Cell culture, transfection and labellingCell culture<\/p>\n
COS-7 cells (Sigma, 87021302) and HEK293T cells (Beyotime, C6008) were cultured in Dulbecco\u2019s Modified Eagle Medium (Thermo Fisher, 41965-039) supplemented with 10% (v\/v) fetal bovine serum (FBS; Sigma, F7524), 1% penicillin\u2013streptomycin (Thermo Fisher, 15140-122), 1% l-glutamine (Thermo Fisher, 25030-081) and 1% sodium pyruvate (Thermo Fisher, 11360-070). U-2 OS-CRISPR-NUP96-mEGFP cells originally obtained from Cytion (300174) and provided by Y. Li were maintained in McCoy\u2019s 5A (Procell, PM150710) supplemented with 10% (v\/v) FBS and 1% penicillin\u2013streptomycin. Cells were cultured at 37\u2009\u00b0C in a humidified incubator containing 5% CO2 and were passaged every 2\u20133 days. All experiments were performed using cells in 20 passages.<\/p>\n
To generate a doxycycline-inducible U-2 OS-CRISPR-NUP96-mEGFP cell line expressing importin-\u03b2, lentiviral particles were produced in HEK293T cells by cotransfection of pTRIPZ-importin-\u03b2-3\u00d7FLAG-ALFA-P2A-tagBFP (derived from the pTRIPZ; Addgene, 206981), psPAX2 (Addgene, 12260) and pMD2.G (Addgene, 12259) at a plasmid ratio of 4:3:1. Viral supernatants were collected 48 and 72\u2009h after transfection and concentrated by polyethylene-glycol-8000 precipitation. U-2 OS-CRISPR-NUP96-mEGFP cells were transduced for 48\u2009h and selected with puromycin (1\u2009\u03bcg\u2009ml\u22121; Yeasen, 727136ES03) for 4\u2009days. For MINFLUX imaging, expression of importin-\u03b2 was induced with doxycycline (0.5\u2009\u03bcg\u2009ml\u22121; MCE, HY-N0565) for 24\u2009h before fixation.<\/p>\n
Cell morphology was routinely monitored during culture. The engineered U-2 OS-CRISPR-NUP96-mEGFP\/importin-\u03b2 cell line was also verified by NUP96-mEGFP fluorescence and doxycycline-inducible importin-\u03b2 expression. No in-house short tandem repeat profiling was performed. All cell lines were regularly tested for mycoplasma contamination by PCR and with the MycoBlue Mycoplasma Detector Kit (Vazyme, D101-01), with negative results.<\/p>\n
Transfection<\/p>\n
COS-7 cells were seeded on 35-mm glass-bottom imaging dishes (ibidi, 81158) 24\u2009h before transfection to reach 60\u201370% confluency. Cells were transfected with plasmids listed in Supplementary Table 1<\/a> using jetPRIME (Polyplus) according to the manufacturer\u2019s instructions. At 4\u20135\u2009h post-transfection, the medium was replaced with fresh culture medium supplemented with 10\u2009mM HEPES and either 50\u2009\u03bcM BCN for site-specific labelling or 50\u2009\u03bcM BOC for control experiments. Where indicated, 10\u2009\u03bcM Thiamet-G (MCE, HY-12588) or 10\u2009\u03bcM OSMI-4 (MCE, HY-114361) was added at this stage and maintained throughout the experiment.<\/p>\n Live-cell labelling<\/p>\n At 20\u201324\u2009h following transfection, cells were washed with medium containing 50\u2009\u03bcM BOC and 10\u2009mM HEPES and incubated for 2\u2009h at 37\u2009\u00b0C to allow excess BCN to clear. Cells were then labelled with 2\u2009\u03bcM HD653 in serum-free medium for 30\u2009min at 37\u2009\u00b0C. For O-GlcNAc perturbation experiments, 10\u2009\u03bcM Thiamet-G or 10\u2009\u03bcM OSMI-4 was included during labelling to maintain treatment conditions. Where indicated, SiR-tetrazine (Spirochrome, SC008) or JF646-tetrazine (Tocris, 7279) was used following the same protocol. After labelling, cells were washed with 1\u00d7 PBS and imaged immediately in FluoroBrite Dulbecco\u2019s Modified Eagle Medium (Thermo Fisher, A1896701) supplemented with 10% (v\/v) FBS, 1% l-glutamine, 1% sodium pyruvate and 10\u2009mM HEPES. Imaging was performed at room temperature with the dish sealed to ensure stable conditions during the roughly 2-h acquisition period.<\/p>\n Immunostaining of endogenous importin-\u03b2<\/p>\n COS-7 cells labelled with HD653 were fixed with 2% paraformaldehyde (PFA) in PBS for 10\u2009min, permeabilized with 0.5% Triton X-100 in PBS for 15\u2009min and blocked with 3% bovine serum albumin in PBS for 90\u2009min. Cells were incubated with an anti-KPNB1 antibody (Abcam, ab2811; 1:1000 dilution) followed by an Alexa Fluor 488-conjugated anti-mouse secondary antibody (Thermo Fisher, A-11001; 1:1000 dilution). Immunofluorescence imaging confirmed localization of endogenous importin-\u03b2 at the nuclear envelope following live-cell labelling (Extended Data Fig. 1b<\/a>).<\/p>\n Estimation of importin-\u03b2 concentration at the nuclear pore<\/p>\n To estimate the local concentration of importin-\u03b2 at the nuclear pore, solutions containing free Alexa Fluor 488 at known concentrations (1\u2009\u03bcm\u20131\u2009mM) were added to immunostained cells. Nuclear pore fluorescence remained distinguishable from the background in the presence of up to 100\u2009\u03bcM free dye but became indistinguishable at 1\u2009mM (Extended Data Fig. 2a<\/a>), indicating that the effective local concentration of importin-\u03b2 at the nuclear pore is in the millimolar range.<\/p>\n Assessment of expression levels of exogenous importin-\u03b2 by immunoblotting<\/p>\n The doxycycline-inducible U-2 OS-CRISPR-NUP96-mEGFP cell line described above was treated with doxycycline (0.5\u2009\u03bcg\u2009ml\u22121) for 0, 6, 10, 15 or 24\u2009h. Non-transduced U-2 OS-CRISPR-NUP96-mEGFP cells without doxycycline treatment were used as a parental control. Cell lysates were collected at the indicated time points and analysed by immunoblotting using an anti-FLAG antibody (Proteintech, 66008-4-Ig; 1:1,000 dilution) to detect exogenous importin-\u03b2 and an anti-KPNB1 antibody (1:2,500 dilution) to detect both endogenous and exogenous importin-\u03b2. \u03b1-Tubulin detected with an anti-\u03b1-Tubulin antibody (ABclonal, AC012; 1:5,000 dilution) was used as a loading control. Doxycycline induction resulted in detectable FLAG-tagged importin-\u03b2 expression, whereas the total KPNB1 signal showed no substantial increase compared with the parental control, consistent with near-endogenous expression of the exogenous protein (Supplementary Figs. 19<\/a> and 20<\/a>).