Intermediate filaments (IFs) provide resistance to the mechanical stresses of the cellular spaces with the robust network in eukaryotic cells (Herrmann et al., 2007; Ondrej et al., 2008). All IFs consist of the N-terminal head, central α-helical rod, and C-terminal tail domains (Coulombe and Wong, 2004; Herrmann et al., 2007; Karantza, 2011). The parallel coiled-coil dimer with the central rod domains is the fundamental soluble unit of IFs (Herrmann and Aebi, 2016; Lupas et al., 2017). The nuclear IF lamins are evenly distributed in meshworks on the inner surface of nuclear envelopes, protect from mechanical pressures (Stiekema et al., 2020; Ungricht and Kutay, 2017). Compared to the cytoplasmic IFs, such as vimentin and keratins, nuclear IF lamins have additional Ig-like domains in the C-terminal tail region (Ahn et al., 2021; Herrmann et al., 2007).

The central rod domain adopts the α-helical conformation and has been divided into subdomains: coil 1a, linker L1, coil 1b, linker L12, and coil 2 (Chernyatina et al., 2015) (Supplementary Fig. S1). The periodicities and lengths of the subdomains within the central rod domain are critical for proper filament formation, although the molecular reasons are not fully understood (Herrmann and Strelkov, 2011; Smith et al., 2002). The coil 1a and coil 1b regions are in the heptad repeats exhibiting the typical left-handed coiled-coil dimeric conformation in crystal structures (Ahn et al., 2019; Chernyatina et al., 2012; Karantza, 2011; Strelkov et al., 2002). The crystal structure of lamin further visualized that the linker regions L1 and L12 are in the α-helical conformations with substantial bends between the neighbouring coiled-coils (Ahn et al., 2019).

The coil 2 region consisted of the hendecad (residues 240-277 in human lamin A/C), heptad (residues 278-319), stutter (residues 320-330), and heptad repeats (residues 331-381). The hendecad repeat region of coil 2 showed the parallel (untwisted) coiled-coil conformation (Ahn et al., 2019). The heptad repeat regions of coil 2 showed the left-handed coiled-coil structure, as predicted from the sequence periodicity (Lupas et al., 2017; Nicolet et al., 2010) (Fig. 1A, Supplementary Fig. S1). The stutter region comprised 11 residues and exhibited a short dragged coiled-coil, interrupting the long left-handed coiled-coils of the coil 2 heptad regions in lamin A/C, vimentin, and keratin (Lee et al., 2012; Nicolet et al., 2010; Strelkov et al., 2004) (Supplementary Fig. S2).

The recent results, including the crystal structure and in situ cryo-electron tomography (cryo-ET) images, suggested that the lamin coiled-coil dimers form the 3.5-nm-thick filament structure via two alternative binding modes: A11 and A22 (Ahn et al., 2019; Turgay et al., 2017; Turgay and Medalia, 2017; Vermeire et al., 2021). The A11 binding mode of four coil 1b was well-defined at atomic resolution by the crystal structures (Ahn et al., 2019; 2022; Lilina et al., 2020). The A22 binding mode represents the antiparallel interaction between the two coil 2 dimers. The researchers believed that the ACN binding mode, representing the head-to-tail interaction between coil 2 and coil 1a, is derived from the A11 and A22 in IF proteins. Recently, sophisticated chemical cross-linking mass analyses suggested that the ACN binding interaction consists of a parallel four-helix bundle model by the overlapping coil 1a, which was approximately 6.5 nm long, and coil 2 (Makarov et al., 2019; Stalmans et al., 2020). However, the in situ cryo-ET structure model, combined with the crystal structure of lamin fragment, showed 40-nm spacing for a parallel coiled-coil dimer, implicating an approximately 10-nm-long overlapping between coil 1a and coil 2 (Ahn et al., 2019; Turgay and Medalia, 2017) (see Discussion section for detail). At the molecular level, the overall lamin filament assembly mechanism is required to resolve the discrepancy of the overlapping lengths in the ACN binding mode.

This study determined the crystal structure representing the A22 binding mode, which further derived the ACN binding mode in the lamin filaments assembly. We further presented the fully assembled filament model, which provides the structural basis for the elasticity and stiffness of the lamin filaments with molecular insights into the assembly mechanism of other IF proteins.

