Matrix stiffness drives drop like nuclear deformation and lamin A/C tension-dependent YAP nuclear localization

Synthesis and functionalization of polyacrylamide hydrogels

Polyacrylamide hydrogels were prepared as described in ref. 84. Acrylamide and bis-acrylamide (Bio-Rad Laboratories) were mixed in concentrations of 5%/0.1%, 8%/0.2%, and 15%/1.2% to prepare gels with Young’s modulus (E) of 1, 22, and 308 kPa, respectively, as described in ref. 11. The precursor solution was degassed, mixed with 0.5% v/v ammonium persulphate (ThermoFisher Scientific) and 0.1% v/v tetramethylethylenediamine (ThermoFisher Scientific) to initiate polymerization, and 100 μl of the mixture was layered between a hydrophobic glass surface and a hydrophilic 18-mm diameter glass coverslip at room temperature for 20 min. The gels were functionalized using sulfosuccinimidyl 6-(40-azido-20-nitophenylamino) hexanoate (G-Biosciences) and coated with rat tail collagen type I (0.2 mg/ml; Corning) before cell seeding.

Cell culture

All cancer cell lines were maintained in a humidified incubator at 37 °C and 5% CO2. Human breast adenocarcinoma cells MDA-MB-231 (ATCC, HTB-26), human head and neck cancer cells BHY and HN (Deutsche Sammlung von Mikroorganismen und Zellkulturen GmbH), and MDCK cells (obtained from Jennifer Lippincott-Schwartz lab) were cultured in Dulbecco’s Modified Eagle’s Medium with 4.5 g/l glucose (Corning), supplemented with 10% v/v donor bovine serum (Gibco) and 1% v/v penicillin/streptomycin (Corning). Human fibrosarcoma cells HT-1080 (ATCC, CCL-121), human pancreatic carcinoma cells PANC-1 (ATCC, CRL-1469), mouse fibroblasts NIH-3T3 (ATCC, CRL-1258), and retroviral packaging cells Phoenix-Ampho (ATCC, CRL-3213) were maintained in Dulbecco’s Modified Eagle’s Medium with 4.5 g/l glucose (Corning), supplemented with 10% v/v fetal bovine serum (FBS; Gibco) and 1% v/v penicillin/streptomycin (Corning). Mouse lung cancer cells 344SQ (a generous gift from Jonathan Kurie lab) were cultured in Roswell Park Memorial Institute medium (ThermoFisher Scientific), supplemented with 10% v/v FBS (Gibco) and 1% v/v penicillin/streptomycin (Corning). For 3D acinar cultures, Nunc Lab Tek II 8-well chamber slides (ThermoFisher Scientific) were coated with 40 μl of growth-factor-reduced (GFR) Matrigel (Corning) and allowed to gel for at least 1 h at 37 °C. Trypsinized 344SQ cells from tissue culture plates were suspended in growth medium supplemented with 2% v/v Matrigel to achieve a final concentration of 10 cells/ml, and 400 μl was added to each well of the chamber slide where the cells were allowed to form acini for 7–12 days before fixation. The growth medium was changed every 3–5 days.

Plasmid and stable cell line generation

MDCK cells with inducible mCherry-dominant-negative (DN) KASH1 were generated as previously described85. MDCK cells expressing lamin A/C strain sensor (Lamin-SS) or lamin A/C truncated control sensor (Lamin-TM) were generated as previously described50. pBABE-puro-GFP-wt-lamin A plasmid was a gift from Tom Misteli86 (Addgene; plasmid #17662). GFP-fusion lamin A was stably expressed in cancer cell lines by retroviral transduction. Phoenix-Ampho cells were transfected with the pBabe plasmid DNA using lipofectamine 3000 (ThermoFisher Scientific) according to the manufacturer’s protocol. Transfected Phoenix-Ampho cells were incubated at 37 °C for 8 h, refed with fresh culture medium, and maintained at 32 °C for 48 h. The culture medium containing packaged retrovirus was filtered through a 0.45-μm filter (ThermoFisher). Filtered medium supplemented with polybrene (2.5 μg/ml; Sigma–Aldrich) was added to the target cancer cells. The target cells were incubated at 37 °C for 48 h and refed with a culture medium containing puromycin (Sigma–Aldrich) for selection of viral integration. After 2–3 days of antibiotic selection, the expression of GFP-lamin A in cancer cells was verified using immunofluorescence and immunoblot analysis.

