Fibrillar adhesion dynamics govern the timescales of nuclear mechano-response via the vimentin cytoskeleton

Cell culture, transfections and drug treatments

Human TIFFs (a kind gift from J.I.) were cultured in high-glucose Dulbecco’s modified Eagle’s medium (Thermo Fisher Scientific) supplemented with 20% fetal bovine serum (v/v; Thermo Fisher), 2% of 1-M HEPES (v/v; H0887 Sigma) and 1% penicillin–streptomycin (v/v; 10378016, Thermo Fisher). For stretch experiments, media were changed to CO2-independent media (18045054, Thermo Fisher) supplemented with the same concentrations of fetal bovine serum, HEPES and penicillin–streptomycin, as done previously. Mammary epithelial cells (MCF10A) were purchased from ATCC (category number CRL-10317) and cultured in Dulbecco’s modified Eagle’s medium–F12 (21331-020, Life Technologies) with 5% horse serum, 1% penicillin–streptomycin, EGF (20 ng ml−1), hydrocortisone (0.5 μg ml−1), cholera toxin (100 ng ml−1) and insulin (10 μg ml−1). All cells were maintained at 37 °C with 5% CO2. Cell cultures were routinely checked for the presence of mycoplasma.

Transfections were conducted using the Neon Transfection System (Thermo Fisher Scientific) following the manufacturer’s instructions. TIFF cells were subjected to a single voltage pulse of 1,650 V with a width of 20 ms. Cells were transfected the day before the experiments, and the cells were seeded ~4 h before the experiment, unless otherwise stated.

Plasmids used for transfections

The Sencyt mechano-reporter was generated in the laboratory from a previous study8. Plectin 1f-GFP and plectin 1f-8-GFP were generated from a previous study75. GFP-paxillin was generated in the laboratory from a previous study3. Membrane marker N-terminal Neuromodulin-GFP was a kind gift from F. Tebar. Tensin1-eGFP was a kind gift from J.I. EGFP-Vimentin-7 was a gift from M. Davidson (Addgene plasmid number 56439; RRID: Addgene_56439).

For the pharmaceutical inhibitor experiments, cells were seeded on fibronectin-coated substrates for a minimum of 4 h (unless otherwise stated) to allow FB formation. All compounds were diluted and stored according to manufacturer’s instructions. Immediately before the experiments, compounds were diluted in cell culture media and warmed to 37 °C before adding to the cells.

The drugs and concentrations used were bleb (25 µM, B0560, Sigma), cytoD (1 µM, C2618, Sigma), Y-27 (25 µM, 688001, Sigma) and latA (0.5 µM, L5163, Sigma). Control cells were incubated with DMSO (Sigma), where the volume added was equal to the maximum volume of the drug conditions.

For the activation of α5β1 integrin by Mn2+, after trypsin cells were resuspended in media containing 5 mM of Mn2+ and seeded onto 1.5-kPa polyacrylamide gels. This concentration of Mn2+ was maintained throughout the duration of the experiment.

Fibril-blocking approaches

The PUR4 (also known as FUD) peptide (sequence, KDQSPLAGESGETEYITEVYGNQQNPVDIDKKLPNETGFSGNMVETEDT) and the scrambled control (sequence, EKGYSKPPVGNEGGDQVDEYDTMSQTKLEDEGNTLISPITFENATEQVN) were synthesized by Thermo Fisher Scientific without any tags or modifications. In all the experiments, after trypsin, the cells were resuspended in media containing the PUR4 or scramble peptide at a final concentration of 500 nM. The peptide was maintained in the media for the duration of the experiment.

For blocking α5β1 integrin, cells in suspension were incubated for 20 min at 37 °C in the blocking antibody (α5β1 integrin, clone JBS5, Sigma) or control antibody (IgG) before seeding onto 10 µg ml−1 of fibronectin-coated glass surfaces. Both blocking antibodies were used at a concentration of 10 µg ml−1.

Gluteraldehyde-blocked surfaces were prepared as described previously47. Briefly, glass surfaces were coated with 10 μg ml−1 of fibronectin overnight at 4 °C or 1 h at 37 °C. Surfaces were then treated with 1% gluteraldehyde (Sigma-Aldrich) in MilliQ H2O solution for 10 min at room temperature. Surfaces were then thoroughly rinsed with H2O and left to incubate in freshly prepared 1% bovine serum albumin (Sigma-Aldrich) solution for at least 20 min at 37 °C before cell seeding.

siRNA treatment

siRNA treatment was applied using reverse transfection by incubating detached TIFFs with DharmaFECT 1 Transfection Reagent complexes preincubated with 100 nM of the corresponding siRNA (ON-TARGETplus Non-targeting Pool 20 µM, reference number 77D-001810-10), ON-TARGETplus SMART pool SYNE3 (reference number L-016637-01) and ON-TARGETplus SMART pool VIM (reference number L-003551-00) (all from Dharmacon). The cell suspension with the siRNA complexes was seeded and incubated for 24 h before changing the media, and cells were used after 72 h.

