Molecular mechanisms of inorganic-phosphate release from the core and barbed end of actin filaments

The release of inorganic phosphate (Pi) from actin filaments constitutes a key step in their regulated turnover, which is fundamental to many cellular functions. The mechanisms underlying Pi release from the core and barbed end of actin filaments remain unclear. Here, using human and bovine actin isoforms, we combine cryo-EM with molecular-dynamics simulations and in vitro reconstitution to demonstrate how actin releases Pi through a ‘molecular backdoor’. While constantly open at the barbed end, the backdoor is predominantly closed in filament-core subunits and opens only transiently through concerted amino acid rearrangements. This explains why Pi escapes rapidly from the filament end but slowly from internal subunits. In a nemaline-myopathy-associated actin variant, the backdoor is predominantly open in filament-core subunits, resulting in accelerated Pi release and filaments with drastically shortened ADP-Pi caps. Our results provide the molecular basis for Pi release from actin and exemplify how a disease-linked mutation distorts the nucleotide-state distribution and atomic structure of the filament.


Introduction
The dynamic turnover of actin filaments (F-actin) controls the shape and movement of eukaryotic cells and is driven by changes in the molecular identity of the adenine-nucleotide bound to actin [1][2][3] . While monomeric actin (G-actin) displays only very weak hydrolysis activity towards ATP 4 , actin polymerization results in the flattening of the protein and a rearrangement of amino acids and water molecules near the nucleotide-binding site [5][6][7][8] . Accordingly, the ATPase activity of F-actin increases about 42,000 fold and hydrolysis takes place within seconds of filament formation (rate 0.3 s -1 ) (ref. 9 ). Because the release of the cleaved inorganic phosphate (Pi) occurs at a much slower rate than ATP hydrolysis 10 , the cap of a growing filament is generally rich in ADP-Pi-bound subunits 11 , whereas 'aged' F-actin primarily adopts the ADP-bound state. In vivo, these changes in the nucleotide state are sensed by a variety of actin-binding proteins (ABPs) [12][13][14] . For instance, ADF/cofilin family proteins efficiently bind and sever the ADP-bound state of the filament, but bind only weakly to ADP-Pi-F-actin [15][16][17] .
Thus, the release of Pi from the F-actin interior represents a crucial step in the control of filament turnover.
For a long time, it was debated whether or not the Pi release rate of a given F-actin subunit depends on the nucleotide state of its neighboring subunits 10,18,19 . Finally, singlefilament experiments provided experimental evidence that Pi release from the F-actin core is a stochastic process; each ADP-Pi-subunit in the filament releases its bound phosphate molecule with equal probability at a rate of 0.002 to 0.007 s -1 , which corresponds to a half-time t of several minutes 10,[20][21][22][23][24] . Interestingly, under depolymerization conditions, actin subunits at the barbed end release Pi more than 300-fold faster (~2 s -1 ) than those that reside in the filament core, even though the equilibrium constants of Pi binding to barbed end and filament core are essentially the same 20,25 . These observations therefore imply that Pi binding is also much faster at the barbed end of F-actin 25 .
At the atomic level, Pi release from actin has been investigated by pioneering molecular dynamics (MD) simulation studies in the late 1990s (refs. 26,27 ), which suggested that the disruption of the ionic bond between Pi and the nucleotide-associated divalent cation (Mg 2+ or Ca 2+ ) could represent the rate limiting step for Pi release, because actin rearrangements were not required for Pi to exit. These studies furthermore predicted that Pi escapes through an open 'backdoor' in the actin molecule, with residues arginine-177 (R177) and methylated histidine-73 (H73) as potential mediators of Pi release. However, a central limitation of the simulations was that they were performed on a G-actin structure 28 , because no high-resolution F-actin structures were available at the time. In 2015, the first sub-4 Å cryo-EM structures of F-actin revealed that within the flattened conformation of the filament, Pi cannot freely diffuse out of the F-actin interior 29 ; R177 participates in a hydrogen bonding network with the side chain of N111 and the backbones of H73 and G74, defining a closed backdoor conformation in F-actin.
Accordingly, recently published cryo-EM structures of F-actin bound to ADP-Pi and ADP at resolutions beyond 2.5 Å showed a closed backdoor in both the pre-and post-release states 8,30 .
These data therefore suggest that Pi release from the filament interior occurs through a transient, high-energy state of F-actin that requires substantial rearrangements, but is difficult to capture with static imaging techniques such as cryo-EM. In a more recently proposed model for Pi-release, a rotameric switch of residue S14 from a hydrogen-bond interaction with the backbone amide of G74 to the one of G158 would enable Pi to approach the R177-N111 backdoor and egress 31 . However, in the absence of experimental validation, the molecular principles that underlie Pi release from F-actin remain elusive, and further evidence is required to determine whether the phosphate molecule exits the filament interior through the postulated backdoor or through potential other egress routes. Additionally, the structural basis for the orders-of-magnitude faster Pi release from actin subunits at the barbed end compared to those that reside in the filament core is still unknown.
Here, we uncover that Pi release from subunits at the filament core and at the barbed end occurs through a common backdoor pathway. For internal subunits, the backdoor is predominantly closed and its transient opening is kinetically limited, whereas at the barbed end, the backdoor is open and Pi is capable of escaping from the ultimate subunit without large protein rearrangements. Strikingly, we also characterize an actin disease variant (N111S) that adopts an open backdoor arrangement in internal F-actin subunits and, hence, releases Pi without considerable delay. Our results provide a detailed molecular description of Pi release from F-actin and highlight a general approach of studying the mechanism of disease-linked actin variants.

