Controlling Cellular Volume via Mechanical and Physical Properties of Substrate

Article

Controlling Cellular Volume via Mechanical and Physical Properties of Substrate Kenan Xie,1 Yuehua Yang,1 and Hongyuan Jiang1,* 1 CAS Key Laboratory of Mechanical Behavior and Design of Materials, Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui, China

ABSTRACT The mechanical and physical properties of substrate play a crucial role in regulating many cell functions and behaviors. However, how these properties affect cell volume is still unclear. Here, we show that an increase in substrate stiffness, available spread area, or effective adhesion energy density results in a remarkable cell volume decrease (up to 50%), and the dynamic cell spreading process is also accompanied by dramatic cell volume decrease. Further, studies of ion channel inhibition and osmotic shock suggest that these volume decreases are due to the efflux of water and ions. We also show that disrupting cortex contractility leads to bigger cell volume. Collectively, these results reveal the ‘‘mechanism of adhesion-induced compression of cells,’’ i.e., stronger interaction between cell and substrate leads to higher actomyosin contractility, expels water and ions, and thus decreases cell volume.

INTRODUCTION Mechanical and physical properties of substrate, such as substrate stiffness, substrate topography, adhesion energy density, and available adhesion area, play an important role in regulating many cell functions and behaviors. For example, it has been shown that cells undergo directed migration in response to the gradient of substrate stiffness (durotaxis) (1,2), graded adhesion (haptotaxis) (3), or the asymmetric geometrical cues of substrate (4,5). Increasing substrate stiffness also promotes cell spreading and proliferation (6), and the cells cultured on stiffer substrates appear to be significantly stiffer (7,8). Strikingly, when mesenchymal stem cells are grown on substrates with high, intermediate, and low stiffness, they exhibit preferential differentiation to osteoblasts, myoblasts, and neurons (6,7). The size and shape of adhesive islands can also remarkably affect cell differentiation (9,10) and many other cell properties, such as cell viability (11), focal adhesion assembly (12), and protein synthesis (13). In addition, increased substrate stiffness leads to malignant phenotypes of cancer cells (14). Recently, it has also been found that the composition (15), pore size (16), and the geometrical topography (17) of the substrate contribute to the malignant phenotype

Submitted July 14, 2017, and accepted for publication November 28, 2017. *Correspondence: [email protected] Kenan Xie and Yuehua Yang contributed equally to this work. Editor: Cecile Sykes. https://doi.org/10.1016/j.bpj.2017.11.3785

of cancer cell. Although these studies have shown that the mechanical and physical properties of substrate can influence many cell functions and behaviors, how they influence cell volume is still elusive. In fact, recently researchers began to realize that cell volume is an underestimated hidden parameter in cells. It has been shown that the change of cell volume impacts not only cell mechanical properties (18,19) but also cell metabolic activities (20) and gene expression (21). This might be because the volume change could result in nucleus deformation and then impact chromatin condensation (22,23). Furthermore, the change of cell volume can provide the driving force for the dorsal closure of Drosophila (24), wound healing (25), vesicle trafficking (26), and cell migration in confined microenvironments (27). Lastly, cell volume can even regulate cell viability (28,29), cell growth (30), and cell division (31). Therefore, it is of great interest to investigate the mechanism of cellular volume regulation. Usually, osmotic shocks are used to manipulate cell volume (22,32). However, there is accumulating evidence that the change of cell volume can also be induced by mechanical stimuli from the microenvironment. Indeed, cell volume can decrease by 30% under shear stress (33) or mechanical impact (29). The adhesion of cells to substrate is also a mechanical stimulus from the microenvironment, and a recent theoretical study showed that the volume change can significantly affect the shape and dynamics of

Ó 2017 Biophysical Society.