<\/p>\n Assessment of cellular O-GlcNAc levels by immunoblotting<\/p>\n To verify modulation of cellular O-GlcNAcylation, COS-7 cells were treated with 10\u2009\u03bcM Thiamet-G or 10\u2009\u03bcM OSMI-4 as described above and lysed directly in Laemmli sample buffer. Proteins were separated by sodium dodecyl sulfate polyacrylamide gel electrophoresis (SDS\u2013PAGE), transferred to nitrocellulose membranes and probed with the anti-O-GlcNAc antibody RL2 (Invitrogen, MA1-072; 1:1,000 dilution). Bound antibody was detected using an IRDye 800CW goat anti-mouse IgG secondary antibody (LI-COR Biosciences, 926-32210; 1:10,000 dilution) and visualized using an Odyssey imaging system (Fig. 4b<\/a>).<\/p>\n Measurement of nuclear-import rates in live cells<\/p>\n Live-cell nuclear-import assays were performed as described previously49<\/a> with minor modifications. COS-7 cells expressing NES\u2013mCherry\u2013LINuS were treated with 10\u2009\u03bcM Thiamet-G or 10\u2009\u03bcM OSMI-4 and imaged 24\u2009h after transfection following Hoechst 33342 staining (10\u2009\u03bcg\u2009ml\u22121, 10\u2009min). Imaging was performed on a Zeiss LSM 980 confocal microscope. Nuclear import was induced by 488-nm illumination and monitored by mCherry fluorescence using 561-nm excitation. Images were acquired every 10\u2009s for 820\u2009s. Nuclear regions were segmented using Hoechst fluorescence, and nuclear mCherry intensity was quantified over time and normalized to the pre-activation signal. Apparent nuclear-import rate constants were obtained by fitting fluorescence accumulation curves to y\u2009=\u20091\u2009+\u2009(b\u2009\u2212\u20091)(1\u2009\u2212\u2009e\u2212kt), where b is the plateau fluorescence intensity and k is the apparent nuclear-import rate constant.<\/p>\n Protein expression, purification and labellingExpression and purification of NUP98 FG domain<\/p>\n The human NUP98 FG domain (residues 1\u2013505) was cloned into a pQE-14his-TEV vector. As described previously26<\/a>,59<\/a>, the GLEBS domain (residues 157\u2013213) was excluded to avoid misfolding of this structured region on rapid dilution from denaturant during phase separation (see \u2018In vitro phase separation assay\u2019 below); intrinsically disordered FG regions, by contrast, readily regain their dynamic ensemble under native buffer conditions. The construct was transformed into Escherichia coli BL21-AI cells and grown in terrific broth supplemented with kanamycin (50\u2009\u00b5g\u2009ml\u22121) at 37\u2009\u00b0C with shaking at 200\u2009rpm. Protein expression was induced when optical density at 600\u2009nm (OD600)\u2009\u2248\u20090.6 with 0.02% (w\/v) arabinose and 1\u2009mM iIsopropyl \u03b2-D-1-thiogalactopyranoside, followed by incubation for 16\u2009h at 18\u2009\u00b0C.<\/p>\n Cells were collected and lysed using a high-pressure cell disruptor (CF1, Constant Systems) in lysis buffer containing 6\u2009M guanidine hydrochloride (GdmCl), 0.2\u2009mM tris(2-carboxyethyl)phosphine (TCEP), 20\u2009mM imidazole and 50\u2009mM Tris-HCl (pH 8.0). Following clarification by centrifugation (12,000g, 1\u2009h, 4\u2009\u00b0C), lysates were incubated with nickel-nitrilotriacetic acid (Ni-NTA) resin for 2\u2009h at 4\u2009\u00b0C. Bound protein was washed with 2\u2009M GdmCl buffer and eluted with 500\u2009mM imidazole in 2\u2009M GdmCl and 50\u2009mM Tris-HCl (pH\u20098.0). After dialysis into 0.5\u2009M GdmCl and 50\u2009mM Tris-HCl (pH 8.0), the N-terminal His-tag was removed by overnight TEV protease digestion. The cleaved protein was separated from uncleaved protein and TEV protease by a second Ni-NTA purification step and further purified by size-exclusion chromatography (Superdex 200 Increase 10\/300 GL, Cytiva, 28990944) in 2\u2009M GdmCl, 0.2\u2009mM TCEP and 50\u2009mM Tris-HCl (pH 8.0). Purity was confirmed by SDS\u2013PAGE and Coomassie staining. Protein fractions were concentrated to about 15\u2009mg\u2009ml\u22121, quantified using a bicinchoninic acid assay and stored at \u221280\u2009\u00b0C.<\/p>\n In vitro O-GlcNAcylation of NUP98 FG domain<\/p>\n The purified NUP98 FG domain was enzymatically glycosylated using recombinant OGT1 and UDP-GlcNAc (Sigma, U4375). The reaction mixture contained 10\u2009\u00b5M NUP98 FG domain, 1\u2009\u00b5M OGT1 and 1\u2009mM UDP-GlcNAc in glycosylation buffer (50\u2009mM Tris-HCl, pH 7.5, 200\u2009mM NaCl, 20\u2009mM MgCl2, 0.2\u2009mM TCEP and 1% Tween-20). Samples were incubated for 16\u2009h at room temperature with gentle rotation. Following O-GlcNAcylation, His-tagged OGT1 was removed using Ni-NTA resin. O-GlcNAcylated NUP98 FG domain was further purified by size-exclusion chromatography (Superdex 200) in 2\u2009M GdmCl, 0.2\u2009mM TCEP and 50\u2009mM Tris-HCl (pH 8.0) and concentrated to about 40\u2009mg\u2009ml\u22121. O-GlcNAcylation efficiency was assessed by mass spectrometry, confirming successful modification of the NUP98 FG domain (Extended Data Fig. 8c<\/a>).<\/p>\n For experiments requiring higher levels of O-GlcNAc modification, the purified glycosylated protein was subjected to a second round of enzymatic O-GlcNAcylation under identical reaction conditions. Unless otherwise stated, all experiments were performed using NUP98 FG domains that had undergone a single round of O-GlcNAcylation. Proteins subjected to two rounds of O-GlcNAcylation were used only for the experiments shown in Supplementary Fig. 18<\/a>.