Structure of the F-actin barbed end reveals an open backdoor in the ultimate subunit
To elucidate how the conformation of the F-actin barbed end allows for much faster Pi release kinetics during filament depolymerization, we first aimed to obtain structural information on the barbed end by single-particle cryo-EM. Through a novel experimental approach, in which we polymerized free G-actin (native bovine β/γ-actin) in the presence of G-actin:DNase I complex, the FH2 domain of formin mDia1 (mDia1FH2) and the filament-stabilizing toxin phalloidin (see Methods for details), we reproducibly formed short (~50 -150 nm length) filaments and obtained a cryo-EM structure of the barbed-end at 3.6-Å resolution (Fig. 1a, Video 1). Importantly, we did not find any evidence for an ABP remaining bound to the barbed end, defining our structure as the undecorated barbed end of F-actin.
The structure reveals the hallmark actin filament architecture of a double-stranded helix with a right-handed twist (Fig. 1b, d). All actin subunits in our structure adopt the aged ADPnucleotide state ( Supplementary Fig. 2a, b). The arrangements of F-actin subunits that make all available inter-subunit contacts within the filament (A2 and above), as well as that of the penultimate subunit A1, are essentially the same as in previously solved F-actin structures ( Supplementary Fig. 3, Ca rmsd <0.5 Å with pdb 8a2t) 8 . Accordingly, in subunits A1 and above, the predicted R177-N111 backdoor is closed and the Pi-binding site is shielded from the filament exterior (Fig. 1d, Supplementary Fig. 3e). Although the overall arrangement of the ultimate (A0) subunit is also similar (Ca rmsd of 0.9 Å between subunits A0 and A2) and it remains in a flattened conformation ( Supplementary Fig. 3c), we observed several differences when compared to the internal subunit A2, including small rearrangements of the W-loop (residues 165 -172), the hydrophobic plug region (residues 264 -273) and a disordered Factin C-terminus (residues 363 -375) (Fig. 1c). However, the most striking rearrangement is the downward displacement of the Pro-rich loop (residues 107 -112) by ~3 Å (Fig. 1c), which -unlike in internal actin subunits -it is not stabilized by subdomain 4 (SD4) of an adjacent subunit ( Supplementary Fig. 2d). Hence, N111 loses its hydrogen bonds with G74 of the sensor loop (residues 70 -77) and SD3-residue R177, and instead interacts within its own local loop with E107 (Fig. 1d, Supplementary Fig. 3f). Interestingly, this E107-N111 interaction is commonly observed in G-actin structures ( Supplementary Fig. 3f). Strikingly, residue H161, which flips rotameric position during the G-to F-actin transition and is important for ATP hydrolysis in F-actin 7,8 , also adopts its G-actin-like rotameric position in the A0 subunit and points towards R177. As a result, R177 can no longer interact with the sensor loop (Fig. 1d,   Supplementary Fig. 3f). When taken together, the hydrogen-bonding network formed by R177, N111, H73 and G74 is fully abolished, which opens a ~5 Å diameter hole in the structure that connects the internal nucleotide-binding site to the filament exterior (Fig. 1e, Supplementary Video 1). This defines the predicted 27 Pi release backdoor as open. Thus, our structure provides evidence that, under depolymerization conditions, Pi can dissociate from the nucleotidebinding site at the barbed end without large protein rearrangements, thereby revealing the structural basis for the orders-of-magnitude faster Pi release rates from the ultimate barbed end subunit compared to those within the filament core.