Immunofluorescence staining and microscopy

Cultured cells were fixed in 4% paraformaldehyde (PFA, Alfa Aesar) for 20 min at room temperature, permeabilized with 0.1% Triton X-100 (ThermoFisher Scientific) in phosphate-buffered saline (PBS), and blocked with 1 mg/ml bovine serum albumin (ThermoFisher Scientific) for 1 h at room temperature. Cells were incubated with primary antibodies rabbit anti-lamin B1 (Abcam, ab229025; dilution 1:1000), mouse anti-YAP (Santa Cruz Biotechnology, sc-101199; dilution 1:100), mouse anti-lamin A/C (Invitrogen, MA5-35284; dilution 1:250), mouse anti-α-Tubulin (Cell Signaling, #3873; dilution 1:100), rabbit anti-H3K9me3 (Abcam, ab8898; dilution 1:100), or mouse anti-H3K27me3 (Abcam, ab6002; dilution 1:100) overnight at 4 °C. The cells were then washed with PBS and incubated with secondary antibodies Alexa Fluor 488 goat anti-rabbit (Invitrogen, A11034; dilution 1:250), Alexa Fluor 594 goat anti-rabbit (Invitrogen, A11012; dilution 1:200), Alexa Fluor 594 goat anti-mouse (Invitrogen, A11032; dilution 1:200), Alexa Fluor 647 goat anti-rabbit (Invitrogen, A21244; dilution 1:200), or Alexa Fluor 647 goat anti-mouse (Invitrogen, A21235; dilution 1:200) for 2 h at room temperature. DNA was stained with Hoechst 33342 (Sigma–Aldrich), and F-actin was stained using phalloidin conjugated to Alexa Fluor 405 or 488 (Invitrogen; dilution 1:400). The cells cultured on polyacrylamide hydrogels were mounted on 35-mm glass dishes (World Precision Instruments) before imaging. For staining tissue microarrays, 5-μm-thick formalin-fixed paraffin-embedded (FFPE) tissue samples were deparaffinized with xylene, rinsed in ethanol, and rehydrated with ethanol to deionized water gradient. Heat-induced antigen retrieval was performed in an instant pot with a 1× universal antigen retrieval solution (Abcam). After blocking with 3% w/v bovine serum albumin, 1% v/v goat serum, and 0.1% Triton X-100 in PBS, samples were incubated with primary antibodies rabbit anti-lamin B1 (Abcam, ab229025; dilution 1:2000) and guinea pig anti-pan-cytokeratin (LS-Bio, LS-B16812; dilution 1:50) overnight at 4 °C, followed by incubation with secondary antibodies Alexa Fluor 488 goat anti-rabbit (Invitrogen, A11034; dilution 1:500) and Alexa Fluor 594 goat anti-guinea pig (Invitrogen, A11076; dilution 1:500) for 1 h at room temperature and then mounted. Imaging was performed on an Olympus FV3000 confocal microscope using a 60×/1.3 NA silicone oil-immersion objective (Olympus Scientific Solutions Americas Corp.) or on a Zeiss LSM900 confocal microscope using a C Plan-Apochromat 63×/1.4 NA oil-immersion objective (Carl Zeiss Jena GmbH). A pinhole size of 1 Airy disk and a z-step size of 130 nm were used for 3D confocal imaging to ensure overlapping z-stacks and sampling at less than half the focus depth to satisfy the Nyquist criterion87:

$$frac{{rm{FWHM}}}{2}=frac{1}{2}cdot frac{0.88cdot {lambda }_{{rm{ex}}}}{n-sqrt{{n}^{2}-{{rm{NA}}}^{2}}}=frac{1}{2}cdot frac{0.88cdot 488{rm{nm}}}{1.5-sqrt{{1.5}^{2}-{1.4}^{2}}}approx 223{rm{nm}}, > , 130{rm{nm}}$$

