LINC complex branching through structurally diverse SUN-KASH 6:6 assemblies Authors

The LINC complex mechanically couples cytoskeletal and nuclear components across the nuclear envelope to fulfil a myriad of cellular functions, including nuclear shape and positioning, hearing and meiotic chromosome movements. The canonical model of the LINC complex is of individual linear nucleocytoskeletal linkages provided by 3:3 interactions between SUN and KASH proteins. Here, we provide crystallographic and biophysical evidence that SUN-KASH is a constitutive 6:6 complex in which two SUN trimers interact back-to-back. A common SUN-KASH topology is achieved through structurally diverse 6:6 interaction mechanisms by distinct KASH proteins, including zinc-coordination by Nesprin-4. The SUN-KASH 6:6 complex is incompatible with the current model of a linear LINC complex and instead suggests the formation of a branched LINC complex network. In this model, SUNKASH 6:6 complexes act as nodes for force distribution and integration between adjacent SUN and KASH molecules, enabling the coordinated transduction of large forces across the nuclear envelope.


Introduction
The nuclear envelope partitions nuclear components from the cytoskeleton, thereby necessitating their mechanical coupling across the nuclear envelope to enable cytoskeletal function in the structure and positioning of nuclear contents. This is achieved by the Linker of Nucleoskeleton and Cytoskeleton (LINC) complex, which traverses the nuclear envelope and binds to cytoskeletal and nuclear structures to mediate force transduction between these partitioned components (Starr and Fridolfsson, 2010) ( Figure 1a). In this capacity, the LINC complex is essential for cellular life, performing critical functions in nuclear structure, shape and positioning, in addition to tissue-specific functions including sound perception in the inner ear and chromosome movements during meiosis (Lee and Burke, 2018;Meinke and Schirmer, 2015;Starr and Fridolfsson, 2010). Further, mutations of the LINC complex and its interacting partners are associated with human laminopathies, including Hutchison-Gilford progeria syndrome and Emery-Dreifuss muscular dystrophy (Meinke et al., 2011;Mejat and Misteli, 2010).
The LINC complex is formed of SUN (Sad1 and UNC84 homology) domain and KASH (Klarsicht, ANC-1 and Syne homology) domain proteins (Meinke and Schirmer, 2015;Starr and Fridolfsson, 2010), which interact immediately below the outer nuclear membrane, through complex formation between their C-terminal eponymous SUN and KASH domains (Sosa et al., 2012;Wang et al., 2012;Zhou et al., 2012). SUN proteins then traverse the approximately 50 nm peri-nuclear space and cross the inner nuclear membrane, enabling their N-termini to bind to nuclear contents, including reported interactions with the nuclear lamina (Crisp et al., 2006;Haque et al., 2006;Haque et al., 2010), chromatin (Chi et al., 2007) and the telomeric ends of meiotic chromosomes (Shibuya et al., 2014). Similarly, KASH domain proteins cross the outer nuclear membrane and have large cytoplasmic extensions to enable their Ntermini to bind to the cytoskeleton (Spindler et al., 2019;Starr and Fridolfsson, 2010). Thus, the LINC complex axis is established by a peri-nuclear SUN-KASH core interaction and mechanically couples the cytoskeleton and nuclear contents (Figure 1a).
In mammals, there are five SUN proteins, of which SUN1 and SUN2 are widely expressed and perform partially redundant functions Zhang et al., 2009). There are similarly multiple KASH proteins, four of which are Nesprins (Nuclear Envelope Spectrin Repeat proteins). Nesprin-1 and Nesprin-2 are widely expressed, perform overlapping functions and contain large cytoplasmic spectrin-repeat domains with N-termini that bind to actin (Banerjee et al., 2014;Starr and Fridolfsson, 2010). Nesprin-3 shares a similar KASH domain but its cytoplasmic region binds to plectin, mediating interactions with intermediate filaments (Ketema and Sonnenberg, 2011). The two most divergent KASH proteins, Nesprin-4 and KASH5, exhibit substantial sequence diversity within their KASH domains ( Figure 1b). Nesprin-4 functions in the outer hair cells of the inner ear and is essential for hearing (Horn et al., 2013a). Its N-terminus interacts with kinesin, which mediates microtubule binding and plus-end directed movements that achieve the basal positioning of nuclei (Horn et al., 2013a;Roux et al., 2009).