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cells adhered between two adhesive surfaces (34,35). Therefore, we wonder whether the mechanical properties of substrate can regulate cell volume. In this study, using confocal microscopy and atomic force microscopy, we first measure the cell volume of 3T3 cells cultured on polydimethylsiloxane (PDMS) substrates of varying stiffness, and then we study the cell-volume change during dynamic cell spreading. We further use adhesive islands to control the available spread area and the effective adhesion energy density of substrates, and we explore the effects of these properties on cell volume. Surprisingly, we find that an increase in substrate stiffness, available spread area, or effective adhesion energy density results in a remarkable decrease in cell volume. The disturbance of ion channels and cortical contractility indicates that the volume decrease is due to the increase of cortical contractility and the efflux of water and ions, which is further confirmed by our theoretical model. MATERIALS AND METHODS Cell culture 3T3 mouse fibroblast cells, MCF7, and Hela cells were cultured in Dulbecco’s modified Eagle medium (Gibco; Life Technologies, Carlsbad, CA) supplemented with 10% (vol/vol) fetal calf serum (Gibco; Life Technologies) and 1% penicillin-streptomycin (Gibco; Life Technologies), at 37+ C and 5% CO2 in humid conditions. Cells were trypsinized by 0:05% trypsin-EDTA (Gibco; Life Technologies), centrifuged at 1500 Rpm/min for 3 min and seeded on dishes at low density (2
4  103 cells/cm2 ) to reduce cell-cell interaction. In all the experiments, after cells had had enough time to adhere to the substrate, they were cultured with 2 mM hydroxycarbamide (HU) (Sigma-Aldrich, St. Louis, MO) medium for at least 18 h to block cells in G1/S transition. After this synchronization, cells were further cultured for 6 h before imaging.

Fabrications of substrates with tunable mechanical properties PDMS and Sylgard 184 (Dow Corning, Midland, MI) were used to fabricate substrates with tunable rigidity. Sylgard 184 was prepared as per the manufacturer’s directions, and the rigidity of substrate was controlled by the ratio of base to curing agent. Seven different volume ratios of Sylgard 184 base to curing agent, 3:1, 5:1, 10:1, 15:1, 20:1, 30:1, and 50:1, were evaluated. These blends were mixed and defoamed in a vacuum drier. After the mixing, the PDMS samples were either poured into 12-mm-width, 70-mm-length molds to create rectangle samples for mechanical testing or spin coated onto 22-mm-diameter glass coverslips at 1500 Rpm by spin coater (KW-4A) to create 80- to 120-mm-thick film substrates. All PDMS samples were then cured at 65 C for 12 h and disinfected in ultraviolet light over 15 min. The universal tensile test machine (LS1 Series, Ametek, Berwyn, PA) was used to measure the Young’s moduli of PDMS substrates. The PDMS films were further placed onto glass coverslips for cell seeding. Before cell seeding, the PDMS substrates were treated with plasma cleaner (PDC-002, Harrick, Stockton, CA) in O2 for 1 min to determine hydrophilicity. Microcontact printing was used to fabricate substrates with various available adhesion areas and adhesion energy densities. Briefly, silicon wafers were patterned by standard ultraviolet photolithography (optical aligner MA/BA6, SUSS, Garching bei Munchen, Germany) with AZ6112 and then etched by inductively coupled plasma (PlasmaPro System100

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ICP380; Oxford Instruments, Abingdon, United Kingdom). PDMS stamps (base/agent ratio, 10:1) were replicated from the silicon wafers that were pretreated with Trichloro (1H,1H,2H,2H-perfluorooctyl) silane. The stamps were then treated with O2 plasma for 1 min and inked for 2 h with 10 mg/mL fibronectin solution (Abcam, Cambridge, United Kingdom). The nonfunctional regions on the glass coverslip were blocked by 0.1 mg/mL PLL-gpolyethylene glycol (PEG) solution in 10 mM HEPES. After being dried in air, the stamps were placed in contact with the glass coverslip for 30 min. Then the stamps were released and immersed in phosphate-buffered saline (PBS) and 10 mM HEPES solution for 1 min.

