Structural basis of actin filament assembly and aging

The dynamic turnover of actin filaments (F-actin) controls cellular motility in eukaryotes and is coupled to changes in the F-actin nucleotide state1–3. It remains unclear how F-actin hydrolyses ATP and subsequently undergoes subtle conformational rearrangements that ultimately lead to filament depolymerization by actin-binding proteins. Here we present cryo-electron microscopy structures of F-actin in all nucleotide states, polymerized in the presence of Mg2+ or Ca2+ at approximately 2.2 Å resolution. The structures show that actin polymerization induces the relocation of water molecules in the nucleotide-binding pocket, activating one of them for the nucleophilic attack of ATP. Unexpectedly, the back door for the subsequent release of inorganic phosphate (Pi) is closed in all structures, indicating that Pi release occurs transiently. The small changes in the nucleotide-binding pocket after ATP hydrolysis and Pi release are sensed by a key amino acid, amplified and transmitted to the filament periphery. Furthermore, differences in the positions of water molecules in the nucleotide-binding pocket explain why Ca2+-actin shows slower polymerization rates than Mg2+-actin. Our work elucidates the solvent-driven rearrangements that govern actin filament assembly and aging and lays the foundation for the rational design of drugs and small molecules for imaging and therapeutic applications.

previous high-resolution crystal structures of monomeric G-actin, this has enabled the authors to describe conformational changes and water molecule positions, and to make suggestions relating to the mechanisms underlying ATP hydrolysis, the G-to F-actin transition, the calcium effect, Pi release and the coupling of polymerisation state to actin-binding proteins.
While no entirely new methodology was invented or used, the combination of state-of-the-art sample preparation and cryo-EM data acquisition and data processing yielded maps of truly unprecedented quality of one of the most important molecule in the whole of eukaryotic biology, Factin. The data are impressive, convincing and important. The level of detail obtained justifies the great majority of the claims made, and provides atomic snapshots that will make it possible to determine the molecular mechanisms of actin with absolute certainty, based on the structures and suggestions provided by the authors.
The paper is well written but will need to be re-formatted for Nature. I would suggest presenting hypothetical mechanisms in more cautious language throughout. Also, the number of main figures needs to be reduced, since too much detail is presented in my opinion. The authors might want to remove some of the data on calcium-bound actin from the main figures, for example to increase brevity and clarity.
I think this is definite landmark work in the field of the cytoskeleton (where only filaments that crystallise have reached this level of detail), the work presents a technical advance for cryo-EM, and is of significant interest to those working on, and thinking about atomic mechanisms of enzymes, which is very many people. It is also a showcase for cryo-EM not being a low-resolution method anymore, and that this is now true for many, if not most of samples. The work will also lead to many structures, at high resolutions, of important molecule bound to actin filaments.
A few specific points in no particular order: -p1: Title: "aging" a good word, seems actin specific? "ATP hydrolysis" instead?
-general: Is looking at calcium-bound actin interesting? Given that not normally bound in cells (intro, p3). It is of course interesting in terms of understanding the mechanism better, but it might need to be phrased as such.
-general: Intra-strand contact is sometimes also called longitudinal.
-general: Did you consider/try using a transition-state mimic, such as aluminium fluoride (need to admit that I am not sure this works on actin)? -p4: "All three functional states": is it not possible that there are more functional states that we can't trap? For example, the state where Pi leaves the active site? (see below, p10, missing open "back door" state).
-p6, top: I do not find it "surprising" that there are no extra binding sites for Mg and Pi.
-p6: How can we be sure that F-actin is bound to calcium and not a mix of magnesium and calcium (also: methods)?
-p8: What are the attack angles of the other two water and their distances (list)? -p8 I find the attack angle of Wnuc slightly worrying, given the speed of the reaction involved. Could this have to do with the use of BeF3, which will cause slightly altered geometry and dimensions? Any way to get to true ATP actin? -p8: The putative mechanism of water attack and proton transfer is hypothetical at this point I would suggest. Please phrase as such. This applies to many hypothetical scenarios predicted from the structures, more cautious wording is warranted, generally.
-p9: The putative explanation of slower polymerisation and hydrolysis by calcium actin is quite convincing.
-p10: It is somewhat puzzling that the Pi "back door" is not visible in the ADP-Pi or ADP F-actin structures. See below, how the ADP-Pi state was generated.
