Elastic Properties of Pore-Spanning Apical Cell Membranes Derived from MDCK II Cells

Abstract

The mechanical response of adherent, polarized cells to indentation is frequently attributed to the presence of an endogenous actin cortex attached to the inner leaflet of the plasma membrane. Here, we scrutinized the elastic properties of apical membranes separated from living cells and attached to a porous mesh in the absence of intracellular factors originating from the cytosol, organelles, the substrate, neighbors, and the nucleus. We found that a tension-based model describes the data very well providing essentially the prestress of the shell generated by adhesion of the apical membrane patches to the pore rim and the apparent area compressibility modulus, an intrinsic elastic modulus modulated by the surface excess stored in membrane reservoirs. Removal of membrane-associated proteins by proteases decreases the area compressibility modulus, whereas fixation and cross-linking of proteins with glutaraldehyde increases it.

Introduction

Cell mechanics plays a pivotal role in many biological processes comprising cell adhesion, division, growth, and locomotion, and also on larger scales in embryogenesis and tumorigenesis (1, 2, 3, 4, 5). Thereby, cells experience external mechanical stimuli in a large number of scenarios. They are exposed to osmotic stress, as shear fluid forces, for instance, in the blood stream, endure compressive forces and dynamic tensile forces (6, 7, 8, 9). Most cell types are able to deform rapidly followed by subsequent changes in their biochemical signaling (10, 11). They also sense neighboring cells and respond to elastic properties of their underlying extracellular matrix (12, 13, 14). In essence, the response of cells to mechanical stimuli is biochemically complex and depends on cell type, magnitude of the force, and its rate.

The elastic response of polarized confluent cells to indentation is often described in the framework of established contact models derived from continuum mechanics such as the famous Hertz model (15) or combinations of continuum and tension-based mechanics (16). These models describe the weak elastic deformation of a semiinfinite homogeneous continuum with an axisymmetric indenter. Although these models are useful to cast all cellular properties into a single parameter, i.e., the Young’s modulus of the probed cell, they fail to capture the intricate shell-like architecture of living cells and are only valid for small deformations of a semiinfinite solid. The cell, however, is shaped by the plasma membrane supported by an actomyosin cortex, which is connected to the plasma membrane via specialized adhesion proteins such as those belonging to the ezrin-radixin-moesin protein family (17, 18, 19). The cortex generates a lateral tension that permits the cell to maintain a pressure difference between the cytosol and the extracellular space driving cell deformation or pseudopodia extension necessary for cell locomotion (20). The passive reconstitution of artificial actomyosin networks in giant unilamellar vesicles has recently shown that simple reconstitution is not sufficient to reproduce cell’s abilities to handle high-pressure differences. As in the mentioned study, actomyosin contraction leads to blebbing, and the importance of excess membrane area has also been emphasized (21). Besides cortical tension, plasma membrane tension is produced by adhesion to the cortex. As the plasma membrane is largely inextensible and due to its liquid-crystalline nature cannot bear large strains, rapid adjustments of surface area are required to avoid lysis of the membrane (22). Surface area regulation relies on the existence of a dynamic membrane reservoir, which can be rapidly recruited if the cell changes its surface to volume ratio as it occurs upon deformation triggered by external stimuli but also during intrinsic processes such as cell division, locomotion, or morphogenesis (23). Excess membrane area is usually stored in membrane ruffles, folds such as caveolae (24, 25), and membrane protrusions (26), or kept in associated vesicles that are ready to fuse with the plasma membrane (27). An increase in cell volume, for instance, as it occurs periodically in cardiomyocytes, leads to an increase in membrane tension that is compensated by the loss of caveolae or other membrane reservoirs (28). Investigating cellular mechanics by indentation is impacted by the osmotic effects, the presence of a stiffer nucleus, the substrate, the intermediate filaments, the neighboring cells, and the cytosolic components. Therefore, we recently established a method to transfer isolated apical cell membrane fragments from living cells onto a porous mesh using the sandwich cleavage method (29). The porous mesh allows us to probe the isolated free-standing membrane/cortex in the absence of all aforementioned factors as schematically shown in Fig. 1.