Immunofluorescent staining For living cells, to mark the cell cytoplasm for confocal imaging, cells were loaded with a fluorescent indicator, CellTracker Green (5-chloromethylfluorescein diacetate (CMFDA)). 50 mg lyophilized CMFDA powder was dissolved in 1 mL high-quality DMSO. Cells were then incubated with 30 mL/mL CMFDA solution for 20–30 min at 37 C. After incubating, the medium was removed, and cells were washed three times with PBS, then incubated for another 10 min before imaging. For fixed cells, before staining the nucleus and F-actin, cells were fixed with 4% paraformaldehyde (4 g paraformaldehyde powder dissolved in 100 mL PBS at 68o C; Sigma-Aldrich) for 5 min, then washed three times with PBS. After that, cells were permeabilized with 0.1% TRITON X-100 (40 mL TRITON dissolved in 40 mL PBS) for 5 min. For the immunofluorescent staining of the cell nucleus, cells were loaded with 40 -6-diamidino-2-phenylindole (DAPI) dihydrochloride: 1 mg DAPI powder (Sigma-Aldrich) was dissolved in 1 mL PBS. For the mark of F-actin, cells were loaded with fluorescein-isothiocyanate-labeled phalloidin) (0.1 mg powders dissolved in 2 mL DMSO; Sigma-Aldrich). Cells were incubated with 25 mL/mL DAPI and 30 mL/mL phalloidin at 38 C for 45 min. To remove unbound conjugate, cells were washed three times with PBS.

Drug treatments and osmotic shock All inhibition tests were carried out after the CMFDA treatments. The blebbistatin (myosin II inhibitor; Sigma-Aldrich), latrunculin A (F-actin polymerization inhibitor; Sigma-Aldrich), cytochalasin D (actin polymerization inhibitor; Abcam), Y-27632 (ROCK inhibitor; Sigma-Aldrich), ouabain (Naþ/Kþ ATPase inhibitor; Sigma-Aldrich), 4, 40 -diisothiocyanatostillbene 2, 20 -disulfonic acid disodium salt hydrate (HCO 3 =Cl antiporter inhibitor; Sigma-Aldrich), ethylisopropylamiloride (EIPA) (Naþ/Hþ antiporter inhibitor; Sigma), bumetanide (KþNaþ/2 Cl sysporter inhibitor; Abcam), and nocodazole (microtubule polymerization inhibitor; Sigma-Aldrich) were dissolved in DMSO, subpackaged, and then diluted by DMSO to varying concentrations. In each drug-inhibited experiment, we added the DMSO solution with drug to adjust the DMSO concentration in the last culture solution to 30 mL/mL. The cells were then incubated with these drugs for 1
2 h before confocal imaging. For osmotic experiments, PEG200 (Sigma-Aldrich) was premixed with the cell medium to get a hypertonic solution. For the hypotonic solution, cell medium was premixed with water (Sigma-Aldrich). After osmotic shocks, cells were incubated for 3 h before imaging. After osmotic shock, the 3T3 cells do not recover their volume, so they can retain the effects of the osmotic shocks (36,37). Therefore, we wait for 3 h before imaging so that the cells have enough time to respond to the osmotic shock.

Image acquisition A 35 mm glass-bottom dish with a dye-loaded cell was placed on a Leica DMi8 laser scanning confocal microscope with a 63 oil lens (NA 1.4). For different coverslips that were covered with PDMS, the 20 lens (NA 0.4) was used for cell imaging. The CMFDA dye was excited by a

