The AAA+ ATPase TorsinA polymerizes into hollow tubes with a helical periodicity of 8.5 subunits per turn

TorsinA is an ER-resident AAA+ ATPase, whose single residue deletion of glutamate E303 results in the genetic neuromuscular disease primary dystonia. TorsinA is a highly unusual AAA+ ATPase in that it needs an external activator. Also, it appears not to thread a peptide substrate through a narrow central channel, in contrast to its closest structural homologs. Here, we examined the oligomerization of TorsinA to get closer to a molecular understanding of the still enigmatic function of it. We observe TorsinA to form helical filaments, which we analyzed by cryo-electron microscopy using helical reconstruction. The 4.4 Å structure reveals long hollow tubes with a helical periodicity of 8.5 subunits per turn, and an inner cavity of ∼4 nm diameter. We further show that the protein is able to induce tubulation of membranes in vitro, an observation that may reflect an entirely new characteristic of AAA+ ATPases. We discuss the implications of these observations for TorsinA function.


Introduction
Torsins are essential proteins that belong to the AAA+ (ATPases associated with a variety of cellular activities) superfamily. AAA+ ATPases encompass diverse enzymes, that use ATP hydrolysis to drive protein and nucleic acid remodeling, protein degradation, and other functions [1][2][3][4] . They share a bilobed core of an N-terminal, 200-250aa nucleotide binding domain, and a Cterminal, ~50-80aa small domain. The nucleotide binding site has several characteristic signature motifs, including P-loop, Walker-A and -B, and Sensors-1 and -2 5 . Typically, AAA+ ATPases form hexameric ring or double-ring structures, in which neighboring subunits act as activators for ATP hydrolysis involving a highly conserved arginine residue ('Arg finger') 6 . The small C-terminal domain is critical for ring formation. Mechanical interaction with the substrate often involves threading through the narrow central cavity of the ring structure 7,8 . Torsins are restricted to multicellular eukaryotes and they exclusively reside in the endoplasmic reticulum (ER) and the connected perinuclear space (PNS) 9,10 . Humans have four Torsins, with different tissue-specific expression profiles 11 . From a medical perspective TorsinA is important, since a deletion of glutamate 303 in TorsinA, TorsinADE for short, is the founding mutation for earlyonset primary dystonia 12,13 , a devastating and still incurable neuromuscular movement disorder [14][15][16] .
Torsins are intriguing since they differ from their closest structural homologs in surprising ways.
Among AAA+ ATPases, they are, sequence-wise, most similar to bacterial Clp proteins, well understood molecules engaged in protein unfolding and degradation 17 . However, the similarity to Clp proteins proved to be rather misleading with regard to the search for the elusive Torsin function. Emblematic for this, the two tightly interacting proteins Lamina-Associated Protein 1 (LAP1) and LUminal Domain Like LAP1 (LULL1) were initially considered to be substrates, since they preferentially bind to ATP-bound TorsinA, similar to Clp substrates [18][19][20] . However, we now know that LAP1 and LULL1 are activators of TorsinA, with a curious structural similarity to AAA+ ATPases [21][22][23] . While LAP1 and LULL1 provide the Arg-finger for activating ATP hydrolysis, they are unable to bind nucleotide themselves, due to a lack of the characteristic sequence motifs introduced above 23 . The dystonia mutant TorsinADE weakens the interaction with the activators, which makes it a loss-of-function protein [19][20][21]24 . LAP1 and LULL1 are both transmembrane proteins, which raises the possibility that TorsinA has a novel membraneassociated function. In addition, Torsins are different from other AAA+ ATPases because of a set of highly conserved cysteine residues, positioned in a way that suggests them to be coupled to ATP hydrolysis, and potentially involved in a redox mechanism 20,24,25 . Furthermore, Torsins contain a hydrophobic N-terminal region that likely plays a role in membrane binding 26,27 .
The structural studies on TorsinA and its activators provoked another question, namely the oligomerization state of TorsinA. Based on the similarity of TorsinA to well-known AAA+ ATPases, a heterohexameric ring assembly of 3 TorsinA subunits alternating with 3 activator subunits initially made logical sense 22,23 . In addition, there was circumstantial evidence for this conclusion, such as stoichiometric and low-resolution structural data 22,23 . However, the activators LAP1 and LULL1 lack the small C-terminal domain and their surfaces are not well conserved in the areas that would be expected to interact with TorsinA to form oligomers beyond the catalytically activatable heterodimer 24 , putting a heterohexameric ring assembly in doubt (see discussion in 24,28 ). On the other hand, various publications presented data that suggested oligomerization of TorsinA alone, albeit at limited resolution 11,[28][29][30] . In this study, we probed the oligomeric state of TorsinA in solution. We observed that TorsinA, presumably when ATP-bound, can readily assemble into continuous helical filaments. These structures, again, are different from canonical AAA+ ATPases, since we observe a periodicity of 8.5 subunits per turn rather than 6, and a much larger central channel. Our in vitro experiments performed with liposomes suggest that the hollow core of these filaments may bind directly to membranes, likely relevant to elucidating the enigmatic function of TorsinA.