Plasmid construction

The DNA fragments of the human lamin A/C (residues 244-340) were amplified by inserting them into the pProEx-Hta vector (Thermo Fisher Scientific, USA), which encodes the hexa-histidine tag and tobacco etch virus (TEV) protease cleavage site at the N-terminus of lamin protein. For the S295C, I299C, S303C, and K316C mutants, site-directed mutagenesis was performed.

Purification of recombinant proteins

The resulting plasmid was transformed into the Escherichia coli strain BL21 (DE3; Novagen, USA). The E. coli strain was cultured in 4 L of Terrific broth at 37°C until an OD600 of approximately 1.5, and protein expression was induced using 0.5 mM IPTG at 30°C. After cell harvest by centrifugation, cells were resuspended in a lysis buffer containing 20 mM Tris-HCl (pH 8.0), 150 mM NaCl, and 2 mM 2-mercaptoethanol. The cells were disrupted using a continuous-type French press (Constant Systems, UK) at 23 kpsi pressure and was subjected to centrifugation at 19,000 × g for 30 min at 4°C to remove the cell debris. The supernatant was loaded onto an affinity chromatography column using a cobalt-charged agarose resin (Qiagen, The Netherlands) in lysis buffer. The target protein was eluted with lysis buffer supplemented with 250 mM imidazole and 0.5 mM EDTA. The eluate was treated with TEV protease and then loaded onto a HiTrap Q column (GE Healthcare, USA) to cleave the hexa-His-tag. A linear gradient of increasing NaCl concentration was applied to the HiTrap Q column. The fractions that contained the protein were applied onto a size exclusion chromatography column (HiLoad Superdex 200 26/600 column; GE Healthcare) pre-equilibrated with lysis buffer.

Crystallization, structure determination, and analysis

The K316C mutant lamin fragment (residues 244-340, 7 mg/ml) was crystallised in a precipitation solution containing 4% (v/v) Tacsimate (pH 5.5), and 8% (w/v) PEG3350, supplemented with 100 μM methyl mercury acetate, using the hanging-drop vapour diffusion method at 17°C. The diffraction datasets were collected using an Eiger 9M detector at Beamline 5C at PLS (Korea) and were processed with the HKL2000 package (Otwinowski and Minor, 1997). The partial model was obtained by ab initio phasing using the ARCIMBOLDO_LITE program, and the final structure was determined by molecular replacement-single wavelength anomalous diffraction (MR-SAD) with PHASER in the PHENIX package (Afonine et al., 2010; Caballero et al., 2018; Sammito et al., 2015). The coiled-coil pitch of crystal structures was analysed using the program TWISTER (Strelkov and Burkhard, 2002).

SEC-MALS analysis

The molecular mass of lamin proteins was determined using analytical size exclusion chromatography coupled with multi-angle light scattering (SEC-MALS). The wild-type and mutants (S303C and K316C) of the lamin 244-340 fragments (2 mg/ml) were injected into a Superdex 200 Increase 10/300 GL column (GE Healthcare) pre-equilibrated with 20 mM Tris-HCl pH 7.5 buffer containing 150 mM NaCl. SEC-MALS data was analysed by ASTRA 6 software (WYATT, USA).

Structure prediction using AlphaFold2-multimer

The prediction model of the A22 four-helix bundle, comprising residues 275-330 of lamin A, was generated by AlphaFold2-multimer using the reduced database (Akdel et al., 2021; Evans et al., 2021; Jumper et al., 2021). The predicted aligned error and predicted local distance difference test (pLDDT) on Cα were analysed with ALPHAPICKLE to validate the model.

Molecular dynamics (MD) simulation

The side chains of Cys316 in the crystal structure were substituted with Lys for wild-type structure using Pymol (Schrodinger, 2015). The central region (residues 272-336) was extracted for MD simulation. The topologies and gromacs files were generated using CHARMM36m force field in CHARMM-GUI (Huang et al., 2017; Jo et al., 2008). The structure was solvated in TIP3P water and neutralized by adding 150 mM KCl molecules. Energy minimization, equilibration, and MD simulation were performed using the GROMACS software (Hess et al., 2008; Pronk et al., 2013). The system was subjected to energy minimization using the steepest descent algorithm. The minimized state was equilibrated with a 125 ps NVT (constant number, volume, and temperature) simulation to attain the temperature of 310 K and a 125 ps NPT (constant number, pressure, and temperature) simulation for the target pressure of 1 bar. The MD production run of 10 ns in 2 fs time steps started at the endpoint of equilibration. The root mean square deviation (RMSD) of the simulated structure was calculated from the trajectory data using the GROMACS tool.

