SHORT REPORT

Mechanical stability of the cell nucleus – roles played by thecytoskeleton in nuclear deformation and strain recoveryXian Wang1,2, Haijiao Liu1,2, Min Zhu1,3, Changhong Cao1, Zhensong Xu1, Yonit Tsatskis4, Kimberly Lau3,Chikin Kuok4, Tobin Filleter1, Helen McNeill4,*, Craig A. Simmons1,2,*, Sevan Hopyan3,5,* and Yu Sun1,2,*

ABSTRACTExtracellular forces transmitted through the cytoskeleton candeform thecell nucleus. Large nuclear deformations increase the risk of disruptingthe integrity of the nuclear envelope and causing DNA damage. Themechanical stability of the nucleus defines its capability to maintainnuclear shape by minimizing nuclear deformation and allowing strain tobe minimized when deformed. Understanding the deformation andrecovery behavior of the nucleus requires characterization of nuclearviscoelastic properties. Here, we quantified the decoupled viscoelasticparameters of the cell membrane, cytoskeleton, and the nucleus.The results indicate that the cytoskeleton enhances nuclearmechanical stability by lowering the effective deformability of thenucleus while maintaining nuclear sensitivity to mechanical stimuli.Additionally, the cytoskeleton decreases the strain energy releaserate of the nucleus and might thus prevent shape change-inducedstructural damage to chromatin.

KEY WORDS: Nuclear mechanics, Viscoelasticity, Cytoskeleton,Strain recovery, AFM

INTRODUCTIONExtracellular forces can deform the cell nucleus via thecytoskeleton, which transmits forces from the cell membrane tothe nuclear envelope (Haase et al., 2016). Large nucleardeformations can cause localized loss of nuclear envelopeintegrity, leading to uncontrolled exchange of nucleo-cytoplasmiccontents, DNA damage and cell death (Denais et al., 2016). Theability of the nucleus to avoid extreme deformation and extremestrain energy release rate is important for its mechanical stability(Rowat et al., 2006). Quantitative measurements of nucleardeformation and recovery are important for understanding howthe nucleus responds to forces and maintains nuclear mechanicalstability.Existing methods for studying nuclear mechanics include

micropipette aspiration (Pajerowski et al., 2007), atomic forcemicroscopy (AFM) indentation (Ivanovska et al., 2017), the use ofmagnetic (Guilluy et al., 2014) or optical tweezers (Schreiner et al.,

2015), substrate strain testing (Lombardi et al., 2011) andmicrofluidic approaches (Hanson et al., 2015). However, themajority of measurements have been made on isolated nuclei orindirectly induce large deformations on a cell to probe the cellnuclear properties (Table S1). We previously used a sharp AFMprobe to penetrate the cell membrane to directly measure theelasticity of nuclei (Liu et al., 2014). However, the elasticity alone isinsufficient to describe nuclear deformation behavior. Theviscoelastic properties of the cytoskeleton and the nucleus greatlyimpact on nuclear deformation and strain recovery by dissipatingstrain energy stored because of the deformation (Corbin et al.,2016).

Here, to characterize the viscoelastic properties of the intactnuclei, the nucleus is directly loaded by means of an AFM probe-mediated deformation (Fig. 1A,B) undertaken at various speeds.The AFM probe first deforms and penetrates the cell membrane(section A in Fig. 1C), then loads the nucleus until penetration ofthe nuclear envelope (section B in Fig. 1C). The probe positionwas recorded by conducting AFM measurement and confocalz-stack scanning simultaneously (Fig. 1D; Fig. S1). The force–displacement data collected at various loading speeds were usedto quantify the viscoelastic parameters of the cell membrane,cytoskeleton and nucleus by fitting the data into viscoelasticmodels. The results revealed that the cytoskeleton stiffens thenucleus owing to its linkage to the nucleus; the nucleus has theinherent capability to rapidly release the strain energy stored underdeformation and the cytoskeleton slows down this high strainenergy release rate to protect chromatin structures.

RESULTS AND DISCUSSIONQuantification of elastic modulus and viscosity of the cellmembrane, cytoskeleton and nucleusWhen extracellular forces deform the cell membrane, they aretransmitted to the nucleus through the cytoskeleton (Fig. 2A).Fig. 2B shows the mechanical model we propose, where the cellmembrane, cytoskeleton and nucleus are connected in series witheach represented by a spring and a damper in the form of the Kevin–Voigt model (K-V model). Other models have also been used inprevious cell mechanics studies (Swift et al., 2013; Guilluy et al.,2014); however, as detailed in the Materials and Methods, the K-Vmodel was chosen here for describing AFM indentation onviscoelastic solids. The proposed model describes deformation asa function of both the magnitude and the rate of the force stimulus.The force stimulus rate was varied in the AFM indentation, fromwhich the elastic portion (spring, rate independent) and the viscousportion (damper, rate dependent) in the model were quantified(Eqn 5).

In our model, the cytoskeleton mechanically supports the cellmembrane (Fig. 2A). When the cell membrane is deformed by theAFM probe, the cytoskeleton also contributes to the mechanicalReceived 15 August 2017; Accepted 14 May 2018

1Department of Mechanical and Industrial Engineering, University of Toronto,Toronto, Ontario, Canada M5S 3G8. 2Institute of Biomaterials and BiomedicalEngineering, University of Toronto, Toronto, Ontario, CanadaM5S 3G9. 3Program inDevelopmental and Stem Cell Biology, Research Institute, The Hospital for SickChildren, Toronto, Ontario, Canada M5G 1X8. 4Lunenfeld-Tanenbaum ResearchInstitute, Mt. Sinai Hospital, Toronto, Ontario, Canada M5G 1X5. 5Division ofOrthopaedic Surgery, Hospital for Sick Children and University of Toronto, Toronto,Ontario, Canada M5G 1X8.