Self-assembly of TorsinA
To examine the homo-oligomerization of TorsinA, we designed a series of constructs to recombinantly express TorsinA in bacteria with different solubility tags. An N-terminally MBPtagged human TorsinA construct (residues 51-332) was produced in high yield and purity ( Supplementary Fig. 1a,b). We obtained large amounts of MBP-TorsinA through a one-step affinity purification at a purity greater than 95%. Subsequent gel filtration analysis revealed that the majority of the protein eluted in the void volume of the column, indicating a size of over 600 kDa, thus higher-order oligomerization ( Supplementary Fig. 1c).
To understand the exact nature of these MBP-TorsinA assemblies, we first performed a negative-stain analysis of the affinity-purified protein. The sample grids showed TorsinA assembled into filamentous structures with an obvious internal order, suggesting that helical reconstruction may be a feasible approach for structure determination ( Supplementary Fig. 1d).
Next, we explored options to obtain even longer filaments. Proteolytically cleaving MBP with 3C protease, combined with ATP-containing buffer resulted in longer filaments, which were then suitable for helical reconstruction.

Structural analysis of TorsinA filaments
The longer TorsinA filaments obtained after 3C cleavage, clustered into thick bundles on negatively stained EM grids at low-ionic-strength buffers, whereas at high-ionic-strength conditions they remained separated ( Supplementary Fig. 1e,f). We obtained the most suitable sample for structural analysis at a buffer condition containing 300 mM NaCl. We next prepared frozen-hydrated cryo-EM grids in this improved buffer condition to helically reconstruct TorsinA filaments at higher resolution. We were able to collect useful images from the grid areas containing very thin ice (Fig. 1a). Using 75,909 overlapping particles from 602 micrographs, we helically reconstructed TorsinA at ~4.4 Å resolution (Fig. 1, Supplementary Fig. 2 and Table 1).
The resulting structure showed TorsinA to assemble into a helical filament with an outer diameter of ~14.5 nm. Surprisingly, and in contrast to most AAA+ ATPases, we observe that the filament has a wide open channel in the core with a diameter of ~4 nm. The filaments have a right-handed 1-start helix with a pitch of ~47 Å, and they contain 8.5 TorsinA molecules per turn with an axial rise of 5.5 Å per subunit (Fig. 1b-d). Non-hexameric assemblies of AAA+ ATPases, while rare, have been observed before, particularly in DNA-remodeling enzymes (see discussion below). The EM density for the small domain of TorsinA is less well defined than the large domain, potentially indicating some flexibility. Also, each of the helical turns in the TorsinA filament is in close contact with a neighboring turn ( Fig. 1d and Supplementary Fig. 3b).
Interestingly, the disease-causing ∆E mutation lies in the proximity of these contact sites and the ∆E mutant did not polymerize as judged by negatively stained EM grids (Supplementary Figs. 3b and 4f).
The superposition of filamentous TorsinA with its heterodimeric LULL1-bound state 24 shows that the protein rearranges significantly (Fig. 1e,f). The conformation of TorsinA in the LULL1bound state is incompatible with filament formation due to steric hindrance. The biggest change occurs at the non-catalytic face of TorsinA. There, the rearrangement of residues 232-262, is critical to prevent steric clashes with the nucleotide bound to the neighboring unit ( Fig. 1f and Supplementary Fig. 3a). A highly conserved glycine (G251) in this region is likely to be pivotal for the structural rearrangement to occur. To prove this point, we mutated this glycine to tyrosine (G251Y). As expected, the mutant protein did not polymerize, as judged by negative stain EM ( Supplementary Fig. 4c). Notably, residue G251 has been mutated also in a previous study 28 , disrupting TorsinA's oligomerization behavior in vitro and its physiological functioning in vivo.
Helix α0, the loops following the helix α3, and the rearranged region reside at the subunitsubunit interface of the TorsinA helical tube ( Supplementary Fig. 3a). Mutating the conserved residues D188 and D264 (D188A/Y, D264A) in this region also prevents filament formation, as observed by negative stain EM ( Supplementary Fig. 4a,b,d).