<\/p>\n Labelling of NUP98 FG domain<\/p>\n NUP98 FG-domain variants containing a single cysteine substitution (residue 36, 100, 221, 312, 387 or 482) were exchanged into 4\u2009M GdmCl, 1\u00d7 PBS, 0.1\u2009mM EDTA and 0.2\u2009mM TCEP (pH 7.0). Proteins were labelled overnight at 4\u2009\u00b0C with Cy3B maleimide (GE Healthcare, PA63131) or Alexa Fluor 594 maleimide (Thermo Fisher Scientific, A10256) at a protein\/dye molar ratio of 1:2. Excess dye was quenched with 10\u2009mM dithiothreitol and removed by ultrafiltration (3\u2009kDa molecular-weight cutoff), followed by size-exclusion chromatography (Superdex 200). Protein concentrations and labelling efficiencies were determined spectroscopically using a Duetta fluorometer (Horiba). Labelled proteins were flash-frozen in liquid nitrogen and stored at \u221280\u2009\u00b0C.<\/p>\n Expression and purification of importin-\u03b2<\/p>\n The human importin-\u03b2 coding sequence was cloned into a pTXB3-intein-CBD-12His vector and transformed into E. coli BL21-AI cells. Cultures were grown in terrific broth supplemented with kanamycin (50\u2009\u03bcg\u2009ml\u22121) at 37\u2009\u00b0C with shaking (200\u2009rpm). Protein expression was induced at OD600\u2009=\u20090.4\u20130.6 with 0.02% (w\/v) arabinose and 1\u2009mM iIsopropyl \u03b2-d-1-thiogalactopyranoside, followed by incubation for 5\u20136\u2009h at 37\u2009\u00b0C. Cells were lysed by high-pressure homogenization in 50\u2009mM Tris, 650\u2009mM NaCl, 5\u2009mM MgCl2, 5\u2009mM imidazole, 1\u2009mM phenylmethylsulfonyl fluoride and 0.2\u2009mM TCEP (pH 7.0). After clarification by centrifugation (12,000g, 1\u2009h, 4\u2009\u00b0C), lysates were incubated with Ni-NTA resin for 2\u2009h at 4\u2009\u00b0C. Bound protein was washed with lysis buffer containing 10\u2009mM imidazole and 1.5\u2009M NaCl and eluted with 400\u2009mM imidazole. The eluate was dialysed into imidazole-free buffer and subjected to a second Ni-NTA purification step. Importin-\u03b2 was further purified by size-exclusion chromatography (Superdex 200) in 50\u2009mM Tris, 650\u2009mM NaCl, 5\u2009mM MgCl2 and 0.2\u2009mM TCEP (pH 7.0). Purity was confirmed by SDS\u2013PAGE. Purified protein was concentrated to about 500\u2009\u03bcM, flash-frozen in liquid nitrogen and stored at \u221280\u2009\u00b0C.<\/p>\n In vitro phase separation assays<\/p>\n Purified NUP98 FG domains stored in 2\u2009M GdmCl were induced to phase separate by rapid dilution into transport buffer (20\u2009mM HEPES, 110\u2009mM KOAc, 5\u2009mM NaOAc, 2\u2009mM Mg(OAc)2, 1\u2009mM EGTA and 2\u2009mM dithiothreitol, pH\u20097.3). Unless otherwise indicated, 1\u2009\u03bcl protein solution was mixed with 24\u2009\u03bcl transport buffer on a chambered coverslip (ibidi, 81507) immediately before imaging. Wild-type NUP98 FG domains were used at a final concentration of 10\u2009\u03bcM mixed with 2\u2009nM labelled FG domain. The residual GdmCl concentration after dilution was about 80\u2009mM and did not interfere with condensate formation.<\/p>\n Because O-GlcNAcylated FG domains exhibited reduced phase-separation propensity, a final concentration of 25\u2009\u03bcM was used for the experiments in Fig. 4g\u2013i<\/a> to generate condensates of comparable size and morphology to those formed by wild-type FG domains.<\/p>\n For cophase separation assays, importin-\u03b2 was diluted into transport buffer to the desired concentration before mixing with FG domains. Wild-type FG domains were used at 10\u2009\u03bcM unless otherwise indicated. Glycosylated FG\u2013importin-\u03b2 condensates were prepared from 25\u2009\u03bcM glycosylated FG domains and 10\u2009\u03bcM importin-\u03b2 to obtain condensates comparable to those formed by wild-type FG domains. The final concentration of GdmCl was maintained at 80\u2009mM across all conditions.<\/p>\n Quantification of FG-condensate phase concentrations<\/p>\n Dense- and dilute-phase concentrations of NUP98 FG condensates were determined using trace amounts of Alexa Fluor 594-labelled NUP98 FG domain. Condensates were formed from mixtures of unlabelled wild-type NUP98 FG domain and labelled tracer protein at molar ratios of 2,000:1, 5,000:1 or 10,000:1, as described above. Immediately after formation, condensates were sedimented by centrifugation at 4,300g for 5\u2009min.<\/p>\n Dense-phase fluorescence was measured on a custom-built confocal microscope equipped with a 560-nm pulsed laser. Dense-phase regions were identified from their high fluorescence intensity and characteristic condensate morphology. Fluorescence intensities were converted to protein concentrations using calibration curves generated from known concentrations of free Alexa Fluor 594 measured under matched buffer conditions. Differences in fluorescence quantum yield between free dye and dye-conjugated protein were measured independently using a Duetta fluorometer and used to correct the calculated protein concentrations.<\/p>\n Dilute-phase concentrations were measured by focusing well above the condensate layer and applying the same calibration and quantum-yield correction. An unlabelled\/labelled protein ratio of 20:1 was used to increase dilute-phase signal while minimizing perturbation of phase behaviour. Small dynamic nanoclusters were occasionally observed in the dilute phase of wild-type NUP98 FG condensates in the absence of importin-\u03b2 (Extended Data Fig. 3d<\/a>).<\/p>\n The experimentally determined dense- and dilute-phase concentrations were used to constrain FG\u2013importin-\u03b2 interaction strengths in the coarse-grained molecular-dynamics simulations (Extended Data Fig. 3e<\/a>).<\/p>\n O-GlcNAcylation-dependent selective partitioning of FG domains<\/p>\n To examine the effect of O-GlcNAcylation on FG-domain partitioning, NUP98 FG domains containing a cysteine substitution at residue 221 were site-specifically labelled with fluorescent maleimide dyes. Unglycosylated NUP98 FG domains were labelled with Alexa Fluor 488 maleimide, whereas unglycosylated, modestly O-GlcNAcylated (single-round glycosylation) and highly O-GlcNAcylated (two-round glycosylation) NUP98 FG domains used as probe molecules were labelled with LD655 maleimide.