RNA isolation and quantitative polymerase chain reaction

Total RNA was isolated by using the High Pure RNA Isolation Kit according to the manufacturer’s instructions. Then, 500 ng of RNA was used to generate the corresponding cDNA with the iScript Reverse Transcription Supermix (Bio-Rad). SYBR Green-based quantitative reverse-transcription polymerase chain reactions (Fast SYBR Green Master Mix, Applied Biosystems) were run in triplicate in a StepOnePlus System (Applied Biosystems). The expression level of individual genes was analysed by the ΔCt method and normalized according to the expression of the housekeeping gene RNA18S. Primers sequences are listed in Supplementary Table 1.

Western blotting

Cells were lysed in RIPA buffer (Merck Millipore) with protease and phosphatase inhibitor cocktails (1%; both from Sigma-Aldrich) on ice and then centrifuged at 13,000g for 10 min at 4 °C. The protein concentration was determined using the bicinchoninic acid assay method. Here 10 µg of proteins for each sample were loaded in on 4%–20% polyacrylamide gels (Bio-Rad), run at 110 V for 1.5 h and then transferred to a nitrocellulose membrane (GE Healthcare LifeScience) at 30 V overnight. Membranes were blocked with 5% bovine serum albumin in Tris-buffered saline with Tween 20, incubated with diluted primary antibody (anti-nesprin 3, ab186746, Abcam, 1:1,000), anti-vimentin (ab92547, Abcam, 1:2,000), anti-GAPDH (sc-32233, Santa Cruz Biotechnology, 1:1,000) in 5% bovine serum albumin in Tris-buffered saline with Tween 20 at 4 °C overnight, and then probed with the proper secondary horseradish-peroxidase-linked antibody (Jackson ImmunoResearch) at room temperature for 1 h. ImageQuant LAS 4000 mini imaging system (Bio-Rad) was used to detect chemiluminescence.

Immunostainings

Cells were fixed with 4% paraformaldehyde for 10 min at room temperature and rinsed thrice with phosphate-buffered saline (PBS). Cells were permeabilized with 0.1% Triton X for 5 min and then blocked with 0.5% fish gelatin (Sigma-Aldrich) for 1 h (except manganese-treated cells, which were permeabilized using 0.5% Triton X for 15 min). Cells were incubated with the primary antibody for 1 h, diluted in the 0.5% fish gelatin blocking solution, washed with the blocking solution for 30 min and incubated with the secondary antibody labelled with an Alexa fluorophore (Thermo Fisher, 1:300 dilution) for 1 h. In the case of actin staining, phalloidin (Sigma-Aldrich, 1:1,000) was added with the secondary antibody. Hoechst (1:2,000) was added for 5 min to label the nuclei, and the samples were washed thoroughly.

Primary antibodies and their dilutions

YAP (1:300, sc-101199, Santa Cruz Biotechnology) or (1:300, 14074S, Cell Signaling); integrin α5, clone SNAKA51 (1:300, MABT201, Millipore); laminB (1:300 ab16048, Abcam); paxillin (1:300, ab32084, Abcam); twist (1:100, SC-81417, Santa Cruz Biotechnology); snail (1:50, Ab224731, Abcam); tensin1 (1:200, ab233133, Abcam); fibronectin (1:300, F3648, Sigma); vimentin (1:600, ab92547, Abcam); γH2Ax (1:300, 2577, Cell Signaling).

Polyacrylamide gel

Polyacrylamide gels of variable rigidities were prepared as previously described8. Briefly, glass-bottom dishes (MatTek) or glass coverslides were treated with a solution of 3-(trimethoxysilyl)propyl methacrylate (Sigma), acetic acid and 96% ethanol (1:1:14) for a minimum of 10 min. The glass was then thoroughly rinsed in 96% ethanol and dried. Gels were prepared by mixing different concentrations of acrylamide and bis-acrylamide to produce gels of different rigidities according to a previous characterization8, with 2% v/v 200-nm-diameter fluorescent carboxylate-modified beads (FluoSpheres, Thermo Fisher Scientific), 0.05% v/v ammonium persulfate (Sigma-Aldrich) and 0.05% tetramethylethylenediamine (Sigma-Aldrich) in PBS 1×. To cast the gels, 22 μl was placed on top of the treated glass and then covered with an 18-mm circular coverslip. Gels were left for 45 min to polymerize at room temperature. Finally, gels were submerged in PBS 1× and the top coverslip was removed. To coat gels, we prepared a mixture containing 10% HEPES (0.5 M, pH 6.0), 0.004% bis-acrylamide, 0.05% Igracure 2959 and 4% acrylic-acid N-hydroxysuccinimide/DMSO (10 mg ml−1, A8060, Sigma) in MilliQ water. Gels were coated in this mixture and then illuminated with UV light for 8 min. Gels were then washed twice in 50 mM of HEPES at pH 7 and twice in PBS 1×, and incubated with 10 µg ml−1 of fibronectin in PBS overnight at 4 °C, sterilized by UV treatment in a laminar-flow hood, washed once with PBS and immediately used.