*Authors for correspondence (sun@mie.utoronto.ca; sevan.hopyan@sickkids.ca;simmons@mie.utoronto.ca; mcneill@lunenfeld.ca)

X.W., 0000-0002-1501-2544; Y.S., 0000-0001-7895-0741

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© 2018. Published by The Company of Biologists Ltd | Journal of Cell Science (2018) 131, jcs209627. doi:10.1242/jcs.209627

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properties measured on the membrane. Instead of considering themeasured results as cell membrane properties alone, the measureddata (section A of Fig. 1C) reflects the combined effect of the cellmembrane and the cytoskeleton (reduced elastic modulus andreduced viscosity of cell membrane E* and η*) but does notrepresent any nuclear effects. As the cytoskeleton is connected tothe nucleus through the LINC complex, the measured data when theprobe deforms the nucleus (section B of Fig. 1C) reflects thecombined effects (reduced elastic modulus and reduced viscosity ofnucleus E** and η**) of the nucleus and the cytoskeleton but doesnot represent any effects from the membrane.To decouple the properties of the cell membrane, cytoskeleton

and nucleus based on the measured combined effects (E* and E**,η* and η**), we also conducted the mechanical measurementon isolated nuclei, reflecting only the properties of the nucleus(En and ηn). To quantify the elastic modulus and viscosity of thecytoskeleton, the reduced modulus calculated from combinedeffects of the nucleus and cytoskeleton (E** and η**) wassubstituted with the elastic modulus and viscosity of the nucleusinto the reduce modulus equations (Eqns 10–13). Similarly, theelastic modulus and viscosity of the cell membrane were decoupledfrom the combined effects of the cell membrane and cytoskeleton(E* and η*) by substituting the elastic modulus and viscosity of thecytoskeleton into the reduced modulus equations. Elastic modulusvalues were determined to be 2.98±0.04 kPa, 4.28±0.33 kPa,and 2.01±0.10 kPa for the membrane, cytoskeleton, and nucleus,respectively. Viscosity values were 4.10±0.06 kPa, 5.43±0.55

kPa·s, and 0.97±0.08 kPa·s for the membrane, cytoskeleton, andnucleus, respectively (results in main text given as mean±s.e.m.).These values fit into the range of other reported measurements(Guilak et al., 2000; Dahl et al., 2005). In the decoupling process,the cytoskeleton was assumed to be homogeneous. In reality,the cortex underlying the cell membrane is rich in actin, andpotentially explains the higher elastic modulus and viscosity ofthe membrane.

A separate experiment with a tipless AFM probe was performed(Fig. 2E), and the results were compared to finite element simulationresults. Experimentally, indentation depths of 1 µm, 2 µm and 3 µmwith rates of 1 µm/s, 5 µm/s and 10 µm/s were applied withoutpenetrating the cells (n=10). The probe–cell contact area wasrecorded for converting the force–displacement curves into thestrain–stress curves (Fig. 2F). A 3D multi-layered computationalmodel was constructed (Fig. 2G; Karcher et al., 2003; Lau et al.,2015). The material properties assigned to these three layers werefrom experimentally determined values (Fig. 2D), and the cell andnucleus geometries were constructed from confocal z-stackreconstruction. The same mechanical loads as in the experimentswere used as values for the force input on the cell surface of themodel, and strain–stress curves were recorded and compared withthose from experiments. The results showed good agreementbetween model-calculated values and the experimental results bothin terms of shape and in values with no significant differences(Fig. 2H–J, correlation coefficient R>0.9), indicating the validity ofthe measured and decoupled parameters.

Fig. 1. AFM method used to measure cellular and intracellular mechanics. (A,B) A focused ion beam (FIB)-processed AFM probe enables the penetrationof the membrane and nuclear envelope for mechanical measurements. (C) Representative force–displacement data. Force first increases when the probecontacts and loads the membrane until membrane penetration (section A), after which force decreases until the probe contacts the nuclear envelope when forceincreases again until it penetrates the nuclear envelope (section B). (D) Images of an AFM probe penetrating both the cell membrane and nuclear envelope.

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The cytoskeleton stiffens the cell nucleus to preventextreme nuclear deformationFrom the cell membrane, cytoskeleton and nucleus, the nucleusexhibited the lowest elastic modulus (2.01±0.10 kPa), implying thatthe nucleus can be easily deformed when standing alone. This lowelastic modulus almost doubled (3.81±0.21 kPa) when the nucleuswas tethered to the cytoskeleton, implying that the cytoskeletonstiffens the nucleus to prevent extreme nuclear deformation under

extracellular forces. The cytoskeleton has a high elastic modulusand is connected to the nucleus through nucleo-cytoskeletalcoupling. It enhances the mechanical stability of the nucleus viastiffening of the nucleus to avoid extreme nuclear deformation.When the actin filaments and microtubules in the cytoskeleton wereinhibited by treatment with cytochalasin D and nocodazole,respectively, we observed a significant decrease in the reducedelastic modulus of the nucleus (Fig. 3A). Anti-cytoskeletal drug

Fig. 2. Viscoelastic properties of the cell membrane, cytoskeleton and nucleus. (A) Schematic showing the mechanical structures within a cell.(B) Cell mechanics model for interpreting AFM data. (C)Without cytoskeletal effects, the modulus of nucleus can be assessed by direct measurement on isolatednuclei. (D) Decoupled elastic modulus and viscosity of cell membrane (Em, ηm), cytoskeleton (Em, ηc) and nucleus (Em, ηn) of T24 cells, mean±s.e.m., n=31,*P< 1×10−10, **P < 1×10−14. (E) Schematic of validation experiments using a tipless AFMprobe. (F) The tipless AFMprobe deforms a cell while force–deformationdata is recorded. (G) The constructed three-layer computational model. (H–J) Strain–stress curves: comparison between experiments and model-calculatedvalues, with indentation depths of 1 µm (H), 2 µm (I) and 3 µm (J).