<\/p>\n Preformed condensates were generated from unglycosylated NUP98 FG domains (final concentration roughly 10\u2009\u03bcM supplemented with 4\u2009nM Alexa Fluor 488-labelled protein) as described above. Samples were incubated for 30\u2009min at room temperature to allow condensate maturation before probe addition. LD655-labelled probe proteins (unglycosylated, modestly glycosylated or highly glycosylated NUP98 FG domains) were then added to the chamber at a 1:1 volume ratio, yielding a final probe concentration of 20\u2009nM. The incorporation of probe molecules into preformed condensates was monitored by time-lapse confocal microscopy using a Zeiss LSM 980 microscope (Supplementary Fig. 18<\/a>).<\/p>\n TRFA measurementsInstrument configuration<\/p>\n TRFA measurements were conducted on a custom-built confocal microscope equipped with picosecond pulsed laser diodes (560\u2009nm: LDH-D-TA-560, PicoQuant; 660\u2009nm: LDH-D-C-660, PicoQuant) controlled by a Sepia II PDL 828 multichannel laser driver26<\/a>. The excitation beam was delivered through a single-mode polarization-maintaining optical fibre (KineFLEX-P-2-S-405\/640-2.5-2.5-p2), passed through a Glan-laser polariser (Thorlabs), directed through a FLIMbee laser scanning system (PicoQuant) and focused onto the sample through a \u00d760 water immersion objective lens (SR Plan Apo IR, 1.27 NA, Nikon). Fluorescence emission was collected through the same objective, spatially filtered using a pinhole (100\u2009\u03bcm for live-cell measurements and 50\u2009\u03bcm for in vitro measurements) and separated into parallel and perpendicular polarization components using a polarizing beam splitter. Each component was further separated spectrally by dichroic filters (ZT561 RDC and T647 LPXR, Chroma), passed through bandpass filters (Cy3B: 612\/69 BrightLine HC, Semrock; HD653: ET700\/75m, Chroma) and detected with hybrid photon-counting detectors (PMA Hybrid 40, PicoQuant). Photon arrival times were recorded with a HydraHarp 400 time-correlated single-photon-counting module at 16-ps resolution. Data were acquired using SymPhoTime 64 software (v.2.6, PicoQuant).<\/p>\n Instrument response functions (IRFs) were measured daily using Erythrosine B in saturated potassium iodide solution and used for reconvolution analysis. Detection channels were aligned using the measured IRFs. We note that a small discontinuity around 4\u2009ns is observed in the raw anisotropy-decay curves; this arises from weak optical reflections in the time-correlated single-photon-counting setup and is accounted for in the analysis by reconvolution with the measured IRFs.<\/p>\n Live-cell measurements<\/p>\n HD653 fluorescence intensity at the nuclear rim was first verified under 660-nm laser excitation (optimized to 50\u2009\u03bcW average power at 40\u2009MHz) to assess the expression level, ensuring comparable expression levels and avoiding overexpression artefacts. Data acquisition was performed using T3 mode, with fluorescence photons collected separately by parallel and perpendicular detectors. Imaging parameters included a pixel size of 100\u2009nm, an image size of 256\u2009pixels\u2009\u00d7\u2009256\u2009pixels, a pixel dwell time of 150\u2009\u00b5s and an imaging time of 5\u2009min. Regions of interest corresponding to the nuclear rim were selected, where thresholding algorithms were applied to identify regions of interest on the basis of pixel intensity and average fluorescence lifetime. The time-resolved intensity curves for parallel and perpendicular channels were extracted for further analysis.<\/p>\n In vitro measurements<\/p>\n Condensates were imaged immediately after formation as described above. Fluorescence photons were collected in T3 mode using 560-nm excitation (40\u2009MHz repetition rate). To minimize photobleaching and ensure representative sampling, the imaging field was changed every 5\u2009min to examine different condensates throughout the measurement period. Imaging parameters included a pixel size of 150\u2009nm, an image size of 256\u2009pixels\u2009\u00d7\u2009256\u2009pixels, a pixel dwell time of 203\u2009\u03bcs and a time resolution of 16\u2009ps. Condensates were identified on the basis of fluorescence intensity and morphology, and time-resolved intensity curves were extracted from condensate regions using SymPhoTime 64 software.<\/p>\n For measurements of individual FG chains in solution, purified and labelled FG domains were diluted in transport buffer to a final concentration of 10\u2009nM. Data acquisition and analysis were performed as described above for condensate measurements.<\/p>\n TRFA decay analysisFitting procedures<\/p>\n TRFA decay, r(t), was calculated from fluorescence emissions collected parallel (\\({I}_{\\parallel }(t)\\)) and perpendicular (\\({I}_{\\perp }(t)\\)) to the excitation polarization according to60<\/a><\/p>\n $$r(t)=\\frac{G{I}_{{||}}(t)-{I}_{\\perp }(t)}{(1-3{L}_{2})G{I}_{{||}}(t)+(2-3{L}_{1}){I}_{\\perp }(t)}$$<\/p>\n \n (1)\n <\/p>\n where L1 and L2 are polarization mixing factors caused by the high numerical aperture of the objective lens and G accounts for the differential detection efficiencies between the parallel and perpendicular polarization components:<\/p>\n $$G=\\frac{{\\eta }_{\\perp }}{{\\eta }_{{||}}}$$<\/p>\n \n (2)\n <\/p>\n To determine L1 and L2, the fluorescence decays of a reference sample, yellow fluorescent protein (YFP), were measured. YFP has a known fluorescence rotational relaxation time (\u03c1\u2009=\u200916\u2009ns) (ref.