-p11 & Movie S4: very minor changes are being discussed … how can we be confident these are real differences, especially given that all atomic model building progressed from one model as far as I understood?
-p12: Does rabbit actin have all the modifications as human actin (since human cofilin was used)?
-p13: Not everything that affects rates is visible in atomic structures. For example, electrostatic interactions can drive affinities very significantly (Ca vs Mg / ATP vs ADP actin). ADP F-actin can have a much lower longitudinal affinity, purely based on changed electrostatics (2 vs 3 phosphates). This is thought to drive de-polymerisation in tubulin-like proteins, for example.
-p15: I note in the methods that the ADP-Pi state was created by adding Pi to ADP-actin, not by hydrolysis. That state could be different from a state that resulted from hydrolysis of ATP, and this may have shown the Pi "back door" open? I am aware that hydrolysis is much more difficult to control.
-p17: What particle, CTF and aberration parameters where refined in Bayesian polishing in RELION?
-p18: For the water molecules: was chemical plausibility taken into account when deciding on the positions of water molecules? How were waters distinguished from ions bound to the proteins? Some waters are not very round … Crystallography has developed many tools for this to be done more objectively … - Figure 1: Very well presented. I would have added stereo versions of these as supplement.
- Figure 2: No bond is shown here for Be to Pbeta? - Figure 4a: Again, what is the distance of Wbridge to Be? To me, the attack angle looks better for Wbridge? (The atomic model and/or stereo would help the reader to form an opinion).
-I think there are too many figures … -As far as I can see, only preliminary PDB validation reports have been provided. I thought submissions required full validation reports and PDB IDs these days to make sure structures have actually been submitted and accepted, before manuscript review?
-Line numbers would have been helpful throughout.
-A personal note to the editor: I find the reporting summary etc not useful and they create a lot of work for authors and give the impression of a degree of experimental precision that is not really attainable in most situations (certainly not in my own group).

Author Rebuttals to Initial Comments:
Point-to-point response to the reviewers' comments We thank the reviewers for their positive and constructive feedback, which aided us to further improve the manuscript. Below is a point-by-point response to all comments and a detailed description of all changes we have made to our manuscript after considering their suggestions. The changes are highlighted in yellow in the revised manuscript.

Reviewer #1
[1.1] The authors use well-established nucleotide ATP-like analogues to infer the ATP F-actin structural state. However, at the resolutions at which the authors are working and at the level of individual water molecules, can they really be certain that these analogues are truly structurally analogous at atomic resolution? It would be very exciting and novel to see the authors apply their processing methods to dynamic actin filaments, enabling them to capture physiologically relevant nucleotide-dependent structural transitions that do not rely on analogues.
Reply 1.1 (see also Reply 2.11): The BeF3group, which represents the -phosphate mimic in our studies, cannot be considered "truly analogous" of phosphate as it is comprised of different atoms. However, as mentioned in the manuscript, the orientation and bond lengths of ADP-BeF3in our F-actin structures are highly similar to those of ATP in X-ray structures of G-actin. Thus, BeF3represents a suitable -phosphate analog for elucidating structures of F-actin in a state that resembles the ATP ground state. Importantly, ADP-BeF3has been characterized as an ATP ground state analog based on high-resolution structures of a wide range of molecular machines, such as maltose transporters (see Oldham and Chen, PMID: 21825153) and sarcoplasmic Ca 2+ -ATPases (see Møller et al, PMID: 20809990).
We fully agree with the reviewer that it would be very exciting to capture a true pre-hydrolysis state of F-actin. However, actin hydrolyzes ATP within seconds of polymerization (rate 0.3 s -1 ). Therefore, to obtain a cryo-EM sample in which the majority of filaments are in the ATP state, one would have to vitrify actin on a cryo-EM grid within a second of polymerization. This would require fast mixing of G-actin-ATP with a high-salt buffer to reach 100 mM KCl and 2 mM CaCl2/MgCl2 final concentration and spraying onto a grid. Unfortunately, this is unattainable with our standard vitrification protocols using a Vitrobot Mark IV. Instead, this time-resolved cryo-EM approach would rather require a specialized mixing/spraying device. There are only a few examples worldwide where these devices have been successfully used by specialized labs after years of fine-tuning and optimization. Therefore, such an approach is not feasible within our current study but on our list of future investigations.