(1)

where ({rm{FWHM}}) is the full width at half maximum, ({{rm{lambda }}}_{{rm{ex}}}) is the excitation wavelength, ({rm{n}}) is the refractive index of the immersion medium, and ({rm{NA}}) is the lens numerical aperture. For live imaging of cell spreading and mitosis, NIH-3T3 and HT-1080 cells stably expressing GFP-lamin A cultured in tissue culture plates were incubated with SPY650-FastAct (Cytoskeleton; dilution 1:1000) for 2 h to label F-actin. Then, the cells were passaged onto 8-well glass chamber slides (ThermoFisher Scientific) and maintained in a stage-top heated and humidified chamber (Tokia Hit USA Inc.). Live time-lapse cell imaging was performed with a time step of 5–6 min and a z-step size of 1 μm to provide sufficient temporal resolution and minimize phototoxicity and photobleaching of fluorescent probes.

Photobleaching and trypsinization experiments

NIH-3T3 and HT-1080 cells stably expressing GFP-lamin A were seeded in a complete medium onto 8-well glass chamber slides (ThermoFisher Scientific) coated with 20 μg/ml of fibronectin (Corning) for 12 h for cell attachment and were then placed in a stage-top heated and humidified chamber (Tokia Hit USA Inc.). Using the 488 nm line of a 400-mW Kr/Ar laser, cells within a region of interest were photobleached with a “T” pattern at the basal, middle, and apical nuclear planes to create three fluorescent lamina arcs. The well was washed with PBS to remove traces of serum, and 0.25% trypsin (Corning) was added to the well. Confocal mid-plane images of cell nuclei were captured before the PBS wash and approximately 40 s after the addition of 0.25% trypsin.

To prepare fixed samples of spread cells, NIH-3T3 and HT-1080 cells stably expressing GFP-lamin A were seeded in a complete medium on 35-mm glass dishes (World Precision Instruments) coated with 20 μg/ml of fibronectin (Corning) for 12 h for the cell to adhere. Cells were fixed with 4% paraformaldehyde (Alfa Aesar) at room temperature for 15 min and washed with PBS prior to imaging. For preparation of suspended cells, NIH-3T3 and HT-1080 cells stably expressing GFP-lamin A were trypsinized and centrifuged at 1000 RPM for 5 min. The cell pellet was gently washed with PBS, fixed with 4% paraformaldehyde (Alfa Aesar) at room temperature for 15 min, then washed and carefully resuspended in PBS and transferred to a 35-mm glass dish for imaging.

Micropattern fabrication and contact printing

PDMS stamp micropatterns were designed in AutoCAD 2018 and fabricated in PDMS using a two-step photolithography master mold fabrication process. This was followed by a soft lithography process of replica molding for the final PDMS device from the master mold. First, the AutoCAD design was patterned on a chrome-coated glass mask using a Heidelberg DWL66+ Laser Pattern Generator. Second, to create the master mold, a layer of photosensitive epoxy (Kayaku, SU-8) was patterned on a three-inch diameter silicon substrate (3″ N/Ph (1-0-0) 10–20 ohm-cm, 381 ± 25 μm PRIME SILICON WAFER, SSP, 2 SEMI FLATS) by spin coating SU-8 2015 (Microchem) at 2200 rpm for 30 s and soft baking at 95 °C for 5 min to obtain a thickness of 20 μm. It was then exposed to UV light using photolithography (EVG 610 Double-Slide Mask Aligner) at an exposure energy equal to 160 mJ/cm2 through a photomask, followed by a post-exposure bake at 95 °C for another 5 min. Next, the wafer was developed with an SU-8 developer (Microchem). The master mold was then coated with (tridecafluoro1,1,2,2-tetrahydro octyl) trichlorosilane (United Chemical Technologies Inc., T2492) (≈50 nm thick using Chemical Vapor Deposition) for 30 min to facilitate PDMS release from the master mold after replication. The PDMS devices were replicated from the master mold by pouring PDMS prepolymer (Krayden, Sylgard 184 Clear Kit; 5:1 mixture) on the mold, mixed vigorously for 5 min, degassed for 30 min under vacuum to remove air bubbles, and cured at 85 °C for 45–60 min. To make the PDMS micropatterns hydrophilic for easy cell and culture medium loading, the PDMS layers were treated with oxygen plasma (Harrick Plasma) for 90 s.