Molecular modelling of the snake-shaped lamin filament

Overall modelling procedures were performed manually using Pymol (Schrodinger, 2015) to align the fragments and COOT (Emsley and Cowtan, 2004) for model building and connection. GalaxyRefineComplex (Heo et al., 2016) further refined all models for energy minimization and MD simulation-based relaxation. The model of the ACN four-helix bundle, consisting of residues 27-66 and residues 338-381, was constructed by referring to the ACN bundle model suggested by Stalmans et al. (2020). After structure refinement of the ACN bundle, the Leu338 residues of the ACN bundle and Leu337 residues of the crystal structure of the A22 bundle were manually connected, and the crashing regions of coil 2A were slightly adjusted. The ACN-A22-ACN model was well-refined by GalaxyRefineComplex (Heo et al., 2016).

Before linking the A11 tetramer, packing interactions of the crystal structure of the lamin A11 tetramer were eliminated by energy minimization and relaxation using GalaxyRefineComplex (Heo et al., 2016). The ACN-A22-ACN bundle and the relaxed A11 tetramer were aligned and connected based on the overlapping regions consisting of residues 27-66. The overlapping residues of 244-247 in coil 2A were removed and refined using the GalaxyRefineComplex (Heo et al., 2016). The extended assembly models were constructed by repeating the simple connection between the A22, ACN, and A11 bundles, as below.

Structure of lamin coil 2 fragment

To elucidate the A22 interaction at the molecular level, we attempted to crystallize diverse coil 2 fragments. We finally determined the crystal structure of a coil 2 fragment (residues 244-340) harbouring the K316C mutation at 1.8 Å resolution using ab initio molecular replacement and MR-SAD experiments (Supplementary Table S1). The K316C mutation was introduced by referencing the corresponding residue of lamin B1 in the sequence alignment (Fig. 1A, Supplementary Fig. S1). We found that the purified K316C mutant protein made a higher oligomer in the gel filtration chromatography compared to dimeric wild-type proteins (Supplementary Fig. S3).

To better describe this structure, we divided the coil 2 region into four subparts based on the periodicities of the sequence: coil 2A (residues 240-277; hendecad repeat), coil 2B (residues 278-319; heptad repeat), stutter (residues 320-330), and coil 2C (residues 331-381; heptad repeat) (Fig. 1A, Supplementary Fig. S1). Therefore, the crystal structure contains coil 2A, coil 2B, stutter, and coil 2C, except for the three N-terminal residues and 41 C-terminal residues (Figs. 1A and 1B). The asymmetric unit contained two α-helices interacting in opposite directions (chains A and B; Fig. 1B, Supplementary Fig. S4A). The crystallographic two-fold operation of the asymmetric unit created four α-helices closely interacting (chain A, B, A’, and B’; Fig. 1B, Supplementary Fig. S4B). The four α-helices are arranged tail-to-tail along with the coiled-coils, forming a typical antiparallel four-helix bundle in the central overlapping region. The antiparallel-interacting regions between the parallel dimers (A-A’ and B-B’) consist of coil 2B and stutter (coil 2B-stutter) (Figs. 1B and 1C; left). Contrastingly, the two coil 2A α-helices of the hendecad repeats were arranged parallelly without apparent interactions (Figs. 1B and 1C; right).

Antiparallel four-helix bundle of coil 2B-stutter

The antiparallel four-helix bundle of the lamin coil 2B-stutter region showed the typical hydrophobic a-d core along with the central space of the four α-helices, formed by the residues at the a and d positions of the heptad repeats (Fig. 1, Supplementary Fig. S5), as observed in the repressor of primer (Rop) protein (Protein Data Bank [PDB] code: 4DO2), which is a widely used model system of antiparallel four-helix bundles (Deng et al., 2006).

