Mechanical stability of the cell nucleus – roles played by the cytoskeleton in nuclear deformation and strain recovery

Extracellular forces can deform the cell nucleus via the cytoskeleton, which transmits forces from the cell membrane to the nuclear envelope (Haase et al., 2016). Large nuclear deformations can cause localized loss of nuclear envelope integrity, leading to uncontrolled exchange of nucleo-cytoplasmic contents, DNA damage and cell death (Denais et al., 2016). The ability of the nucleus to avoid extreme deformation and extreme strain energy release rate is important for its mechanical stability (Rowat et al., 2006). Quantitative measurements of nuclear deformation and recovery are important for understanding how the nucleus responds to forces and maintains nuclear mechanical stability.

Existing methods for studying nuclear mechanics include micropipette aspiration (Pajerowski et al., 2007), atomic force microscopy (AFM) indentation (Ivanovska et al., 2017), the use of magnetic (Guilluy et al., 2014) or optical tweezers (Schreiner et al., 2015), substrate strain testing (Lombardi et al., 2011) and microfluidic approaches (Hanson et al., 2015). However, the majority of measurements have been made on isolated nuclei or indirectly induce large deformations on a cell to probe the cell nuclear properties (Table S1). We previously used a sharp AFM probe to penetrate the cell membrane to directly measure the elasticity of nuclei (Liu et al., 2014). However, the elasticity alone is insufficient to describe nuclear deformation behavior. The viscoelastic properties of the cytoskeleton and the nucleus greatly impact on nuclear deformation and strain recovery by dissipating strain energy stored because of the deformation (Corbin et al., 2016).

Here, to characterize the viscoelastic properties of the intact nuclei, 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 of the nuclear envelope (section B in Fig. 1C). The probe position was recorded by conducting AFM measurement and confocal z-stack scanning simultaneously (Fig. 1D; Fig. S1). The force–displacement data collected at various loading speeds were used to quantify the viscoelastic parameters of the cell membrane, cytoskeleton and nucleus by fitting the data into viscoelastic models. The results revealed that the cytoskeleton stiffens the nucleus owing to its linkage to the nucleus; the nucleus has the inherent capability to rapidly release the strain energy stored under deformation and the cytoskeleton slows down this high strain energy release rate to protect chromatin structures.

When extracellular forces deform the cell membrane, they are transmitted to the nucleus through the cytoskeleton (Fig. 2A). Fig. 2B shows the mechanical model we propose, where the cell membrane, cytoskeleton and nucleus are connected in series with each represented by a spring and a damper in the form of the Kevin–Voigt model (K-V model). Other models have also been used in previous cell mechanics studies (Swift et al., 2013; Guilluy et al., 2014); however, as detailed in the Materials and Methods, the K-V model was chosen here for describing AFM indentation on viscoelastic solids. The proposed model describes deformation as a function of both the magnitude and the rate of the force stimulus. The force stimulus rate was varied in the AFM indentation, from which the elastic portion (spring, rate independent) and the viscous portion (damper, rate dependent) in the model were quantified (Eqn 5).

In our model, the cytoskeleton mechanically supports the cell membrane (Fig. 2A). When the cell membrane is deformed by the AFM probe, the cytoskeleton also contributes to the mechanical properties measured on the membrane. Instead of considering the measured results as cell membrane properties alone, the measured data (section A of Fig. 1C) reflects the combined effect of the cell membrane and the cytoskeleton (reduced elastic modulus and reduced viscosity of cell membrane E* and η*) but does not represent any nuclear effects. As the cytoskeleton is connected to the nucleus through the LINC complex, the measured data when the probe deforms the nucleus (section B of Fig. 1C) reflects the combined effects (reduced elastic modulus and reduced viscosity of nucleus E** and η**) of the nucleus and the cytoskeleton but does not 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 measurement on isolated nuclei, reflecting only the properties of the nucleus (E_n and η_n). To quantify the elastic modulus and viscosity of the cytoskeleton, the reduced modulus calculated from combined effects of the nucleus and cytoskeleton (E** and η**) was substituted with the elastic modulus and viscosity of the nucleus into the reduce modulus equations (Eqns 10–13). Similarly, the elastic modulus and viscosity of the cell membrane were decoupled from the combined effects of the cell membrane and cytoskeleton (E* and η*) by substituting the elastic modulus and viscosity of the cytoskeleton into the reduced modulus equations. Elastic modulus values 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, and nucleus, 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, and potentially explains the higher elastic modulus and viscosity of the membrane.