Two plausible Pi egress routes from the F-actin core
The barbed end structure revealed a Pi release pathway similar to the path predicted in the MD simulation study by Wriggers and Schulten from 1999 (ref. 27 ). Accordingly, when we performed MD simulations on Pi release from barbed end subunit A0, we observed that virtually all Pi escape events occurred through the open R177-N111 backdoor ( Supplementary Fig. 4a,   b). However, we reasoned that for actin subunits in the filament core, which make all available inter-subunit contacts and release Pi at much slower rates, other Pi exit routes might exist. We therefore set out to develop an MD protocol to investigate the Pi release mechanism from the F-actin filament core, using our recently reported ~2.2-Å structure of F-actin in the Mg 2+ -ADP-Pi state 8 as high quality starting model (Fig. 2a). Because Pi release from the F-actin core is a slow, stochastic event with a half-time t >100 seconds, it is unattainable to study the Pi escape path using conventional MD simulations. Instead, we developed an enhanced-sampling simulation protocol based on meta-dynamics, which applies a history-dependent repulsive potential on the Pi Cartesian coordinates to progressively drive it out of the nucleotide-binding site 32 , without favoring any egress route a priori (see Methods for details).
Using this approach, we collected dozens of Pi release events from the F-actin core and identified sterically accessible egress pathways (Fig. 2b). We then analyzed the predicted pathways for physical plausibility and first dismissed all pathways that entailed unrealistic distortions of F-actin or the nucleotide ( Supplementary Fig. 4c-e). Secondly, we made the assumption that Pi exits the F-actin interior near the binding sites of phalloidin and jasplakinolide, as both toxins strongly inhibit Pi release [33][34][35] . This analysis resulted in two remaining egress pathways that are physically plausible. In the first one, a side-chain movement of Q137 allows Pi to move into a hydrophilic pocket between E107 and H161, where it also interacts with the Pro-rich loop residues. From there, Pi is observed to escape either by disrupting the R177-N111 hydrogen bond (leading to an open backdoor, similar to the conformation adopted by the barbed end) (Fig. 2c, Supplementary Video 2), by leaving close to residues N115 and R116, or by exiting near residues T120 and V370. Of note, phalloidin and jasplakinolide stabilize the R177-N111 interaction ( Supplementary Fig. 2c), but would not interfere with Pi egress near N115-R116 or T120-V370, suggesting that the exit path that requires the disruption of the R177-N111 interaction is the most probable. In the second plausible pathway, Pi first breaks the hydrogen bond between S14 and G74 to enter a pocket between H73 and R183. Then, Pi escapes to the intra-filament space upon breaking the strong electrostatic interaction with R183 (Fig. 2d). Interestingly, the disruption of the S14-G74 hydrogen bond was previously proposed to play a role in Pi release, albeit via a different mechanism 31 . Furthermore, phalloidin and jasplakinolide would prevent the opening of the H73-R183 pocket. Thus, in addition to the predicted route, there exists another physically realistic egress pathway for Pi.

Actin filaments harboring the N111S mutation release Pi rapidly
To experimentally probe the two possible Pi release pathways from the F-actin core, we mutated key residues in β-actin that pose a barrier for Pi release in each pathway. For the first pathway, we introduced the N111S mutation to potentially disrupt the hydrogen-bonding network of the R177-N111 backdoor. For the second pathway, we aimed to destabilize the R183-mediated backdoor by R183W and R183G mutations. Importantly, all actin mutants studied here are associated with human diseases; the R183W mutation was identified in β-actin of patients suffering from deafness, juvenile-onset dystonia and development malfunctions 36,37 , whereas the R183G and N111S mutations have been found in a-actin of nemaline myopathy patients 38,39 , highlighting the relevance of these actin variants.
We developed a fluorescence-based assay to synchronously monitor seeded actin polymerization using pyrene fluorescence and subsequent Pi release via a fluorescent phosphate sensor in the same experiment (Fig. 3a). This allowed us to determine the respective reaction rates by fitting the data to a kinetic model (see Methods for details). Because we performed the experiments at actin concentrations (10 µM) that allow for rapid filament growth and seeded the reaction with spectrin-actin seeds to circumvent slow nucleation, we effectively monitored Pi release from internal F-actin subunits and not from the barbed end. The assay revealed that wild type β-actin released Pi at a slow rate k-Pi of 0.0065 s -1 (half time t ~107 s) 8 ( Fig. 3b), which falls within the range of values previously reported for rabbit skeletal aactin 10,20,24 , indicating that slow Pi release after polymerization and ATP-hydrolysis is a feature conserved between mammalian actin isoforms. R183G-and R183W-actin released Pi at a slightly increased rate of, respectively, 0.0117 s -1 and 0.0190 s -1 , corresponding to a 1.8-and 2.9-fold increase compared to wild-type β-actin (Fig. 3b). Strikingly, N111S-actin exhibited ultrafast Pi release kinetics without appreciable delay after polymerization. In fact, the reaction time-courses of Pi release slightly outpaced the observed polymerization kinetics (Fig. 3b) making it impossible to determine an exact Pi release rate for N111S-actin. However, when estimated conservatively (see Methods, Supplementary Fig. 5c, d), N111S-actin releases Pi at a rate ≥0.1 s -1 , which is at least 15-fold faster than wild-type actin. Thus, the R183 mutants release Pi somewhat faster but still display the characteristic delay between polymerization/ATP-hydrolysis and Pi release, whereas in contrast, N111S-actin appears to release Pi without appreciable delay.