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treatments did not cause significant changes in the elastic modulusand viscosity of isolated nuclei (Fig. S3C), suggesting that changesin the cytoskeleton do not significantly affect the decoupledproperties of nuclei.Forces from the extracellular matrix are transmitted through the

cytoskeleton and cause nuclear deformation. The higher elasticmodulus of the cytoskeleton relative to the nucleus facilitatesnuclear sensitivity to the force transmitted from the cytoskeleton forcausing nuclear deformation. Nuclear deformation could promotethe expression of tenascin C (Chiquet et al., 2009), which is anadhesion-modulating protein inhibiting cellular adhesion tofibronectin, and thereby decrease the force transmitted from theextracellular matrix. For isolated nuclei, forces applied on nesprin-1induce emerin phosphorylation and lamin A/C reinforcement(Guilluy et al., 2014). Strengthening of the lamin network resultsin the stiffening of isolated nuclei, thereby potentially protectingchromatin from excessive mechanical stress.

The cytoskeleton slows down the strain recovery process ofthe cell nucleusWhen an applied stress is removed, the deformation of the nucleusgradually decreases, the stress on nuclear structures is released, andthe strain energy stored via the deformation of the spring is graduallydissipated through the damper (Fig. 2B). The stress–strain

relationship during strain recovery is ɛ(t)=((σ0)/E)(1−e−(t/(η/E))),where ɛ(t) is the strain, σ0 is the maximum stress before the strainrecovery, η is the viscosity, and E is the elastic modulus. The ratio ofviscosity over elastic modulus (time constant), η/E, determines thespeed of the exponential decay of strain. The time constant alsodescribes the strain energy release rate in strain recovery, as strainenergy decreases linearly with the square of strain, U=(1/2)VEɛ(t)2,whereU is strain energy and V represents the volume of the nucleus.A larger time constant means a longer duration of strain relaxationand a lower strain energy release rate (Vincent, 2012).

For an isolated nucleus, strain recovery is rapid as the nucleusbehaves mostly elastically with a small time constant (0.48±0.05 s,Fig. 3B), which has also been previously observed in micropipetteaspiration and in AFM indentation experiments (Dahl et al., 2005).Because of the high viscosity, the cytoskeleton (time constant1.27±0.13 s) requires a longer time for strain recovery thanthe nucleus. Therefore, when the nucleus is tethered by thecytoskeleton, the cytoskeleton significantly slows down the strainrecovery of the nucleus (intact versus isolated of 0.76±0.02 s versus0.48±0.05 s), thus giving a lower strain energy release rate. A highstrain energy release rate (i.e. a small time constant) indicates ahigher risk of structural damage. During strain recovery, the strainenergy stored in the elastic portion (Fig. 2B) is dissipated as shearand crack propagation on the structures (Koop and Lewis, 2003),

Fig. 3. Nuclear mechanics after drug treatments and SUN protein knockdown. (A) Experimentally quantified elastic modulus and viscosity, mean±s.e.m.,n=31, *P<0.01, #P<0.001 after treatment with the indicated drugs. (B) Time constant of the nucleus coupled to the cytoskeleton, nucleus and cytoskeleton,mean±s.e.m., n=31, *P= 3×10−6, #P= 4×10−7. (C,D) qRT-PCR to determine the effect of individual siRNAs targeting SUN1 (C) and SUN2 (D), mean±s.d., n=4,*P< 0.01, ***P< 0.0001, #P< 0.0001. (E) Reduced modulus and reduced viscosity of nuclei with SUN domain proteins knocked down, mean±s.e.m., n=15,*P< 0.02, #P< 0.005.

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which potentially tear chromatin and chromatin–protein bindings,and trigger epigenetic changes (Miroshnikova et al., 2017).Structurally, the cytoskeleton tethers to the nuclear lamina, whichis connected to chromatin. The high viscosity of the cytoskeletonsignificantly slows down the nuclear strain recovery process andlowers the strain energy release rate, potentially providing cushioneffects to stabilize chromatin structure.Anti-cytoskeletal drug treatments revealed both the redundant and

distinct role of actin filaments and microtubules in stiffening thenucleus and slowing down strain recovery.On the one hand, disturbingboth actin filaments and microtubules resulted in significant softernuclei than disturbing only actin filaments or only microtubules(Fig. 3A), suggesting that actin filaments andmicrotubules both play arole in preventing extreme nuclear deformations. On the other hand,disturbing both actin filaments and microtubules resulted in a similarviscosity value to that seen upon disturbing either one of them(Fig. 3A). These data prove the necessity of having both actin filamentsand microtubules in order to maintain a high viscosity of the nucleusand slow down the strain recovery process.In addition, to study the role of LINC complex (LInker of

Nucleoskeleton and Cytoskeleton) in nuclear mechanics, the SUNdomain proteins, the major component of the LINC complex, wereknocked down using both an siRNA pool and individual siRNA, asconfirmed by quantitative real-time PCR (qRT-PCR) (Fig. 3C–E;Fig. S2), and the properties of the membrane, cytoskeleton, nucleusand isolated nucleusweremeasured (Fig. 3E; Fig. S2).After knockingdown the SUN proteins, the reduced elastic modulus and reducedviscosity became significantly lower than the control, suggesting thenecessity of cytoskeleton–nucleus coupling for the cytoskeleton tostiffen the nucleus, prevent extreme deformations and slow downstrain recovery. It was noticed that the depletion of SUN1 or SUN2alone had a significant effect on nuclear stiffness, indicating that theyhave potentially distinct roles in nuclear mechanics (Fig. 3C,E).