KASH5 functions in meiosis and is essential for fertility (Horn et al., 2013b;Morimoto et al., 2012). Its N-terminus interacts with dynein-dynactin (Horn et al., 2013b;Morimoto et al., 2012), which mediates microtubule binding and minus-end directed motility that drives rapid chromosomal movements to facilitate homologous chromosome pairing (Lee et al., 2015;Zetka et al., 2020). Thus, KASH proteins execute a range of LINC complex functions in transmitting actin forces, plus-/minus-end directed microtubule movements and the tensile strength of intermediate filaments into the nucleus.
The canonical model of the LINC complex is based on crystal structures of the SUN-KASH domain complexes formed between SUN2 and Nesprin-1/2 (Sosa et al., 2012;Wang et al., 2012). The SUN domain adopts a 'three-leaf clover'-like structure, in which a globular trimer extends from a short Nterminal trimeric coiled-coil (Sosa et al., 2013). KASH domains are intertwined between SUN protomers and their path is defined by three distinct regions. The KASH C-terminus contains a triple proline motif that packs between the globular cores of SUN protomers. The KASH mid-region winds around the trimeric arc and is wedged between the globular core of one SUN protomer and a β-turnβ loop, known as the KASH-lid, of the adjacent protomer. The KASH N-terminus then turns by >90˚ to radiate out from the trimer axis and forms a disulphide bond with a SUN protomer (between SUN2 and KASH1 amino-acids C563 and C8774, respectively), which is predicted to enhance the tensile strength of SUN-KASH (Jahed et al., 2015;Sosa et al., 2012). The biological unit of SUN-KASH was interpreted from the crystal lattice as a 3:3 complex, comprising three KASH domains bound to a single SUN trimer (Sosa et al., 2012;Wang et al., 2012). On this basis, it was proposed that the LINC complex consists of a SUN-KASH 3:3 complex that is orientated vertically to allow KASH proteins to cross the outer nuclear membrane and SUN to form an extended trimeric coiled-coil that spans the peri-nuclear space (Sosa et al., 2013;Sosa et al., 2012) (Figure 1a). Thus, the canonical model of the LINC complex is of individual linear structures that provide independent nucleocytoskeletal couplings. Whilst it has been proposed that branching or higher-order assembly between LINC complexes may be advantageous in distributing large forces and achieving coordinated motions (Jahed et al., 2018;Lu et al., 2008;Sosa et al., 2013;Wang et al., 2012;Zhou et al., 2012), we have hitherto lacked structural evidence in favour of this hypothesis.
Here, we provide crystallographic and biophysical evidence in support of the LINC complex forming a branched network rather than individual linear structures. We find that SUN-KASH complexes between SUN1 and Nesprin-4, KASH5 and Nesprin-1 are 6:6 structures that consist of constitutive back-to-back interactions between SUN trimers. The three distinct KASH domains provide structurally diverse but related 6:6 interfaces that achieve the same topology with potential hinge-like motion between SUN trimers. The SUN-KASH 6:6 complex is incompatible with the current model of a linear LINC complex, and instead suggests the formation of a branched LINC complex network. Thus, we propose that SUN-KASH domain complexes act as nodes for branching and integration between LINC complexes to achieve the coordinated transduction of large forces across the nuclear envelope.