Figure 1.

Schematic representation of membrane patches yielded by sandwich cleavage. The membrane (red) on a porous mesh (gray) is still containing actin (green) and linker proteins (blue). To see this figure in color, go online.

In contrast to previous work (30, 31), we now precisely capture the elastic properties of pore-spanning membranes at large strain, where stretching dominates, by taking the indenter geometry into account. The setup permits us to neglect bending and bulk properties of cells. We found that the mechanical response of the native membrane fragments resembles the one of living cells, which is fundamentally different from that of artificial bilayers (32). This elastic response can be captured by the tension model (33, 34) and similar compressibility moduli to those of living cells are found, confirming that the cortex-membrane-composite is most relevant for the mechanical response of a cell to external poking. These findings pave the way to a better understanding of how cellular mechanics is biochemically controlled and will serve as a benchmark for the assembly of artificial systems that mimic the elastic properties of cells.

Materials and Methods

Cell culture

Madin-Darby canine kidney cells, strain II (MDCK II; Health Protection Agency, Salisbury, UK) were cultured in minimum essential medium (MEM) with Earle’s salts, 2.2 g/L NaHCO₃, 10% fetal bovine serum, and 4 mM L-glutamine in a humidified incubator set to 37°C and 5% CO₂. Cells were released using trypsin/EDTA (0.05:0.02%) and subcultured three times per week. Two days before experiments, 35-mm Petri dishes (TPP, Trasadingen, Switzerland) were incubated with poly-d-lysine (PDL, 50 μg/mL, mol wt > 300,000; Sigma-Aldrich, Steinheim, Germany) for 2 h and rinsed with Dulbecco’s phosphate-buffered saline (PBS, without Ca²⁺ and Mg²⁺; Biochrom, Berlin, Germany). 500,000 cells were seeded on freshly prepared Petri dishes and incubated at 37°C and 7.5% CO₂ in a humidity chamber (Thermo Fisher Scientific, Waltham, MA).

Sandwich cleavage protocol to obtain apical membranes from MDCK II cells

Silicon substrates (FluXXion, Eindhoven, the Netherlands) with pores of 1.2 μm diameter and 800 nm depth, accessible from both sides. were used for membrane preparation. Each substrate contains 140 fields of porous surfaces, separated by areas that are nonporous, to provide mechanical stability. The substrates were cleaned in argon plasma, coated with 2–3 nm chromium followed by 20–25 nm gold, and incubated with PDL (0.2 mg/mL, 2 h). The cultured cells were rinsed with ultrapure water and incubated in ultrapure water for 2 min. The coated substrates were then placed on top of cultured cells facing upside-down, pressed down gently and incubated for 30 min. Afterwards the substrates were lifted off the Petri dish and placed in a self-made sample holder filled with PBS. Samples were either used immediately or treated additionally with glutaraldehyde (GDA, 0.5$\%$ in PBS; Sigma-Aldrich) for 10 min or treated with Pronase E (2 mg/mL in water; Sigma-Aldrich) for 1 h.

Immunostaining

Before the sandwich cleavage, every sample was rinsed with PBS and incubated with a staining solution of CellMask Orange (1:500 in MEM; Thermo Fisher Scientific) for 10 min at 37°C and 7.5% CO₂. Cells were rinsed subsequently with MEM and kept under MEM until sandwich cleavage. Staining of F-actin was performed after sandwich cleavage. Between each step, samples were rinsed three times with PBS. Cells were fixed using 4$\%$ paraformaldehyde in PBS for 20 min. Unspecific binding of antibodies was blocked using bovine serum albumin (5$\%$ w/v, BSA; Sigma-Aldrich) mixed with Triton X-100 (0.3$\%$ v/v; Sigma-Aldrich) in PBS for 30 min. A solution of AlexaFluor 488 Phalloidin (6.6 μM; Thermo Fisher Scientific) was added subsequently and incubated for 45 min.