[1.2] The authors state (p10) that their data show that the Ca2+ ion is more mobile within the actin catalytic site and that this could decrease filament stability and explain these filaments' higher depolymerization rate. It is not clear how reduced stability arises from ion mobility. Does this reduced stability manifest in their structures? If not, why not? Reply 1.2: Thank you for pointing this out. In the nucleotide-binding site of the Ca 2+ -ADP-bound Factin structure, we do not observe lower local resolution, less resolved sidechains and higher B-factors of amino acids compared to the other structures. Thus, there is no structural evidence for a reduced stability. We have therefore removed the sentence: "This difference at the active site probably decreases the stability of the filament and could explain the higher depolymerization rates of Ca 2+ -actin compared to Mg 2+ -actin 18 " from the manuscript. The higher depolymerization rates of Ca 2+ -F-actin may depend on differences that we cannot observe in our structures, such as for example different conformations at the filament ends. Figure 5, evidence for the actin subunit back door by which Pi is released is inferred to be formed by the side chains of R177 and N111 and the backbones of methylated histidine 73 (H73) and G74, and is in a closed conformation in both ADPPi and ADP states of Mg2+-F-actin and Ca2+ of F-actin. Can more extensive EM data processing in this area provide more direct evidence for conformational change in this region? Could the authors include molecular dynamics experiments to provide evidence about the behaviour of the back door? Reply 1.3 (see also Reply 2.15): The evidence that the Pi-release back door is formed by R177, N111, H73 and G74 is largely based on a pioneering molecular dynamics study by Wriggers and Schulten from 1999 (PMID: 10223297). This study was based on a ATP-G-actin-gelsolin segment-1 complex. Our high-resolution structures of F-actin provide no evidence for any flexibility within the region of the proposed back door, nor in any other potential back doors. Because no flexibility is observed and the density is of high quality, we believe that more extensive processing will not yield additional insights.

[1.3] As depicted in
Our observations strongly indicate that Pi release occurs in a transient, high-energy state of F-actin, which is a new finding by itself. We indeed think that state-of-the-art MD simulations could provide new insights into the path of Pi release. However, as Pi release occurs in the range of minutes (rate 0.006 s -1 ), such simulations would require extensive optimization and CPU time and hence represent a completely new project that could easily take more than a year of work. Including MD simulations was therefore not within the scope of the current study. In fact, we would like to emphasize that our work highlights that Pi release from the F-actin interior is far from completely understood, contrary to statements from many articles that consider the release mechanism through the R177-back door as solved. Thus, the mechanism of Pi release could represent a prevalent theme of future research within the actin field.
[1.4] In figure 6, several rearrangements of the D-loop and the C-terminus at the intrastrand interface in the actin filament, in the presence of Ca2+ and Mg2+, are described, but more information is needed about the methodology used during the focused classification steps. Specifically, the authors should clearly explain why and how they used two initial model in order to classify the particles. In particular, how did they mitigate the possibility of model bias arising from the use of high value of T (500) combined with a high-resolution filtering of initial models (4 Å). Could alternative image processing strategies -e.g. with the use of signal subtraction combined with mask classification and refinementprovide additional validation of the structural interpretations arising from these analyses?
Reply 1.4: The reviewer highlights an important point. We have described our classification approach now in more detail within the methods section of the revised manuscript.
Firstly, the D-loop is a very tiny region of ~10 amino-acid residues. It is expected that for such a small region within the map (and hence a very small mask compared to the full box), more weight needs to be put on the experimental data, resulting in a higher regularization parameter T. This has been discussed in posts on the ccpem mailing list, see for example https://www.jiscmail.ac.uk/cgi-bin/wajisc.exe?A2=ind1909&L=CCPEM&P=R114857. We updated the manuscript accordingly: "After optimization of the tau2fudge parameter, which required a high value due to the small size of the mask compared to the full box, this classification …".
We have also attempted to use signal subtraction, but that did not yield in improved classification results. Class3D with a high T value was performed without image alignment to exclude strong bias during the classification. It is also clear from the data that we have a mix of 'closed' and 'open' D-loop conformations. Thus, although we require classification with two references to separate the particles in two conformations, we do not look for conformations that are not there. In the subsequent refinement (in which image alignment is performed again) was performed with a reference of the pre-classification map. However, we understand the concern of Reviewer #1 and have now refined the "closed" and "open" particle sets with an initial model low-pass filtered to 8 Å, in which the D-loop conformation is indistinguishable. The manuscript now states: "… with mixed D-loop conformation (filtered to 8.0 Å, at which the D-loop conformation is indistinguishable) as reference …" These refinements yielded the same results as our previous study: the intra-strand interface for the central subunit is separated, but all other intra-strand interfaces within the map (that were not used in the masked classification) display a mixed conformation.