Substrate Properties Tune Cell Volume 488 nm laser and its emission was detected in the band from 510 to 530 nm. DAPI was excited by a 405 nm laser and its emission was detected in the band from 432 to 480 nm. Phalloidin was excited by a 488 nm laser and its emission was detected in the band from 502 to 578 nm. The separation between two z-stacks of confocal images is 0.3
0.5 mm. When objects get further from the focal planes on which they are imaged, the precision of the z-planes decreases. This blurring effect is also accompanied by a distortion in the z-plane. Thus, to determine the cellular boundary, we first find a rough boundary in the differential-interference-contrast channel, and then we adjust the laser intensity to make the pixels inside this rough cellular boundary almost overexposed in the fluorescence channel. In this way, we can regard the overexposure region as the actual cell profile. For atomic force microscopy (AFM) imaging, after cells were incubated for 12 h, the cell-culture dish was placed onto the AFM (BioScope Resolve, Bruker, Karlsruhe, Germany). AFM imaging was performed in PeakForce tapping mode with a PeakForce QNM-Live Cell (PFQNM-LC) probe (Bruker AFM probes: tip length, 17 mm; tip radius, 65 nm; opening angle, 15 ; spring constant, 0.093 N/m). The scanning size was adjusted according to the cell size, and the scanning frequency was smaller for bigger cells.

Cell-stiffness measurements The cell stiffness was measured under PFQNM model on AFM. The MLCT-BIO-D probe (Bruker AFM probes: tip length, 6 mm; tip radius, 24 nm; opening angle, 25 ; spring constant, 0.012 N/m) was oscillated at 2 kHz with a peak force amplitude of 100 nm. The peak-force set point was adjusted to 1.661 nN. The Derjaguin, Muller, Toropov (DMT) modulus, E , was calculated by fitting the retract curve with the DMT model. Since the DMT model includes the effect of the adhesion force, we would use the retraction curve, which includes more information about the adhesion force, to calculate the cell stiffness. The sample modulus, Es , can be calculated from




 1  n2t 1  n2s E ¼ þ ; Et Es 

where Et is the modulus of the probe tip, nt is the Poisson’s ratio of the tip, and ns is the Poisson’s ratio of the biological sample. Assuming that the tip modulus is much larger than the sample modulus, the sample modulus can be deduced from

1  n2s Es ¼ : E All data analyses were done with Nanoscope Analysis software (Veeco Instruments, Santa Barbara, CA).

Cell volume measurements For the volume measurements based on confocal images, 3D cell morphologies were reconstructed by stacking XY scan images through the entire height of cell. A region of interest encompassing a single cell was chosen for three-dimensional reconstruction and volume quantification. For the AFM scanning, cell volumes were calculated from the height images. After first-order flattening and low-pass filtering to eliminate noise, the height images were exported in ASCII text file format in the Nanoscope Analysis software so that the volume could be calculated. First, a height threshold was adjusted to isolate the cell from the substrate; then the cell volume was calculated using the formula

X

dV ¼

X

z  dA ¼

X

z  dx  dy;

where z is the height of a data point and dA is the area element, which is the product of the distance of two pixels in the horizontal and vertical directions.

Accuracy of volume measurements To quantify the cell volume, we reconstruct the 3D cell morphology from a series of z-stack confocal microscopy images. This method might include systematic errors during the reconstructions of cell morphology. To characterize the precision of 3D reconstruction method, spherical silicon dioxide (SiO2) beads with a radius of 10 or 5.5 mm were prepared after washing five times with deionized water. The SiO2 beads were mixed with 30 mg/mL rhodamine 110 solution. Then we added 100 mL bead solution to the glass-bottom dish, which was treated with plasma in O2 for 30 s. The refractive index of an SiO2 bead is
1.46, which is close to the refractive index of 3T3 cells (1.36) (38,39). We first measure the bead diameter, D, by identifying the largest cross section in the z-plane. We assume the beads are perfect spheres. Thus, the true value of the bead volume is V ¼ 1=6pD3 . Alternatively, we can also use the 3D confocal reconstruction to measure the bead volume. We can obtain the precision of volume measurement with the 3D confocal reconstruction by comparing the bead volumes deduced by these two methods. We find that the error of the volume measurement with 3D confocal reconstruction is in the range 8.7
14% (Fig. S3 c). As shown in Fig. 1 d, the cell heights on soft substrate, measured by AFM scanning and 3D confocal reconstruction, are 11.6 and 13.7 mm, respectively. We have found that the absolute error of height deduced from 3D reconstruction (due to the distortion in z-plane) is
2.3 mm (Fig. S3 d). The difference between cell height measured by AFM scanning and that measured by 3D reconstruction is 2.1 mm, which is also in the range of the cell-height error measured by the 3D confocal reconstruction method (
2.3 mm). Another error comes from the estimation of lamellipodium thickness, since it is difficult to extract the actual lamellipodium thickness (
100 nm) from the z-stack images. In addition, we assume the thickness of the lamellipodia to be the depth separation between two z-stack images (0.3
0.5 mm). Assuming that the actual thickness is 200 nm, then the error in estimation of the actual lamellipodium thickness is 0.1
0.3 mm. Thus, for a spread area of
1200 mm2, which is almost the biggest spread area measured in our experiments, the maximal volume-error results from the 3D reconstruction are in the range 120
360 mm3.