SUN-KASH complexes are 6:6 hetero-oligomers
The previously reported crystal structures of SUN-KASH complexes between SUN2 and Nesprins 1-2 revealed almost identical structures that were interpreted as 3:3 hetero-oligomers (Sosa et al., 2012;Wang et al., 2012). The KASH domains of Nesprin-4 and KASH5 exhibit sequence divergence from Nesprins 1-3, including the presence of conserved N-terminal motifs of 381-CCSH-384 and 545-PPP-547, respectively ( Figure 1b). On this basis, we reasoned that Nesprin-4 and KASH5 may impose unique SUN-KASH structures that differ from the classical architecture of Nesprin 1-3 complexes, which may underlie their specialised functional roles. We thus solved the X-ray crystal structures of SUN-KASH complexes formed between the SUN domain of SUN1 and KASH domains of Nesprin-4 and KASH5 (herein referred to as SUN1-KASH4 and SUN1-KASH5). The SUN1-KASH4 structure was solved at a resolution of 2.75 Å and revealed a 6:6 assembly in which two globular 3:3 complexes are held in a back-to-back configuration through zinc-coordination by opposing KASH4 molecules across the 6:6 interface ( Figure 1c, Table 1 and Supplementary Figure 1a Is the 6:6 assembly unique to SUN-KASH complexes formed by Nesprin-4 and KASH5? We next solved the crystal structure of the SUN-KASH complex between SUN1 and Nesprin-1 (herein referred to as SUN1-KASH1). The SUN1-KASH1 structure was solved at 1.82 Å resolution and demonstrated a similar 6:6 back-to-back assembly, albeit with less extensive interface-spanning interactions provided solely by opposing KASH-lids ( Figure 1c, Table 1 and Supplementary Figure 1a,d). Importantly, the SUN1-KASH1 structure closely matches the previous SUN2-KASH1/2 structures, in which similar 6:6 interfaces were present in the crystal lattice but were dismissed as crystal contacts (Supplementary Figure 1e) (Sosa et al., 2012;Wang et al., 2012). It was thus critical to determine whether SUN1-KASH1 is a 6:6 complex in solution. We utilised size-exclusion chromatography multi-angle light scattering and we failed to detect 3:3 complexes in any biochemical conditions tested. Thus, we conclude that SUN-KASH complexes are 6:6 hetero-oligomers in which two 3:3 complexes interact in back-to-back configurations. The SUN-KASH 6:6 structure is incompatible with the current model of a linear LINC complex and instead demonstrates a constitutive interaction between SUN trimers that mediates the physical coupling of adjacent LINC complexes within the peri-nuclear space.

Structural diversity within the SUN-KASH 6:6 interface
Our SUN-KASH crystal structures reveal the formation of similar 6:6 architectures through diverse back-to-back interfaces. Whilst the C-termini of all three KASH domains adopt the same structure, their N-termini differ substantially (Figure 2a Figure   3c). Overall, the three structures demonstrate alternative SUN-KASH 6:6 interaction mechanisms that are differentially exploited by KASH proteins. SUN1-KASH4 and SUN1-KASH1 represent extreme states of this spectrum in which the 6:6 interface is mediated solely by KASH-mediated metal coordination and SUN1 KASH-lids, respectively. In contrast, SUN1-KASH5 adopts an intermediate structure that utilises both KASH and KASH-lid interaction mechanisms to form a fully enclosed 6:6 interface.

SUN1-KASH1 complex formation depends on KASH-lid 6:6 interactions
On the basis of their crystal structures, we predicted that KASH-lid tip-to-tip interactions are essential for 6:6 hetero-oligomer formation in solution by SUN1-KASH1 but not SUN1-KASH4. We tested this by generating glutamate mutations of KASH-lid tip amino-acids I673 and F671, which mediate interface-  Table 2). The failure to observe smaller hetero-oligomers demonstrates that SUN1-KASH1 3:3 complexes are unstable in absence of the 6:6 interface, indicating that SUN1-KASH1 is a constitutive 6:6 hetero-oligomer. In agreement with the equal roles of KASH domain and KASH-lid interactions at its 6:6 interface, SUN1-KASH5 exhibited intermediate phenotypes upon I673E and F671E mutation, with retention of complex formation but reduction in oligomer size to species that likely reflect partially dissociating 6:6 complexes (Figure 3a,b and Supplementary Figure 4d,e). We conclude that the diverse roles of KASH-lids at the 6:6 interfaces of SUN-KASH crystal structures are truly reflective of their solutions states and that KASH-lid tip-to-tip interactions are essential for assembly of a constitutive SUN1-KASH1 6:6 hetero-oligomer.