Structural basis for the ultrafast Pi-release kinetics of N111S-actin
To structurally understand the differences in Pi release rates between the R183W and N111S mutants, we determined the filament-core structures of these variants in the Mg 2+ -ADP-bound state at ~2.3-Å by cryo-EM ( Fig. 4a, 8a-c). Globally, we observed no major differences between the two β-actin mutants and Mg 2+ -ADP-bound a-actin filaments (pdb 8a2t, rmsd <0.7 Å) (Supplementary Fig. 8d) but, importantly, we identified small but impactful rearrangements.
We first examined the atomic arrangement near the mutated residues. In wild-type F-actin structures, the R183 sidechain interacts with D157 and the carboxyl moieties of S14 and I71 ( Fig. 4c). As expected for R183W-F-actin, these interactions are abolished and the W183 sidechain points away from the mentioned residues (Fig. 4c). Nevertheless, the S14-G74 hydrogen bond remains intact and we did not observe an open cavity near W183 through which Pi could escape (Fig. 4c); the R177-N111 backdoor is also intact in the R183W-F-actin structure (Fig. 4d, e).
In N111S-F-actin, the introduced mutation induces a more drastic conformational change; residue S111 is too short to interact with R177 and G74. Instead, S111 hydrogen bonds with E107, the backbone of A108 and a water molecule within its local environment in the Pro-rich 9 loop (Fig. 4d, Supplementary Fig. 8c). Additionally, the density for the sidechain of R177 is fragmented ( Supplementary Fig. 8c), indicating that the residue is more flexible than in wildtype F-actin structures. As a result, the interaction between the sensor loop and Pro-rich loop is disrupted and a ~4-Å diameter hole is observed, yielding an open backdoor (Fig. 4d, e).
Hence, the conformation of F-actin subunits harboring the N111S mutation is reminiscent of the arrangement of the ultimate subunit of the barbed end structure (Fig. 1d). Further consistent with the barbed end structure, we identified that H161 adopts a mixture of rotameric states and that it partially adopts a G-actin-like conformation (Fig. 4d, Supplementary Fig. 8c). This observation suggests that repositioning of the H161 sidechain represents a key feature of backdoor opening. Conversely, the S14-G74 interaction is not affected in N111S-F-actin (  Supplementary Fig. 8e). Although residue R183 does not directly interact with ADP in wild-type F-actin, it resides in close proximity to the nucleotide and, importantly, it is positioned in a negatively-charged cluster of acidic residues ( Supplementary Fig. 9). Hence, R183W-F-actin harbors a more negatively charged nucleotide-binding site ( Supplementary   Fig. 9), which may explain why the positively charged Mg 2+ repositions in the mutant structure to compensate the charge imbalance. Thus, R183W-F-actin displays an altered nucleotidebinding site but does not reveal any conformational changes that would allow for Pi egress, indicating that the R183-backdoor does not encompass the dominant Pi escape path in wildtype actin. Although we cannot exclude that this release path is marginally sampled, we propose that, alternatively, Pi still mainly exits through the R177-N111 backdoor in the R183 mutants. In that scenario, the more negatively charged nucleotide-binding pocket may explain why the negatively charged Pi is released slightly faster from R183W-and R183G-actin compared to wild-type actin (Fig. 3b, c).

N111S-actin filaments display dramatically shortened ADP-Pi caps
Next, we hypothesized that N111S-actin, which releases Pi rapidly in bulk assays and adopts an open backdoor, should also display strong differences in nucleotide state distribution at the single filament level compared to wild-type actin. Specifically, we reasoned that filaments harboring the N111S mutation should form a drastically shortened ADP-Pi cap, which we tested in microfluidic flow-out assays using total internal reflection fluorescence (TIRF) microscopy ( Fig. 5a, Supplementary Video 4). Filaments were elongated from surfaceimmobilized spectrin actin seeds using either wild-type-or N111S-actin and then rapidly switched to depolymerization with buffer lacking soluble actin (see Methods). For wild-type β-actin, the speed of filament depolymerization after flow-out gradually increased over a few minutes to converge to a maximal rate (Fig. 5b, c). Since ADP-Pi-bound actin depolymerizes at slower rates than ADP-bound actin, this change is caused by the filament depolymerizing region slowly maturing from an ADP-Pi-rich to an ADP-rich composition through Pi release.
The measured depolymerization velocities are well described by a kinetic model (Fig. 5d, see Methods) with parameters similar to those previously measured from single-filament assays on skeletal a-actin 20 , as well as from our own bulk measurements (Fig. 3b, Fig. 5d). Strikingly, we observed that filaments grown from N111S actin depolymerized at a high velocity (vdepol,ADP = 14.80 s -1 ) (Fig. 5b, c). More importantly, we found no appreciable change in the depolymerization velocity after buffer flow-out ( Fig. 5c), indicating that the ADP-Pi to ADPactin transition is very fast and not captured within the resolution of our experiment. This allowed us to estimate a lower bound for the rate of phosphate release from the filament interior k-Pi ≥ 0.154 s -1 for N111S actin (Fig. 5d, Supplementary Fig. 5e). Hence, our data reveal in high mechanistic detail that the rapid rate of Pi release indeed results in drastically shortened ADP-Pi caps in N111S-actin filaments.
To also investigate the effect of the N111S mutation in vivo, we compared the growth rates of yeast strains expressing either wild type or N111S variants of S. cerevisiae actin. Under normal conditions, we observed no major differences in growth phenotype between the two strains ( Fig. 5e). However, when exposed to the toxin Latrunculin A, which sequesters G-actin and accelerates F-actin depolymerization 40 , the yeast strain expressing N111S-actin displayed a dramatically reduced growth rate compared to that of the strain expressing wild-type-actin ( Fig. 5e). This high sensitivity to Latrunculin A-induced stress suggests that N111S-actin filaments are more labile and prone to depolymerization. Thus, the phenotype observed for S. cerevisiae N111S-actin in vivo is in line with our in vitro experiments on human-β N111Sactin, where we observed faster Pi release and filament depolymerization rates compared to wild-type actin.
Taken together, our experiments provide strong evidence that the first Pi egress pathway identified by enhanced sampling MD, encompassing the R177-N111 backdoor, is the dominant route for the exit of Pi from the F-actin interior. Hence, Pi is released from the core and barbed end of F-actin through similar exit routes, although F-actin subunits in the filament core require additional conformational rearrangements to transiently open the R177-N111 backdoor.