Filamentous TorsinA is likely ATP bound
The resolution of our helical reconstruction is not high enough to directly determine the nature of the bound nucleotide. We presume that the TorsinA filaments are nucleotide-bound for two reasons: first, we observed EM density at the nucleotide binding site (Fig. 1g), and second, we observed robust filament formation only in ATP-containing buffer. We also examined whether TorsinA filaments are catalytically active. We performed an NADH-coupled ATPase assay and observed no ATPase activity ( Supplementary Fig. 5). This experiment suggests that it is the lack of an Arg-finger in TorsinA that prevents ATP hydrolysis. To directly prove that ATP is present in the nucleotide binding pocket we also purified an ATP-trap mutant, MBP-TorsinA E171Q (residues 51-332), which should allow stable retention of ATP. Intriguingly, we did not observe this mutant forming filaments on negative stain EM grids ( Supplementary Fig. 4e). Considering this observation, and the flexible state of the small domain/sensor-2 motif, we conclude that ATP is likely bound in a non-canonical or transition state in the TorsinA helical assembly. In the E171Q mutant, the ATP molecule may not be able to adopt this conformation.

Membrane tubule formation by TorsinA
TorsinA helical tubes have a wide inner cavity, with an approximate diameter of ~4 nm. The electrostatic surface along the inner cavity of TorsinA shows an undulating pattern of positively and negatively charged stripes ( Fig. 2a-d). Most of the positively charged residues inside the channel are well conserved (Fig. 2e). Based on numerous publications that show TorsinA's potential role in membrane remodeling 13,31-34 , we asked whether TorsinA may engage with phospholipid membranes through its inner cavity. Such behavior would be reminiscent of dynamin-or BAR domain-like membrane remodelers [35][36][37] .
To test this hypothesis, we prepared small acidic liposomes and incubated TorsinA with them under a variety of conditions. We either incubated liposomes, MBP-tagged TorsinA and 3C protease for about 6 hours, long enough to cleave off about 50% of the MBP fusion tags (as judged by SDS-PAGE analysis) or, alternatively, we pre-cleaved the MBP tags overnight (about 80% cleavage efficiency) and mixed the long TorsinA filaments with liposomes for about an hour. We also performed these experiments at different ionic strength conditions to evaluate the effect of electrostatic interactions between TorsinA and lipids. Subsequently, we examined all our samples on negatively stained EM grids. At relatively low ionic strength conditions (80-100 mM NaCl) we observed numerous protrusions extending from the liposomes ( Fig. 3a-f). Since we did not observe these protrusions in a higher ionic strength buffer, TorsinA likely mediated their formation by acting electrostatically on lipids. The protrusions appeared to be decorated with a coat of TorsinA molecules, which suggests that membrane extrusion happened through the inner cavity. However, we noted that these TorsinA-coated membrane tubules were noticeably larger in diameter (mean: 20 nm) than the membrane-free TorsinA filaments (mean: 15.5 nm) (Fig. 3g). The larger diameter suggests that filaments were arranged differently, presumably with more TorsinA molecules per helical turn, in order to establish a wider inner cavity. Furthermore, we noticed that TorsinA did not only coat the protrusions, but rather the entire membrane surface ( Fig. 3c-f).
In order to understand how the lining of the inner cavity of TorsinA may affect polymerization as well as the formation of membrane tubules, we introduced mutations on three highly conserved lysine residues (K148, K174, K184) and histidine H140 of the inner channel ( Supplementary   Fig. 6, Table 2). H140N, K174A, and K174E mutants all form filaments. While H140N and K174E did not tubulate membranes, K174A did. In contrast, K148E and K184E mutants did not form helical filaments. However, while the K184E mutant, tubulated liposomes similar to wildtype TorsinA, the K148E mutant did not. These observations suggest that filament formation and membrane tubulation are not directly linked and are, according to our data, at least partially independent of each other.
Finally, we tested whether TorsinA hydrolyzes ATP while remodeling liposomes, different from the enzymatically inactive TorsinA filaments. To test this, we performed an NADH-coupled ATPase assay with our liposome-TorsinA mixtures ( Supplementary Fig. 5). Again, we did not observe ATPase activity. Since the Walker B mutant (E171Q) of TorsinA also triggers membrane tubulation on liposomes (data not shown), while it cannot form membrane-free filaments, further supports the notion that the two helical arrangements are substantially different.