Photodegradable compound synthesis

Photodegradable precursors were prepared as previously described57. Briefly, the acrylate-functionalized photodegradable monomer was synthesized by suspending 4-[4-(1-hydroxyethyl)-2-methoxy-5-nitrophenoxy]butyric acid (0.0166 mol, Sigma-Aldrich) in anhydrous dichloromethane (90 ml). The mixture was purged with argon; triethylamine (0.0664 mol) was added to the flask by syringe; and acryloyl chloride (0.0547 mol) in dry dichloromethane was added dropwise at 0 °C. The reaction was kept under an argon atmosphere and allowed to proceed overnight at room temperature. The reaction mixture was then added to deionized water (0.5 l) and allowed to stir for 2 h at room temperature, before being extracted with chloroform (5 × 200 ml washes). The organic phase was dried over NaSO4 and concentrated by rotary evaporation to obtain the acrylate-functionalized photodegradable crosslinker.

To synthesize the photodegradable PEG crosslinker (PEGdiPDA), the acrylate-functionalized photodegradable monomer (6 mmol) was dissolved in N-methyl-2-pyrrolidone (15 ml) and purged with argon. The coupling agent 2-(1H-benzotriazole-1-yl)-1,1,3,3-tetramethyluronium hexafluorophosphate (6.6 mmol), 1-hydroxybenzotriazole (6.6 mmol) and diisopropylethylamine (0.012 mol) were then added to the reaction mixture and stirred for 5 min before the addition of PEGdiamine (0.6 mmol, 2 kDa) in N-methyl-2-pyrrolidone. The reaction mixture was heated and vortexed until all the reactants had completely dissolved, and left to stir overnight at room temperature. The reaction mixture was then precipitated in diethyl ether at 0 °C and collected by centrifugation. The macromer product was redissolved in water and centrifuged to yield a dark brown pellet with a clear supernatant. The supernatant was collected, dialysed (SpectraPor 7; CO, 1,000 g mol−1) and lyophilized to produce a white powder (39% yield) that was used in experiments.

Characterization of photodegradable gel mechanical properties

Photodegradable gels were prepared by first mixing 5.4 wt% of PEGdiPDA, 9.6 wt% of PEG400acrylate and 6.6 mM of sodium acrylate in PBS before degassing for 5 min on ice. Polymerization was initiated by the addition of 200-mM tetramethylethylenediamine and 100-mM ammonium persulfate, which were preincubated on ice, and drops were added between Sigmacote (Sigma-Aldrich)-treated glass slides with either 200-µm spacers for 12-µl gels or 100-µm spacers for 6-µl gels. The gels were left to polymerize for 10 min before the top glass slide was removed and the hydrogels were transferred to a well plate with PBS (500 µl). Following equilibration for 30 min in PBS, the hydrogels were transferred to a rheometer (DHR-3, TA Instruments) equipped with a light curing accessory (OmniCure 1000, Lumen Dynamics) and an 8-mm parallel-plate tool to measure the shear properties of the hydrogel. The 6-µl gels were used to track the in situ network evolution during irradiation (365 nm, 10 mW cm−2), and the 12-µl gels were used to evaluate the rheological properties of equilibrium swollen samples before and after preselected doses of irradiation. All the rheological characterization experiments utilized a strain of 1% and a frequency of 1 Hz.

Photodegradable gel cell experiments

Glass-bottom dishes were activated using the same protocol as the polyacrylamide gels. Photodegradable gels were prepared by first mixing 5.4 wt% of PEGdiPDA, 9.6 wt% of PEG400acrylate and 6.6 mM of sodium acrylate in PBS before degassing for 5 min on ice. Polymerization was triggered by the addition of 5% tetramethylethylenediamine and 10% ammonium persulfate (2 M), which were preincubated on ice, and a 22-μl drop of gel mixture was placed in the centre of the glass-bottom dish and covered with an 18-mm coverslip to achieve uniform spreading. The gels were left to polymerize for 10 min before the addition of PBS and the removal of the top coverslip.