Visualization of the transient state that allows for Pi-release from the F-actin core
Finally, we sought to understand how Pi is released through the R177-N111 backdoor from the wild-type F-actin core. Our enhanced-sampling MD suggested Pi escape pathways through the backdoor (Fig. 2c), but this protocol is aggressive and may not reflect a realistic order of molecular motion. Therefore, we first ran unbiased MD simulations to investigate the backdoor conformation in F-actin. The simulations revealed the disruption and reformation of the R177- inter-subunit contacts within the filament remained intact. We then evaluated the Pi release efficiency of structures extracted along these key timepoints in the SMD trajectories using our previously introduced metadynamics-based protocol. While we did not observe a major effect of the charge of meHis73 on backdoor opening, our simulations revealed a high probability (pBD) (Fig. 6c, Supplementary Fig. 12a, b, 13, see Methods) for Pi to escape through the backdoor when the R177-N111 interaction was disrupted and the H161 sidechain was flipped, suggesting that both events are required to stabilize an open backdoor conformation. Thus, although only the backbone movement was steered in our SMD setup, the simulations elucidate the sidechain rearrangements that lead to the transient opening of the backdoor in the F-actin core (Fig. 6). allowing F-actin to adopt its low-energy state with a closed backdoor. In the N111S-actin mutant, which is linked to nemaline myopathy, the backdoor is predominantly open in all subunits because the introduced S111 sidechain is too short to maintain the interactions that keep the door closed. Hence, N111S-F-actin releases Pi rapidly upon polymerization, thereby drastically reducing the fraction of ADP-Pi-bound subunits in the filament. Thus, our data provide conclusive evidence that the Pi release rate from F-actin is controlled by steric hindrance through the backdoor rather than by the disruption of the ionic bond between Pi and Mg 2+ at the nucleotide-binding site as previously proposed 27 .

Discussion
The open backdoor arrangement in the ultimate subunit at the barbed end explains how remaining Pi can be rapidly released during filament depolymerization. In contrast, under filament growth conditions, the barbed end growth velocity (~10 -500 monomers s -1 , dependent on the actin concentration) 41 is much faster than the ATP hydrolysis rate of F-actin (0.3 s -1 ) 9 , indicating that barbed end subunits effectively only adopt the ATP state before becoming internal subunits. During the G-to F-actin transition, the sidechain of residue H161 13 flips towards ATP, which triggers the relocation of water molecules near the nucleotide and, as a result, creates a favorable environment for ATP-hydrolysis 7,8 . In contrast, in our barbed end structure, H161 adopts its G-actin like rotameric position and points away from the nucleotide in the ultimate subunit, which suggests that, regardless of the filament growth velocity, the last subunit only becomes ATP-hydrolysis competent when another actin subunit is added to the filament. This provides implications that the complete G-to F-form transition of a given actin subunit should be considered as a multi-step process, which not only encompasses the initial incorporation of that subunit into the filament, but also requires the subsequent binding of the next actin subunit. Formal proof for such a mechanism will require future structural investigations of the barbed end of F-actin in the ATP state.
Can our results explain how the N111S mutation leads to nemaline myopathy, a disease affecting skeletal muscle a-actin? Although actin filaments in striated muscle are expected to undergo less turnover than cytoplasmic actin isoforms, it is well established that actin-severing proteins such as cofilins are expressed in muscle sarcomeres to control actin (thin) filament length during sarcomerogenesis and actin turnover [42][43][44] . Since cofilins preferably sever ADPover ADP-Pi-bound F-actin, we propose that the ultrafast Pi-release kinetics of N111S-actin may contribute to the pathophysiology of the disease in these patients. Moreover, it will be interesting to study the effects of the N111S mutation in actin in non-muscle tissue. Because N111S actin does not majorly populate the ADP-Pi state, it could represent a unique tool for investigating the role of this metastable actin state both in vivo and in vitro. In general, we envision that our approach of studying actin mutants R183W and N111S, where we combined biochemical experiments with high-resolution cryo-EM, will also be instrumental in elucidating the molecular mechanisms of other disease-associated actin mutants. Specifically, visualizing the mutations' impact on the F-actin atomic structure will allow for the formulation of new hypotheses on how the mutations affect cellular processes and how this is linked to disease. Therefore, this approach may ultimately contribute to the development of new therapeutic strategies for the treatment of human diseases that are characterized by mutations in actin genes.