Late-stage cancer cells reveal a lower elastic modulus,viscosity and time constantGene instability is known to be a hallmark of late-stage cancer cells(Simi et al., 2015). Therefore, we next compared the intact nuclei ofearly (RT4, Stage I) and late stage (T24, Stage III) human bladder

cancer cells. For intact RT4 and T24 cells, T24 nuclei exhibit a lowerelastic modulus, lower viscosity and smaller time constant than RT4cells (Fig. 4A,B). Actin and tubulin staining confirmed that T24 cellshave a significantly lower cytoskeleton density, leading to a lowerelastic modulus and viscosity of the cytoskeleton (Fig. 4C–F, Kimet al., 2014).After anti-cytoskeletal drug treatment (cytochalasinDandnocodazole), the reduced elastic modulus of the nuclei decreased from4.33±0.36 kPa to 3.45±0.20 kPa, the reduced viscosity decreased from4.47±0.35 kPa·s to 2.54±0.21 kPa·s, and time constant decreasedfrom 1.35±0.25 s to 0.81±0.40 s. After anti-cytoskeletal drugtreatment, the reduced elastic modulus and viscosity of RT4 cellsexhibited no significant difference from those of T24 nuclei(Fig. 4A), suggesting the cytoskeleton difference is responsible forthe difference in mechanical properties between RT4 and T24nuclei. However, we also note that the isolated nuclei of RT4 weresignificantly stiffer than T24 nuclei, which cannot be explained bycytoskeleton differences. The higher stiffness of isolated nuclei ofRT4 versus T24 cells could potentially be attributed to the higherdensity of laminA/C in RT4 (Fig. 4E,F), which is themajor nuclearenvelope structural protein (Swift et al., 2013).

ConclusionsOur findings indicate that the nucleus is a soft organelle relative tothe cytoskeleton and that coupling with the stiff cytoskeleton helpsnucleus avoid extreme nuclear deformations. Large deformationscan impose higher stress onto the nuclear envelope, lamins,chromatin and other structures inside the nucleus. High stresson the nuclear envelope could induce local rupture and causeuncontrolled material exchanges between intranuclear andextranuclear environments, and DNA damage (Denais et al.,2016; Irianto et al., 2017). High stress also has the potential toalter the conformation of chromatin, binding between chromatin andtranscription factors, and to cause histone modifications (Mattoutet al., 2015). Tethering between the cytoskeleton and nucleus mayhelp to lower the risk of genetic instability when an extracellularforce is exerted on the cell.

Previous work has shown that there are abnormalities in actin andmicrotubules in a large number of late-stage cancer cell lines (Sunet al., 2015; Sakthivel and Sehgal, 2016), which is consistent with

Fig. 4. Late-stage cancer cells possess a lower elastic modulus and viscosity. Shown data were all measured on intact nuclei (i.e. not isolated). (A) Elasticmodulus comparison between T24 and RT4 nuclei, mean±s.e.m., RT4 n=24, T24 n=31, *P=0.04 (B) Viscosity comparison between T24 and RT4 nuclei,mean±s.e.m., RT4 n = 24, T24 n=31, *P= 3×10−4. (C–F) Difference in the intensity of cytoskeleton components and lamin as determined by immunostaining.Chromatin intensity was used for normalizing the intensities. T24 cells express less tubulin, less actin, and less lamin than RT4 cells. Results are mean±s.e.m.,RT4 n=30, T24 n=30, *P= 3×10−12, **P= 3×10−4, ***P= 3×10−6.

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the differences between RT4 and T24 shown in the present study.The structural differences in cytoskeleton imply that there aredistinct mechanical properties in late-stage cancer cells in general,although further studies are required for characterizing more typesof cancer cells. During metastasis, cancer cells need to travelthrough confined spaces (Denais et al., 2016), which causeschromatin stretching and DNA damage (Irianto et al., 2017). In thisprocess, the low elastic modulus (thus large deformation) and smalltime constant (thus high strain energy release rate) of cancer cellscould play an instrumental role in inducing gene mutations, theadaption of the cells to new microenvironments and in facilitatingmetastasis (Burrell et al., 2013).

MATERIALS AND METHODSCell cultureHuman bladder cancer T24 and RT4 cells were obtained from the AmericaType Culture Collection (ATCC, Manassas, VA). Cells were cultured inATCC-formulated McCoy’s 5A modified medium with 10% FBS and 1%penicillin–streptomycin (complete culture medium) at 37°C and 5% CO2.Subculture was conducted before cells reached confluency. Before AFMand confocal experiments, T24 and RT4 cells were passaged and seeded at2500 cells/cm2 in 35 mm Petri dishes and 35 mm glass bottom dishes(P35G-1.0-20-C, uncoated glass bottom dishes, MatTeck Corporation),respectively, for 24 h.

Nucleus isolationHuman bladder cancer T24 cells were removed from the Petri dish by gentlyscraping with a cell lifter and transferred to a pre-chilled conical tube afterthey were rinsed with nuclear extraction buffer (Active Motif ). The cellsuspension was subsequently centrifuged for 5 min at 200 g, and theresulting pellet was resuspended in 1× hypotonic buffer (40010, NuclearExtract Kit, Active Motif ) and incubated as a cell suspension. The nucleiwere then separated from the cellular debris by a 30 s centrifugation at14,000 g at 4°C. The supernatant (cytoplasmic fraction) was discarded andthe pellet (containing nuclei) was then resuspended and transferred to a35 mm Petri dish in complete culture medium for 8 h before the AFMmeasurements, allowing the nuclei to precipitate and weakly attach to thedish surface.

Drug treatmentCells were treated with either cytochalasin D (0.2 µg/ml in cell medium,C8273, Sigma-Aldridge) or nocodazole (5 µg/ml in cell medium, M1404,Sigma-Aldridge) to specifically depolymerize actin or tubulin, respectively.The cytochalasin D powder was first dissolved in DMSO to give aconcentration of 0.2 mg/ml, and then 1 µl cytochalasin D solution wasadded into 1 ml culture medium as the working medium. Similarly, thenocodazole powder was dissolved in DMSO to give a concentration of5 mg/ml, and 1 µl nocodazole solution was added into 1 ml culture mediumas the working medium. For the double-treatment experiments, in whichboth drugs were used to treat the cells, both cytochalasin D powder andnocodazole powder were dissolved in DMSO at concentration of 0.2 mg/mland 5 mg/ml in DMSO. Then, 1 µl of the DMSO solution with both drugswas added to the cell. 1 µl DMSO was added to control group to control forany influence from DMSO. Each working medium was added to the cell60 min prior to the experiment. For staining, the drug solution was added tothe 24-well cell culture plate with the coverslip 60 min prior to fixing.