TorsinA function at the inner nuclear membrane
The hallmark of Torsin loss and/or loss-of-function in cells is nuclear blebs arising from the inner nuclear membrane (INM) 13,32,33,38,39 . Since the neck of these blebs is occupied by nuclear pore complex (NPC) -like structures, it is reasonable to speculate that TorsinA is involved in NPC assembly 34 . We inquired whether a membrane remodeling activity of TorsinA as observed in our in vitro liposome assays contributes to the blebbing phenotype. For this, we first generated a HeLa cell line containing a triple knock-out of TorsinA/TorsinB/Torsin3A using CRISPR/Cas9 engineering ( Supplementary Fig. 7a). Ultrastructural characterization of the sections obtained from these cells revealed a robust and pronounced blebbing phenotype at the INM (Fig. 4a,b).
Next, we stably expressed TorsinA constructs in the triple KO TorsinA/TorsinB/Torsin3A cells at near endogenous levels ( Supplementary Fig. 7b). We expected that introducing the wild-type TorsinA would rescue the blebbing phenotype, while introducing the TorsinA mutants would not if the mutations were to interfere with a blebbing-relevant function. Since H140N, K148E and K174E mutations impeded the ability of TorsinA to tubulate the liposomes in vitro, we expressed these mutants in our triple KO cells to examine their effects. Intriguingly, we observed that the wild-type along with all of the mutant TorsinA constructs rescued nuclear blebbing ( Fig. 4c-f, Table 2). Thus, our data suggests that the membrane remodeling of TorsinA is either not directly linked to the blebbing phenomenon or that the in vivo experiment is less sensitive than the liposome assay.