[1.5] The results of the cofilin cosedimentation assay in the presence of Ca2+-F-actin are used to derive a new nucleotide-dependent recognition mechanism for cofilin binding. The relevant text (p12-13) only refers to Ca2+ data but Mg2+ data are also presented in ED16/17 figure and should be incorporated into the description. Only a single concentration of cofilin is used in these experiments -do the observations hold up when a more complete titration is performed? This is important given the cooperative nature of cofilin binding to F-actin.
Reply 1.5: Thank you for highlighting this point. The original manuscript indeed did not refer to Mg 2+ -F-actin data, this has now been adjusted in the revision: "To assess this, we incubated cofilin-1 and Mg 2+ -or Ca 2+ -bound F-actin in three nucleotide states and measured cofilin-dependent filament severing." To validate our observations that the D-loop conformation does not represent the only sensor for cofilin binding and severing, we have, based on the reviewer's suggestions, now repeated the experiment using a broad range of cofilin concentrations (5, 10 and 20 μM). To highlight that the function of cofilin is Factin severing, rather than just binding, we calculated the cofilin-dependent F-actin severing based on three independent experiments. These experiments reveal that, over the entire concentration range tested, cofilin-1 only efficiently severs both Mg 2+ -and Ca 2+ -F-actin in the ADP state, and not in the other nucleotide states. This supports our statement that cofilin senses the -phosphate moiety in Factin.

Reviewer #2
[2.1] The paper is well written but will need to be re-formatted for Nature. I would suggest presenting hypothetical mechanisms in more cautious language throughout. Also, the number of main figures needs to be reduced, since too much detail is presented in my opinion. The authors might want to remove some of the data on calcium-bound actin from the main figures, for example to increase brevity and clarity.
Reply 2.1: We are grateful for the feedback from Reviewer #2. Also based on editorial comments, we have shortened the manuscript, reduced the number of main figures and have moved some of the Ca 2+ -F-actin figures to the Extended Data.
Reply 2.2: We appreciate the suggestion from Reviewer #2. However, changing "aging" to "ATP hydrolysis" would yield a title that does not fully cover the contents of our manuscript; for instance, we also present insights into the ADP-bound state. Therefore, we prefer to keep "aging" in the title. [2.4] general: Is looking at calcium-bound actin interesting? Given that not normally bound in cells (intro, p3). It is of course interesting in terms of understanding the mechanism better, but it might need to be phrased as such.

Reply 2.4: Reviewer #2 is correct that Ca 2+ probably only marginally binds the actin-nucleotide in vivo.
In the revised manuscript, we therefore focus more on Mg 2+ -actin and have reduced the part of Ca 2+actin. Nevertheless, we believe that a molecular understanding of Ca 2+ -actin polymerization is highly relevant for the field, in addition to scientists interested in mechanisms of enzymes. Ca 2+ has been standardly used in actin purifications, many in vitro studies and most G-actin crystal structures over the last 80 years. The reason for this is, that Ca 2+ -ATP-bound G-actin exhibits slower polymerization kinetics and a higher critical concentration of polymerization. However, what causes the slow polymerization rates of Ca 2+ -actin has so far remained unknown and our structures provide the molecular explanation for this phenomenon. We have rephrased the respective paragraph in the introduction to make this aspect clearer to the reader.
[2.5] general: Intra-strand contact is sometimes also called longitudinal.
Reply 2.5: In the first sentence in which the term "intra-strand" is introduced, we added "or longitudinal" between brackets to also make the reader familiar with this definition: "We next examined the nucleotide-state dependent conformational mobility of the D-loop (residues 39-51) and the Cterminus at the intra-strand (or longitudinal) interface in the actin filament 21,40 ".
[2.6] general: Did you consider/try using a transition-state mimic, such as aluminium fluoride (need to admit that I am not sure this works on actin)?
Reply 2.6: Reviewer #2 is right to assume that AlF4can bind to ADP-F-actin (see e.g., Combeau and Carlier, PMID: 2808407) and that ADP-AlF4bound F-actin is proposed to mimic a transition state. However, our current research focused on elucidating the ground nucleotide states in detail. The extensive biochemical and structural characterization of a potential transition state was therefore not within the scope of the current study, but we definitely will consider it for follow-up work.