Individual siRNA and siRNA pool treatmentThe siRNA pool is a combination of multiple siRNAs targeting the samegene. The SMARTpool SUN1 siRNA from Daharmacon includes fourtypes of siRNAs targeting SUN1, and the SMARTpool SUN2 siRNAincludes four types of siRNAs targeting SUN2. Using the siRNA pool canreduce the off-target effect, but might cause more non-specific transcriptiondecreases of other genes. Individual siRNAs can be more specific than thesiRNA pool, but might have more off-target effects than an siRNA pool. Toensure sufficient knockdown and minimize any potential off-target effects

or non-specific decrease of other genes, so as not to affect the measurednuclear mechanics, we here used both an siRNA pool and individualsiRNAs to knockdown SUN1 and SUN2 proteins, after which the reducedelastic modulus and reduced viscosity of the nucleus were measured.

The siRNAs for SUN1 and SUN2 knockdown were purchased fromDharmacon (human SUN1 SMARTpool siRNA L-025277-00 andindividual siRNA J-025277-05, and human SUN2 SMARTpool siRNAL-009959-01 and individual siRNA J-009959-09). The cells were treatedwith 10 nM siRNA for 72 h prior to measurements. ON-TARGETplusNon-targeting siRNA (D-001810-01) from Dharmacon was used in thecontrol group.

Fabrication of sharp AFM probe tipsSharp AFM probe tips were formed by processing standard AFM cantilevers(MLCT-D, Bruker) with a focused ion beam (FIB)-scanning electronmicroscope (SEM) dual beam system (HITACHI NB5000 FIB-SEM).Individual AFM cantilevers were mounted on the SEM stage with probetips facing upwards. The AFM pyramidal tips were then milled into sharpcylinders by dual ion beams (beam 25-1-80). The milling process wasmonitored by SEM imaging. The machining process typically costs 10 min/probe. The resulting tips were 120–150 nm in diameter and 3–5 µm in length.AFM cantilevers with a sharp tip were used in characterizing the mechanicalproperties of the cell membrane, cytoskeleton, and nucleus. Only a smalldeformation was produced before the rupture of the cell membrane occurred,conforming to the small-strain assumption of the Hertz model in contactmechanics. The tension effect was minimized via the use of sharp AFM tipsthat produced a small contact area and small indentation depth.

AFM measurement and data analysisForce–displacement data were collected at room temperature using an AFM(Bioscope Catalyst, Santa Barbara, CA) mounted on a Nikon confocalmicroscope. As opposed to in a substrate strain test, in which forceapplication is along the cell substrate direction, and micropipette aspiration,in which applied forces are transmitted through a much larger region ofcytoskeleton, measurements made in this work were significantly morelocally as achieved by use of a sharp AFM probe that applied a normal forceperpendicular to cellular structures. Measurement of cells in each Petri dishwas completed within 20 mins after being taken out of incubator. The AFMprobes used in experiments were FIB modified as described above, with anominal spring constant of 0.03 N/m. The spring constant of each probewascalibrated via thermal spectroscopy (Nanoscope 8.10). The loading speedswere set to be 15 µm/s, 30 µm/s and 45 µm/s, at each of which force–displacement data were collected.

Force–displacement–speed data were measured at the cell center wherea distinct separation of plasma membrane and nuclear envelope can bevisualized. Data analysis for quantifying reduced modulus from force–displacement–speed data, and decoupling elastic modulus and viscosity fromreduced modulus was conducted in MATLAB. The force–displacement datafrom AFM measurement have a displacement resolution of 0.2 nm and forceresolution of 10 pN, which is capable of capturing the rupture of the cellmembrane due to the large force change caused by cell membrane penetration.The force drop after cell membrane penetration is typically larger than 100 pN(Fig. S1B–D; Bitterli, 2012; Obataya et al., 2005; Angle et al., 2014;Liu et al., 2014), and there is also a significant change in the elasticmodulus, which rules out a mere sudden change of force without cellmembrane rupturing. The MATLAB code for data analysis used forrejecting the non-rupture case is available for download at https://github.com/XianShawn/Nuclear_Mechanics.

Viscoelastic modelThe viscoelastic model uses springs and dashpots to describe the elastic andviscous properties. The spring–dashpot model provides more informationthan previous studies on nuclear mechanics, most of which only focusedon the elastic property. The model is commonly used for describingviscoelastic properties of cellular structures as it describes both time-variant(the dashpot) and time-invariant (the spring) relationships between stressand strain (Swift et al., 2013; Guilluy et al., 2014).

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Among spring–dashpot models, the K-V model, Maxwell model andSLS model are the most commonly used models (López-Guerra andSolares, 2014). The K-V model, where a damper and a spring areconnected in parallel, is commonly used to describe the force–displacement–speed behavior of viscoelastic solids. The parallelconnection of the spring and the damper separates the force–displacement curve into the speed-invariant portion (Felastic) and speed-dependent portion (Fviscous), namelyF=Felastic+Fviscous. With differentindentation speeds of the AFM probe, the speed-invariant portion(Felastic) and the speed-dependent portion (Fviscous) can be separated andanalyzed through linear regression (Eqns 7,9) to quantify the elasticmodulus E and viscosity η. The Maxwell model, where a damper and aspring are connected in series, is used to describe the relaxation behaviorof a material but does not describe creep under indentation (López-Guerraand Solares, 2014). The AFM technique used in this work is in essence acreep test (indentation). Using the Maxwell model to describe creepunder indentation would result in an extremely high viscosity value andan extremely low elastic modulus value, since the Maxwell modelassumes the material under testing flows and does not reach the steadystate in a creep test. The standard linear solid (SLS) model can be used fordescribing both viscoelastic solids and viscoelastic fluids. However,compared to the K-V model (two components) and the Maxwell model(two components), the SLS model contains three components while AFMforce–displacement–speed data does not contain the stress rate ( _s)information that is necessary for fitting all the three parameters in the SLSmodel. Direct fitting force–displacement–speed data from our AFMmeasurement using the SLS model resulted in a correlation coefficient aslow as 0.4±0.2 (based on 30 force–displacement–speed curves capturedin experiments). Thus, in this work, the SLS model was not chosen fordata analysis.