Hinge-like motion of the SUN-KASH 6:6 interface
How is the SUN-KASH 6:6 complex orientated within the nuclear envelope? Its back-to-back assembly suggests a horizontal orientation, parallel to the outer nuclear membrane, with SUN trimers organised obliquely within the peri-nuclear space. In this configuration, tension forces carried by SUN and KASH molecules would exert bending moments on the structure, favouring a hinge-like angulation between opposing 3:3 complexes. We thus utilised small-angle X-ray scattering (SAXS) to determine whether  Table 2). In case of large-scale motion, we performed SAXS-based rigid-body modelling using two SUN1-KASH1 3:3 complexes as independent rigid bodies. We consistently obtained models that closely fitted experimental data (χ 2 = 1.56) in which 3:3 complexes interact back-to-back with a bend of approximately 60˚ relative to the crystal structure (  Table 2). In this model, two pairs of KASH-lid tip-to-tip interactions by I673 and F671 are retained, whilst the third is disrupted, and an additional interface is formed between opposing central KASHlids. Thus, KASH-lids act as a hinge at the 6:6 interface, opening the linear crystal structure into an angled conformation that is seemingly more stable in solution. This hinged structure is suited to force transduction between oblique SUN and KASH molecules and places all six KASH1 N-termini in favourable positions to cross the outer nuclear membrane.
Is a similar hinge-like angulation possible for SUN1-KASH4 and SUN1-KASH5? Whilst their extensive 6:6 interfaces retain linear structure in solution (Supplementary Figure 6a-c and Table 2), angulation may be achieved by tension forces. We thus performed normal mode analysis to determine whether angled structures are conformationally accessible. We observed low frequency normal modes corresponding to hinge-like angulation at the 6:6 interface for all SUN-KASH complexes (Figure 4b), indicating that angled conformations are accessible flexible states. We thus conclude a model in which hinged SUN-KASH 6:6 complexes, parallel with the outer nuclear membrane, act as nodes for the integration and distribution of tension forces between oblique SUN trimers and KASH molecules within a branched LINC complex network ( Figure 5).