[2.7] p4: "All three functional states": is it not possible that there are more functional states that we can't trap? For example, the state where Pi leaves the active site? (see below, p10, missing open "back door" state).

Reply 2.7:
We agree that F-actin is capable of adopting functional states that cannot be trapped with current experimental methodology, and that the "All three functional states" statement is misleading. We have changed the sentence to: "Here, we present six ~2.2 Å cryo-EM structures of rabbit skeletal -actin filaments in three functional states, polymerized …" [2.8] p6, top: I do not find it "surprising" that there are no extra binding sites for Mg and Pi.
Reply 2.8: We initially wrote "surprisingly" because we do not observe extra binding sites for Mg and Pi, even though these binding sites were previously predicted. Nevertheless, we now have removed the term "surprisingly" from the text.
[2.9] p6: How can we be sure that F-actin is bound to calcium and not a mix of magnesium and calcium (also: methods)?
Reply 2.9: The final step of the purification of actin from rabbit muscle acetone powder is dialysis in "G-buffer" for 2 days, with multiple buffer exchanges. G-buffer contains 0.2 mM CaCl2 and no Mg 2+salts. Thus, all Mg 2+ ions that were present in the sample are infinitely diluted and removed. Combined with data that the affinity of Ca 2+ for ATP-bound G-actin is slightly higher than that of Mg 2+ and, that exchange is relatively fast (see Estes et al PMID: 1527214), it can be concluded that the divalent cation bound to G-actin after the purification is Ca 2+ . Therefore, actin that was polymerized in the absence of MgCl2 does not harbor a Mg 2+ -ion in the active site. To clarify this, we added the following sentence to the methods section, after describing the dialysis: "This ensured that Ca 2+ was the divalent cation bound in the active site of G-actin." [2.10] p8: What are the attack angles of the other two water and their distances (list)?
Reply 2.10: For the Mg 2+ -F-actin structures, the distance to the Be-atom of the modelled water proposed to represent Wnuc is 3.6 Å with an angle of 144°; Wbridge is 4.0 Å with an angle of 134°; and the third water is 6.6 Å with an angle of 125°. For the Ca 2+ -F-actin structures, the distance to the Be-atom of the modelled water proposed to represent Wnuc is 3.7 Å with an angle of 137°; Wbridge is 4.0 Å with an angle of 125°; and the third water is 6.2 Å with an angle of 127°. We have added a table to Extended Data Fig. 6i in which these distances are now listed.
[2.11] p8 I find the attack angle of Wnuc slightly worrying, given the speed of the reaction involved. Could this have to do with the use of BeF3, which will cause slightly altered geometry and dimensions? Any way to get to true ATP actin?
Reply 2.11: Although we propose in the manuscript that Wnuc may adopt hydrolysis competent and hydrolysis less competent configurations, we indeed cannot exclude that the orientation of the nucleotide is slightly altered when ADP-BeF3is used. We have now added a sentence to the manuscript to underline this: "Although it cannot be excluded that nucleotide orientation is slightly altered between ADP-BeF3 --bound and ATP-bound F-actin, inspection …". The development of a time-resolved approach for the elucidation of a true ATP state of F-actin was unfortunately not feasible within the current study. We also refer Reviewer #2 to our elaborate Reply 1.1.
[2.12] p8: The putative mechanism of water attack and proton transfer is hypothetical at this point I would suggest. Please phrase as such. This applies to many hypothetical scenarios predicted from the structures, more cautious wording is warranted, generally.

Reply 2.12:
We agree that the proposed mechanism of ATP hydrolysis is hypothetical, although we believe that our predictions are justified by the experimental data. We have adjusted the manuscript and have introduced more cautious wording (more cautious wording is highlighted in bold): "Wbridge may represent a Lewis base with a high potential to activate Wnuc and potentially act as an initial proton acceptor during hydrolysis, followed by transfer of the proton to D154, as previously predicted by simulations 57,58 , or alternatively, to H161. In conclusion, we propose that Q137 coordinates Wnuc but that the hydrogen bond network comprising Wbridge, D154 and H161 is responsible for the activation of Wnuc and proton transfer".