As the nucleus, cytoskeleton and cell membrane behave more asviscoelastic solids, the K-V model was assumed to describe theforce–displacement–speed behavior of the materials. The time constantof the strain recovery process quantitatively describes how fast strainrecovery occurs in K-V model. Comparisons made between the resultswith of the nucleus only and the results with the nucleus coupled withcytoskeleton revealed the role played by cytoskeleton in the strainrecovery process.

For a viscoelastic material, the stress–strain relationship in the K-Vmodel is:

s ¼ E1þ hd1

t; ð1Þ

where σ is stress, ɛ is strain, (dɛ/t) is the strain rate, E is the elastic modulusand η is the viscosity of the sample.

In terms of forces, the K-V model combines the elastic portion and theviscous portion as:

F ¼ Felastic þ Fviscous: ð2ÞThe Hertz model for a cylindrical tip (the shape of the fabricated AFM probetips) was applied to determine Felastic, according to Wallace (2012):

Felastic ¼ 4

3

Es

1� v2sR

12d

32 ; ð3Þ

where Es is the measured sample elastic modulus,vs is the Poisson’s ratio ofthe sample, R is the tip radius and d is the displacement of the tip.

As the mechanical strain is calculated asɛ=((Δl )/l )=((vt)/l ), then:

Fviscous ¼ Ssviscous ¼ pRd � h d1ðtÞt

¼ hv

lpRd; ð4Þ

where the contact area S=πRd, according to the Hertz model.Combining the elastic portion and the viscous portion in the K-V model,

the relationship between force, displacement, and speed is:

F ¼ Felastic þ Fviscous ¼ 4

3ER1=2d3=2 þ h

v

lpRd: ð5Þ

Determination of reduced elastic modulus and reducedviscosity, E*, η*, E** and η**

The cell model proposed in this work (Fig. 2A,B) is based on the K-Vmodelfor viscoelastic materials. The cell membrane, cytoskeleton and nucleus areeach represented by a spring and a damper connected in parallel. The cellmembrane is supported underneath by the cytoskeleton. When measuringthe mechanical properties of the cell membrane by analyzing the force–displacement–speed data, the data reflect the coupled mechanical propertiesof both the cell membrane and cytoskeleton. As shown in Fig. 2B, the elasticmodulus and viscosity extracted from ‘section A’ of Fig. 1C were reducedmodulus E* andη*, which describe the combined material properties of thecell membrane and cytoskeleton. Similarly, the nucleus is tethered by thecytoskeleton. The measured mechanical properties from the force–displacement–speed data reflect the coupled mechanical properties ofboth the nucleus and cytoskeleton. As shown in Fig. 2B, the elastic modulusand viscosity extracted from ‘section B’ of Fig. 1C were reduced modulusE** andη**, which describe the combined material properties of nucleusand cytoskeleton. Because the tip is sharp and capable of penetrating the cellmembrane, distinct separation between the membrane indentation processand the nucleus indentation process was observed. Thus, it was assumed thatthere is no effect from the nucleus when indenting the cell membrane andthere is no effect from the cell membrane when indenting the nucleus.

To determine the reduced elastic modulus and reduced viscosity, the rawAFM data were imported into MATLAB. Baseline subtraction and region ofinterest (ROI) selection were conducted. The ROI for quantifying thereduced elastic modulus of the cell membrane and nucleus correspond tosection A and section B in Fig. 1C, respectively. After filtering the highfrequency noise and interpolation, differentiation of data was conducted forfurther regression.

Differentiating Eqn 5 with respect to d results in:

_F ¼ 2E�R1=2d1=2 þ hv

lpR; ð6Þ

where E* linearly relates to d1/2 and _F. Based on Eqn 6, regression gives:

_F ¼ k1d1=2 þ b1; ð7Þ

where k1 and b1 are linear regression parameters. Then, the reduced elasticmodulus of the cell membrane coupled with cytoskeleton was calculatedfrom regression as

E� ¼ k12R1=2

: ð8Þ

To calculate the reduced viscosity, ΔF was defined as the force differencebetween two indentation speeds, namely DF ¼ Fv1 � Fv2 . Accordingto Eqn 5,

DF ¼ h� DvlpRd; ð9Þ

where Δv equals tov1− v2, and the reduced viscosity η* linearly relates to dandΔF.

Then, the regression function is constructed as:

DF ¼ k2d þ b2;

where k2 and b2 are linear regression parameters.The reduced viscosity of the cell membrane coupled to the

cytoskeleton is:

h� ¼ k2ððDvÞ=lÞpR : ð10Þ

The analysis for determining the reduced elastic modulus E** and reducedviscosity η** for cell nucleus coupled with cytoskeleton is the same asthe above.

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Decoupling elastic modulus and viscosity from reduce modulusand reduced viscosityThe relationship between the reduced elastic modulus and reduced viscosityare given by:

1

E� ¼1

Emþ 1

Ec; ð11Þ

1

E�� ¼�1

Ecþ 1

En; ð12Þ

where E* and E** are the reduced elastic modulus of the cell membraneand nucleus, respectively; Em, Ec, and En are the elastic modulus of themembrane, cytoskeleton, and nucleus, respectively.