\u200961<\/a>). The fluorescence decays for the parallel and perpendicular components of YFP were globally fitted using the following equations61<\/a>:<\/p>\n $${I}_{||}(t)=\\frac{1}{3}{I}_{0}{e}^{-\\frac{t}{\\tau }}\\left\\{1+\\frac{2}{5}(2-3{L}_{1}){e}^{-\\frac{t}{\\rho }}\\right\\}$$<\/p>\n \n (3)\n <\/p>\n $${I}_{\\perp }(t)=\\frac{1}{3}{I}_{0}{e}^{-\\frac{t}{\\tau }}\\left\\{1-\\frac{2}{5}(1-3{L}_{2}){e}^{-\\frac{t}{\\rho }}\\right\\}$$<\/p>\n \n (4)\n <\/p>\n where I0 is the initial fluorescence intensity, \u03c4 is the fluorescence lifetime and \u03c1 is the rotational correlation time of YFP. The G factor was determined by measuring the ratio of the average intensities in the perpendicular and parallel channels using a solution of tris(2,2\u2019-bipyridyl)dichlororuthenium(II) chloride ([Ru(bpy)3]Cl2), which exhibits isotropic rotational motion.<\/p>\n For IDPs, r(t) can be modelled using a double-exponential decay32<\/a>:<\/p>\n $$\\begin{array}{l}r(t)=\\left[({r}_{0}-{r}_{{\\rm{p}}}){e}^{-\\frac{t}{{\\rho }_{\\mathrm{fast}}}}+{r}_{{\\rm{p}}}\\right]{e}^{-\\frac{t}{{\\rho }_{\\mathrm{slow}}}}\\\\ \\,\\,=\\,{r}_{0}\\left[\\left(1-\\frac{{r}_{{\\rm{p}}}}{{r}_{0}}\\right){e}^{-\\frac{t}{{\\rho }_{\\mathrm{fast}}}}+\\frac{{r}_{{\\rm{p}}}}{{r}_{0}}\\right]{e}^{-\\frac{t}{{\\rho }_{\\mathrm{slow}}}}\\end{array}$$<\/p>\n \n (5)\n <\/p>\n where r0 is the fundamental anisotropy of the fluorophore, \u03c1fast is the fitted rotational correlation time associated primarily with local dye\/linker motion, rp is the residual anisotropy remaining after fast local motion and reflecting slower, larger-scale chain motions and \u03c1slow is the fitted slow-component timescale used here as an apparent segmental-motion parameter. Values approaching the upper fitting bound of 1,000\u2009ns were interpreted as indicating very slow apparent segmental motion and were not considered well resolved.<\/p>\n When \u03c1fast is much smaller than \u03c1slow, equation (5<\/a>) can be approximated and simplified to<\/p>\n $$\\begin{array}{l}r(t)\\approx {r}_{0}\\left[\\left(1-\\frac{{r}_{{\\rm{p}}}}{{r}_{0}}\\right){e}^{-\\frac{t}{{\\rho }_{\\mathrm{fast}}}}+\\frac{{r}_{{\\rm{p}}}}{{r}_{0}}{e}^{-\\frac{t}{{\\rho }_{\\mathrm{slow}}}}\\right]\\\\ \\,=\\,{r}_{0}\\left({\\beta }_{\\mathrm{fast}}{e}^{-\\frac{t}{{\\rho }_{\\mathrm{fast}}}}+{\\beta }_{\\mathrm{slow}}{e}^{-\\frac{t}{{\\rho }_{\\mathrm{slow}}}}\\right)\\end{array}$$<\/p>\n \n (6)\n <\/p>\n where \u03b2fast\u2009=\u20091\u2009\u2212\u2009rp\/r0 and \u03b2slow\u2009=\u2009rp\/r0 represent relative amplitudes of the fast (local) and slow (segmental) components, respectively.<\/p>\n The fluorescence lifetime (\u03c4) was first determined by fitting the total fluorescence decay obtained from the parallel and perpendicular emission channels. The resulting \u03c4 value was then fixed during the subsequent global fitting of the parallel and perpendicular fluorescence decays using the 2_exp_rot model implemented in TauFit in the PAM package62<\/a>, where IRFs were included through reconvolution analysis. Here we interpret \u03c1slow primarily as an apparent segmental-motion parameter for relative comparisons rather than as a precise absolute rotational correlation time. Rotational components slower than the fluorescence lifetime can nevertheless influence the measured anisotropy decay and be estimated by model-based fitting, with precision depending strongly on photon statistics and decreasing as the correlation time increasingly exceeds the fluorescence lifetime63<\/a>,64<\/a>. Although three-exponential models were also evaluated, the additional component was consistently negligible or degenerate with existing components and therefore did not improve the fits.<\/p>\n To calculate steady-state anisotropy (rss), the integrated intensities of the fluorescence emissions collected in the parallel (\\({I}_{\\parallel }\\)) and perpendicular \\(({I}_{\\perp }\\)) channels were used. The steady-state anisotropy was computed using the equation<\/p>\n $${r}_{\\mathrm{ss}}=\\frac{G{I}_{{||}}-{I}_{\\perp }}{(1-3{L}_{2})G{I}_{{||}}+(2-3{L}_{1}){I}_{\\perp }}$$<\/p>\n \n (7)\n <\/p>\n The steady-state anisotropy value provides a single, time-averaged measurement of the overall fluorescence anisotropy, which complements the dynamic information obtained from TRFA decay analysis.<\/p>\n Statistical analysis<\/p>\n For live-cell measurements, single-cell anisotropy-decay traces were used for subsequent analysis. In Fig. 1i<\/a>, the fitted slow-component parameter (\u03c1slow) was calculated on a per-cell basis to capture relative temporal trends in apparent segmental motion. For all other experiments, a non-parametric bootstrap strategy was applied to improve signal-to-noise and ensure robust curve fitting.<\/p>\n For each condition, 200 bootstrap replicates were generated by resampling single-cell decay traces with replacement, summing photon counts and fitting the resulting decays in TauFit62<\/a>. Bootstrap depth was selected on the basis of convergence analysis (Supplementary Fig. 2<\/a>). Differences between conditions were assessed using two-sided bootstrap tests. P values were calculated as the proportion of null resamples with absolute differences greater than or equal to the observed effect. Percentile confidence intervals were derived from the empirical distribution of independent bootstrap differences.<\/p>\n For in vitro measurements, anisotropy decays were analysed every 5\u2009min and fitted individually. Reported values represent the mean\u2009\u00b1\u2009s.d. from three independent experiments.