Rhodamine-conjugated fibronectin circle patterns 30, 40, and 50 µm in diameter were printed on 35-mm tissue culture dishes (ibidi, µ-Dish) using a microcontact printing technique88. Briefly, Sylgard 184 Silicone Elastomer base (Dow Corning) was mixed with Sylgard 184 Silicone Elastomer Curing Agent at a 10:1 ratio, then poured on the silicon wafer, degassed in a vacuum chamber, and cured in the oven at 65 °C for 2 h. After curing, the PDMS was removed and cut into approximately 1 cm × 1 cm stamps that were placed in a petri dish with the feature side up. The surface of the PDMS stamps was treated with a low-frequency plasma cleaner unit (PlasmaEtch, Inc., PE-25) for 2 min before 100 µl of rhodamine-conjugated fibronectin (Cytoskeleton) at 0.1 mg/ml was applied to the surface for 1 h to allow adsorption of rhodamine fibronectin onto the surface of the stamps. The 35-mm ibidi µ-Dishes were plasma treated for 2 min, and the stamps were placed feature down on the center of the dishes. The stamps remained in contact with the dishes for 30 min and then the stamps were gently removed. To prevent protein adsorption and cell adhesion on the non-micropatterned regions of the dishes, 200 µg/ml PLL-g-PEG [poly(L-lysine)-g-poly (ethylene glycol)] solution (Surface Solutions AG) was applied overnight at 4 °C.

Model for axisymmetric cell and nuclear shapes

Fully spread cells commonly have characteristics that consist of surfaces of constant mean curvature89 for the joint nuclear/cell surface spherical cap (with mean curvature, ({{rm{H}}}_{{rm{cap}}})), the cell surface exterior between the cytoplasm and cell (with mean curvature, ({{rm{H}}}_{{rm{cell}}})), and the nuclear surface at the interface of the nucleus and cytoplasm (with mean curvature, ({{rm{H}}}_{{rm{nuc}}})) (see Fig. 3f). Generally, an axisymmetric surface of constant mean curvature is characterized by radius ({rm{R}}({rm{phi }})) vs. vertical position ({rm{z}}left({rm{phi }}right)), parameterized by variable ({rm{phi }}), with constant mean curvature H. The equations for ({rm{R}}({rm{phi }})) and ({rm{z}}left({rm{phi }}right)) are

$$R(phi )=sqrt{{alpha }^{2}{cos }^{2}phi+{beta }^{2}{sin }^{2}phi }$$

(2)

$$zleft(phi right)=alpha Eleft(phi,kright)+beta Fleft(phi,kright)$$

(3)

where ({rm{F}}left({rm{phi }},{rm{k}}right)) and ({rm{E}}left({rm{phi }},{rm{k}}right)) are incomplete elliptical integrals of the first and second kinds, respectively, and

$$alpha=frac{1+sqrt{1-4{CH}}}{2{rm{H}}}$$

(4)

$$beta=frac{1-sqrt{1-4{CH}}}{2H}$$

(5)