The reduced viscosity of the cell membrane and the nucleus are given by:

1

h� ¼1

hmþ 1

hcð13Þ

1

h�� ¼�1

hcþ 1

hnð14Þ

where η* and η** are the reduced viscosity of the cell membrane andnucleus, respectively; and ηm, ηc, and ηn are the viscosity of the membrane,cytoskeleton, and nucleus, respectively.

The reduced elastic modulus E*, E**and reduced viscosity η* and η**were calculated according to the data analysis procedure described in theabove section. The elastic modulus and viscosity of cell nucleus, En and ηnwere calculated based on the measurement on isolated cell nuclei.

Error propagationOwing to variation across cells and due tomeasurement errors, themechanicalparameters calculated from experimental data have uncertainties. From dataanalysis, the standard error of reduced modulusE*,E**, En, η*,η**, ηn, wasquantified via one-way ANOVA.When the modulus was decoupled from thereduced modulus, the error from reduced modulus would propagate to thedecoupled modulus.

According to Ku (1966), the elastic modulus Em and Ec are:

Ec ¼ EnE��

E�� � Enð14Þ

Em ¼ EcE�

Ec � E� ð15Þ

Similarly, the viscosity ηm andηc are:

hc ¼hnh

��

h�� � hnð16Þ

hm ¼ hch�

hc � h� : ð17Þ

From the above equations, uncertainty (standard error of the mean,denoted Se in equations) was calculated as

SeðEcÞ ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffidEc

dEnSeðEnÞ

� �2

þ dEc

dE�� SeðE��Þ� �2

s; ð18Þ

SeðEmÞ ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffidEm

dEcSeðEcÞ

� �2

þ dEm

dE� SeðE�Þ� �2

s; ð19Þ

SeðhcÞ ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffidhc

dhnSeðh3Þ

� �2

þ dhc

dh�� Seðh��Þ� �2

s; ð20Þ

SeðhmÞ ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffidhm

dhcSeðh2

� �Þ2 þ dhm

dh� Seðh�� �

Þ2s

: ð21Þ

Model validationModel geometryA computational model was developed to simulate the application of forcesexerted by the tipless AFM probe on the cell structure. The model iscomposed of three layers, including the cell membrane, cytoskeleton andnucleus, reconstructed from confocal imaging. The default mesh size andnode number were set to be 46386 and 26931, respectively.

Boundary conditionA zero-displacement boundary condition was imposed at the bottom surfacebecause in the experiments, cells were cultured on a rigid (compared withthe mechanical properties of the cell) substrate (a glass slide or Petri dish).Adjacent layers were connected, and the cytoskeleton is fixed to the cellmembrane and nucleus.

Mechanical propertiesThe mechanical properties of the cell membrane, cytoskeleton, and nucleusfrom the experimental results were assigned to the computation model.The K-V model was used to interpret experimental data.

ExperimentExperiments were performed using a tipless AFM probe with differentindentation depths (1 µm, 2 µm and 3 µm) and rates (1 µm/s, 5 µm/s and10 µm/s). Confocal imaging was performed simultaneously with a rate of 8frames/s recording the probe–cell contact area changes, which were used forcalculating stress on the cell membrane.

Applied loadThe mechanical loads with identical displacement magnitude and rate as intipless AFM experiments were applied to the cell structure. The strain–stressrelationship on the surface of the cell, and the deformation of the nucleus,were extracted from the computational model and compared with thosemeasured in experiments (indentation depth, 1 µm, 2 µm and 3 µm; rate,1 µm/s, 5 µm/s and 10 µm/s).

Self-consistency of the computation modelMesh sensitivity was investigated to ensure the independence of the resultsfrom the computational mesh size. Three mesh sizes were used. The coarse(default mesh from ANSYS workbench), medium and fine meshesconsisting of 86381, 46386 and 20438 nodes were used for comparison.All three meshes resulted in similar solution patterns. The solution patternsdid not depend on the patterns of the mesh lines. At all time-points, themaximum differences between three computational meshes were less than3% for maximum stress on cell surface, less than 5% for maximumdeformation of cell in the z-direction. The results proved the self-consistencyof the computation model.

Error sourceThe main error source is the variance across cells, as differences in cellgeometries and mechanical properties of cellular structures exist. However,comparisons between different cell types (RT4 and T24) show that they aredistinct and significantly different compared to the variances within eachcell type. Error can also stem from the multiple regression process duringdata analysis, including data transformation and linear regressions, and thiserror was accounted for during the calculation of error propagation andincluded in the final results.

ImmunostainingThe plasma membrane of a cell was stained with the CellMask Deep Redstain (C10046, CellMask Membrane Stain, ThermoFisher Scientific), andthe cell nucleus was stained with the standard Hoechst dye (33258, Sigma-Aldrich). The working solution with concentration of 10 μg/ml of CellMaskand 50 μg/ml of Hoechst was prepared by mixing the two stocking solutionsin warm PBS before confocal imaging. The cells were rinsed with PBS andincubated with the stain working solution for 20 min. Then, after removal ofall the staining solution, the cells were rinsed three times with PBS and thenthe cells were immediately imaged via confocal microscopy in live-cell

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imaging solution (Invitrogen). The AFM probe tips were first treated withplasma activation for 2 min. 3-(aminopropyl)triethoxysilane (APTES; 99%)(Sigma-Aldrich) was diluted to 2% in a mixture of 95% ethanol and 5% DIwater. The AFM probe tips were placed into the APTES solution for 10 minand then rinsed with ethanol, dried with nitrogen, and incubated at 120°C for1 h. The Alexa Fluor 555 NHS ester (Invitrogen) was dissolved in DMSO to100 μg/ml and used immediately. The tips were then placed into the stainsolution and incubated for 1 h at room temperature, and then washed withPBS and deionized water and dried with nitrogen. In experiments, AFMmeasurement and cell imaging were performed simultaneously (Fig. 1D).