Reply 2.13: We already refer to these mutants in the manuscript: "Indeed, the ATP hydrolysis rates of the Q137 to alanine (Q137A) actin mutant are slower but not abolished 34 , whereas the triple mutant Q137A/D154A/H161A-actin exhibits no measurable ATPase activity 35 ." -which refers to previous studies that investigated the effect of alanine mutations of these residues on ATP hydrolysis. Because these mutants have been characterized previously by our group ( [2.14] p9: The putative explanation of slower polymerisation and hydrolysis by calcium actin is quite convincing.
Reply 2.14: Thank you for the positive feedback.
[2.15] p10: It is somewhat puzzling that the Pi "back door" is not visible in the ADP-Pi or ADP F-actin structures. See below, how the ADP-Pi state was generated.
Reply 2.15: See also Reply 1.3. The proposed "back door" of Pi release is indeed closed in all our structures, as well as any other potential back door, which let us to propose that Pi release occurs transiently in a high energy state. This hypothesis is further supported by kinetic data. Namely, Pi remains bound to F-actin in the range of several minutes, whereas its affinity is low (~1.5 mM, see Carlier and Pantaloni, PMID: 3335528). Accordingly, the binding and dissociation of -phosphate mimics such as BeF3from ADP-F-actin is, as described in previous studies, "very slow" (see Combeau and Carlier, PMID: 3182855). Thus, phosphate molecules/mimics do not freely diffuse in and out of the F-actin active site, which supports that binding and dissociation occur in a short-lived state that we cannot easily trap with averaging methods such as cryo-EM. Of note: we incubated our samples >6 hours in BeF3or Pi to ensure saturation of the binding site (see methods).
[2.16] p11 & Movie S4: very minor changes are being discussed … how can we be confident these are real differences, especially given that all atomic model building progressed from one model as far as I understood?
Reply 2.16: We would like to emphasize that our high-resolution structures now, for the first time, allow us to discriminate minor changes because we can confidently model the positions of waters and amino-acid sidechains. All six presented structures are highly similar, it was therefore convenient to use the Ca 2+ -ADP bound F-actin structure as starting model for modelling. However, in the subsequent elaborate, iterative process of manual modeling in Coot and real-space refinement in phenix, all residues and solvent molecules were refined in the experimental density map of the specific state. The observed differences can therefore be attributed to changes between the different states.
[2.17] p12: Does rabbit actin have all the modifications as human actin (since human cofilin was used)?
Reply 2.17: Rabbit skeletal -actin indeed harbors the same hallmark post-translational modifications as human skeletal -actin, such as N-terminal acetylation and the methylation of residue H73. In general, the majority of biochemical studies on the actin-cofilin complex have been performed with rabbit actin, simply because it is the most convenient to purify in large quantities. Thus, the established purification protocol and well-characterized biochemistry also made rabbit actin a prime candidate for our structural studies.
[2.18] p13: Not everything that affects rates is visible in atomic structures. For example, electrostatic interactions can drive affinities very significantly (Ca vs Mg / ATP vs ADP actin). ADP F-actin can have a much lower longitudinal affinity, purely based on changed electrostatics (2 vs 3 phosphates). This is thought to drive de-polymerisation in tubulin-like proteins, for example.
Reply 2.18: This is an excellent suggestion. In the conclusion section of the manuscript, we now refer to a study that shows that the nucleotide state affects the mechanical properties of the filament.
[2.19] p15: I note in the methods that the ADP-Pi state was created by adding Pi to ADP-actin, not by hydrolysis. That state could be different from a state that resulted from hydrolysis of ATP, and this may have shown the Pi "back door" open? I am aware that hydrolysis is much more difficult to control.
Reply 2.19: See also Replies 1.3 and 2.15. Pi release occurs in the order of minutes, but it is expected that some Pi molecules, especially those close to the filament ends, will be released faster. Therefore, a protocol aimed to capture ADP-Pi right after polymerization and hydrolysis would effectively result in a mixture between ATP, ADP-Pi and ADP states of F-actin. With the used protocol, we could ensure that the Pi-binding site in F-actin was saturated and that we isolated a full ADP-Pi state. Indeed, the cryo-EM densities of the P and P of ADP and of Pi are of comparable intensity, indicating full occupancy. It is generally accepted within the actin field that Pi binding is reversible from a kinetic perspective (see e.g., Carlier and Pantaloni, PMID: 3335528 and Fujiwara et al, PMID: 17517656). Indeed, previous cryo-EM studies by other groups (see e.g., Chou and Pollard, PMID: 30760599 and 33214556) have used a similar approach of generating the ADP-Pi state. In addition, structures of Factin copolymerized with cyclic peptide toxins jasplakinolide and phalloidin (see Pospich et al, PMID: 32084355) have revealed a Pi-binding site highly similar to that in our current structures (including a closed back door). The toxins strongly inhibit Pi release and therefore, these structures show Pi that is the product of ATP hydrolysis. Therefore, combined with Reply 2.14, we do not believe that a different preparation of the ADP-Pi state would yield an open back door.