In addition to ({rm{H}}), ({rm{C}}) is a 2nd parameter that establishes the specific shape of the cell cortical surface (({{rm{C}}}_{{rm{cell}}})) or nucleus ({{rm{C}}}_{{rm{nuc}}})). (See Dickinson and Lele34 for a detailed mathematical derivation). For a spherical cap, C = 0. Let ({{rm{R}}}_{1},{{rm{z}}}_{1})) be the junction point between the joint spherical cap (with mean curvature, ({{rm{H}}}_{{rm{cap}}})), the cortical cell surface (with mean curvature, ({{rm{H}}}_{{rm{cell}}})), and the free nuclear surface (with mean curvature, ({{rm{H}}}_{{rm{nuc}}})). Matching the three surface tangents ({rm{dR}}/{rm{dz}}) at ({{rm{R}}}_{1}) requires

$${C}_{{rm{cell}}}=left({H}_{{rm{cap}}}-{H}_{{rm{cell}}}right){{R}_{1}}^{2}$$

(6)

$${C}_{{rm{nuc}}}=left({H}_{{rm{cap}}}-{H}_{{rm{nuc}}}right){{R}_{1}}^{2}$$

(7)

Further, the radius ({{rm{R}}}_{{rm{n}}0}) where the nucleus surface impinges tangentially on the substratum is given by

$${R}_{{rm{n}}0}={R}_{1}sqrt{1-frac{{H}_{{rm{cap}}}}{{H}_{{rm{nuc}}}}}$$

(8)

For a given cell spread radius, specific cell and nuclear shapes can be calculated by solving for the values of ({{rm{H}}}_{{rm{cap}}}), ({{rm{H}}}_{{rm{cell}}}), and ({{rm{H}}}_{{rm{nuc}}}) that satisfy specified values of cell volume, nuclear volume, and nuclear surface area. For a nuclear surface area greater than that of a sphere of the same nuclear volume, the resulting nuclear shapes are flattened against the surface (see Fig. 3g). In addition, assuming the Law of Laplace applies, the ratio of the surface tensions of the nuclear to cell surfaces is given by

$$frac{{tau }_{{rm{nuc}}}}{{tau }_{{rm{cell}}}}=frac{left({H}_{{rm{cap}}}-{H}_{{rm{cell}}}right)}{{({H}_{{rm{nuc}}}-{H}_{{rm{cap}}})}}$$

(9)

The solution yields unique cell and nuclear shapes for spreading radii up to a maximum radius where the cell edge becomes perpendicular to the substratum. Below a certain spreading radius, a unique solution with a non-zero spherical cap region requires ({{rm{H}}}_{{rm{cell}}}) > ({{rm{H}}}_{{rm{cap}}}) which would imply a negative tension on the lamina surface (by Eq. 9). However, since the nucleus is not attached to the cortex, this shape is not physically realized; rather the same constraints on cell volume, nuclear volume, and nuclear surface area, can be satisfied with the nucleus separated from the cell cortical surface, yielding a spherical cap-shaped cell cortical surface, and an undetermined, but possibly irregular nuclear shape without surface tension.

Synthesis and fabrication of gelatin-based hydrogels

Gelatin methacrylol (GelMA) hydrogels reinforced with polyethylene glycol (PEG)-dopamine-coated iron oxide nanoparticles (8 nm) were synthesized according to previously defined methods56. Precursor solutions consisted of GelMA (5% w/v), DI water, and 0 or 0.5 µg/ml of nanoparticles to achieve elastic moduli of 1–3 or 10–15 kPa, respectively. Hydrogel precursors were mixed with MDA-MB-231 cells (4 × 105 cells/ml) at 37 °C, then cast in droplets on glass coverslips and crosslinked under ultraviolet (UV) light (OmniCure Series 2000) at an intensity of 30 mW/cm2 for 60 s. Crosslinked gels were submerged in media for 5 days prior to cell fixation and immunofluorescent imaging.