<\/p>\n Validation of HD653 for anisotropy measurements<\/p>\n To assess the suitability of HD653 as a probe for TRFA, control experiments were performed using a globular protein with known rotational properties. Purified EGFP containing a single BCN at residue 39 was site-specifically labelled with either HD653 or the rigid, well-characterized anisotropy dye Cy3B30<\/a>,31<\/a>. TRFA measurements were conducted on both unlabelled and labelled EGFP at 10\u2009nM in 1\u00d7 PBS. The rotational correlation times were obtained by fitting TRFA decay curves using the 2_exp_rot model function in TauFit62<\/a>. For globular EGFP, the fitted slow component, \u03c1slow, corresponds to its overall rotational correlation time and was used to determine the hydrodynamic radius:<\/p>\n $${R}_{{\\rm{h}}}={\\left(\\frac{3{k}_{{\\rm{B}}}T{\\rho }_{\\mathrm{slow}}}{4\\pi \\eta }\\right)}^{1\/3}$$<\/p>\n \n (8)\n <\/p>\n where kB is the Boltzmann constant, T is the absolute temperature and \\(\\eta \\) is the solvent viscosity. Hydrodynamic radii determined for labelled EGFP were consistent with wild-type EGFP and previously reported values65<\/a>,66<\/a>, confirming HD653 as a reliable anisotropy probe and supporting its use for segmental dynamics measurements in live-cell and in vitro assays.<\/p>\n MINFLUX measurementsSample preparation for MINFLUX imaging<\/p>\n Doxycycline-induced U-2 OS-CRISPR-NUP96-mEGFP cells expressing importin-\u03b2-3\u00d7FLAG-ALFA were prepared as described above. Cells were fixed with 4% PFA for 10\u2009min, washed three times with 1\u00d7 PBS containing 100\u2009mM glycine and permeabilized and blocked for at least 30\u2009min at room temperature in blocking buffer consisting of 3% bovine serum albumin, 10% donkey serum and 0.3% Triton X-100 in 1\u00d7 PBS.<\/p>\n DNA docking strand-conjugated anti-GFP and anti-ALFA nanobodies (Massive Photonics) were diluted 1:200 in antibody incubation buffer (Massive Photonics) and incubated with cells for 1\u2009h at room temperature. Samples were washed three times with washing buffer (Massive Photonics) and post-fixed with 2.4% PFA for 8\u2009min. Gold nanoparticles (250\u2009nm diameter; BBI Solutions) were then added for 10\u2009min as fiducial markers for active drift correction, followed by extensive washing with 1\u00d7 PBS.<\/p>\n Cy3B-labelled DNA-PAINT imager strands (Massive Photonics) were diluted in imaging buffer (Massive Photonics) to a final concentration of 200\u2013500\u2009pM. Samples were mounted in custom imaging chambers, and imager solution was added immediately before imaging. All MINFLUX measurements were completed within 2\u2009days of sample preparation.<\/p>\n Two-colour DNA-PAINT MINFLUX imaging<\/p>\n Two-colour DNA-PAINT MINFLUX measurements were performed on a commercial MINFLUX microscope (Abberior Instruments) based on an Olympus IX83 inverted microscope equipped with a \u00d7100 UPlanXApo objective and controlled by Imspector software. The excitation beam pattern and pinhole position were calibrated daily using fluorescent calibration nanoparticles (Gold 150\u2009nm and 2C Fluor 120\u2009nm; Abberior Instruments).<\/p>\n Cells expressing the inducible importin-\u03b2 construct were identified by tagBFP fluorescence. Imaging was performed at the basal surface of the nucleus adjacent to the coverslip. Transient DNA-PAINT binding events were verified by rapid confocal imaging before MINFLUX acquisition. At least three gold fiducials were present in each field of view and were used by the active stabilization system to correct real-time drift, maintaining subnanometre lateral stability throughout acquisition.<\/p>\n Regions of interest were imaged using the standard two-dimensional MINFLUX acquisition sequence with a pinhole diameter of 0.83\u2009Airy units. Following acquisition of the first target, imager strands were exchanged using a custom perfusion system while maintaining uninterrupted MINFLUX acquisition and active stabilization. Buffer exchange was performed at about 10\u2009\u03bcl\u2009s\u22121 until DNA-PAINT binding events were no longer detected, indicating complete removal of the first imager strand. The second imager strand was subsequently introduced and imaging resumed. Sequential two-colour imaging and strand exchange typically required roughly 4\u2009h.<\/p>\n NPC alignment and radial density analysis<\/p>\n NPCs were analysed using custom MATLAB routines adapted from the published MINFLUX_NPC_Tracking workflow14<\/a>. Candidate NPCs were selected from the NUP96 channel and filtered using geometry-based quality-control criteria to exclude incomplete or poorly resolved pores.<\/p>\n For each NPC, the pore centre was determined from NUP96 localizations and used for spatial registration. The eightfold rotational phase was estimated from the angular distribution of NUP96 localizations using the complex order parameter \\({z}_{8}=\\langle {e}^{i8\\theta }\\rangle \\). Individual NPCs were rotated into a common eightfold reference frame, and the same rigid-body transformation was applied to the corresponding importin-\u03b2 localizations. Aligned NUP96 coordinates were rendered directly to preserve the native octagonal architecture of the NPC scaffold.<\/p>\n Because importin-\u03b2 localizations did not exhibit a robust eightfold angular organization, their spatial distribution was quantified using radial density analysis relative to the NUP96-defined pore centre. Localizations were binned by radial distance, corrected for annular area, normalized in each NPC and averaged across pores. Individual radial profiles were smoothed before calculation of the population mean and s.e.m. The resulting mean radial density profile was rotationally symmetrized to generate the final importin-\u03b2 density map. To assess the contribution of radial geometry, a uniform random two-dimensional distribution was generated in the analysed pore radius and processed using the same radial binning, annular-area correction, normalization, smoothing and symmetrisation as the experimental localizations (Fig. 3g<\/a>).