For functionalization, we prepared a mixture containing 100 mM of 1-ethyl-3-(3′-dimethylaminopropyl)carbodiimide hydrochloride (8510070025, Sigma) and 200 mM of N-hydroxysuccinimide (130672, Sigma) in 20 mM of HEPES buffer at pH 7. Gels were incubated in this mixture for 20 min at 37 °C. The gels were rinsed once with HEPES buffer and once with PBS. The gels were then incubated with 10 µg ml−1 of fibronectin overnight at 4 °C. To initiate gel softening, gels were placed under a UV lamp (UVP; 365 nm, 15 W) for 4.5 min. We measured the pH and osmolality of the cell culture media before and after the UV illumination protocol and observed no significant differences.

Live–dead assay

To quantify the extent of cell death from UV illumination during gel softening experiments, cells were seeded on 15-kPa polyacrylamide gels in either PUR4 or scramble peptide. After 4 h, cells were subjected to a 4.5-min UV illumination and left for 1 h. Cells were then incubated for 10 min in media containing 500 nM of Sytox green nucleic acid stain (Invitrogen) and Hoechst. After washing out the Sytox-containing media, cells were imaged using a ×20 objective and the percentage of Sytox-positive cells was calculated.

EdU assay

Cell proliferation was assessed using the Click-iT Plus 5-ethynyl-2′-deoxyuridine (EdU) Cell Proliferation Kit (Thermo Fisher Scientific), according to the manufacturer’s protocol. Briefly, cells were seeded onto fibronectin-coated glass-bottom wells and incubated for 4 h in the presence of either scramble or PUR4 peptide. Cells were then treated with either DMSO or cytoD for the indicated duration. EdU was added to the culture medium 1 h before fixation. Cells were fixed with 4% paraformaldehyde in PBS for 10 min at room temperature, permeabilized with 0.5% Triton X-100 and stained using the Click-iT EdU kit reagents followed by Hoechst 33342 to label the nuclei. Samples were imaged using a ×10 objective on an epifluorescence microscope, with each field of view containing approximately 20 cells. The number of EdU-positive cells was quantified per field of view, and the mean across all fields was calculated for each biological replicate.

Image acquisition

Epifluorescent images were obtained and time-lapse microscopy was performed using an inverted microscope (Nikon ECLIPSE Ti) equipped with thermal, CO2 and humidity control. Microscopes were equipped with an ORCA Flash4.0 camera (Hamamatsu) and controlled with MetaMorph (v. 7.7.1.0) or Micro-Manager. Most images were taken with a ×60 objective (Plan Apo; numerical aperture (NA), 1.2; water immersion), unless otherwise stated.

For time-lapse acquisition of the change in mechano-reporter Sencyt localization with drug treatments, a single image was acquired before pharmacological treatment, and then, the images were acquired every 5 min for a total duration of 1 h. For time-lapse acquisition of the change in mechano-reporter Sencyt localization on in situ photodegradable gel softening, images were taken on a Nikon TiE inverted microscope equipped with a spinning-disc confocal unit (Andor) and a Sona scientific complementary metal–oxide–semiconductor camera (Andor), using a ×40 objective (Plan Fluor; NA, 0.75) controlled using Fusion software. A single z stack was acquired before UV softening. Gels were then softened for 4.5 min with a UV lamp, and the z-stacked images were taken every 10 min for 2 h. For all experiments involving transfected cells, only cells positive for the GFP expression were imaged and analysed.

Confocal images of nuclear height and plectin 1f were acquired a ZEISS LSM880 inverted confocal microscope using ZEISS ZEN2.3 SP1 FP3 (black edition; v. 14.0.24.201) using a ×63, 1.46-NA oil-immersion objective. Confocal images of the vimentin network were taken using a Nikon TiE inverted microscope with a spinning-disc confocal unit (CSU-WD, Yokogawa) and a Zyla 4.2 scientific complementary metal–oxide–semiconductor camera (Andor) using a ×60 objective (Plan Apo; NA, 1.2; water immersion) controlled with Micro-Manager.

Traction force microscopy

Traction force microscopy experiments were performed as described previously76. Briefly, cells were seeded on 15-kPa polyacrylamide gels embedded with fluorescent beads. Images of the cells and the beads were acquired before pharmacological treatment and 30 min after pharmacological treatment. Cells were then removed from the gel using trypsin to obtain a reference image of the beads. Local gel deformation was computed using a custom particle imaging velocimetry software77 in MATLAB (MathWorks). Traction forces were computed using Fourier traction microscopy with a finite gel thickness and the mean of each cell was calculated.