Micropost fabrication

Sylgard 184 Silicone Elastomer base (Dow Corning) was mixed with Sylgard 184 Silicone Elastomer Curing Agent at a 10:1 ratio, degassed, poured onto the micropost mold, and cured at 65 °C overnight. Micropost stamps were peeled off and used to make upright microposts on 35-mm glass dishes (World Precision Instruments). The dishes were coated with 0.1 mg/ml rhodamine-conjugated fibronectin (Cytoskeleton) for 1 h at room temperature, washed three times with PBS, and then cells were passaged on the microposts, incubated overnight at 37 °C and processed for immunofluorescence staining and microscopy.

Transfection of siRNAs

Cells were cultured in 12-well plates in an antibiotic-free medium at 80% confluency at the time of transfection. The transfection solution consisted of 0.5% lipofectamine RNAiMAX transfection reagent (Invitrogen) and 0.5% siRNA (Dharmacon, siGENOME Non-Targeting siRNA Pool #2, D-001206-14-05, target sequences: UAAGGCUAUGAAGAGAUAC, AUGUAUUGGCCUGUAUUAG, AUGAACGUGAAUUGCUCAA, UGGUUUACAUGUCGACUAA; LMNA siGENOME SMARTpool siRNA, D-004978-01, target sequence: GAAGGAGGGUGACCUGAUA; LMNB1 siGENOME SMARTpool siRNA, D-005270-01, target sequence: GAAGGAAUCUGAUCUUAAU) in the reduced serum Opti-MEM medium (Gibco). The culture medium was replaced with transfection solutions, and cells were incubated in 5% CO2 for 3 days. On day 3, cells were collected for polymerase chain reaction (PCR) assay to verify siRNA knockdown and were passaged on microposts or polyacrylamide hydrogels.

Reverse transcriptase-quantitative PCR

To determine the efficiency of siRNA knockdown, cells were harvested and lysed using the RNeasy Plus Kit (Qiagen), and RNA was purified and quantified. The cDNA was prepared by mixing RNA, reverse transcriptase, oligo primers, and nucleotide triphosphates (dNTPs) (iScript™ Advanced cDNA Synthesis Kit, Bio-Rad Laboratories) in PCR-grade nuclease-free water (Invitrogen). The reaction mixture was incubated in the Bio-Rad thermocycler at the appropriate temperature and duration for reverse transcription. Forward and reverse primer sets (GAPD: VHPS-3541, forward (5′–3′): GAGTCAACGGATTTGGTCGT, reverse (5′–3′): TTGATTTTGGAGGGATCTCG, RealTimePrimers; LMNA: Ref# 460260112 & 13, forward sequence: ATGAGGACCAGGTGGAGCAGTA, reverse sequence: ACCAGGTTGCTGTTCCTC-TCAG; LMNB1: Ref# 460260114 & 15, forward sequence: GAGAGCAACATGATGCCCAAGTG, reverse sequence: GTTCTTCCCTGGCACTGTTGAC, IDT) were used to target the cDNA of the genes of interest. The PCR reaction combined cDNA, primers, DNA polymerase, dNTPs, and iQ™ SYBR® Green Supermix reaction buffer (Bio-Rad Laboratories). PCR amplification was performed using appropriate cycling conditions recommended by Bio-Rad. The standard curves and Ct values were used to quantify gene expression levels for the genes of interest normalized to the expression level of GAPD in the treatment group relative to the normalized gene expression levels in the siSCRM group.