DNA constructs and yeast strains
Throughout the manuscript, we used human β-actin amino-acid numbering that is consistent with the numbering in the corresponding UniProt entry (P60709, ACTB_HUMAN), with the initiator methionine numbered as residue 1, even though this methionine is cleaved off during actin maturation. Hence, the used amino-acid numbers for β-actin are in register with the sequences of mature human and rabbit skeletal a-actin, as well as S. cerevisiae actin, facilitating a direct comparison between all actin isoforms used in this study.
The plasmid for the expression of recombinant, human β-actin (p2336 pFL_ACTB_C272A) was described previously 45 . All mutations were introduced via QuikChange PCR, using p2336 as template. All β-actin constructs contain the C272A substitution (including the protein referred to as wild type), as C272 is prone to oxidation in aqueous solutions 46 . The equivalent residue in human skeletal a-actin is also alanine. The FH2 domain of M. musculus mDia1 (mDia1FH2) (amino acids 750-1163) was cloned into an pETMSumoH10 expression vector by Gibson assembly.
S. cerevisiae strains were grown in minimal medium containing yeast nitrogen base without amino acids (Difco) containing glucose and supplemented with tryptophane, adenine, histidine, and/or uracil if required. S. cerevisiae strains were transformed using the lithiumacetate method 47 . Yeast actin mutagenesis was performed as described previously 48 . Yeast viability in the presence or absence of Latrunculin A was analyzed by drop test assays: 5-fold serial dilutions of cell suspensions were prepared from overnight agar cultures by normalizing OD600 measurements, then plated onto agar plates and incubated at 30°C for 2 days.

Protein expression and purification
Native bovine, cytoplasmic β-actin and γ-actin mixture was purified from bovine thymus tissue as described previously 41,49 . Bovine β and γ-actin both display 100% amino-acid sequence identity to their corresponding human orthologs.
Human cytoplasmic b-actin variants were recombinantly expressed as fusion proteins, with thymosin β4 and a deca-His-tag fused to the actin C-terminus 45  Spectrin-actin seeds were purified and biotinylated as described previously 51 .

Synchronous measurement of actin polymerization and Pi release in bulk assays
On the day of the assay, aliquots of all purified b-actin variants (frozen as G-actin) were thawed and centrifuged at 100,000g for 20 -30 minutes to remove aggregates. To ensure that all variants were in exactly the same buffer, we exchanged the buffer to G-buffer-v2 (5 mM Tris prepared. We confirmed that the presence of trace amounts (1.5%) of pyrene-labeled, wildtype a-actin, which releases Pi with slow kinetics, did not significantly contribute to the overall readout by the phosphate sensor, which was dominated by Pi release from the actin mutant present in vast excess (98.5%) (Supplementary Fig. 5a). 36 µl of G-actin solution was then mixed with 4 µl 10xME (5 mM EGTA pH 7.5, 1 mM MgCl2) and incubated at room with A monomeric ATP-actin, B filamentous ADP-Pi-actin, C filamentous ADP-actin. The model contains three kinetic parameters, two of which were fixed. The first-order rate of polymerization (kpoly), that formally combines the processes of polymerization and ATP hydrolysis was fixed to the experimentally measured polymerization rate for each actin variant (see above). The second-order association rate constant for binding of inorganic phosphate (k+Pi) was fixed to 0.000002 µM -1 s -1 as measured previously for wild-type a-actin and assumed to be the same for all actin variants 11,25 . This assumption likely does not hold, because the chosen mutations can be anticipated to similarly accelerate both release and binding of Pi.
However, we determined that k+Pi can be varied by more than 1000-fold without significantly affecting the obtained first-order rate of phosphate release (k-Pi). More importantly, we can exclude that rebinding of Pi contributes significantly under our experimental conditions: Pi is i) generated only in minor amounts (10 µM) during the course of the assay and ii) potently sequestered by the phosphate sensor that is present in molar excess (30 µM) and binds Pi with 10000-fold higher affinity (KD = 0.1 µM) 52 compared to actin (KD = 1.5 mM) 11,25 .
For the N111S mutant, we could not determine the exact rate constant of Pi release in this manner, because the average observed rate of Pi release slightly exceeded the average observed polymerization rate (Fig. 3b). This should formally not be possible because the latter has to precede the former and the reason for this inversion remains unknown. To nonetheless obtain a conservative estimate for the increase in the Pi release rate in this case, we carried out kinetic simulations in KinTek Explorer to systematically explore the dependence of the observed Pi release reaction kinetics on the rate enhancement of Pi release ( Supplementary Fig.   5c, d). This showed that a rate enhancement of Pi release by more than 15-fold is required, for the observed Pi release rate to fall within the error margin of the observed polymerization rate.
Hence, we consider 0.1 s -1 the lower bound for the rate of Pi release for the N111S mutant.