Discussion
The LINC complex is essential for nuclear shape and positioning in almost all eukaryotic cells, and fulfils a number of specialised roles, such as in hearing and meiotic cell division (Lee and Burke, 2018;Meinke and Schirmer, 2015;Starr and Fridolfsson, 2010). As a mechanical transducer, the structure-function relationship underlies the highly diverse cellular roles of the LINC complex. Specifically, the structure and oligomeric assembly of its protein components dictate the topology of the LINC complex and thereby its mechanism of force transduction within the nuclear envelope. On the basis of their X-ray crystal structures and solution states, we report that the globular SUN-KASH cores of diverse LINC complexes are constitutive 6:6 hetero-oligomers in which SUN trimers interact back-to-back. This topology is incompatible with the current model of individual linear 3:3 LINC complexes (Sosa et al., 2013;Sosa et al., 2012), and instead indicates the formation of a branched LINC complex network.
A branched network is an attractive means for force transduction as it can transmit forces of magnitudes far in excess of those carried by single molecules, is impervious to disruption of individual linkages, and allows communication and coordination between adjacent molecules. Thus, SUN-KASH 6:6 hetero-oligomers enable force distribution and integration between adjacent molecules to achieve coordinated actions within the nucleus. In this capacity, LINC complex branching by SUN-KASH 6:6 assembly explains previous cellular observations of higher-order LINC complex structures, including its immobility within the nuclear envelope (Lu et al., 2008), foci formation within the meiotic nuclear envelope (Ding et al., 2007;Horn et al., 2013b;Morimoto et al., 2012), and the formation of transmembrane actin-associated nuclear (TAN) lines (Luxton et al., 2010).
The back-to-back nature of SUN-KASH 6:6 complexes suggests their orientation parallel to the outer nuclear membrane, with SUN trimers organised obliquely within the peri-nuclear space ( Figure 5). Our SAXS analysis of SUN1-KASH1 indicates that it adopts a hinged conformation in solution, stabilised by two KASH-lid tip-to-tip interactions and the lateral association of central KASH-lids. This provides a more extensive interface than the tripod of KASH-lid tip-to-tip interactions within the crystal structure, explaining its preferential formation outside of a crystal lattice. In contrast, SUN1-KASH4 and SUN1-KASH5 have extensive 6:6 interfaces that preserve linearity in solution. Nevertheless, normal mode analysis predicted that hinged structures of all three SUN-KASH complexes are conformationally accessible states. Thus, SUN-KASH 6:6 hetero-oligomers may become angled in response to tension forces carried by obliquely orientated SUN and KASH molecules. All three SUN-KASH 6:6 interfaces consist of circumferential exteriors and hollow cores that are largely hydrophobic in nature. Thus, we envisage that the SUN-KASH hinged structure may be stabilised by interaction of its 6:6 interface with phospholipids of the outer nuclear membrane, potentially forming an integrated membrane-bound complex between a 6:6 hetero-oligomer and the transmembrane regions of its six KASH proteins.
How do the diverse 6:6 interfaces provided by KASH proteins facilitate their specialised functions? An intriguing observation is that Nesprin-4 and KASH5, which transduce microtubule forces (Horn et al., 2013a;Horn et al., 2013b;Morimoto et al., 2012;Roux et al., 2009), demonstrate extensive interactions at their 6:6 interfaces. In contrast, a far less extensive 6:6 interface is found in classical Nesprins, which transduce actin forces and the tensile strength of intermediate filaments (Banerjee et al., 2014;Ketema and Sonnenberg, 2011;Starr and Fridolfsson, 2010). Thus, cytoskeletal components may have differential requirements for the strength, structure and stability of SUN-KASH 6:6 hetero-oligomers. Further, their diverse interfaces may provide disparate mechanisms for the timely assembly and disassembly of LINC complex networks during miotic and meiotic cell cycles. This could be achieved by inhibition of the 6:6 interface, which is sufficient to disrupt the SUN1-KASH1 globular complex. Further, as the SUN1-KASH4 6:6 interface is mediated by zinc-coordination sites, its formation could be regulated by zinc availability and sequestration within the peri-nuclear space.
The SUN-KASH 6:6 hetero-oligomer provides the first structural evidence, but perhaps not the sole structural means, of LINC complex network formation. Additional branching events could result from variation in oligomer state along the SUN-KASH axis. Whilst SUN is assumed to form a trimeric coiledcoil extending from its globular core, its protein sequence is inconsistent with formation of a single continuous coiled-coil. Instead, it suggests the presence of short discrete coiled-coils, of potentially distinct oligomers, that are connected by unstructured linkers. Further, C526 residues of SUN1 are reported to form disulphide bonds (Lu et al., 2008), suggesting tethering between SUN trimers from separate SUN-KASH 6:6 complexes. Thus, oligomer variation and disulphide formation may combine with the SUN-KASH 6:6 interface to provide multiple branching events within the peri-nuclear space.
Whilst there is no reported structural information regarding KASH proteins, we find that KASH5 is dimeric (Manickam & Davies, unpublished findings), indicating branching between SUN-KASH 6:6 complexes and their cytoskeletal attachments. Thus, we propose that coordinated force transduction is achieved by a highly branched LINC complex network. In this model, the lowest degree of branching supported by current structural evidence is of SUN-KASH 6:6 hetero-oligomers mediating force distribution and integration between three KASH dimers and two SUN trimers ( Figure 5).

Size-exclusion chromatography multi-angle light scattering (SEC-MALS)
The absolute molar masses of protein samples and complexes were determined by size-exclusion chromatography multi-angle light scattering (SEC-MALS). Protein samples at >1 mg/ml (unless otherwise states) were loaded onto a Superdex™ 200 Increase 10/300 GL size exclusion chromatography column (GE Healthcare) in 20 mM Tris pH 8.0, 150 mM KCl, 2 mM DTT, at 0.5 ml/min using an ÄKTA™ Pure (GE Healthcare). The column outlet was fed into a DAWN® HELEOS™ II MALS detector (Wyatt Technology), followed by an Optilab® T-rEX™ differential refractometer (Wyatt Technology). Light scattering and differential refractive index data were collected and analysed using ASTRA® 6 software (Wyatt Technology). Molecular weights and estimated errors were calculated across eluted peaks by extrapolation from Zimm plots using a dn/dc value of 0.1850 ml/g. SEC-MALS data are presented as differential refractive index (dRI) profiles with fitted molecular weights (MW) plotted across elution peaks.