A separate experiment with a tipless AFM probe was performed (Fig. 2E), and the results were compared to finite element simulation results. Experimentally, indentation depths of 1 µm, 2 µm and 3 µm with rates of 1 µm/s, 5 µm/s and 10 µm/s were applied without penetrating the cells (n=10). The probe–cell contact area was recorded for converting the force–displacement curves into the strain–stress curves (Fig. 2F). A 3D multi-layered computational model was constructed (Fig. 2G; Karcher et al., 2003; Lau et al., 2015). The material properties assigned to these three layers were from experimentally determined values (Fig. 2D), and the cell and nucleus geometries were constructed from confocal z-stack reconstruction. The same mechanical loads as in the experiments were used as values for the force input on the cell surface of the model, and strain–stress curves were recorded and compared with those from experiments. The results showed good agreement between model-calculated values and the experimental results both in terms of shape and in values with no significant differences (Fig. 2H–J, correlation coefficient R>0.9), indicating the validity of the measured and decoupled parameters.

From the cell membrane, cytoskeleton and nucleus, the nucleus exhibited the lowest elastic modulus (2.01±0.10 kPa), implying that the nucleus can be easily deformed when standing alone. This low elastic modulus almost doubled (3.81±0.21 kPa) when the nucleus was tethered to the cytoskeleton, implying that the cytoskeleton stiffens the nucleus to prevent extreme nuclear deformation under extracellular forces. The cytoskeleton has a high elastic modulus and is connected to the nucleus through nucleo-cytoskeletal coupling. It enhances the mechanical stability of the nucleus via stiffening of the nucleus to avoid extreme nuclear deformation. When the actin filaments and microtubules in the cytoskeleton were inhibited by treatment with cytochalasin D and nocodazole, respectively, we observed a significant decrease in the reduced elastic modulus of the nucleus (Fig. 3A). Anti-cytoskeletal drug treatments did not cause significant changes in the elastic modulus and viscosity of isolated nuclei (Fig. S3C), suggesting that changes in the cytoskeleton do not significantly affect the decoupled properties of nuclei.

Forces from the extracellular matrix are transmitted through the cytoskeleton and cause nuclear deformation. The higher elastic modulus of the cytoskeleton relative to the nucleus facilitates nuclear sensitivity to the force transmitted from the cytoskeleton for causing nuclear deformation. Nuclear deformation could promote the expression of tenascin C (Chiquet et al., 2009), which is an adhesion-modulating protein inhibiting cellular adhesion to fibronectin, and thereby decrease the force transmitted from the extracellular matrix. For isolated nuclei, forces applied on nesprin-1 induce emerin phosphorylation and lamin A/C reinforcement (Guilluy et al., 2014). Strengthening of the lamin network results in the stiffening of isolated nuclei, thereby potentially protecting chromatin from excessive mechanical stress.

When an applied stress is removed, the deformation of the nucleus gradually decreases, the stress on nuclear structures is released, and the strain energy stored via the deformation of the spring is gradually dissipated 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 strain recovery, η is the viscosity, and E is the elastic modulus. The ratio of viscosity over elastic modulus (time constant), η/E, determines the speed of the exponential decay of strain. The time constant also describes the strain energy release rate in strain recovery, as strain energy decreases linearly with the square of strain, U=(1/2)VEɛ(t)², where U is strain energy and V represents the volume of the nucleus. A larger time constant means a longer duration of strain relaxation and a lower strain energy release rate (Vincent, 2012).