Preparation of functionalized glass slides
Functionalized glass slides coated with 5% Biotin-PEG and 95% Hydroxy-PEG were prepared as described 53 . Briefly, high-precision glass coverslips (22 x 60 mm, 1.5H) were asymmetrically cut at one corner using a diamond pen to distinguish the functionalized surface from the non-functionalized one. Glass slides were cleaned by incubating in 3 M NaOH solution for 15 min, rinsed in water and then incubated in freshly prepared Piranha solution (3:2 mixture of 95-97% Sulfuric acid and 30% Hydrogen peroxide) for 30 min. Slides were rinsed with water to remove residual acid and then air dried with nitrogen gas. Dried glass slides were sandwiched with 3 drops of GOPTS (3-Glycidyloxypropyltrimethoxysilane) and then stored in closed Petri dishes, which were further incubated in an oven at 75 °C for 30 min.
Sandwiched glass slides were rinsed in acetone and separated with a pair of tweezers.
Following separation, the glass slides were rinsed again in fresh acetone. Separated glass slides were air dried with nitrogen gas and placed in pre-warmed Petri dishes with their functionalized surface facing up. The functionalized surfaces were sandwiched with 75 µL of a 150 mg/ml mixture of 95% Hydroxy-amino-PEG (ɑ-Hydroxy-ω-amino PEG-3000) and 5% Biotinylamino-PEG (ɑ-Biotinyl-ω-amino PEG-3000) dissolved in acetone. Sandwiched glass surfaces were incubated in closed Petri dishes in an oven at 75 °C for 4 hrs. Following incubation, the glass slides were separated with a pair of tweezers, rinsed multiple times in water and air dried with nitrogen gas.

Preparation of microfluidic devices
Microfluidic devices were prepared from PDMS (polydimethylsiloxane) casted onto a silicon mold designed to incorporate up to 4 inlets and 1 outlet. A mixture of PDMS and its curing agent (10:1 mass ratio, SYLGARD™ 184 Silicone Elastomer Kit) was thoroughly mixed and poured onto the silicon mold. The PDMS cast was degassed in a desiccator under vacuum for 3 hrs to remove bubbles from the cast. After removal of bubbles, the cast was incubated in an oven at 75 °C for another 4 hrs to complete the curing process. On completion of the curing process, the PDMS microfluidic devices were cut out from the cast, rinsed with isopropanol and air dried with nitrogen gas.

Microfluidic experiments and TIRF microscopy of single filaments
The surface of a flow channel was prepared by first passivating the surface to avoid unspecific interactions, then coating the biotinylated surface with streptavidin and finally coating the surface with biotinylated spectrin actin seeds. Image acquisition was carried out using a TIRF microscope with a 60x objective and a 1.5x zoom lens under TIRF conditions. Time-lapse images were acquired every 5 s with 2% laser power, 2 s exposure time, 150 gain and emitted light was filtered through an emission filter of 525 nm with 50 nm bandpass. All images were acquired at a bit-depth of 16 bits.

Filament tracking and data analysis
Timelapse TIRF microscopy images of actin filaments were first denoised using the Non-Local We estimated lower bounds for the Pi release rate of the N111S actin mutant by assuming the ADP-Pi-depol to either be equal or twice that of wt actin. The latter assumption was motivated by the observation that the '()*+,-./ rate of N111S mutant was about 2.2 times that of wt actin (Fig. 3d, Supplementary Fig. 5e).

Cryo-EM grid preparation
All cryo-EM grids were prepared through a common protocol; 2.8 µl of F-actin sample was applied to a glow-discharged R2/1 Cu 300 mesh holey-carbon grid (Quantifoil). Excess solution was blotted away and the grids were plunge frozen in liquid ethane or a liquid ethane/propane mixture using a Vitrobot Mark IV (Thermo Fisher Scientific, operated at 13 °C). The short β/γ-actin filaments, which allowed for the structure determination of the barbed end, were blotted with a blotting force of 0 for 3 seconds. The long filaments of recombinant β-actin with the N111S or R183W mutation were blotted with a blotting force of -20 for 8 seconds.