Reply 2.20: Bayesian polishing and contrast transfer function (CTF) refinement refer to two separate image processing steps that improve the quality and resolution of the reconstruction. During cryo-EM data collection, the electron beam induces movements of the protein within the vitreous ice layer. To correct for this beam-induced motion, cryo-EM micrographs are typically collected as 'movies' that consist of frames (60 -80 frames in our experiments). At the start of image processing, these frames are aligned to correct for the motion. During the processing, correction with the contrast-transfer function is essential for obtaining high-resolution reconstructions. The contrast-transfer function is dependent on the used defocus and is initially estimated per micrograph. Bayesian polishing and CTF refinements are used in later stages of processing after an initial good-quality density map is obtained. Bayesian polishing employs a Bayesian approach to estimate improved particle trajectories of beaminduced motion and performs dose-weighting. With CTF refinements, the CTF per particle is estimated, which is a more accurate estimation than "per micrograph". Namely, the ice thickness in each micrograph is never fully uniform, which will affect the CTF. We furthermore used CTF refinements to estimate aberrations caused by microscope imperfections: beam tilt, 3-fold (trefoil) astigmatism, Cs and 4-fold (tetrafoil) astigmatism and anisotropic magnification. More information can be found in the publications describing Bayesian Polishing (Zivanov et al, PMID: 30713699) and CTF refinements (Zivanov et al, PMID: 32148853). The methods section has been slightly adjusted to make this clearer: "Within Relion 3.1.0, the particles were subjected to Bayesian polishing 60 for improved estimation of particle movement trajectories caused by beam-induced motion; and to CTF refinements 61 to estimate per-particle defocus values and to correct for beam tilt, 3-fold (trefoil) astigmatism, Cs and 4-fold (tetrafoil) astigmatism, and anisotropic magnification".
[2.21] p18: For the water molecules: was chemical plausibility taken into account when deciding on the positions of water molecules? How were waters distinguished from ions bound to the proteins? Some waters are not very round … Crystallography has developed many tools for this to be done more objectively … Reply 2.21: Due to the relative "young age" of high-resolution cryo-EM, tools to verify modelled ligands and waters are not as far developed as those for macromolecular crystallography. Therefore, we indeed have paid much attention to model only solvent molecules that make chemical sense (e.g., hydrogen-bonded to amino-acid residues). The Mg 2+ and Ca 2+ ions bound to the nucleotide could be modelled based on their geometry and coordination by the nucleotide. Besides the ions in the nucleotide-binding site, we did not identify any solvent density that we, based on geometry and coordinating residues, could unambiguously attribute to an ion. We therefore modelled all these densities as waters. The manuscript states: "Although earlier studies predicted additional Mg 2+ and Pi binding sites outside of the F-actin nucleotide-binding pocket 25,40,41 , we did not find evidence for these secondary ion-binding sites in any of our reconstructions". Specifically, Scipion et al (PMID: 30254171) inventoried all cation binding sites in G-actin crystal structures, and predicted that some of these sites may also be present in F-actin. We specifically inspected these sites in all our structures but did not observe clear density for ions, supporting our decision to only model waters.  Fig. 1. Additionally, the maps and models are deposited to, respectively, the EMDB and PDB, which will allow interested readers to look at the structures in 3D.
[2.23] Figure 2: No bond is shown here for Be to Pbeta? Reply 2.23: This was indeed not consistent. We now show the bond between the P and Be in Fig. 2 and Extended Data Fig. 6. [2.24] Figure 4a: Again, what is the distance of Wbridge to Be? To me, the attack angle looks better for Wbridge? (The atomic model and/or stereo would help the reader to form an opinion). Reply 2.26: Thank you for pointing this out. We are happy to report that all models and maps have now been submitted and that the validation reports did not reveal any large errors. Full validation reports have been included in the present submission.

Reply
[2.27] Line numbers would have been helpful throughout.

Reply 2.27:
We have now added line numbers to the manuscript.