For an isolated nucleus, strain recovery is rapid as the nucleus behaves mostly elastically with a small time constant (0.48±0.05 s, Fig. 3B), which has also been previously observed in micropipette aspiration and in AFM indentation experiments (Dahl et al., 2005). Because of the high viscosity, the cytoskeleton (time constant 1.27±0.13 s) requires a longer time for strain recovery than the nucleus. Therefore, when the nucleus is tethered by the cytoskeleton, the cytoskeleton significantly slows down the strain recovery of the nucleus (intact versus isolated of 0.76±0.02 s versus 0.48±0.05 s), thus giving a lower strain energy release rate. A high strain energy release rate (i.e. a small time constant) indicates a higher risk of structural damage. During strain recovery, the strain energy stored in the elastic portion (Fig. 2B) is dissipated as shear and crack propagation on the structures (Koop and Lewis, 2003), which potentially tear chromatin and chromatin–protein bindings, and trigger epigenetic changes (Miroshnikova et al., 2017). Structurally, the cytoskeleton tethers to the nuclear lamina, which is connected to chromatin. The high viscosity of the cytoskeleton significantly slows down the nuclear strain recovery process and lowers the strain energy release rate, potentially providing cushion effects to stabilize chromatin structure.

Anti-cytoskeletal drug treatments revealed both the redundant and distinct role of actin filaments and microtubules in stiffening the nucleus and slowing down strain recovery. On the one hand, disturbing both actin filaments and microtubules resulted in significant softer nuclei than disturbing only actin filaments or only microtubules (Fig. 3A), suggesting that actin filaments and microtubules both play a role in preventing extreme nuclear deformations. On the other hand, disturbing both actin filaments and microtubules resulted in a similar viscosity value to that seen upon disturbing either one of them (Fig. 3A). These data prove the necessity of having both actin filaments and microtubules in order to maintain a high viscosity of the nucleus and slow down the strain recovery process.

In addition, to study the role of LINC complex (LInker of Nucleoskeleton and Cytoskeleton) in nuclear mechanics, the SUN domain proteins, the major component of the LINC complex, were knocked down using both an siRNA pool and individual siRNA, as confirmed by quantitative real-time PCR (qRT-PCR) (Fig. 3C–E; Fig. S2), and the properties of the membrane, cytoskeleton, nucleus and isolated nucleus were measured (Fig. 3E; Fig. S2). After knocking down the SUN proteins, the reduced elastic modulus and reduced viscosity became significantly lower than the control, suggesting the necessity of cytoskeleton–nucleus coupling for the cytoskeleton to stiffen the nucleus, prevent extreme deformations and slow down strain recovery. It was noticed that the depletion of SUN1 or SUN2 alone had a significant effect on nuclear stiffness, indicating that they have potentially distinct roles in nuclear mechanics (Fig. 3C,E).

Gene instability is known to be a hallmark of late-stage cancer cells (Simi et al., 2015). Therefore, we next compared the intact nuclei of early (RT4, Stage I) and late stage (T24, Stage III) human bladder cancer cells. For intact RT4 and T24 cells, T24 nuclei exhibit a lower elastic modulus, lower viscosity and smaller time constant than RT4 cells (Fig. 4A,B). Actin and tubulin staining confirmed that T24 cells have a significantly lower cytoskeleton density, leading to a lower elastic modulus and viscosity of the cytoskeleton (Fig. 4C–F, Kim et al., 2014). After anti-cytoskeletal drug treatment (cytochalasin D and nocodazole), the reduced elastic modulus of the nuclei decreased from 4.33±0.36 kPa to 3.45±0.20 kPa, the reduced viscosity decreased from 4.47±0.35 kPa·s to 2.54±0.21 kPa·s, and time constant decreased from 1.35±0.25 s to 0.81±0.40 s. After anti-cytoskeletal drug treatment, the reduced elastic modulus and viscosity of RT4 cells exhibited no significant difference from those of T24 nuclei (Fig. 4A), suggesting the cytoskeleton difference is responsible for the difference in mechanical properties between RT4 and T24 nuclei. However, we also note that the isolated nuclei of RT4 were significantly stiffer than T24 nuclei, which cannot be explained by cytoskeleton differences. The higher stiffness of isolated nuclei of RT4 versus T24 cells could potentially be attributed to the higher density of lamin A/C in RT4 (Fig. 4E,F), which is the major nuclear envelope structural protein (Swift et al., 2013).

