (30 -34), whereas Stu2/ XMAP215 proteins encode multiple tumor-overexpressed gene (TOG) domains that bind tubulin heterodimers and promote their incorporation at the plus ends of microtubules (35). For some of these proteins, sequence variations among isoforms give rise to binding sites with differing affinities for actin or tubulin. These variations have been demonstrated to produce significant effects on polymer assembly rates (36 -38). Similarly, modification of the number of tandem binding sites either by duplication or by increasing the oligomeric state of the protein has also been shown to modulate polymer elongation rates (38,39).
Proteins in the Ena/Vasp family contain dual binding sites that bind actin monomers and filaments. These tetrameric proteins interact with filament barbed ends via their F-actinbinding site and mediate actin elongation by delivering actin subunits bound to their G-actin-binding (GAB) sites to the barbed end (36,39,40). Elongation rates mediated by Vasp isoforms are positively correlated with the affinity of the GAB sites for actin, and full saturation of all binding sites promotes a maximal elongation rate (36). In contrast, a lower affinity for filaments promotes faster elongation (36), suggesting that, like formins, interactions of Ena/Vasp proteins with the filament itself dictate the rate at which subunits can be delivered continuously from the monomer-binding sites to the barbed end. The constraint on the rate of elongation imposed by the lifetime of the Ena/Vasp-filament association might also limit the number of effective monomer-binding sites, as engineering additional GAB sites into Vasp does not increase the rate of filament elongation to the same extent as does increasing the oligomeric state (39).
In contrast to our observations with formins, the two TOG domains encoded by the S. cerevisiae microtubule-polymerizing protein Stu2p contribute to microtubule elongation in an additive manner (38). Ultimately, the rate of polymerization mediated by Stu2p is governed by a balance between lifetimes of TOG-tubulin association and interactions between a stretch of basic residues in Stu2 with the microtubule lattice (38). The competition between these two sets of interactions is similar to the interplay between FH2 gating and FH1-profilin-binding interactions in regulating actin polymerization by formins.
Sequence variations and modulation of the numbers of actin or tubulin-binding sites encoded by cytoskeletal nucleationpromoting factors influence the rates at which these proteins mediate polymer assembly. Our work with formins suggests that the optimal number of tandem subunit-binding sites encoded by a polymerization-promoting protein depends on its mechanism of interaction with the elongating filament. Together, the rate of availability of the filament end, the affinity of binding sites for actin monomers or tubulin dimers, the flexibility of intrinsically disordered regions between binding sites, the inherent processivity of the polymerization-promoting protein, and the lifetime of interactions with the filament impose practical limitations on the number of subunit-binding sites a protein might encode. Future studies will undoubtedly reveal how many aspects of the formin mechanism are conserved across divergent nucleation-promoting proteins, and the ways in which they differ.

Protein purification
Variant FH1-FH2 constructs of Cdc12p (residues 882-1375) and Bni1p (residues 1227-1776) were cloned into pGEX-4T-3 plasmids (GE Healthcare). In addition to the N-terminal GSH S-transferase (GST) tag that is encoded by pGEX vectors, constructs contained an N-terminal TEV protease recognition sequence and a C-terminal His 6 tag. In variant constructs, individual polyproline tract sequences were replaced with a repetitive Gly-Gly-Gly-Ser sequence of the same length. All proteins were expressed at 16°C overnight in 1-liter cultures of BL21 DE3 RP Codon Plus cells (Agilent Technologies). Unless otherwise specified, all chemicals were purchased from Millipore Sigma.
Cdc12p and Bni1p variant constructs were purified via GST affinity chromatography followed by overnight incubation with 2-5 M TEV protease and further purification by nickel affinity chromatography. Cells expressing Cdc12p constructs were lysed by sonication in 20 mM Tris (pH 7.5), 200 mM NaCl, 5% glycerol, 5 mM dithiothreitol (DTT), whereas cells expressing Bni1p constructs were lysed in 50 mM Tris (pH 8.0), 500 mM NaCl, 1 mM DTT. Following centrifugation at 16,000 rpm for 40 min to remove insoluble material, lysate supernatants were incubated with 2 ml of GSH-agarose resin (Gold Biotechnology) with rotation for 1 h at 4°C. The resin and protein solutions were then transferred to an empty column and washed with 20 ml of lysis buffer, followed by 20 ml of low-salt wash buffer (20 mM Tris (pH 7.5), 100 mM NaCl, 5% glycerol, 1 mM DTT for Cdc12p constructs, and 50 mM Tris (pH 8.0), 100 mM NaCl, 1 mM DTT for Bni1p constructs). Each protein was eluted with 6 ml of 100 mM GSH (pH 8.0) in low-salt wash buffer and incubated with 2-5 M TEV protease overnight at 4°C. Purified proteins were separated from residual TEV protease and GST by nickel-affinity chromatography, concentrated using 30,000 MWCO spin columns (Millipore Sigma), dialyzed into KMEI buffer (50 mM KCl, 1 mM MgCl 2 , 1 mM EGTA, 10 mM imidazole (pH 7.0)) with 1 mM DTT, flash-frozen, and stored at Ϫ80°C. We used ProtParam (ProtParam Tool, RRID:SCR_018087 (41)) to calculate extinction coefficients for all constructs.
S. pombe and S. cerevisiae profilin were expressed from pMW172 vectors in BL21 DE3 pLysS cells and purified as described (15,20). We used extinction coefficients of 19,940 and 19,060 M Ϫ1 cm Ϫ1 at ϭ 280 nm for S. pombe and S. cerevisiae profilin, respectively. Skeletal muscle actin was purified from an acetone powder prepared from frozen chicken breasts (Trader Joe's) via one cycle of polymerization and depolymerization (42). Actin was labeled on cysteine 374 with Oregon Green 488 iodoacetamide (Thermo Fisher Scientific) (43). Monomers were gel-filtered on S-300 resin (GE Healthcare) in G-Buffer (2 mM Tris (pH 8.0), 0.2 mM ATP, 0.5 mM DTT, 0.1 mM CaCl 2 ) and stored at 4°C. We used extinction coefficients of 26,000 M Ϫ1 cm Ϫ1 at ϭ 290 for unlabeled actin and 78,000 M Ϫ1 cm Ϫ1 at ϭ 491 for Oregon Green, and the following relation to calculate the concentration of Oregon Greenlabeled actin: [total actin] ϭ (A 290 Ϫ (A 491 ⅐0.171))/26,000 M Ϫ1 cm Ϫ1 .