Staining for actin, microtubules and the nucleus was achieved usingphalloidin fluorescent conjugate (A12379, Alexa Fluor 488 Phalloidin,ThermoFisher Scientific), tubulin–RFP (C10503, CellLight Tubulin-RFP,BacMam 2.0, ThermoFisher Scientific) and Hoechst 33258 (94403 Hoechst33258 solution, Sigma-Aldrich), separately. BacMam 2.0 was addeddirectly to the cells after passage. The concentration of BacMam wasdetermined based on the protocol provided by ThermoFisher Scientific.After 18 h of incubation, cells were rinsed with PBS and fixed with 4%paraformaldehyde for 15 min at room temperature. The cell membrane wasthen permeabilized with 0.05% Triton X-100 in PBS for 15 min at roomtemperature. After rinsing in PBS, cells were then treated with phalloidinconjugate for 1 h. The nuclei were labeled with Hoechst 33258.

Staining for lamin A/C was achieved using anti-lamin A/C antibody(MA3-1000, 1:200, Lamin A/C Monoclonal Antibody, ThermoFisherScientific) as primary antibody and anti-mouse-IgG secondary antibody[A-21202, 1:1000, donkeyanti-Mouse IgG (H+L) SecondaryAntibody,AlexaFluor 488, ThermoFisher Scientific]. The immunofluorescence staining forSUN1/2 proteins was achieved using primary antibody (kind gifts fromDidierHodzic, Washington University School of Medicine in St. Louis, USA) andsecondary antibodies according to Crisp et al. (2006). The immunostainingprocess is similar to the procedure described for actin staining. In short, cellswere fixed, permeabilized, treated with primary antibody, secondary antibodyand DAPI (D1306 DAPI, ThermoFisher Scientific).

Quantitative confocal imaging and image analysisIn the sample preparation for quantitative confocal imaging, the samemounting medium, coverslip and fluorophore were used for RT4 and T24cells. In the imaging process, targets were first found under bright-fieldimaging to minimize photo bleaching. Microscope settings (e.g. laserintensity, gain, exposure time and illumination) were kept the same foracquiring images in RT4 and T24 cells. Image acquisitions were conductedfor the minimum duration to minimize bleaching, while avoidingsaturations. In image analysis, the normalized intensity for actin andtubulin was quantified by dividing actin or tubulin intensity by thechromatin intensity for individual cells.

qRT-PCR for detection of siRNA-induced mRNA silencingRNA was extracted by using an RNAeasy Micro Kit (Qiagen, 74004),then treated with DNaseI (Thermo, 18068-015) and reverse-transcribedwith SuperScript III (Thermo, 18064) following the manufacturers’instructions. qRT-PCR was performed with Power SYBR Green PCRMasterMix (Thermo, 4368706) using a CFX384 Touch Real-Time PCRDetection System (Bio-Rad). The PCR program was 95°C for 10 min, 40cycles of 95°C for 30 s, 60°C for 30 s, 72°C for 30 s, and followed by thedefault dissociation curve program. GAPDH served as reference gene.Statistical analyses were performed in Prism 6. Primers (F representsforward, and R represents reverse) were: GAPDH_F, 5′-GGAGCGAG-ATCCCTCCAAAAT-3′; GAPDH_R, 5′-GGCTGTTGTCATACTTCTC-ATGG-3′ SUN1_F, 5′-ATGTCCCGCCGTAGTTTGC-3′; SUN1_R, 5′-CCGTCGAGTCACAGCATCC-3′; SUN2_F, 5′-CCAGTCACCCCGA-GTCATC-3′; SUN2_R, 5′-ATGCTCTAAGGTAACGGCTGT-3′

Statistical testsThe elastic modulus and viscosity of cell membrane, cytoskeleton, andnucleus were reported as mean±s.e.m. The s.e.m. for calculated values werequantified base on error propagation. The comparisons of each group wereconducted by one way ANOVA and Student–Newman–Keuls test for

pairwise comparisons in JMP software and the statistical significance ineach comparison was evaluated as P<0.05 for significance level.

AcknowledgementsThe authors thank K. Fenelon and H. Tao for their helpful suggestions. The authorsalso thank Dr Didier Hodzic’s from Washington University School of Medicine inSt. Louis for providing the anti-SUN protein antibodies.

Competing interestsThe authors declare no competing or financial interests.

Author contributionsConceptualization: X.W., H.L., C.C., T.F., Y.S.; Methodology: X.W., H.L., C.C., Z.X.,Y.T., H.M.; Software: X.W.; Validation: X.W., H.L., C.C., Z.X., C.K.; Formal analysis:X.W.; Investigation: X.W., H.L., M.Z.; Resources: X.W., H.L.; Data curation: X.W.,M.Z., K.L.; Writing - original draft: X.W.; Writing - review & editing: H.L., T.F., H.M.,C.A.S., S.H., Y.S.; Visualization: X.W., Z.X., Y.T., K.L.; Supervision: H.M., C.A.S.,S.H., Y.S.; Project administration: X.W., S.H., Y.S.; Funding acquisition: H.M., Y.S.

FundingThis work was supported by the Natural Sciences and Engineering ResearchCouncil of Canada via an NSERC Steacie Memorial Fellowship, the CanadaResearch Chairs program and the Canadian Institutes of Health Research (143319to H.M.).

Data availabilityThe AFM datasets, microscope images and custom-made code for data analysis areavailable through the link https://github.com/XianShawn/Nuclear_Mechanics. TheMATLAB code is for the purpose of reproducible research and not for commercialusage. The other data that support the findings of this study are available from thecorresponding author upon reasonable request.

Supplementary informationSupplementary information available online athttp://jcs.biologists.org/lookup/doi/10.1242/jcs.209627.supplemental

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