Cell stretch experiments and quantification

Stretchable polydimethylsiloxane (PDMS) (SYLGARD 184 Silicone Elastomer Kit, Dow Corning) membranes were prepared as previously described9. Briefly, a base-to-crosslinker mix (10:1) was spun for 1 min at 500 rpm and cured at 65 °C overnight on plastic supports. Once polymerized, membranes were peeled off and assembled onto the stretching device. The PDMS membranes were functionalized with 10 µg ml−1 of fibronectin overnight at 4 °C. TIFF cells were seeded for at least 4 h (unless otherwise stated) before the stretch experiment. Immediately before stretch, the cell media were changed to CO2-independent media. The stretch experiments were performed by mounting the stretching device on an upright microscope (Nikon ECLIPSE Ni-U) equipped with temperature control and controlled using Metamorph. Calibration of the system was performed using PDMS coated with fluorescent beads, to ensure that the vacuum applied a 10% stretch to the PDMS membrane. Each membrane was stretched for a maximum of six times per experiment. The percentage change in the area of the nucleus and cell membrane on stretch was calculated by segmenting the fluorescent signal from the Hoechst or membrane marker, respectively, before and during stretch. For DNA damage experiments, cells were subjected to five cycles of 30 s of 10% stretch and 10 s of release. The stretch system was immediately removed from the microscope and the cells were fixed and stained with γH2Ax and Hoechst. The Hoechst signal was used to segment the nuclei, and the mean intensity of each nucleus was measured correcting for the background.

Adhesion disassembly times

To measure the disassembly times of focal adhesions compared with FBs, TIFF cells were transfected with either paxillin-GFP or tensin1-GFP, respectively. Transfections were performed 24 h before the experiment. On the day of the experiment, cells were seeded on fibronectin-coated glass-bottom dishes (MatTek) of polyacrylamide gels and left to form adhesions for a minimum of 4 h. Adhesion dynamics were acquired using a ZEISS LSM880 inverted confocal microscope with a ×63 1.46-NA oil-immersion objective. For cells expressing paxillin-GFP, images were acquired every 120 s for approximately 2.5 h. For cells expressing tensin1-GFP, images were acquired every 300 s for approximately 10 h. The adhesion intensity was tracked with time, from the initial formation until disappearance. The plot of adhesion intensity was then fit with a Gaussian, and the disassembly time was measured at the time from the Gaussian peak until the return to background levels.

Micropatterning experiments

Single rectangular adhesive patterns were generated on glass substrates using PRIMO2 UV light patterning system (Alvéole) mounted on an inverted microscope (Nikon ECLIPSE Ti2). Glass coverslips were prepared for patterning by 1-min plasma cleaning followed by immediate incubation with poly-L-lysine for 30 min. The glass slides were profusely washed with 0.1-M HEPES buffer (pH 8.5), and incubated for 1 h in 70 mg ml−1 of PEG-SVA (Mw, 5,000; Laysan Bio). Glass coverslips were then washed in MilliQ water and left to dry in a laminar-flow hood. Finally, PLPP gel (Alvéole), diluted at 1:10 in 70% ethanol, was placed on the coverslips and allowed to dry completely. After UV patterning, coverslips were washed thoroughly and then incubated for 5 min with fibronectin (0.1 mg ml−1) and fibrinogen-647 (0.01 mg ml−1) to facilitate pattern visualization.

Image analysisN/C ratio analysis

The N/C ratio was quantified by measuring the mean fluorescence intensity of a nuclear region (Inucleus) and the intensity of a cytoplasmic region immediately adjacent to it (Icytoplasm). The nuclear region was determined from the Hoechst staining. The ratio was calculated using the following formula:

$$\frac{{\rm{Nucleus}}}{{\rm{Cytoplasm}}}=\frac{{I}_{{\rm{nucleus}}}-{I}_{{\rm{background}}}}{{I}_{{\rm{cytoplasm}}}-{I}_{{\rm{background}}}},$$

(1)

where Ibackground is the mean fluorescence intensity of a region outside of the cell. For the quantification of the mechano-reporter Sencyt with time, the N/C ratio was calculated at each time point. For all drug treatment experiments, the N/C ratio at each time point was normalized to the N/C ratio before the addition of the compound. For quantification of the N/C mechano-reporter Sencyt ratio during in situ gel softening experiments, a single confocal plane was selected and the N/C ratio was normalized between the presoftened N/C ratio and the ratio at the final time point.

FB quantification

FBs were marked with integrin α5, clone SNAKA51 antibody (or tensin1 antibody for the blocking antibody experiments). To quantify the extent of FB formation, the fibrils in the area under the nucleus (determined from Hoechst staining) were detected using the Fiji Ridge Detection plug-in, and the percentage area occupied by the fibrils was computed. For cells seeded on soft gels, the length of the FBs was calculated to circumvent changes in the focal plane across the whole cell. For each cell, the length of almost five representative FBs under the nucleus were measured.

Focal adhesion length

Focal adhesion length was obtained by measuring the length of almost five representative focal adhesions at the cell periphery for each cell.

Nuclear height

Nuclear height was measured from z-stacked confocal images of laminB-stained nuclei. Each nucleus was resliced along the long axis, an intensity profile was created and the height was measured from the distance between the two peaks of maximum laminB intensity.