Competition limits elongation rates mediated by formins Microscopy and data analysis
Glass slides and coverslips (22 ϫ 50 mm; Thermo Fisher Scientific) were sonicated in 2% Hellmanex III (Millipore Sigma), rinsed extensively with water, and sonicated in water. Chambers were assembled as described previously (15). Chambers were stored at room temperature and used within 1 week.
Chambers were prepared via subsequent incubations with 0.5% Tween 20 in HS-TBS (50 mM Tris (pH 7.5), 600 mM NaCl), ϳ1 M N-ethylmaleimide-inactivated chicken skeletal muscle myosin (43) in HS-TBS, and 100 mg/ml bovine serum albumin (BSA) in HS-TBS. The chamber was washed with HS-TBS following each incubation step and with KMEI prior to the introduction of a polymerization reaction.
Time-lapse images of elongating actin filaments were collected by through-objective TIRF microscopy on an Olympus Ti83 motorized microscope equipped with a CellTIRF system using a 60ϫ 1.49 N.A. objective and a 488-nm laser. Images were taken every 10 s using a C9100-23B ImagEM X2 EMCCD (Hamamatsu) camera and CellSens Dimension software (Olympus).
Time-lapse movies of growing filaments were processed with ImageJ software (National Institutes of Health (44)). For each reaction, changes in length for 10 -15 formin-bound and 10 control (i.e. not formin-bound) filaments were measured, typically over a span of at least 20 frames or 200 s. To determine elongation rates, linear fits were applied to plots of filament length over time using Kaleidagraph software (Synergy Software). We measured the fluorescence intensities of control and formin-bound filaments by performing line scans along filaments and neighboring background regions using ImageJ. To avoid any influence of photobleaching on our fluorescence measurements, we performed the line scans along 5-10-m stretches at filament barbed ends.

Calculation of FH1-mediated elongation rates
In each polymerization reaction, the rate of filament elongation mediated by the formin's FH1 pathway was calculated as described previously (21). Briefly, the fluorescence intensities of formin-bound filaments were normalized to those of control filaments. The fraction of unlabeled actin subunits incorporated via the FH1 pathway (FH1 black ) was calculated using Equation 1, where fluorescence formin-bound is the normalized fluorescence intensity of the formin-bound filaments in the reaction. where green PA is the fraction of profilin-bound actin that is labeled, and black PA is the fraction of profilin-bound actin that is unlabeled. These values were calculated using published affinities of S. cerevisiae and S. pombe profilin for unlabeled actin and actin that is labeled at cysteine 374 (2.9 and 29 M for S. cerevisiae profilin and 0.2 and 2 M for S. pombe profilin (22,25,45)) and Equation 3, The total fraction of actin subunits incorporated via the FH1 pathway was then calculated by summing FH1 black and FH1 green , and the polymerization rate mediated through the FH1 pathway was obtained by multiplying this sum by the overall elongation rate mediated by the formin in each reaction.