Our findings indicate that the nucleus is a soft organelle relative to the cytoskeleton and that coupling with the stiff cytoskeleton helps nucleus avoid extreme nuclear deformations. Large deformations can impose higher stress onto the nuclear envelope, lamins, chromatin and other structures inside the nucleus. High stress on the nuclear envelope could induce local rupture and cause uncontrolled material exchanges between intranuclear and extranuclear environments, and DNA damage (Denais et al., 2016; Irianto et al., 2017). High stress also has the potential to alter the conformation of chromatin, binding between chromatin and transcription factors, and to cause histone modifications (Mattout et al., 2015). Tethering between the cytoskeleton and nucleus may help to lower the risk of genetic instability when an extracellular force is exerted on the cell.

Previous work has shown that there are abnormalities in actin and microtubules in a large number of late-stage cancer cell lines (Sun et al., 2015; Sakthivel and Sehgal, 2016), which is consistent with the differences between RT4 and T24 shown in the present study. The structural differences in cytoskeleton imply that there are distinct mechanical properties in late-stage cancer cells in general, although further studies are required for characterizing more types of cancer cells. During metastasis, cancer cells need to travel through confined spaces (Denais et al., 2016), which causes chromatin stretching and DNA damage (Irianto et al., 2017). In this process, the low elastic modulus (thus large deformation) and small time constant (thus high strain energy release rate) of cancer cells could play an instrumental role in inducing gene mutations, the adaption of the cells to new microenvironments and in facilitating metastasis (Burrell et al., 2013).

Human bladder cancer T24 and RT4 cells were obtained from the America Type Culture Collection (ATCC, Manassas, VA). Cells were cultured in ATCC-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 AFM and confocal experiments, T24 and RT4 cells were passaged and seeded at 2500 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.

Human bladder cancer T24 cells were removed from the Petri dish by gently scraping with a cell lifter and transferred to a pre-chilled conical tube after they were rinsed with nuclear extraction buffer (Active Motif). The cell suspension was subsequently centrifuged for 5 min at 200 g, and the resulting pellet was resuspended in 1× hypotonic buffer (40010, Nuclear Extract Kit, Active Motif) and incubated as a cell suspension. The nuclei were then separated from the cellular debris by a 30 s centrifugation at 14,000 g at 4°C. The supernatant (cytoplasmic fraction) was discarded and the pellet (containing nuclei) was then resuspended and transferred to a 35 mm Petri dish in complete culture medium for 8 h before the AFM measurements, allowing the nuclei to precipitate and weakly attach to the dish surface.

Cells 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 a concentration of 0.2 mg/ml, and then 1 µl cytochalasin D solution was added into 1 ml culture medium as the working medium. Similarly, the nocodazole powder was dissolved in DMSO to give a concentration of 5 mg/ml, and 1 µl nocodazole solution was added into 1 ml culture medium as the working medium. For the double-treatment experiments, in which both drugs were used to treat the cells, both cytochalasin D powder and nocodazole powder were dissolved in DMSO at concentration of 0.2 mg/ml and 5 mg/ml in DMSO. Then, 1 µl of the DMSO solution with both drugs was added to the cell. 1 µl DMSO was added to control group to control for any influence from DMSO. Each working medium was added to the cell 60 min prior to the experiment. For staining, the drug solution was added to the 24-well cell culture plate with the coverslip 60 min prior to fixing.

The siRNA pool is a combination of multiple siRNAs targeting the same gene. The SMARTpool SUN1 siRNA from Daharmacon includes four types of siRNAs targeting SUN1, and the SMARTpool SUN2 siRNA includes four types of siRNAs targeting SUN2. Using the siRNA pool can reduce the off-target effect, but might cause more non-specific transcription decreases of other genes. Individual siRNAs can be more specific than the siRNA pool, but might have more off-target effects than an siRNA pool. To ensure sufficient knockdown and minimize any potential off-target effects or non-specific decrease of other genes, so as not to affect the measured nuclear mechanics, we here used both an siRNA pool and individual siRNAs to knockdown SUN1 and SUN2 proteins, after which the reduced elastic modulus and reduced viscosity of the nucleus were measured.