Vimentin spreading

To calculate the area occupied by vimentin, confocal stacks were acquired for cells stained with actin and vimentin. The area of the actin and vimentin networks was calculated by thresholding the z projection (sum) of each channel. The percentage area of the vimentin network with respect to the total cell area (from the actin network) was computed for each cell.

Actin anisotropy

The actin anisotropy was analysed using the FibrilTool plug-in in ImageJ78.

Computational modelScope and limitations of the model

The scope of the computational model presented here is that of cellular and nuclear mechanics. It has been designed to capture the essential mechanical interactions governing nuclear deformation and adaptation timescales. It seeks to understand whether the role of FBs as anchors between the intermediate filament cytoskeleton and the substrate can explain how FBs regulate nuclear shape in response to the two types of mechanical stimulus applied experimentally: actomyosin contractility inhibition and cell stretch. In this regard, it does not address aspects upstream (such as the molecular regulation leading to different timescales for focal adhesions and FBs) or downstream (such as how nuclear deformation regulates YAP nucleocytoplasmic transport).

The model is deterministic, with flexibility of the parameter space, which can be adjusted to reflect different cell types, substrate rigidities or pharmacological perturbations, thereby enabling the exploration of qualitative trends across a range of conditions. The model is not intended to provide exact quantitative predictions for all cellular contexts, but rather to highlight the relative contributions of cytoskeletal contractility, vimentin anchoring and FB stability to nuclear mechanics. Limitations include the absence of stochasticity in adhesion bond dynamics, the assumption of isotropy within cytoskeletal elements and the treatment of the nucleus as a linearly elastic material, without explicitly incorporating potential viscoelastic relaxation timescales. Although such viscoelastic effects could shift the magnitude of nuclear deformations, they would not alter the qualitative conclusion that FB anchoring regulates the persistence of nuclear mechanotransduction.

Constitutive models for the cell, nucleus and substrate

To fully describe the effect of mechanical stress (generated due to cellular contraction and/or applied stretch) on the nucleus, we consider the following key components in our computational model: (1) contraction due to myosin motors (Fig. 3m, red), (2) actin filaments (Fig. 3m, blue), (3) VIFs (Fig. 3m, green), (4) microtubules (Supplementary Fig. 3, brown) and (5) FBs. In our model, the cell cytoskeleton is considered to consist of spatially varying representative volume elements, each of which comprises components (1)–(4) described above (Supplementary Fig. 3a). We initially assume uniform and isotropic distribution of these elements and describe how—due to the action of contractile forces and the resulting stress field—these cytoskeletal components are redistributed in a more anisotropic manner, facilitating force transfer from the cell cytoskeleton to the nucleus. Also, the ECM is modelled as a linear elastic material with an elastic modulus of 70 kPa, whereas the nucleus is similarly modelled as an elastic material with the Young modulus and shear modulus values listed in Supplementary Table 2. We describe each of these components here.

Cytoskeletal contraction due to myosin molecular motors

Myosin motors are treated as force dipoles (pair of equal but oppositely oriented forces) that bind to actin filaments and generate cellular contractility79 (Fig. 3m). The volume-averaged density of the bound motors can be represented by a symmetric tensor \({\rho }_{{ij}}\), whose components represent cytoskeletal contractility along different directions80. Within our coarse-grained approach, the contraction due to myosin motors is represented as an isotropic stress tensor (ρ11 = ρ22 = ρ33 = ρ) with a magnitude of 1.5 kPa, applied at every point in the cell cytoskeleton. Due to cytoskeletal contraction, compressive stress \({C}_{{ijkl}}^{\,({\rm{A}})}{\varepsilon }_{{kl}}^{({\rm{A}})}\) are generated in components in compression (like vimentin), whereas tensile stresses \({s}_{{ij}}\) are generated in the cytoskeletal components under tensile strain (actin filaments). By force balance, the contractility is given as

$${\rho }_{{ij}}=-{C}_{{ijkl}}^{\,\left({\rm{A}}\right)}{\varepsilon }_{{kl}}^{\left({\rm{A}}\right)}+{s}_{{ij}},$$

(2)

where \({C}_{{ijkl}}^{\,\left({\rm{A}}\right)}\) and \({\varepsilon }_{{kl}}^{\left({\rm{A}}\right)}\) are the stiffness tensor and strain of the components in compression (Supplementary Fig. 3), respectively, namely, the microtubules and vimentin.

Actin filaments and actin–vimentin interactions

The actin filaments experience tension as the cell contracts and, hence, are in series with the myosin element. VIFs interact with actin through direct physical contact facilitated by crosslinkers and direct binding81. Hence, the VIFs in contact with actin also experience tensile stresses and are added in series to the nonlinear elastic element representing actin filaments (Supplementary Fig. 3).