Fluorescence recovery after photobleaching

Fluorescence recovery experiments were carried out with a confocal laser scanning microscope setup (LSM 710; Zeiss, Jena, Germany) and recovery was evaluated according to Axelrod et al. (35).

Atomic force microscopy

Membrane patches were localized on the substrates using an upright epifluorescence microscope (BX51; Olympus, Tokyo, Japan) using the membrane fluorescence. Substrates were then transferred to an atomic force microscope (MFP-3D Origin; Asylum Research, Santa Barbara, CA). Indentation experiments were carried out using MLCT-cantilever (k_nom = 0.01 N/m; Bruker AFM Probes, Camarillo, CA). The spring constant of each cantilever was determined before the experiment using the thermal noise method according to Hutter and Bechhoefer (36), refined by Butt and Jaschke (37) and Butt et al. (38). Membrane patches were localized according to fluorescence micrographs and force-distance curves (FDCs) were acquired at constant velocity of 5 μm/s during approach to a peak force of 500 pN. Maps of FDCs were taken with a lateral resolution of ∼170 nm.

Scanning ion conductance microscopy

Surface roughness was examined on MDCK II cells seeded on Petri dishes (35 mm; TPP) and grown to confluency over the course of 2 days. Cells were fixed using 4$\%$ paraformaldehyde in PBS for 20 min. Scanning ion conductance microscopy (SICM) images were acquired with an Ionscope ICNano2000 setup (OpenIOLabs, Cambridge, United Kingdom). Nanopipettes were obtained from glass capillaries before each measurement using a P-1000 pipette puller (Sutter Instruments, Novato, CA).

Theory

Here, we present a straightforward approach that allows us to assess the shape of punched membranes and force response upon indentation. The key assumption is that the restoring force to indentation relies on the membrane’s lateral tension. Due to the size of the pores in the micrometer regime and the thickness of the membrane-cortex shell only in the nanometer regime, we neglect bending as a possible source of energy opposing deformation (30, 39). Therefore, linear in-plane stretching and detachment from the pore rims are the only considered sources of restoring force. That bending at the tip of a perfect cone would be infinite is also neglected because, in reality, the radius of the tip is ∼20 nm and the curvature remains constant during deformation. Membrane theory permits us to describe the contour of the membrane as a function of compression depth. This allows us to derive a fitting function that permits us to access both prestress T₀ and the area compressibility modulus K_A from experimental force indentation curves. For the case of a prestressed but unstretched membrane, see Norouzi et al. (40) as well as Bhatia and Nachbar (41). A thorough discussion on the impact of bending on the force-indentation curve is given by Steltenkamp et al. (39) and Mey et al. (30). A reasoning for neglecting bending is given in the Results and Discussion.

Conical indenter

Fig. 2 shows the parameterization of a conical indenter, pushing into a pore-spanning membrane at its center.

Figure 2.

Parameterization of a conical indenter (empty triangle) with half-opening angle 90°−θ poking into a flat circular membrane. Without indentation, the membrane will be at the same height as the rim (black boxes left and right), giving u(r) = 0. During indentation to a total indentation depth of u_tot, the membrane (red line) will be deformed into the pore. Two parts of the membrane will be treated separately; the inner part will stick on the conus’ surface, whereas at the certain movable contact point (r = a, u = u_a) the membrane will free itself from the conus. To see this figure in color, go online.