The typical a-d core four-helix bundle structures contain inter-chain polar interactions between the residues of e and e (e-e) and g and g (g-g) positions on the surface of the four-helix bundle (Deng et al., 2006; Lupas and Bassler, 2017; Lupas et al., 2017) (Fig. 2A). Of these, the polar interaction networks Glu317-His289-R321-Glu324 and K319-E291-Q312-R298-Q308 seem important in stabilizing the four-helix bundle on the e and g positions (Fig. 2A). Notably, both ends of the four-helix bundle are disrupted by hydrophilic residues Gln281 and Glu330 at the d positions, limiting further elongation of the four-helix bundle (Figs. 1B and 1C).

The wild-type structure was modelled by restoring Lys316 from the K316C mutant in silico. The mutated Cys316 residue in the K316C mutant was at the d position of the four-helix bundle, which is more suitable for the four-helix bundle formation than the wild-type Lys residue. However, the MD simulation of the wild-type model suggested that the four-helix bundle conformation is also stabilized in the wild-type structure, indicating that the wild-type structure is not significantly different from the K316C structure presented in this study (Supplementary Fig. S6).

The A22 binding mode

This structure shows the antiparallel interaction between coil 2 regions, which is directly matched to the classical A22 binding mode (Steinert, 1993; Vermeire et al., 2021). To test whether the four-helix bundle structure of the coil 2 fragment (residues 244-340) represents the classical A22 interaction, we analysed the molecular sizes of the coil 2 fragment harbouring the S303C mutation. Because Ser303 is at the center of the antiparallel arrangement of this structure, the mutant coil 2 fragment would be within favourable distance to form a disulfide bond in the S303C mutant coil 2 fragments (Fig. 2B). Unlike the wild-type coil 2 fragment that formed the coiled-coil dimer in solution, SEC-MALS analysis showed that the S303C mutation created the disulfide-mediated tetrameric complex, as expected from the crystal structure (Fig. 2B, Supplementary Fig. S3). Also, we performed the SEC experiment with the S295C and I299C mutant proteins, which showed only dimeric sizes unlike the tetrameric size of S303C (Supplementary Fig. S7). These observations indicate that this structure represents a snapshot of the assembly process in the A22 binding mode. Furthermore, the genetic laminopathy-related mutations were found at the residues of the e-e and g-g interfaces of the four-helix bundle, such as S303C/P, Q294P, R298C, and E317K (Dittmer and Misteli, 2011; Szeverenyi et al., 2008). These findings indicate that the four-helix bundle formation is an important step in forming the proper nuclear envelope structure, although the further experimental confirmation is required (Fig. 2). Thus, we concluded that this structure of the coil 2 fragment represents the A22 interaction as the first atomic model.

Three sequential four-helix bundles

This structure of the A22 interaction showed that the C-terminal region of coil 2C after Glu338 (residues 338-381) did not form the coiled-coil interaction due to the phase shift caused by four additional amino acids of the stutter region (Supplementary Fig. S8). This unpaired coiled-coil region at the after-stutter coil 2C part gave the structural hints in the assembly process between the A11 tetramers. The unpaired coiled coils have a high potential to provide the platforms for the molecular interactions.

We noted that the coil 1a region of the other A11 tetramer as the binding part of the unpaired coil 2C region in the assembly process. The parallel four-helix bundle models were built to represent the ACN binding mode of coil 2C and coil 1a suggested by Makarov et al. (2019) and Stalmans et al. (2020). We built this model by trimming and refining the four-helix bundle models used in the previous research (Jeong et al., 2022). Then, this model (residues 338-381 in the coil 2C part) was linked to the C-terminal ends of the A22 four-helix bundle model (residues 244-337) (Figs. 3A and 3B), posing into the spaces between the coil 2A α-helices of the other dimers in the A22 four-helix bundle (Fig. 3C). This model, similar to the ACN models proposed by Makarov et al. (2019) and Stalmans et al. (2020), is strongly supported by cross-linking mass analyses (Supplementary Fig. S9).

Then, we laterally arranged the coil 2A regions alongside the central ACN four-helix bundle because the ACN interaction was not affected by the presence of the coil 2A part in our previous results (Fig. 3C) (Ahn et al., 2019; 2020). This arrangement of coil 2A makes a cross-section of the six α-helices, which was observed in the cryo-ET images (Turgay and Medalia, 2017). This coil 2-full-coverage model with the coil 1a from the adjacent unit formed an approximately 24-nm-long assembly, comprising the three sequential four-helix bundles with the internal 2-fold symmetry around the Ser303 residue: ACN-A22-ACN (Fig. 3C).