<\/p>\n Molecular-dynamics simulationsResidue-based coarse-grained model of NPC and importin-\u03b2<\/p>\n We adapted a previously established coarse-grained model of the NPC26<\/a> to incorporate importin-\u03b2 proteins. In this model, each amino acid (p) of NPC and importin-\u03b2 proteins is represented by a single bead, the nuclear envelope is modelled using fixed membrane particles (m), and the solvent is treated implicitly. Protein residues are divided into three sub-categories: scaffold residues (sc) and FG residues (FG) of NPC proteins and importin-\u03b2 residues. The potential energy of the system is given by<\/p>\n $$\\begin{array}{l}U={U}_{{\\rm{LJ}}}+{U}_{{\\rm{FENE}}}+{U}_{{\\rm{C}}}\\\\ \\,=\\,4{k}_{B}T\\sum _{i < j,{r}_{{ij}} < {r}_{c}^{\\alpha },\\,i,j\\in \\{p,m\\}}\\left\\{{\\widetilde{{\\epsilon }}}_{{ij}}\\left[{\\left(\\frac{{\\sigma }_{{ij}}}{{r}_{{ij}}}\\right)}^{12}-{\\left(\\frac{{\\sigma }_{{ij}}}{{r}_{{ij}}}\\right)}^{6}\\right]-{U}_{{\\rm{LJ}}}({r}_{c}^{\\alpha })\\right\\}\\\\ +\\,4{k}_{B}T\\sum _{\\langle i,j=i+1\\rangle ,{i,j\\in \\{p\\},r}_{{ij}} < {2}^{\\frac{1}{6}}\\sigma }\\left[{\\left(\\frac{\\sigma }{{r}_{{ij}}}\\right)}^{12}-{\\left(\\frac{\\sigma }{{r}_{{ij}}}\\right)}^{6}+\\frac{1}{4}\\right]\\\\ -\\,\\sum _{\\langle i,j=i+1\\rangle ,\\,i,j\\in \\{p\\}}0.5{k}_{{\\rm{FE}}}{R}_{{\\rm{FE}}}^{2}\\,\\mathrm{ln}\\left[1-{\\left(\\frac{{r}_{{ij}}}{{R}_{{FE}}}\\right)}^{2}\\right]\\\\ +\\,{k}_{c}\\sum _{\\,i\\in \\{{\\rm{Imp}}-{\\rm{\\beta }}\\},\\,{r}_{{xy},i} > {R}_{c}}{({r}_{{xy},i}-{R}_{c})}^{2}\\end{array}$$<\/p>\n \n (9)\n <\/p>\n Non-bonded interactions between particles i and j are described by Lennard\u2013Jones potentials, whose strength \\({\\widetilde{{\\epsilon }}}_{{ij}}\\), length \u03c3ij and cutoff values \\({r}_{{\\rm{c}}}^{{\\rm{\\alpha }}}\\) are provided in Supplementary Table 2<\/a>. The Lennard\u2013Jones potentials were shifted by their values at the corresponding cutoff radii: that is, \\({U}_{{\\rm{LJ}}}({r}_{c}^{\\alpha })\\). The bond potential between adjacent beads of the FG-protein was modelled using the finitely extensible nonlinear elastic potential67<\/a> with kFE\u2009=\u200930kBT and RFE\u2009=\u20091.5\u03c3. The radiall positions of importin-\u03b2 were confined by a half-harmonic potential with stiffness kc\u2009=\u2009100kBT\/\u03c32, limiting their radial distance to r\u2009\u2272\u2009Rc\u2009=\u200981\u03c3\u2009\u2261\u200948.6\u2009nm.<\/p>\n Simulations were performed in LAMMPS (Release Sept. 2021)68<\/a>,69<\/a>. Time is reported in units of \\(\\tau =\\sqrt{m{\\sigma }^{2}\/{k}_{{\\rm{B}}}T}\\), where m is the bead mass (identical for all bead types). Following earlier work26<\/a>, we determined the reduced length scale of Lennard\u2013Jones potential obtained as \u03c3\u2009\u2261\u20090.6\u2009nm by matching the root-mean-square inter-residue distance (RE) of a single NUP98 FG chain (amino acids 1\u2013499) in both the homopolymer model and the corresponding Martini representation in the weakly interacting regime70<\/a>. We found that \\(\\widetilde{{\\epsilon }}\\)FG\u2013FG\u2009=\u20090.5 reproduces the RE of a single NUP98 FG chain measured by single-molecule FRET, whereas \\(\\widetilde{{\\epsilon }}\\)FG\u2013FG\u2009=\u20090.42 best matches in situ FLIM\u2013FRET for the NUP98 FG domain in the NPC26<\/a>, reflecting in particular the effects of PTMs.<\/p>\n The membrane particles representing the nuclear envelope were constructed from a 100\u2009\u00d7\u2009100\u2009nm2 coarse-grained POPC bilayer using the Python script insane.py71<\/a>,72<\/a>, with a reduced area per lipid (0.3\u2009nm2) to prevent solvent permeation (command: insane.py -l POPC -x 100 -y 100 -z 100 -a 0.3 -o bilayer.gro). A half-toroidal pore was then generated using BUMPy71<\/a> (command: bumpy.py -s double_bilayer_cylinder -f bilayer.gro -z 10 -g l_cylinder:10 r_cylinder:430 r_junction:120 l_flat:1920). To reduce computational cost, only phosphate beads were retained. NPC scaffold and membrane particles were fixed throughout\u00a0the simulations. To prevent FG domains and importin-\u03b2 molecules from crossing the membrane, a Lennard\u2013Jones potential with a large repulsive range was applied (Supplementary Table 2<\/a>).<\/p>\n We used the constricted NPC model II26<\/a> including the following FG-NUPs: NUP54, NUP58, NUP62, NUP98, POM121, NUP214, NUP153 and NUP358. Importin-\u03b2 was modelled using PDB ID 3W5K<\/a> (ligand Snail1 removed)73<\/a>. Importin-\u03b2 molecules were treated as rigid bodies using a rigid-body integrator with a Langevin thermostat and a damping coefficient 10\u03c4 (LAMMPS command: fix rigid langevin molecule). FG beads were integrated using the Verlet algorithm74<\/a>. NUP98 FG chains were thermalized using Langevin thermostats with damping coefficient 10\u03c4 (ref.\u200975<\/a>).<\/p>\n Preparation and equilibration of importin-\u03b2 inside the NPC<\/p>\n Importin-\u03b2 molecules were added to systems of size 320\u03c3\u2009\u00d7\u2009320\u03c3\u2009\u00d7\u2009400\u03c3. FG-NUPs were first equilibrated at \\(\\widetilde{{\\epsilon }}\\)FG\u2013FG\u2009=\u20090.5 for 106\u03c4, during which they formed a surface condensate on the NPC scaffold. These compact conformations allowed us to efficiently introduce NImp-\u03b2\u2009=\u2009100 importin-\u03b2 molecules76<\/a> with random initial positions and orientations around the NPC. With FG-NUPs frozen and weak interactions (\\(\\widetilde{{\\epsilon }}\\)FG\u2013Imp-\u03b2\u2009=\u20090.1), importin-\u03b2 molecules were allowed to diffuse for 3.4\u2009\u00d7\u2009104\u03c4 with thermostat damping coefficient 1,000\u03c4. Subsequently, the full system was equilibrated with \\(\\widetilde{{\\epsilon }}\\)FG\u2013FG\u2009=\u20090.42 and \\(\\widetilde{{\\epsilon }}\\)FG\u2013Imp-\u03b2\u2009=\u20090.1 for 105\u03c4 using a time step \u03b4t\u2009=\u200910\u22123\u03c4 and thermostat damping coefficient 10\u03c4. Production conditions were then applied by setting \\(\\widetilde{{\\epsilon }}\\)FG\u2013FG and \\(\\widetilde{{\\epsilon }}\\)FG\u2013Imp-\u03b2 to their target values, followed by simulations of at least 106\u03c4. Three independent configurations from the equilibration phase were selected as starting points for independent production runs. Structural visualization was performed using VMD77<\/a>.