The siRNAs for SUN1 and SUN2 knockdown were purchased from Dharmacon (human SUN1 SMARTpool siRNA L-025277-00 and individual siRNA J-025277-05, and human SUN2 SMARTpool siRNA L-009959-01 and individual siRNA J-009959-09). The cells were treated with 10 nM siRNA for 72 h prior to measurements. ON-TARGETplus Non-targeting siRNA (D-001810-01) from Dharmacon was used in the control group.

Sharp AFM probe tips were formed by processing standard AFM cantilevers (MLCT-D, Bruker) with a focused ion beam (FIB)-scanning electron microscope (SEM) dual beam system (HITACHI NB5000 FIB-SEM). Individual AFM cantilevers were mounted on the SEM stage with probe tips facing upwards. The AFM pyramidal tips were then milled into sharp cylinders by dual ion beams (beam 25-1-80). The milling process was monitored 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 mechanical properties of the cell membrane, cytoskeleton, and nucleus. Only a small deformation was produced before the rupture of the cell membrane occurred, conforming to the small-strain assumption of the Hertz model in contact mechanics. The tension effect was minimized via the use of sharp AFM tips that produced a small contact area and small indentation depth.

Force–displacement data were collected at room temperature using an AFM (Bioscope Catalyst, Santa Barbara, CA) mounted on a Nikon confocal microscope. As opposed to in a substrate strain test, in which force application is along the cell substrate direction, and micropipette aspiration, in which applied forces are transmitted through a much larger region of cytoskeleton, measurements made in this work were significantly more locally as achieved by use of a sharp AFM probe that applied a normal force perpendicular to cellular structures. Measurement of cells in each Petri dish was completed within 20 mins after being taken out of incubator. The AFM probes used in experiments were FIB modified as described above, with a nominal spring constant of 0.03 N/m. The spring constant of each probe was calibrated via thermal spectroscopy (Nanoscope 8.10). The loading speeds were 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 where a distinct separation of plasma membrane and nuclear envelope can be visualized. Data analysis for quantifying reduced modulus from force–displacement–speed data, and decoupling elastic modulus and viscosity from reduced modulus was conducted in MATLAB. The force–displacement data from AFM measurement have a displacement resolution of 0.2 nm and force resolution of 10 pN, which is capable of capturing the rupture of the cell membrane 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 elastic modulus, which rules out a mere sudden change of force without cell membrane rupturing. The MATLAB code for data analysis used for rejecting the non-rupture case is available for download at https://github.com/XianShawn/Nuclear_Mechanics.

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

Among spring–dashpot models, the K-V model, Maxwell model and SLS model are the most commonly used models (López-Guerra and Solares, 2014). The K-V model, where a damper and a spring are connected in parallel, is commonly used to describe the force–displacement–speed behavior of viscoelastic solids. The parallel connection of the spring and the damper separates the force–displacement curve into the speed-invariant portion (F_elastic) and speed-dependent portion (F_viscous), namelyF=F_elastic+F_viscous. With different indentation speeds of the AFM probe, the speed-invariant portion (F_elastic) and the speed-dependent portion (F_viscous) can be separated and analyzed through linear regression (Eqns 7,9) to quantify the elastic modulus E and viscosity η. The Maxwell model, where a damper and a spring are connected in series, is used to describe the relaxation behavior of a material but does not describe creep under indentation (López-Guerra and Solares, 2014). The AFM technique used in this work is in essence a creep test (indentation). Using the Maxwell model to describe creep under indentation would result in an extremely high viscosity value and an extremely low elastic modulus value, since the Maxwell model assumes the material under testing flows and does not reach the steady state in a creep test. The standard linear solid (SLS) model can be used for describing 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 AFM force–displacement–speed data does not contain the stress rate (⁠⁠) information that is necessary for fitting all the three parameters in the SLS model. Direct fitting force–displacement–speed data from our AFM measurement using the SLS model resulted in a correlation coefficient as low as 0.4±0.2 (based on 30 force–displacement–speed curves captured in experiments). Thus, in this work, the SLS model was not chosen for data analysis.