Spectrophotometric determination of zinc content
The presence of zinc in protein samples was determined through a spectrophotometric method using the metallochromic indicator 4-(2-pyridylazo) resorcinol (PAR) (Sabel et al., 2009). Protein samples at 90-200 µM, corresponding to SUN1-KASH4 wild-type and CC381/382SS, and a wild-type sample that had been treated with EDTA prior to gel-filtration, were digested with 0.6 μg/μl proteinase K (NEB) at 60°C for 1 hour. 10 μl of the supernatant of each protein digestion was added to 80 μl of 50 μM 4-(2pyridylazo)-resorcinol (PAR) in 20 mM Tris, pH 8.0, 150 mM KCl, incubated for 5 min at room temperature, and UV absorbance spectra were recorded between 600 and 300 nm (Varian Cary 60 spectrophotometer). Zinc concentrations were estimated from the ratio between absorbance at 492 and 414 nm, plotted on a line of best fit obtained from analysis of 0-100 μM zinc acetate standards.

KASH-binding by SUN1 point mutants
The wild-type and individual point mutations I673E, F671E and W676E of SUN1 (as His6-GCN4 fusions) were co-expressed with KASH (as His6-MBP fusion) as described above. Tris pH 8.0, 150 mM KCl at 0.5 ml/min using an Agilent 1200 HPLC system. The column outlet was fed into the experimental cell, and SAXS data were recorded at 12.4 keV, detector distance 4.014 m, in 3.0 s frames. ScÅtter 3.0 (http://www.bioisis.net) was used to subtract, average the frames and carry out the Guinier analysis for the radius of gyration (Rg), and P(r) distributions were fitted using PRIMUS (P.V. Konarev, 2003). Ab initio modelling was performed using DAMMIF (Franke and Svergun, 2009); 30 independent runs were performed in P1 and averaged. Crystal structures and models were fitted to experimental data using CRYSOL (Svergun D.I., 1995). Normal mode analysis was used to model conformational flexibility for fitting to SAXS data using SREFLEX (Panjkovich and Svergun, 2016), and rigid body and flexible termini modelling was performed using CORAL (Petoukhov et al., 2012).

Normal mode analysis of SUN1-KASH structures
Non-linear normal modes were calculated and visualised for SUN1-KASH 6:6 structures using the NOLB algorithm (Hoffmann and Grudinin, 2017) within the normal mode analysis SAMSON element (https://www.samson-connect.net).

Protein sequence and structure analysis
Nesprin sequences were aligned and visualised using MUSCLE (Madeira et al., 2019) and Jalview (Waterhouse et al., 2009). Molecular structure images were generated using the PyMOL Molecular Graphics System, Version 2.3 Schrödinger, LLC.

Data availability
Crystallographic structure factors and atomic coordinates have been deposited in the Protein Data Bank (PDB) under accession numbers 6R15, 6R16 and 6R2I. All other data are available from the corresponding author upon reasonable request.     Hinge-link conformational flexibility within SUN-KASH 6:6 assemblies.
(a) SAXS rigid body model of SUN1-KASH1 in which two constituent 3:3 complexes from its crystal structure were assigned as rigid bodies, with the 6:6 assembly generated by fitting to experimental SAXS data of solution SUN1-KASH1 (χ 2 = 1.56). (b) Normal mode analysis of SUN-KASH complexes in which non-linear normal modes calculated by the NOLB algorithm are shown as the largest amplitude of motion of one constituent 3:3 complex (blue) relative to its original position and its stationary opposing 3:3 complex within the crystal structure (grey) for SUN1-KASH4 (top), SUN1-KASH5 (middle) and SUN1-KASH1 (bottom).

Figure 5
The LINC complex as a branched network of SUN-KASH assemblies.
Model of the LINC complex as a branched network in which SUN-KASH 6:6 complexes act as nodes for force integration and distribution between two SUN trimers and three KASH dimers, which can bind to spatially-separated and distinct nuclear and cytoskeletal components, respectively. This model enables cooperation between adjacent molecules within a LINC complex network to facilitate the transduction of large and coordinated forces across the nuclear envelope.