Snake-shaped model of the lamin filament

The crystal structure of a long lamin fragment (residues 1-300) revealed the different bending angles at the linker regions between the protomers of the tetramer (Ahn et al., 2019). The differential bending at the L1 region seemed to stabilize the left-handed coiled-coil interaction of the coil 1a region in the long lamin fragment, despite the phase shift between coil 1a and coil 1b due to linker L1 (Ahn et al., 2019). The linker L12 region has many non-homologous residues at the a, d, and h positions, which may destabilize the coiled-coil interaction within the parallel dimer. To investigate the conformations and bending angles of the A11 tetramer in the relaxed state, we excluded the crystal packing interactions from the lamin structure by the structure relaxation using GalaxyRefineComplex (Heo et al., 2021). The coil 2 and coil 1a regions were merged, forming a stack of the L1 and L12 from the coil 1b tetrameric core at the relaxed state, resulting in a pseudo-two-fold symmetry at the Ala146 residue (Fig. 3D, Supplementary Fig. S10A). The bending angles at the linker regions were in the range of 46_°-64_° (Supplementary Fig. S10B).

To build the lamin filament model containing the entire central rod domains, we combined the coil 2 full-coverage model of ACN-A22-ACN bundles with the A11 tetramer at the relaxed state. The two models were linked by overlapping the coil 1a regions, keeping the bending angles (Figs. 3D and 3E). Then, we performed the MD refinement on the model using GalaxyRefineComplex (Heo et al., 2021), which did not significantly change the initial bending angle (Fig. 3E).

Next, we built a longer filament containing more repeating units in the same manner, resulting in a snake-like zigzag pattern along the filament axis (Fig. 4A, Supplementary Data 1). Finally, the Ig-like domains were attached to the C-terminal ends of coil 2C in the model (Fig. 4A). The space between the repeating units was in the 40-43 nm range, depending on the bending angles. The snake-like model caused the 20- to 22-nm interval between the adjacent Ig-like domains and the 40- to 43-nm interval between the A11 tetramers (Fig. 4A, Supplementary Data 1).

In this study, we determined the crystal structure of lamin coil 2 fragments, representing the A22 interaction at atomic resolution. This study revealed that the A22 interaction was responsible for the antiparallel four-helix bundle with the coil 2B-stutter regions, whose structure is analogous to the model four-helix bundle protein Rop. Our study provided molecular answers to the functional importance of the length and sequence periodicity in the subdomains. We proposed the sequential arrays of the four-helix bundles of ACN-A22-ACN in the coil 2 region, revealing that each area with a different sequence periodicity has cognate binding partners. The two coiled-coil pairs of coil 2B make an antiparallel four-helix bundle, and the coil 2C pair and coil 1a pair form a parallel four-helix bundle during filament formation. Combining the results, we built a snake-like filament model by combining the A22 four-helix bundle with A11 tetramer from previous structural results, exhibiting the intrinsic curvature along the linear filament axis in the relaxed state.

In particular, the 11-residue-long stutter region has a unique sequence feature in terms of the heptad and hendecad repeat pattern (Arslan et al., 2011; Strelkov et al., 2002). In the soluble dimeric unit of lamin, the stutter poses as a hendecad with an increased coiled-coil pitch between the heptad regions coil 2B and coil 2C without a phase shift, as observed in the crystal structures of lamin, vimentin, and keratin (Supplementary Fig. S2) (Lee et al., 2012; Strelkov et al., 2002; 2004). In contrast, the first seven residues of the stutter were merged into the coil 2B as part of the A22 bundle, while the remaining four residues inhibited the coiled-coil interaction between the coil 2Cs through phase shift (Supplementary Fig. S8). This phase shift in the stutter inhibited coiled-coil interaction within the dimeric unit promotes the ACN interaction with the coil 1a of the different units.