<\/p>\n Martini model of the NPC<\/p>\n To examine how O-GlcNAcylation affects FG-NUP dynamics, we performed molecular-dynamics simulations of the human NPC using the Martini 2.2 coarse-graining scheme. We used the constricted NPC structure (PDB ID: 7R5K<\/a>, ref.\u200939<\/a>). NUPs were grouped into scaffold proteins and disordered FG-NUPs and converted to Martini CG models using the martinize.py script50<\/a>,78<\/a>. FG-NUPs included NUP54, NUP58, NUP62, NUP98, POM121, NUP214 and NUP358 (Supplementary Table 3<\/a>). All scaffold proteins and grafting-anchored ordered domains of FG-NUPs were restrained with a harmonic spring (1,000\u2009kJ\u2009mol\u22121\u2009nm\u22122).<\/p>\n We generated O-GlcNAcylated NPC models at three modification levels (fgly\u2009=\u20090.18, 0.3 and 0.6), where fgly denotes the fraction of O-GlcNAcylated Ser\/Thr sites (Supplementary Fig. 11<\/a>). Potential O-GlcNAcylation sites were predicted using YinOYang79<\/a>, which assigns each residue a probability p\u2009\u2208\u2009[0,1]. Residues with p\u2009\u2265\u2009pth were considered glycosylated. The resulting number of modified sites Ngly determined fgly\u2009=\u2009Ngly\/Ntotal, where Ntotal\u2009=\u200958,768 is the total number of Ser\/Thr residues across all FG-NUPs.<\/p>\n Simulations were performed using GROMACS (v.2020.6 and v.2025.2)80<\/a>,81<\/a>. Interaction strengths for protein\u2013protein, protein\u2013sugar and sugar\u2013sugar interactions were rescaled by parameters \u03b1, \u03bb and \u03b3, respectively70<\/a>,82<\/a>. The optimal \u03b1\u2009=\u20090.78 was determined by matching RE of an untreated NUP98 FG chain to single-molecule FRET measurements (Supplementary Fig. 12<\/a>) and the dense-phase density of FG condensates (Supplementary Fig. 14<\/a> and Supplementary Tables 4<\/a> and 5<\/a>). For O-glycosylated FG-NUPs, interactions involving sugars used \u03bb\u2009=\u20090.15 and \u03b3\u2009=\u20090.5, consistent with experimental osmotic second virial coefficients of aqueous sugars and protein\u2013sugar mixtures83<\/a>,84<\/a>.<\/p>\n Equilibration of the Martini NPC systems<\/p>\n A cubic box (170\u2009nm per side) was constructed to accommodate the NPC. Secondary-structure restraints were assigned using DSSP85<\/a>. Elastic networks in ordered domains were generated using Elastic Network in Dynamics86<\/a> (default parameters; a distance range of 0.9\u2009nm; force constant 500\u2009kJ\u2009mol\u22121\u2009nm\u22122). All FG domains were modelled as coils except for locally ordered regions in NUP358 (Supplementary Table 3<\/a>). The system was solvated with Martini water containing 10% antifreeze beads87<\/a> and neutralized with NaCl to 150\u2009mM. The total number of solvent particles was about 4\u2009\u00d7\u2009107.<\/p>\n Initial energy minimization used steepest descent with maximum step size 0.01\u2009nm and force tolerance 1,000\u2009kJ\u2009mol\u22121\u2009nm\u22121. During this step, position restraints (1,000\u2009kJ\u2009mol\u22121\u2009nm\u22122) were temporarily removed to allow global relaxation. Lennard\u2013Jones and Coulomb potentials were first softened using the GROMACS free-energy framework (parameters: couple-lambda0=vdw-q; sc-alpha\u2009=\u20090.1; sc-coul= yes; sc-power\u2009=\u20092; sc-sigma\u2009=\u20090.3), followed by a second minimization using full potentials.<\/p>\n Equilibration proceeded as follows. First, NVT simulations at 310\u2009K were performed for 100\u2009ns (velocity-rescaling thermostat88<\/a>, time constant 1\u2009ps, time step \u03b4t\u2009=\u20090.015\u2009ps) using reduced interaction scaling (\u03b1\u2009=\u2009\u03b3\u2009=\u2009\u03bb\u2009=\u20090.3) to relax chains into coil-like conformations. Next, NPT equilibration at 310\u2009K and 1\u2009bar was performed for 100\u2009ns (velocity-rescaling thermostat88<\/a>, semi-isotropic Berendsen barostat89<\/a>, time constant 12\u2009ps, compressibility 3\u2009\u00d7\u200910\u22124\u2009bar\u22121). Interaction parameters were then gradually increased. For untreated NPCs, \u03b1 was raised from 0.3 to 0.5 and then 0.6. For O-glycosylated NPCs, \u03b1 was increased from 0.3 to 0.6 and then 0.7, with \u03b3\u2009=\u20090.5 and \u03bb\u2009=\u20090.15. This stage lasted 1.5\u2009\u03bcs. Production simulations were conducted for at least 2\u2009\u03bcs at target \u03b1 values, using the same thermostat and barostat parameters as in the final equilibration step and a time step \u03b4t\u2009=\u20090.02\u2009ps.<\/p>\n Statistics and reproducibility<\/p>\n Sample sizes were not determined by formal statistical power calculations but were based on previous experience with the respective imaging and biophysical assays26<\/a>, practical considerations and the requirements for robust and reproducible measurements. For molecular-dynamics simulations, replicate numbers and trajectory blocks were selected on the basis of convergence and reproducibility criteria. Exact sample sizes, numbers of independent experiments and independent sample preparations are reported in the corresponding figure legends.<\/p>\n For experiments in which representative images are shown, including those in Figs. 1b<\/a>, 2a<\/a>, 3e<\/a> and 4b<\/a>, Extended Data Figs. 1a,b<\/a>, 2a<\/a> and 8e<\/a> and Supplementary Figs. 18<\/a>\u201320<\/a>, experiments were independently repeated at least three times and yielded similar results. Representative images were selected from these independent experiments. Randomization was not applicable because treatments were applied to entire cell cultures or biochemical samples. Experimental variability was minimized by using matched culture, sample-preparation and acquisition conditions.<\/p>\n Reporting summary<\/p>\n