The force balance at the rim (r = R) between membrane and indenter reveals that the restoring force, f, is related to the tension in the membrane with respect to the probe surface (42):

$$f=\underset{C}{\oint }T\left(\mathit{l}\cdot \mathit{z}\right)\text{d}s={\int }_0^{2\pi R}T\frac{u{\left(R\right)}^{\prime }}{\sqrt{g_{\perp }}}\text{d}s,$$ (1)

with g_⊥ = 1 + u(r)^′2 accounting for the projection of z on l. Note that $\text{sin}\left(\beta \right)=\left(u{\left(r\right)}^{\prime }/g_{\perp }\right)$ with l ⋅ z = lz sin (β), the angle between z and l depending on s. Equation 1 simplifies to

$$f={\int }_0^{2\pi R}T\frac{u{\left(R\right)}^{\prime }}{\sqrt{1+u{\left(R\right)}^{\prime 2}}}\text{d}s=2\pi RT\frac{u{\left(R\right)}^{\prime }}{\sqrt{1+u{\left(R\right)}^{\prime 2}}},$$ (2)

where u(r)′ at r = R is obtained from the shape of the membrane using the membrane equation with zero bending rigidity, and excluding momentum effects. Note that the small gradient approximation $\left(\sqrt{1+{\left[{\nabla }^{2}u\left(r\right)\right]}^2}\approx 1/2{\left[\nabla u\left(r\right)\right]}^2\right)$ is used, producing the energy functional $E={\int }_{{\sum }_{\text{free}}}\text{d}{A}_{\parallel }\left[\left(T/2\right){\left(\nabla u\right)}^2\right]$. The corresponding Euler-Lagrange equation is

$$T{\nabla }^{2}u=T\left(\frac{{\partial }^{2}u}{\partial r^2}+\frac{1}{r}\frac{\partial u}{\partial r}\right)=q\left(r\right),$$ (3)

in which q(r) relates to the transverse load on the membrane. The value q(r) depends on the contact radius a:

$$q\left(r\right)=\{\begin{array}{cc}0& a<r<R\\ \frac{f}{2\pi a}& r=a.\end{array}$$ (4)

Whereas the contour of the membrane follows the shape of the indenter up to r = a, the free contour of the membrane at a < r < R can be obtained from integrating:

$$\frac{{\partial }^{2}u}{\partial r^2}+\frac{1}{r}\frac{\partial u}{\partial r}=\mathrm{0,}$$ (5)

leading to

$$u\left(r\right)=A_1\text{ln}\left(\frac{r}{R}\right)+A_2.$$ (6)

A₁ and A₂ depend on the boundary conditions. Assuming that the boundary conditions are u(r = a) = u_a and u(r = R) = 0, one finds the displacement profile and the slope of the displacement profile to be

$$u\left(r\right)=u_a\frac{\text{ln}\left(\frac{r}{R}\right)}{\text{ln}\left(\frac{a}{R}\right)},$$ (7)

and therefore

$$u^{\text{'}}\left(r\right)=\frac{\text{d}u\left(r\right)}{\text{d}r}=\{\begin{array}{cc}\frac{u_a}{r\text{ln}\left(\frac{a}{R}\right)}& r>a\\ \text{tan}\left(\theta \right)& r\le a.\end{array}$$ (8)

The derivative of u(r) at r = a is given by the shape of the indenter:

$$u_a^{\prime }=\frac{u_a}{a\text{ln}\left(\frac{a}{R}\right)}=\text{tan}\left(\theta \right),$$ (9)

which can be used to calculate the contact radius a for a given u_a. The response force f is computed from the slope of u(r) at the rim r = R:

$$f=2\pi RT\frac{u{\left(R\right)}^{\prime }}{\sqrt{1+u{\left(R\right)}^{\prime 2}}}.$$ (10)

The total indentation depth is u_tot = u_a + a tan(θ). Because tension $T=T_0+K_A\left(\Delta A/A_0\right)$ depends on prestress and also on the actual area upon indentation, we need to account for in-plane stretching of the membrane during indentation. The actual area needs to be calculated as a function of u_a or a. The area A₀ before the compression is simply πR². The actual area is

$$A_{cl}=\pi as+2\pi {\int }_a^{R}r\sqrt{1+{\left(\frac{u_a}{r\text{ln}\left(\frac{a}{R}\right)}\right)}^2}\text{d}r,$$ (11)

with $s=\left(a/\text{cos}\left(\theta \right)\right)$. The integral is analytically solvable. Substituting T gives

$$f=2\pi \left(T_0+K_A\left(\frac{\Delta A}{A_0}\right)\right)R\frac{u{\left(R\right)}^{\prime }}{\sqrt{1+u{\left(R\right)}^{\prime 2}}}.$$ (12)

This is a general result and depends only on the boundary condition given by the indenter geometry providing u(R)′. See the Supporting Material for a flat punch and parabolic indenter.