This curved filament model provides a molecular answer to resolving the discrepancy in spacing between the dimeric units in the filamentous form between the in-situ cryo-EM and the other structural predictions. We obtained the 40- to 43-nm spacing between the longitudinal repeating dimeric units of the central rod domain in this model at the curved and relaxed state (Fig. 4). However, the spacing is increased to approximately 46 nm in the fully stretched form considering the α-helical conformations (~1.5 Å rise per residue) of the central rod domain (355 residues) with 6.5-nm overlap of the ACN bundle. Therefore, we propose a reversible transformation between the curved and stretched states depending on the external tensile force applied to the filament. The reversible transformation mechanism meets two controversial observations of the cryo-ET and cross-linking mass analyses (Makarov et al., 2019; Stalmans et al., 2020; Turgay et al., 2017). The 6.5-nm-ACN overlapping is matched to the values obtained from most models that were assessed using cross-linking mass analysis (Makarov et al., 2019; Stalmans et al., 2020). Furthermore, this model explains the 40-nm spacing measured using in situ cryo-ET with the 43-nm interval at the curved state of this filament model, because the 43-nm spacing at the curved form can be decreased by local compression forces on the nuclear membrane (Turgay and Medalia, 2017; Turgay et al., 2017). Makarov et al. (2019) suggested a sliding model of the lamin filament, where the occupied length of the linker regions along the filaments varied with unstructured conformations, explaining the changing spacings. However, the unstructured conformation of linkers was not supported by the crystal structures. It contained a limitation in explaining reversible elasticity against the external tensile force, as the unstructured linkers lacked an intrinsic restoring force.

The reversible transformation mechanism explains how the nuclear structure endures the large external impact to protect highly fragile DNA. The lamin filament could be stretched to the long and straight form by the tensile force, absorbing the external shock without breaking its α-helical conformations (Qin and Buehler, 2011; Sapra et al., 2020). If the tensile forces vanish, the stretched lamin filament would be returned to the original snake-like shape (Fig. 4B). Absorption of the initial eminent external stresses by the lamin filaments would be crucial in protecting the nucleus at the initial impact stage. However, excessive elasticity would result in the abrupt deformation of the nuclear envelopes, eventually causing local pulling and cleavage of the DNA molecules in the nucleus. Therefore, both the stiffness and elasticity of the nuclear envelope are important in protecting the DNA molecules. Once the lamin filaments are fully stretched, it would exhibit a strong resistance against higher tensile forces until the α-helical conformation of the lamin filaments are irreversibly broken (Qin and Buehler, 2011; Sapra et al., 2020). The evenly distributed meshwork of filaments with a balance between the elasticity and the stiffness would be critical in enduring the external large tensile force, especially for the muscle cells, vascular endothelial cells, and lipocytes, which are subject to constant mechanical stresses.

In our previous study (Ahn et al., 2019), we proposed a A22 binding mode, called eA22, which might not be compatible with the results of the antiparallel coiled-coil of coil 2 in this study. We presume that the previous eA22 binding mode might not represent the physiological binding of lamin because it was based on the chemical cross-linkers with the lamin 1-300 fragment, which does not contain the important rest coil 2 in the A22 interaction.

In conclusion, the assembly mechanism of the lamin filaments was a long-unsolved puzzle. In this study, we propose a full assembly model of the lamin filaments at the molecular level, based on the crystal structure representing the A22 binding mode, which was the final missing piece of the puzzle. The assembly model of the lamin filaments provided molecular insights into the physical properties of the nuclear envelopes that were crucial to protecting the DNA molecules. These results will help us understand the assembly mechanism of the other IF proteins, such as vimentin and keratin.

We would like to thank the Pohang Accelerator Laboratory 5C beamline (Pohang, Republic of Korea) for the X-ray diffraction experiments and the Korea Basic Science Institute (Ochang, Republic of Korea) for the SEC-MALS analysis. This research was supported by grants from the National Research Foundation of Korea (2019R1A2C2085135 and 2020R1A4A1019322 to N.-C.H., and 2021R1I1A1A01049976 to J.A.). This work was also supported by the BK21 Plus Program of the Department of Agricultural Biotechnology, Seoul National University, Seoul, Korea.

J.A. and I.J. performed the experiments. J.A., I.J., S.J., J.L., and N.-C.H. conceived the experimental designs and interpretation of data and revised the manuscript.

The authors have no potential conflicts of interest to disclose.