Discussion
This study was motivated by the uncertainty about the oligomeric state of TorsinA, which is an important impediment toward elucidating the biological function of TorsinA. We show, unambiguously, that TorsinA forms long helical filaments in solution, with a periodicity of 8.5 subunits per turn and an inner cavity of ~4 nm diameter. How unusual is this for AAA+ ATPases? While most AAA+ ATPases form hexameric ring structures, TorsinA is not the only exception. A prominent, well-studied example is the MCM2-7 complex, the helicase involved in DNA replication 40,41 . In eukaryotes, the 6 different subunits form a functional head-to-head double hexameric ring assembly 42 . The homologous helicase in archaea, however, only has one distinct subunit and has been shown to assemble into oligomers and polymers. For example, it can form helices with a periodicity of 7.2 subunits per turn, and it can also form 8membered rings 43,44 . In both assemblies, a wide central cavity of ~3-4 nm is observed, similar to what we observed in TorsinA filaments. Widening of the central cavity is a direct consequence of having more subunits per turn. Comparing TorsinA to MCM is somewhat problematic, since MCM has a large N-terminal domain (NTD), absent in TorsinA. This NTD is directly involved in oligomerization, so the assembly structures of TorsinA and MCM only superpose generally. Another example for a non-hexameric AAA+ ATPase assembly is the structure of DnaA, also a component of the replication machinery. Here, helical filaments with an 81 symmetry were observed in a crystal lattice 45 . These DnaA helices are much more elongated with a rise of 17.8 nm per turn, compared to 4.7 nm in TorsinA. Crystal lattices can enforce symmetries, and they need to be carefully examined for physiological relevance. In the DnaA case, the authors argued that the DnaA-interfaces were quite similar to established hexameric units, and that they had a nucleotide bound. Therefore, these assemblies should be physiologically relevant 45 . Using the same argument, we can make a strong case for the TorsinA filaments being biologically relevant, since the interfaces are similar to the established TorsinA-LULL1 interface, albeit with modifications in the 232-262 region. In addition, the filaments presented here are formed in solution rather than in crystals, so we can ignore packing forces associated with the latter. Are helical filaments the only self-assembled form of TorsinA? If this were true, one would argue that the interface between adjacent subunits should be distinct from the canonical hexameric interface of other AAA+ ATPases. We compared the TorsinA assembly with established hexamers of related AAA+ ATPases. The difference between the two assemblies is quite small, and only requires minor rotational adjustment of the large vs. the small domain. In the TorsinA structure we do not recognize any detail that would force a specific relative position of small versus large domain (Fig. 5). Therefore, we argue that TorsinA may adopt multiple oligomeric states in the ER. This is in full agreement with previous publications, where TorsinA was shown to form hexameric and other higher order assemblies 11,[28][29][30] . In a recent article, the higher order assembly of Torsins was discussed in the context of its biological function 28 . The notion of various oligomeric and polymeric states for TorsinA is also supported by our liposome interaction studies. We show that liposomes incubated with TorsinA undergo remodeling (Fig.   3). TorsinA triggers the formation of long protrusions and is able to coat the entire liposome, under the conditions tested. Presumably the long protrusions are TorsinA coated, however, the diameter of these protrusions is wider than that of unbound TorsinA filaments. Unfortunately, the tubular protein coats assembled on liposomes are not amenable to helical reconstruction, so we cannot assess their helical parameters. However, the mean diameter of the protrusions is about 20 nm, compared to 15.5 nm for the membrane-free filaments (Fig. 3g). Assuming a monolayered protein coat, we can estimate a membrane structure with a diameter of ~8.5 nm size, since the protein coat thickness itself would be close to the one observed in the membrane-free environment.
As detailed above, our data suggest that TorsinA can assemble into helical filaments of various diameter, thus presumably with different periodicity. Our construct lacked the N-terminal 30 residues of TorsinA (aa21-50), which remain after signal peptide cleavage and translocation into the ER. This N-terminal peptide is hydrophobic and is suggested to non-specifically interact with membranes 27 . Its location within the filaments is interesting. Sterically, it could be located on the outside or the inside of the helical tube. Possibly, the location may be dictated by the redox state of the conserved cysteines of Torsin. Specifically, Cys162 is spatially close to Cys49/50.
One can entertain the possibility that a disulfide bridge between Cys49/50 and Cys162 may force the hydrophobic N-terminus to be in the inside of the helical tube. A reduction of this potential disulfide bridge may, in contrast, force the N-terminus to be on the outside of the helical tube instead. This is an interesting subject to explore in future studies. The filament structure poses an interesting problem regarding TorsinA activation. To trigger ATP hydrolysis, TorsinA needs to be activated by LAP1 or LULL1, however, they cannot be integrated into the filament. This generates two viable options. In the first scenario, the activator binds to the nucleotide-exposing end of the filament, and hydrolyzes ATP. This could trigger the dissociation of the terminal Torsin molecule, however, it would require an allosteric mechanism.
In other words, the penultimate Torsin-Torsin interface would need to 'sense' the ATP-to-ADP conversion at the LAP/LULL binding site of the terminal Torsin. Sequentially, the filament could be dissolved this way. Alternatively, LAP1 or LULL1 could randomly insert into the filament and break it stochastically at various places. This second scenario depends on the filament being dynamic, which can be assumed based on its in vitro properties. The association of LAP1 and LULL1 with TorsinA is stronger than the homotypic TorsinA interaction, therefore the local concentration of the binding partners is an important determinant of the relevant oligomeric state at a given time.
Taken together, we show that TorsinA can form filaments and that it interacts with membranes, even without the ~30aa hydrophobic N-terminal region present. Going forward, it will be important to further dissect the ATP hydrolysis cycle and to study the protein in situ at higher resolution. TorsinA appears capable of engaging liposome membranes without ATPase activity.
However, in the physiological context this action could be coupled to ATP hydrolysis, raising the possibility that ER/NE membranes are Torsin substrates. No matter where additional findings will lead us it is obvious that TorsinA and its homologs are AAA+ ATPases that continue to defy conventions.