Results and Discussion

Typical results of the sandwich-cleavage method documenting the integrity of the membrane patches were shown in Fig. 3. The membrane patches were stained using CellMask Orange (red) and F-actin was visualized using phalloidin (green). The membrane staining was used in all experiments to identify the patches before force measurements, whereas F-actin staining was only used occasionally after carrying out the force measurements.

Figure 3.

Fluorescence images of membrane patches deposited on porous substrates. Staining of apical membrane in red with CellMask Orange (a) and F-actin in green using phalloidin (b) shows an inhomogeneous distribution of actin on top of the patches. The patch on the top right (arrow) generates almost no intensity from attached actin, whereas the other patches show remnants of the cortex especially associated with microvilli. Staining of F-actin (red, c) and ezrin (green, d) shows colocalization in pointlike structures identified as microvilli. Similar patterns are found in cultured MDCK II cells stained for F-actin (red, e) and ezrin (green, f). Scale bars, 20 μm. To see this figure in color, go online.

The amount of F-actin inferred from the fluorescence signal on top of the patches can vary considerably (Fig. 3, a and b). Some patches show a quite dense actin network, whereas others display only a few filaments that are visible as pointlike clusters (Fig. 3, c and d). These clusters probably originate from the microvilli that are very pronounced on the apical surface of cultured MDCK II cells (Fig. 3, e and f). Fig. 4 shows a SICM image of the apical surface of MDCK II cells for comparison. SICM creates label-free noncontact topographical images of delicate surface structures attached to a soft cell (43, 44).

Figure 4.

Scanning ion conductance microscopy image of the surface of MDCK II cells after fixation with paraformaldehyde. Protrusions from the cell surface, i.e., microvilli, are visible as small bright features. Scale bar, 5 μm.

Microvilli are formed and supported by F-actin and linker proteins like ezrin, and both are found to colocalize on the surface of the apical membrane patch (Fig. 3). The distribution of the proteins is similar to that of living cells, which suggests that the transfer of the apical membrane is faithful and therefore a suitable model system to study cellular mechanics (Fig. 3, c–f).

Membrane staining was also used in fluorescence recovery after photobleaching (FRAP) experiments to confirm the integrity and fluidity of the membrane (see Fig. 5). Due to the strong membrane-substrate adhesion, the diffusion of lipids was expected to be impaired; however, results of FRAP experiments show a complete recovery of the bleached area with a diffusion coefficient of 0.05 μm²/s. This value is very similar to the results of FRAP experiments on the apical membrane of living cells, indicating that the fluidity of the membrane is retained even on the solid support (45). Additionally, the free mobility of membrane constituents is important for membrane mechanics, as stress can be transmitted across the whole patch similarly to the way it occurs in living cells. Thus, the FRAP results further underline the similarity between membrane patches and cellular membranes.

Figure 5.

FRAP of apical membrane patches. Shown are the fluorescence micrographs of membrane-labeled patches before (a) and immediately after bleaching (b). The fluorophores were bleached in four spots on four different patches. After 2 min, the homogenous distribution of fluorophores was restored (c). Bottom-right panel shows the average recovery of fluorescence intensity. Scale bars, 20 μm. To see this figure in color, go online.

Force indentation maps were acquired on membrane patches deposited on porous substrates, and the FDCs obtained from the center of each pore were evaluated employing Eq. 12. Fig. 6 shows a collection of typical FDCs. FDCs on the rim and in the center of uncovered pores show a steep increase due to the stiff silica substrate, but differ in contact height by ∼500 nm. The difference in contact height indicates the maximum indentation depth of covered pore that can be assumed not to be influenced by probe-substrate contact, which is sufficient for all FDCs up to a force of 500 pN.