Cryo-EM grid screening and data collection
The barbed-end dataset was collected on a 200 kV Talos Arctica cryo-microscope (Thermo particles were non-uniformly refined, with the per-particle defocus estimation option switched on, to a reconstruction of 3.51-Å resolution. To further improve the density of subunits at the barbed end, we created a soft mask around the first four actin subunits (from the end) and ran a local refinement in CryoSPARC. The resulting cryo-EM density map was refined to a slightly lower resolution (3.59 Å) but showed an improved local resolution for the penultimate and ultimate subunits at the barbed end.
For the N111S and R183W β-actin datasets, filament segments were picked using the filament mode of SPHIRE-crYOLO 62 , with a box distance of 40 pixels between segments (corresponding to 27.8 Å) and a minimum number of six boxes per filament. This yielded 2,001,281 and 1,569,882 filament segments (from now on referred to as particles) for the N111S and R183W datasets, respectively, which were extracted (384x384 box) and further processed in helical SPHIREv1.4 63 . The used processing strategy was essentially the same as reported in our previous work 8 . Briefly, the extracted particles were first 2D classified using ISAC2 (refs 64,65 ) in helical mode and all non-protein picks were discarded. The particles were then refined using meridien alpha, which imposes helical restraints to limit particle shifts to the helical rise (set to 27.5 Å) to prevent particle duplication, but does not apply helical symmetry 55 . For both datasets, the first refinement was performed without mask using EMD-15109 as initial reference, low-pass filtered to 25 Å. From the obtained reconstruction, a soft mask was created that stretched 85% of the filament length within the box (326 pixels in the Z-direction). Masked meridien alpha refinements then yielded density maps at resolutions of 2.9 Å (N111S dataset) and 3.0 Å (R183W dataset). Subsequently, the particles of both datasets were converted to be readable by RELION through sp_sphire2relion.py. In RELION, the particles were subjected to Bayesian polishing (2x) and CTF refinement, followed by a 3D classification without image alignment into 8 classes. We selected the particles that classified

Model building, refinement and analysis
The barbed-end β/γ-actin structure was modeled as β-actin. Of the 4 amino-acid substitutions between β and γ-actin, three represent N-terminal amino-acids (D2, D3 and D4 in β-actin, E2, E3 and E4 in γ-actin) that are not visible in the density map due to flexibility. Accordingly, the only other residue (V10 in β-actin, I10 in γ-actin) that is different between both isoforms was modeled as valine. To construct an initial model for human b-actin, chain C of the 2.24-Å cryo-EM structure of rabbit skeletal a-actin in the Mg 2+ -ADP state (pdb 8A2T -94% sequence identity to human b-actin, all water molecules removed) was rigid-body fitted in the third actinsubunit from the barbed end (A2) in the cryo-EM density map using UCSF ChimeraX 66 . Rabbit skeletal a-actin residues were substituted with the corresponding residues of human b-actin in

Preparation of structural models for MD simulations
All-atom models of the core and barbed end of F-actin were prepared from respectively pdb

Clustering and analysis of Pi egress paths
To get a broad picture of the main Pi egress paths sampled by metadynamics, we used hierarchical clustering in path space. For this purpose, Pi was considered to have escaped when the distance of the P atom from its initial position in the frame of the actin filament exceeded a cut-off value of 1.4 nm, and frames posterior to escape were discarded for the rest of the proportion using class balancing to preserve the proportion of true positives. The classifier was trained on the training set, and the confusion matrix was evaluated on the test set. scikit-learn was used for these tasks.

Steered MD simulations
To simulate the opening of the R177-N111 backdoor from the filament interior, we used steered molecular dynamics to drive the central actin core subunit towards the barbed-end configuration and away from the actin core configuration. For this purpose, we applied a harmonic restraint (force constant 334124 kJ/mol/nm 2 or 800 kcal/mol/Å 2 ) moving with constant velocity on the ΔRMSD, i.e., the difference in RMSD between actin core and barbed end structures. The biasing potential acting on atomic configuration at time was:      Time courses of the normalized fluorescence intensities from 10 µM actin (either wild-type or mutants as indicated) containing 1.5% wild-type, pyrene α-actin (cyan) and 30 µM MDCC-PBP (red) seeded with 160 nM spectrin-actin seeds after initiation of polymerization (t=0s).
Dark colors indicate averages from three independent experiments whereas light color areas indicate SD. The black dashed lines correspond to fits of the phosphate release data to a kinetic model (see Methods). Rates of Pi release and relative rate enhancement over wild-type actin as determined either from fits to a kinetic model (wild-type, R183G and R183W actin) or estimated from kinetic simulations (N111S, see Methods, Supplementary Fig. 5c, d) are depicted in each graph.   (see Methods, Supplementary Fig. 5e). e Growth phenotype assay with yeast expressing either