Vimentin–microtubule network under compression

VIFs near the perinuclear region interact with microtubule elements and are experimentally reported to stabilize them82,83. To represent this effect, we add another set of vimentin elements in parallel with the microtubules in compression. Hence, there are two sets of VIFs, one that is in direct physical contact with actin and under tension, whereas the other is enmeshed with microtubules under compression, reinforcing them67. Also, VIFs have been observed to stiffen under compressive strains, leading to an overall compressive stiffening of cytoskeletal networks55. To represent the above effects, the cytoskeleton is modelled as a nearly incompressible, hyperelastic solid that stiffens under compressive strains. First, we define the deformation gradient \({F}_{{ij}}=\frac{\partial {x}_{i}}{\partial {X}_{j}}\) as a second-order tensor that maps infinitesimal line elements \({\rm{d}}{\bf{X}}\) in the reference configuration to corresponding infinitesimal line elements \({\rm{d}}{\bf{x}}\) in the current configuration. Further, we define \(C={F}^{{\rm{T}}}F\) to be the right Cauchy–Green deformation tensor whose normal components represent stretch along a given direction, whereas shear components represent a change in angle. A Mooney–Rivlin constitutive equation is used to represent this stiffening behaviour and the strain energy of the cell can be defined as

$${W}_{{\rm{s}}}={C}_{1}\left({\bar{I}}_{1}-3\right)+{C}_{2}\left({\bar{I}}_{2}-3\right)+{\frac{1}{2}K\left(J-1\right)}^{\!2}.$$

(3)

In the above equation, the Jacobian \(J=\det \left({\bf{F}}\right)\) is the determinant of the deformation gradient tensor, whereas \({\bar{I}}_{1}\) and \({\bar{I}}_{2}\) are the first and second invariants of the deviatoric part of \({\bf{C}}\), respectively. The parameters C1 and C2 are Mooney–Rivlin parameters, whereas \(K\) is the bulk modulus of the cell. In the limit of small strains, the parameters \({C}_{1}\) and \({C}_{2}\) can be related to the shear modulus of the cell \(\mu\) as \(\mu =2({C}_{1}+{C}_{2})\). The values of these parameters are listed in Supplementary Table 2, and the elastic modulus of the cell for compressive strains in the range of 0.001 to 0.5 is found to be in the range of 2.1–2.9 kPa, which provides reasonable agreement with the Young modulus measured for living fibroblasts using atomic force microscopy84. The high levels of compressive strain near the nucleus due to the contractile stress leads to the formation of a stiff region representing the vimentin cage observed experimentally (principal stress \({s}_{3}\); Supplementary Fig. 3). By contrast, in the cell cytoskeleton, high tensile stresses are observed close to the basal plane, particularly near the cell periphery (principal stress \({s}_{1}\); Supplementary Fig. 3), representing the actin and VIFs in tension.

Adhesive and frictional forces due to FBs

Due to cytoskeletal contraction, the vimentin cage around the nucleus is gradually pushed down and is anchored by FBs that are present near the centre of the cell. On loss of contractile forces, the nucleus tries to rebound and restore a rounded shape, but this is prevented by the anchored vimentin network. This leads to the application of force from the nucleus to the vimentin network, which is transmitted to the substrate through FBs. We model this as a vertical resistive adhesive force fa mediated by FBs on the edge of the vimentin cage, which remains even when contractile forces are removed. We estimate this force to be of the same magnitude as the contractile force needed to push down the vimentin cage.

FBs are defined by α5β1 integrin and tensin family of proteins, which form bonds with ligands on the ECM. On the application of stretch, the bond between the FBs and the ligands on the ECM (a polymer structure) is ruptured. This rupture corresponds to overcoming energy barriers by thermal activation (note that we assume that the vimentin remains anchored to the FBs as it slides). The disengagement of the FB–ligand bond follows a Hill-type relation, where the velocity of the sliding adhesions decays exponentially as the activation energy associated with bond rupture \({E}_{{\rm{A}}}\) increases:

$${v}_{{\rm{a}}}={v}_{0}\exp (-{E}_{{\rm{A}}}/{E}_{0}),$$

(4)

where \({v}_{0}\) is the maximum sliding velocity (when the activation energy \({E}_{{\rm{A}}}\) is zero) and \({E}_{0}\) is an energy scale related to thermal or active noise. The activation energy can be expressed as the work done by a dissipative force \({f}_{{\rm{d}}}\) in translocating the FBs by a molecular sliding distance \({\rm{A}}\):

$${v}_{{\rm{a}}}={v}_{0}\exp (-{f}_{{\rm{d}}}{\rm{a}}/{E}_{0}).$$

(5)

Assuming that the activation energy associated with the rupture is much smaller than \({E}_{0}\), the above equation can be linearized, and expressed as

$${f}_{{\rm{d}}}={\eta }_{{\rm{d}}}{v}_{{\rm{a}}},$$

(6)

where \({\eta }_{{\rm{d}}}={E}_{0}/{\rm{a}}{v}_{0}\) is a frictional dissipative constant that is inversely related to the mobility of individual FBs85. Setting ηd as zero is equivalent to the case of FBs not anchored to the ECM and is representative of cells lacking FBs.