Figure 6.

Force-distance curves (a) obtained from different locations on substrate-supported apical membrane patches. Indentations performed on the rim (black, left pictogram) as well as on empty pores (blue, right pictogram) show a very steep increase of force due to hard-wall repulsion. Indentations in the center of membrane-covered pores show a complex nonlinear force response (red, green, mid pictogram). Membrane rupture is indicated as a sudden decrease of force (red). The fit (b, line) according to Eq. 12 nicely represents the experimental data (crosses). The results of the computation of membrane shape (small pictograms, jet colormap) during deformation by a cantilever (gray colormap) are shown for indentation depths of 100 nm (left) and 300 nm (right). To see this figure in color, go online.

FDCs on covered pores show a nonlinear force response to indentation, as expected from theory (Eq. 12), where membrane stretching occurs and dominates at larger strain. In some instances, rupture of the membrane sheet was observed as a sudden decrease in repulsive force (Fig. 6 a, red). Interestingly the corresponding holes are stabilized at a certain size and the FDC shows an increase of repulsive force again. This behavior is different from the force response of artificial bilayers, where rupture leads to the loss of the membrane spanning the pore (30). Previous studies have shown that lipid bilayers are almost inextensible and show a linear increase in force to indentation in similar experiments (32). The linear force response to indentation was attributed to prestress in the free-standing bilayer generated by a difference in free energy between the free-standing part and the bilayer adhering to the rim, essentially reflecting the adhesion energy of the bilayer to the substrate per unit length. The stabilization of the FDCs after membrane rupture confirms the presence of a covering membrane in the first place and is also an indication of a characteristic difference in mechanical behavior of cells compared to artificial membranes, where membrane rupture results in the complete collapse of repulsive force and retraction of the membrane from the holes to the rim. It is conceivable that the presence of a cortex attached to the bilayer prevents large-scale rupture of the pore-spanning membrane, limiting hole growth by elastic decoupling of limited membrane areas covered by the actin mesh.

Together with the findings from fluorescence micrographs and FRAP experiments, it is assumed from here that apical membrane sheets are intact and functional. This is in good accordance with other studies, e.g., one by Perez et al. (46), which showed specific binding to membrane receptors even after sandwich-cleavage preparation.

Further investigation of membrane mechanics was performed by acquisition of FDCs in force maps with a lateral resolution of ∼170 nm. For each measured pore, the nine most central FDCs were selected and analyzed individually according to Eq. 12, providing T₀ and K_A for each force curve. The results were averaged to provide one parameter set per pore. The distribution of all parameters is shown in Fig. 7 as a histogram superimposed with a kernel density plot (solid dark line).

Figure 7.

Logarithmically scaled histogram of compressibility moduli K_A (a) and linear histogram of prestress T₀ (b) values obtained from isolated apical membrane sheets deposited on porous materials and subjected to central indentation. Distributions are shown as histograms (bars) with kernel density estimation (dark line). Total number of values is n = 350 with the highest probability at K_A = 27 mN m⁻¹ and T₀ = 0.36 mN m⁻¹. To see this figure in color, go online.

Evaluation of the FDCs according to the tension model (see Eq. 12) allows us to access the prestress T₀ and apparent area compressibility modulus K_A. The prestress of the isolated apical membrane sheets (T₀ ≈ 0.3 mN m⁻¹) is similar to that of living MDCK II cells (T₀ ≈ 0.5 mN m⁻¹ (47) from which the fragments originated. However, due to the loss of cytoplasm and largely the cytoskeleton, the prestress of the membrane sheets originates to a large extent from the membrane-substrate adhesion. The substrate is coated with a positively charged polymer, whereas the plasma membrane carries an overall negative charge. In contrast, prestress in living cells arises mainly due to the actomyosin cortex that contracts in the presence of ATP (29).