Immunoblotting

Cells were washed with ice-cold PBS and lysed on ice with RIPA Buffer (ThermoFisher Scientific) supplemented with 1× Halt Protease and Phosphatase Inhibitor Cocktail (ThermoFisher Scientific). After centrifugation at 15,000 × g for 10 min at 4 °C, the supernatant was collected, and the protein concentration was determined using Pierce BCA Protein Assay Kit (ThermoFisher Scientific) and BioTek Cytation 5 (Agilent). The supernatant was mixed with 4× Laemmli Sample Buffer (Bio-Rad Laboratories) supplemented with 10% β-mercaptoethanol (Bio-Rad Laboratories) and boiled for 5 min. The samples were separated on a 4–15% polyacrylamide gel (Bio-Rad Laboratories) along with Chameleon Duo Pre-stained Protein Ladder (LI-COR Biosciences) and then transferred onto a nitrocellulose membrane (Bio-Rad Laboratories). The membrane was blocked with Intercept Blocking Buffer (LI-COR Biosciences) for 1 h at room temperature and incubated with primary antibodies mouse anti-lamin A/C (Santa Cruz Biotechnology, sc-376248; dilution 1:500) and rabbit anti-GAPDH (Novus Biologicals, NB100-56875; dilution 1:2000) overnight at 4 °C. After multiple membrane washes with TBST (20 mM Tris pH 7.6, 137 mM NaCl, 0.1% Tween 20), the membrane was incubated with secondary antibodies IRDye 680LT goat anti-mouse (926-68020; LI-COR Biosciences; dilution 1:5000) and IRDye 800CW goat anti-rabbit (926-32211; LI-COR Biosciences; dilution 1:5000) for 1 h at room temperature. The membrane was imaged using the Odyssey M imaging system (LI-COR Biosciences). The intensity of the fluorescent bands was quantified using Image Studio 4.0 software (LI-COR Biosciences).

Image analysis

Raw confocal images were loaded into Matlab, and a customized Matlab code was built for nuclear morphometric and phenotypic analysis. Maximum-projection images of the lamin channel were generated and segmented using an Otsu segmentation algorithm to create nuclear masks for the identification of nuclei. Nuclei that touched the image border or had a projected area smaller than the empirically determined lower bounds were removed to exclude small debris or imaging artifacts. The resulting nuclear masks were applied to lamin z-stack images to crop nuclei individually. To quantify nuclear height, mean lamin intensity was calculated for each z-plane, and the onset and offset points from the background intensity were determined as the bottom and top confocal planes. Nuclear height was calculated as the distance between these two confocal planes. Nuclear surface area and volume were quantified using Matlab Image Processing Toolbox.

Nuclear irregularity was quantified using an elliptical Fourier analysis, as we reported previously53, which approximates nuclear shapes through the decomposition of the shape into a series of harmonic ellipses90. We noticed that the bulk masks generated by Otsu segmentation were unable to capture accurate details of folds and wrinkles on nuclear contours. Therefore, we improved the segmentation by tracing the intensity maximum on each normal line along the bulk nuclear periphery to delineate the precise nuclear contour at sub-pixel resolution. The precise nuclear contour was fitted using a series of elliptic harmonics, defined by the Fourier series coefficients calculated from the x and y coordinates of the nuclear outline. A total of 15 harmonic ellipses were used for all the morphometric analyses, which were found to accurately approximate even the most complex, irregular nuclei53,91. The single elliptic harmonic at each frequency can be geometrically visualized as a pair of orthogonal semiaxes. The first-frequency Fourier coefficients describe a rough ellipsoidal shape, and the Fourier coefficients at higher frequencies approximate more convoluted outlines. To quantify the shape irregularity, the elliptic Fourier coefficient (EFC) ratio is defined as the ratio of the length sum of the major and minor semiaxes at the first frequency to the semiaxes length sum for the subsequent 14 harmonics at the higher frequencies. A regular nuclear contour, where the first-frequency elliptic harmonic captures most of the contour with small axes lengths at higher frequencies, has a larger EFC ratio. In contrast, an irregular nuclear contour requires larger axes lengths at higher frequencies, resulting in a lower EFC ratio. In this study, we accommodated the variation of nuclear irregularity across different confocal planes by extracting nuclear contours from the z-plane at 75%, 50%, and 25% of nuclear height to calculate the EFC ratio at the top, middle, and bottom, respectively, and averaging the EFC ratios of three planes for each nucleus.