Model sensitivity analysis

For the different parameters, sensitivity analysis was performed within COMSOL Multiphysics using the built-in sensitivity study node. Each parameter of interest (bulk and shear moduli of the nucleus, cell elastic modulus, Mooney–Rivlin parameters and myosin contractile stress) was defined in the ‘Global Parameters’ node of model builder in COMSOL and systematically perturbed around its baseline value. COMSOL computes sensitivities by differentiating the model equations with respect to each parameter and reports the normalized change in selected output variables. In this case, the primary read-out was nuclear deformation, which served as a proxy for mechanotransduction. The resulting sensitivity coefficients quantify the relative influence of each parameter on nuclear mechanics: negative values indicate that increasing the parameter reduces nuclear deformation, whereas positive values indicate that increasing the parameter amplifies nuclear deformation. This analysis allowed us to identify which mechanical properties and active stresses most strongly control nuclear behaviour in the model. As expected, parameters quantifying stiffness (of the cell and nucleus) reduce nuclear deformations, whereas the contractility parameter increases it, with sensitivities of the same order (Supplementary Table 3).

Time-dependent implementation of adhesion disassembly

To incorporate the different disassembly timescales of focal adhesions and FBs, the corresponding parameters in the COMSOL model were defined as time-dependent functions. Specifically, contractility and adhesion anchoring strengths were assigned linear decay functions in the ‘Global Definitions→Functions’ node, where the slope was set by the experimentally observed rate of disassembly and the function terminated at the experimentally measured final time (20 min for focal adhesions and ~80 min for FBs). Simulations were carried out in a time-dependent study node using the default backward differentiation formula implicit solver, with the total simulated duration set to 100 min to capture the full relaxation process. Nuclear height was extracted as a function of time, providing a direct read-out of how adhesion-dependent anchoring regulated the kinetics of nuclear rebound following loss of contractility.

Geometry, mesh and boundary conditions

The model for the cell cytoskeleton, nucleus and FBs is implemented in COMSOL Multiphysics, within a finite element framework. The cell is modelled as an ellipsoid with semi-axes lengths of 15 and 12 µm, whereas the nucleus is modelled as a spheroid with a radius of 3.7 µm located at the centre of the cell. The substrate is modelled as a rigid cylinder with a radius of 50 µm. Due to rotational symmetry of the cell–substrate system, an axisymmetric analysis is conducted, with horizontal roller boundary conditions applied to the top and bottom ends of the substrate. Although the cell and nucleus fully rest on the substrate, a small hemispherical region around the 0.5-µm-thick nucleus and separated from the nucleus by 0.1 µm is initially separated by a gap of 0.03 µm from the substrate. This represents the vimentin cage that forms on the action of contractile forces and is pushed down and eventually is anchored to the FBs. Standard contact conditions are implemented at the vimentin–nucleus interface, representing the effect of nesprins and other molecules that directly transfer contractile stresses to the nucleus. In addition, the contact boundary conditions are implemented at the vimentin–substrate interface to represent adhesion between the vimentin and FBs near the centre of the cell, using a spring foundation boundary condition with an added friction node. When combined with the frictional contact formulation, this provides a dissipative resistance to tangential motion, capturing the slip–stick behaviour of FBs. In the absence of FBs, the friction node is disabled, whereas the elastic component of the spring foundation is retained, effectively modelling basal substrate contacts and removing the stabilizing contribution of FBs. Triangular mesh elements are used to discretize the cell geometry with a minimum element size of 0.001 µm near the contact zones to accurately resolve the stresses and displacements at contact.

Implementation of simulations

To run the simulations, we first defined the axisymmetric geometry of the cell, nucleus and substrate, and then assigned the parameters listed in Supplementary Table 2 together with the boundary conditions described above. Two types of experimental condition were reproduced. In the first, contractility (ρ) and FB strength were reduced either as a steady-state change or as a time-dependent decay. In the second, substrate stretch was applied through a prescribed displacement using a ramp function. Both conditions were simulated with FBs present and without FBs by setting the FB-related resistive adhesion force (\({f}_{{\rm{A}}}\)) and the frictional viscosity constant (\({\eta }_{{\rm{d}}}\)) to zero. The primary outputs were nuclear height, deformation fields, stress maps and parameter sensitivities.

Statistics and reproducibility

No statistical method was used to predetermine the sample size. No data were excluded from the analyses. Statistical analyses were performed using GraphPad Prism software (v. 9). The names of the statistical tests used and the number of data points and independent replicates are detailed in the figure captions.

Reporting summary

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