In the analysis, we did not consider bending as a major or even significant source of restoring force to indentation. If we consider the limiting case of a pointlike indenter at low indentation depth and pure bending as the only origin of force response, we arrive at

$$f_{\text{bending}}\approx \frac{{\kappa }_{\text{B}}}{R^2}{u}_{\text{tot}},$$ (13)

for the restoring force f_bending assuming low indentation depths on the order of the thickness of the cortex sheet (30). The value κ_B is the bending modulus of the cortex, u_tot is the indentation depth in the center, and R is the radius of the pore. Now, ignoring bending and stretching and solely considering pretension as the main source of force response at low strain, we obtain for the force f_tension

$$f_{\text{tension}}\approx T_0{u}_{tot}.$$ (14)

Comparing the two relations above, it becomes clear that large pore radii combined with thin films foster a tension-dominated response to indentation. Because the bending modulus of the cortex is on the order of 10⁻¹⁸ J, assuming a cortical thickness of ∼100 nm, the ratio between tension response and bending is roughly $\left(f_{\text{tension}}/f_{\text{bending}}\right)=\left(T_0{R}^2/{\kappa }_B\right)\approx {10}^3$, rendering bending only a small contribution to the overall force response. However, smaller pores and thicker cortices require us to consider bending as an important contribution at low strain. At high strain, stretching dominates over prestress and bending. The area compressibility modulus of pore-spanning membrane patches (K_A = 27 mN m⁻¹) is also similar to that of living cells, which was determined to be ∼ K_A = 130 mN m⁻¹ (47), supporting the idea of a largely intact plasma membrane. Although lipid bilayers are extensible up to a maximum of <5%, structured membranes with microvilli should be able to supply their excess area to compensate indentation. The pointlike structures, as shown in the fluorescence micrographs (Fig. 3), indicate that the excess membrane area is still available after the preparation process and thereby can be accessed during indentation, essentially reducing the area compressibility modulus K_A to K_A ⋅ A₀/(A_ex + A₀). Therefore, we refer to apparent area compressibility moduli. A small value for K_A indicates larger accessible membrane reservoirs. The absence of functional myosin motors might increase the available excess area, explaining why K_A values from membrane patches are smaller than those obtained from living cells (29).

To determine the range of mechanical responses of these membrane sheets, we applied two of the most extreme treatments, either using GDA to strengthen the protein network or Pronase E to digest peripheral proteins. Results of these experiments are shown in Fig. 8. Glutaraldehyde is used to cross-link protein domains on the membrane cortex, which stiffens the actin meshwork attached to the membrane to withstand expansion. This stiffening is mirrored in the area compressibility modulus as it rises from a peak at 18.8 mN m⁻¹ for untreated samples to 152 mN m⁻¹ after GDA fixation. The same treatment shows almost no influence on the peak prestress T₀, which is 0.36 mN m⁻¹ on untreated membranes and 0.37 mN m⁻¹ after GDA treatment, confirming the assumption that prestress is governed by substrate adhesion and not cortex composition.

Figure 8.

Kernel density estimates of K_A (a) and T₀ (b) for the different treatments of apical membrane sheets. The apparent area compressibility modulus K_A is highest after treatment with GDA (blue) and lowest after treatment with Pronase E (red), whereas untreated cells (green) show values in between. Prestress values T₀ are very similar regardless of the treatment. To see this figure in color, go online.

Pronase E is used to cleave peptide bonds and thereby destroys protein structures accessible to the soluble enzyme. Incubation with pronase E should therefore weaken the cortical contractility and facilitate expansion during indentation. This weakening was indeed observed, as the peak apparent area compressibility modulus K_A drops from 27 to 12.9 mN m⁻¹. However, the distribution in this case is rather broad and seems to have a shoulder on values even higher than untreated samples. It is possible that cortical integrity is actually important for force transmission along the plasma membrane, and destruction of this cortex leads to an increased inhomogeneity of surface properties from a mechanical perspective of view. Besides, removal of actin might also interfere with accessibility of membrane reservoirs and thereby increase the stiffness at large strain. Regardless of this, the peak prestress T₀ stays quite constant at a value of 0.41 mN m⁻¹, which again indicates that prestress after the given preparation process is largely independent of cortical composition and reflects mainly the adhesion to the pore rims.