Maximum-projection images of the phalloidin channel were generated and segmented using an Otsu segmentation algorithm to create cell masks. Cell spreading area and aspect ratio were quantified using Matlab Image Processing Toolbox. To quantify the nuclear to cytoplasmic ratio of YAP, the nuclear masks and cell masks were applied onto maximum-projection images of the YAP channel, and the nuclear to cytoplasmic YAP ratio was calculated as: [(Nuclear intensity)−(Background intensity)] ÷ [(Cytoplasmic intensity)−(Background intensity)].

For chromatin marker analysis, a customized Matlab code was built based on the previous study75. Briefly, maximum-projection images of the DNA channel were generated and segmented using an Otsu segmentation algorithm to create nuclear masks for determining the nuclear border and the nuclear center for each nucleus. For each pixel inside the nuclear mask, the distance to the nuclear center and the intensities for both H3K9me3 and H3K27me3 markers were measured. Nuclear center distances were normalized to the maximum distance of each corresponding center trajectory. Chromatin marker intensities were normalized to the total intensity per nucleus. Normalized nuclear center distances were binned in 0.01 steps and marker intensities of all pixels in the same bin were averaged for each nucleus.

Fluorescence lifetime imaging microscopy (FLIM)-FRET imaging and analysis

MDCK cells expressing Lamin-SS or Lamin-TM sensor50 were cultured on the fibronectin-coated glass-bottom dishes and allowed to spread overnight. Cells were treated with 10 µg/ml of cytochalasin D (Sigma–Aldrich) for 1 h to induce nuclear wrinkling, followed by fixation with 4% PFA for 15 min. After washing, the samples were stored in PBS without mounting. FLIM imaging was performed on a Leica SP8 confocal microscope using an HC Plan-Apochromat 40×/1.1 NA motCORR CS2 water-immersion objective (Leica Microsystems). A pulsed laser at 440 nm was used to excite the sensors, and fluorescence lifetimes in the 455 to 495 nm range were collected using a HyD X detector to capture photon arrival times specific to the donor. n-Exponential reconvolution fitting model in Leica LAS X software was used to fit the pixel-by-pixel photon arrival times with biexponential decay components to obtain mean lifetimes for individual nuclei.

Cytoskeleton, contractility, and LINC complex disruption experiment

For cytoskeleton disruption experiments, HN cells expressing GFP-LMNA were cultured on soft hydrogels and treated with 4 µM cytochalasin D (Sigma–Aldrich) or 2 µM nocodazole (STEMCELL Technologies) for 1 h. Z-stack live imaging with a 130-nm step size was performed both before and after treatment to assess changes in nuclear wrinkling. F-actin and microtubule disruption were verified through immunofluorescence staining in cells cultured on glass-bottom dishes and fixed after the same treatment. For contractility disruption experiments, HN cells expressing GFP-LMNA were cultured on stiff hydrogels and allowed to spread overnight. Cells were then treated with 50 µM Y-27632 (Sigma–Aldrich), a Rho-associated kinase (ROCK) inhibitor, or 50 µM blebbistatin (Sigma–Aldrich), a direct inhibitor of myosin II activity, for 3 h. Z-stack live imaging with a 130-nm step size was performed both before and after treatment to assess changes in nuclear volume and height. Cells were then fixed and stained for YAP and F-actin and imaged with the same imaging parameters to compare the nuclear to cytoplasmic YAP ratio. For LINC complex disruption experiments, MDCK cells mCherry-DN KASH1 were cultured on 35-mm glass dishes and treated with 1 µg/ml doxycycline (Sigma–Aldrich) for 24 h to induce mCherry-DN KASH1 expression. Cells were then fixed with 4% PFA and stained for lamin B1 and F-actin to compare the nuclear wrinkling and cell spreading.

Statistical analysis

All quantitative data were measured from at least three biological replicates and presented as mean ± standard error of the mean (SEM). GraphPad Prism 10.0 was used for statistical analysis and graphic representations of data. Differences between values were considered statistically significant when p < 0.05 and non-significant (NS) for p > 0.05. The details of experimental conditions and statistical tests are provided in the figure legends.

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.