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

The cell model proposed in this work (Fig. 2A,B) is based on the K-V model for viscoelastic materials. The cell membrane, cytoskeleton and nucleus are each represented by a spring and a damper connected in parallel. The cell membrane is supported underneath by the cytoskeleton. When measuring the mechanical properties of the cell membrane by analyzing the force–displacement–speed data, the data reflect the coupled mechanical properties of both the cell membrane and cytoskeleton. As shown in Fig. 2B, the elastic modulus and viscosity extracted from ‘section A’ of Fig. 1C were reduced modulus E* andη*, which describe the combined material properties of the cell membrane and cytoskeleton. Similarly, the nucleus is tethered by the cytoskeleton. The measured mechanical properties from the force–displacement–speed data reflect the coupled mechanical properties of both the nucleus and cytoskeleton. As shown in Fig. 2B, the elastic modulus and viscosity extracted from ‘section B’ of Fig. 1C were reduced modulus E** andη**, which describe the combined material properties of nucleus and cytoskeleton. Because the tip is sharp and capable of penetrating the cell membrane, distinct separation between the membrane indentation process and the nucleus indentation process was observed. Thus, it was assumed that there is no effect from the nucleus when indenting the cell membrane and there is no effect from the cell membrane when indenting the nucleus.

To determine the reduced elastic modulus and reduced viscosity, the raw AFM data were imported into MATLAB. Baseline subtraction and region of interest (ROI) selection were conducted. The ROI for quantifying the reduced elastic modulus of the cell membrane and nucleus correspond to section A and section B in Fig. 1C, respectively. After filtering the high frequency noise and interpolation, differentiation of data was conducted for further regression.

where η* and η** are the reduced viscosity of the cell membrane and nucleus, respectively; and η_m, η_c, and η_n 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 the above section. The elastic modulus and viscosity of cell nucleus, E_n and η_n were calculated based on the measurement on isolated cell nuclei.

Owing to variation across cells and due to measurement errors, the mechanical parameters calculated from experimental data have uncertainties. From data analysis, the standard error of reduced modulusE*,E**, E_n, η*,η**, η_n, was quantified via one-way ANOVA. When the modulus was decoupled from the reduced modulus, the error from reduced modulus would propagate to the decoupled modulus.

A computational model was developed to simulate the application of forces exerted by the tipless AFM probe on the cell structure. The model is composed of three layers, including the cell membrane, cytoskeleton and nucleus, reconstructed from confocal imaging. The default mesh size and node number were set to be 46386 and 26931, respectively.

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

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

Experiments were performed using a tipless AFM probe with different indentation depths (1 µm, 2 µm and 3 µm) and rates (1 µm/s, 5 µm/s and 10 µm/s). Confocal imaging was performed simultaneously with a rate of 8 frames/s recording the probe–cell contact area changes, which were used for calculating stress on the cell membrane.

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

Mesh sensitivity was investigated to ensure the independence of the results from the computational mesh size. Three mesh sizes were used. The coarse (default mesh from ANSYS workbench), medium and fine meshes consisting of 86381, 46386 and 20438 nodes were used for comparison. All three meshes resulted in similar solution patterns. The solution patterns did not depend on the patterns of the mesh lines. At all time-points, the maximum differences between three computational meshes were less than 3% for maximum stress on cell surface, less than 5% for maximum deformation of cell in the z-direction. The results proved the self-consistency of the computation model.

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

The plasma membrane of a cell was stained with the CellMask Deep Red stain (C10046, CellMask Membrane Stain, ThermoFisher Scientific), and the cell nucleus was stained with the standard Hoechst dye (33258, Sigma-Aldrich). The working solution with concentration of 10 μg/ml of CellMask and 50 μg/ml of Hoechst was prepared by mixing the two stocking solutions in warm PBS before confocal imaging. The cells were rinsed with PBS and incubated with the stain working solution for 20 min. Then, after removal of all the staining solution, the cells were rinsed three times with PBS and then the cells were immediately imaged via confocal microscopy in live-cell imaging solution (Invitrogen). The AFM probe tips were first treated with plasma activation for 2 min. 3-(aminopropyl)triethoxysilane (APTES; 99%) (Sigma-Aldrich) was diluted to 2% in a mixture of 95% ethanol and 5% DI water. The AFM probe tips were placed into the APTES solution for 10 min and then rinsed with ethanol, dried with nitrogen, and incubated at 120°C for 1 h. The Alexa Fluor 555 NHS ester (Invitrogen) was dissolved in DMSO to 100 μg/ml and used immediately. The tips were then placed into the stain solution and incubated for 1 h at room temperature, and then washed with PBS and deionized water and dried with nitrogen. In experiments, AFM measurement and cell imaging were performed simultaneously (Fig. 1D).