Constructs, protein expression and purification
Human TorsinA (residues 51-332), N-terminally fused with a human rhinovirus 3C protease cleavable MBP tag, was cloned into a modified ampicillin resistant pETDuet-1 vector (EMD Millipore). Mutations were introduced by site-directed mutagenesis. TorsinA filaments were observed when the eluted protein was diluted in elution buffer without maltose and negatively stained (see below for details). The filaments grew longer after the MBP fusion tags were cleaved with 3C protease during dialysis against a variety of buffer conditions. For cryo-EM structural analysis of TorsinA, the eluted protein (1-1.5 mg/ml) was mixed with 3C protease and dialyzed overnight at 4°C against 10 mM HEPES/NaOH pH 8.0, 300 mM NaCl, 10 mM MgCl2, and 0.5 mM ATP.

Helical reconstruction
The defocus values and the astigmatism of the micrographs were determined by CTFFIND3 47 .
A total of 602 good micrographs were selected based on the CTF estimation and defocus < 3 μm for subsequent image processing. CTF was corrected by multiplying the images with the theoretical CTF, which correct the phases and improves the signal-to-noise ratio. The e2helixboxer routine within EMAN2 48 was used for boxing the long filaments from the images. A total of 75,909 384px-long overlapping segments (with a shift of 8px between adjacent segments) were extracted from the long filaments for further reconstruction in SPIDER 49 . Using a featureless cylinder as an initial reference, 69,670 segments were used in IHRSR cycles until the helical parameters (a rotation of 42.5° and an axial rise of 5.5 Å per subunit) converged. The resolution of the final reconstruction was determined by the Fourier shell correlation (FSC) between two independent half maps, generated from two non-overlapping data sets, which was 4.4 Å at FSC = 0.143.

Model building and refinement
We used the TorsinA crystal structure (PDB ID: 5J1S, chain A) as an initial template to dock into  Table 1.
To calculate the electrostatic potential of the wild-type and the mutant TorsinA filaments, PDB format files were converted to PQR format with the PDB2PQR server 55 using the PARSE force field and assigned protonation states at pH 7.0, and then applied to the APBS program 56 implemented in UCSF Chimera. The evolutionary conservation of the TorsinA polymer was illustrated using the ConSurf server 57 supplied with the multiple sequence alignment that we generated previously 24 . Protein interfaces within the TorsinA filaments were analyzed using the PDBePISA server 58 . Structure figures were created using UCSF Chimera 50 and PyMOL (Schrödinger LLC).

ATPase activity assay
ATP hydrolysis rates of TorsinA and TorsinA:liposome mixtures were measured by an NADHcoupled assay as described previously 23  Similarly, Cas9 and the sgRNA designed against Tor3A were expressed in pX330-BFP 59 .
Deletion of Torsins were carried out sequentially. First, a TorA KO cell line was generated, and then TorB and Tor3A were simultaneously deleted in that cell line. In each case, cells were transfected with the pX330 constructs using FuGENE HD (Promega) according to the manufacturer's instructions, and clonal populations were isolated by single-cell sorting after 2 days using GFP and/or BFP signal.

Deletion of Torsins was verified via immunoblotting (see below for details).
To confirm deletion of Tor3A, we also performed deep sequencing on the genetic locus enclosing the Tor3A target site. Genomic DNA of cell pellets were extracted in lysis buffer (100 mM Tris pH 8.0, 5 mM EDTA, 200 mM NaCl, 0.2% SDS, supplemented with 0.2 mg/ml Proteinase K from New England Biolabs) at 55°C overnight. Following precipitation in isopropanol, the DNA pellet was washed with 75% ethanol and resuspended in TE buffer. A ~240 bp region centered around the CRISPR target site was PCR amplified using the primers