Reviewer Reports on the First Revision:
Referees' comments: Referee #1 (Remarks to the Author): The manuscript of Oosterheert et al is a high-quality structural study that yields novel insights into the properties of actin filaments. In addition to the authors' response to the reviewers' comments, this manuscript also has to be considered in the context of the work of Reynolds et al, which has recently been deposited on bioRxiv (https://doi.org/10.1101/2022.06.02.494606), and which is also now cited by Oosterheert et al. There is certainly reassuring consistency between the 2 studies with respect to fundamental nucleotide-dependence of F-actin structures. However, with its narrower focus on the enzymology of F-actin, the work of Oosterheert et al suffers in comparison to Reynolds et al, who apply more creative approaches to understanding actin structural dynamics and thereby opens up new ways of understanding the mechanobiology of the cytoskeleton.
In their revision, Oosterheert et al have addressed a subset of the previously raised points: Review point 1.1: While it is positive that the authors see that the future use of rapid spray devices will allow more novel approaches to F-actin cryo-EM sample preparation, it is disappointing that such methodologies have not already been implemented for high resolution structure determination. Kontziampasis et al (2019 PMID 31709058) demonstrated that F-actin could be frozen using a rapid freezing device and that a 5.6 A reconstruction could be determined from a small dataset and without significant optimisation. It can be anticipated that structure determination of such samples will provide critical insight into the true structure of ATP-actin, as oppose to those stabilised by analogues, and would also shed light on the dynamic structural transitions that occur between subunits within filaments as ATP hydrolysis proceeds.
1.2: The authors have acknowledged that their data do not provide an explanation for the reduced stability of Ca-F-actin. They speculate that this phenomenon could arise from effects at the end of filaments. Do their cryo-EM data already provide evidence in support of this idea? In addition, it would be extremely relevant to apply the approaches described by Reynolds et al relating to filament flexibility to explore this phenomenon further.
1.3: The authors' point about the time required to undertake MD simulations to interrogate phosphate release mechanisms is well taken, although such experiments would greatly enrich the current manuscript. Might ADP.Pi F-actin filaments be washed in some way prior to vitrification to stimulate more concerted phosphate release and increase the likelihood of capturing transient release state(s)? Fundamentally, the authors present absence of evidence concerning the phosphate release mechanism which is worthwhile to flag to the field. It would be helpful if the authors were explicit in the manuscript about why current thinking is not correct and how this open question might be addressed in the future.
1.4: The additions to the manuscript concerning classification strategies for the D-loop provides confidence in the methodology applied. The authors should explicitly add to the Methods text how they excluded that the use of very high T value resulted in overfitting of the data. They should also explicitly state in the relevant section of the Methods why two references were used for the first iteration of classification -were they absolutely certain there were only 2 confirmations and if so, how?
1.5: The authors have clarified and added more data to their observations concerning cofilin binding. One explanation for these observations could be the authors' hypothesis that cofilin directly senses the F-actin phosphate state, but as mentioned by one of the reviewers ([2.18] p13: "Not everything that affects rates is visible in atomic structures." This is elegantly explored by Reynolds et al -cofilin-1 binding may also be sensing mechanical filament properties, which are not captured in the Oosterheert study. Referee #2 (Remarks to the Author): Second round review: Oosterheert et al., Nature ms# 422981: The authors did an excellent and thorough job in answering questions and making changes. I would be happy for this work to progress to publication without delay. A few more comments: -I agree that looking at dynamic actin would have be exciting but it is a new and diffcult project as pointed out by the authors. Looking at dynamic, ATP-hydrolysing F-actin, the slightly distorted geometry around the BeF moiety might get resolved and the "back door" issue pointed out in the manuscript and by both reviewers might also get resolved, although that is less clear since it is most likely a transition state and might only occur very briefly. I wanted to challenge the authors on this important goal, but as said, I do not think the current advances are diminished by this future option.
-Reply 1.4: if using 3D classifications without particle alignment (essentially just sorting particles into a few classes), very small parts of the map can be masked successfully and the danger of bias introduction is small. We have done this on stretches of 5 residues in tubulins very successfully (to distinguish alpha and beta). Has this been explored? -It is good to see that the manuscript is now more compact and readable, mostly because of deemphasising the calcium angle, which I am not so keen on as it is non-physiological (but mechanistically interesting, as pointed out by the authors correctly).
-Wording has been changed to more hypothetical phrases in important places, which is good to see since mechanisms are deduced from snapshots, only, and from the use of analogues.