Staining for actin, microtubules and the nucleus was achieved using phalloidin fluorescent conjugate (A12379, Alexa Fluor 488 Phalloidin, ThermoFisher Scientific), tubulin–RFP (C10503, CellLight Tubulin-RFP, BacMam 2.0, ThermoFisher Scientific) and Hoechst 33258 (94403 Hoechst 33258 solution, Sigma-Aldrich), separately. BacMam 2.0 was added directly to the cells after passage. The concentration of BacMam was determined 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 was then permeabilized with 0.05% Triton X-100 in PBS for 15 min at room temperature. After rinsing in PBS, cells were then treated with phalloidin conjugate 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, ThermoFisher Scientific) as primary antibody and anti-mouse-IgG secondary antibody [A-21202, 1:1000, donkey anti-Mouse IgG (H+L) Secondary Antibody, Alexa Fluor 488, ThermoFisher Scientific]. The immunofluorescence staining for SUN 1/2 proteins was achieved using primary antibody (kind gifts from Didier Hodzic, Washington University School of Medicine in St. Louis, USA) and secondary antibodies according to Crisp et al. (2006). The immunostaining process is similar to the procedure described for actin staining. In short, cells were fixed, permeabilized, treated with primary antibody, secondary antibody and DAPI (D1306 DAPI, ThermoFisher Scientific).

In the sample preparation for quantitative confocal imaging, the same mounting medium, coverslip and fluorophore were used for RT4 and T24 cells. In the imaging process, targets were first found under bright-field imaging to minimize photo bleaching. Microscope settings (e.g. laser intensity, gain, exposure time and illumination) were kept the same for acquiring images in RT4 and T24 cells. Image acquisitions were conducted for the minimum duration to minimize bleaching, while avoiding saturations. In image analysis, the normalized intensity for actin and tubulin was quantified by dividing actin or tubulin intensity by the chromatin intensity for individual cells.

RNA was extracted by using an RNAeasy Micro Kit (Qiagen, 74004), then treated with DNaseI (Thermo, 18068-015) and reverse-transcribed with SuperScript III (Thermo, 18064) following the manufacturers' instructions. qRT-PCR was performed with Power SYBR Green PCR MasterMix (Thermo, 4368706) using a CFX384 Touch Real-Time PCR Detection System (Bio-Rad). The PCR program was 95°C for 10 min, 40 cycles of 95°C for 30 s, 60°C for 30 s, 72°C for 30 s, and followed by the default dissociation curve program. GAPDH served as reference gene. Statistical analyses were performed in Prism 6. Primers (F represents forward, and R represents reverse) were: GAPDH_F, 5′-GGAGCGAGATCCCTCCAAAAT-3′; GAPDH_R, 5′-GGCTGTTGTCATACTTCTCATGG-3′ SUN1_F, 5′-ATGTCCCGCCGTAGTTTGC-3′; SUN1_R, 5′-CCGTCGAGTCACAGCATCC-3′; SUN2_F, 5′-CCAGTCACCCCGAGTCATC-3′; SUN2_R, 5′-ATGCTCTAAGGTAACGGCTGT-3′

The elastic modulus and viscosity of cell membrane, cytoskeleton, and nucleus were reported as mean±s.e.m. The s.e.m. for calculated values were quantified base on error propagation. The comparisons of each group were conducted by one way ANOVA and Student–Newman–Keuls test for pairwise comparisons in JMP software and the statistical significance in each comparison was evaluated as P<0.05 for significance level.

The authors thank K. Fenelon and H. Tao for their helpful suggestions. The authors also thank Dr Didier Hodzic's from Washington University School of Medicine in St. Louis for providing the anti-SUN protein antibodies.