These findings suggest that isolated membrane sheets exhibit a mechanical behavior similar to that of plasma membranes of living cells (29). This supports the concept of a tension-based mechanical model that is able to describe the mechanics of apical membranes in both living cells and isolated fragments, and confirms and quantifies expected changes of mechanics due to cortex modifications. The change of the compressibility modulus independent of prestress underlines that two independent parameters are required to characterize the mechanical response of membranes to surface expansion during indentation instead of using a uniform parameter like the Young’s modulus. Depending on the cell type, the latter might in fact be biased by the indenter geometry, as demonstrated recently using blunt spherical indenters that provide smaller Young moduli in contrast to a sharp conical tip generating larger values (29). It will be interesting to see how viscoelasticity differs between isolate fragments and living cells.

Conclusions

The mechanical properties of cells have been recognized to constitute an important biomedical phenotype reporting on cytoskeletal remodeling, malignancy of cells, and vitality, just to name a few examples. Although it is widely accepted that the membrane-cortex composite dominates the cell’s response to external deformation, it remains unclear to what extent cytosolic components such as the nucleus, or the viscoelastic properties of the cytoplasm, including its organelles, contribute to the elastic properties of the cell subject to external deformation.

Based on our previous work on the mechanics of pore-spanning membranes, we then investigated the elastic properties of isolated apical membrane sheets with intact cortex and functional microvilli deposited on micrometer-sized pores using a tension-based model identical to that used for living cells. We enlarged the parameter space of previous works by addressing the nonlinear regime of the force distance curve explicitly, i.e., the large deflection of the membrane cortex, using a model that includes stretching of the composite shell at large deformation and precisely takes the geometry of the indenter into account, which has not been done before. Prestress T₀ (i.e., lateral tension due to adhesion of the membrane to the rim) and area compressibility modulus K_A are shown to be two independent parameters that represent complementary information on the elastic properties of the composite shell. Essentially, the identical model only with a modified geometry has been used to describe the force response of living adherent cells (33, 34). Apart from geometry issues that alter mechanical properties of cells in a deterministic way, the only intrinsic mechanical parameter, the area compressibility modulus, obtained from pore-spanning membrane sheets, is close to what has been found for living cells. Interestingly, strengthening the actomyosin cortex by cross-linking of proteins with GDA leads to increase of the area compressibility modulus, whereas removal by enzymatic digestion decreases it, indicating the importance of the underlying network for recruiting excess membrane area in response to deformation of the membrane.

Our results clearly indicate that the impact of cytosol and organelles can be neglected and the membrane cortex dominates the mechanical response. In particular, the presence of membrane reservoirs that relax external tension upon deformation are essential for the overall mechanical response. It is clear that cells can adapt to external stress such as osmotic imbalance or direct mechanical manipulation by surface area regulation and thereby—in contrast to artificial bilayer—can sacrifice membrane reservoirs to prevent lysis if in-plane tension rises. Rearrangement of cortical actin on a whole cell level has been shown to occur rapidly as a response to wounding of the cell cortex and can lead to long-term changes of gene expression, underlining the dominance of the actin cortex in cell mechanics. As postulated previously, the membrane itself, due to its limited extensibility, in contrast to the actin cortex has a much greater contribution to the overall strength of confluent epithelial cells than expected from studies on mesenchymal cells such as fibroblasts (48).

Author Contributions

S.N. performed the AFM measurements. A.J. did the theoretical analysis and designed the research. S.N. and A.J. wrote the manuscript.

Editor: Stephen Evans.