RESULTS Cell volume is 50% smaller on stiff substrate First, we study how the substrate stiffness affects cell volume. To this end, 3T3 cells are seeded on PDMS substrates of varying stiffness. We prepare a series of PDMS substrates with Young’s modulus in the range 27 kPa to 2.2 MPa by varying the base/cross-linker ratio from 50:1 to 3:1 (Fig. S1). Cells are synchronized to the G1/S transition and then cultured for 6 h before observation, since the cell volume is different in different mitotic phases. Also, the culture time after synchronization cannot be >10 h, because some cells may have divided by this culture time (Fig. S2). To measure cell volume, spread area, and cell height, we label the cytoplasm with a fluorescent indicator, CellTracker Green CMFDA, and reconstruct the 3D cell morphology from a series of z-stack confocal microscopy images. To make sure the 3D reconstruction measurement is reliable, we also use AFM scanning to measure the cell morphology (Figs. S4 and S5). We find that the results from these two methods agree with each other very well (Fig. 1, c–e); especially when the substrate is stiff enough, the cell volumes determined from 3D confocal reconstruction and

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glass

723kPa

285kPa

152kPa

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FIGURE 1 The volume of adherent cells decreases with substrate stiffness and also during cell spreading. (a and b) Snapshots of 3T3 fibroblast living (a) and fixed (b) cells adhered to PDMS substrates of varying stiffness. Scale bar, 20 mm. (c–e) The spread area, cell height, and cell volume, respectively, as a function of substrate stiffness (n ¼ 12
17). The blue (circle), magenta (diamond), and black curves are the results found for living cells using 3D confocal reconstruction, atomic force microscopy (AFM), and the theoretical model (see the 17 coupled differential-algebraic equations in Theoretical Model), respectively. The green (triangle) curves are the results for fixed cells. The red dots in (c)–(e) are the results for suspension cells (S). The differences between the results for suspension cells and those for cells cultured on very soft substrate are due to the effects of the chemical term, Gc , in the adhesion energy density (see Theoretical Model for details). (f) The differential interference contrast (DIC) image, cell morphology from 3D confocal reconstruction, and cell morphology scanned by AFM, and the overlaps between these images. Scale bars, 10 mm. (g and h) The time-dependent changes of cell spread area and cell volume during dynamic cell spreading (n ¼ 13
15). Error bars represent the standard deviations. To see this figure in color, go online.

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Substrate Properties Tune Cell Volume

AFM scanning are almost identical (Fig. 1 e). In this case, the 3D cell morphologies scanned by AFM and reconstructed from confocal images overlap with each other very well (Fig. 1 f). We further characterized the precision of the 3D reconstruction method using spherical SiO2 beads. We first measure the bead diameter, D, by identifying the largest width in the z-plane; then we calculate the bead volume with V ¼ 1=6pD3 . Then we compare these volumes deduced from bead geometry to the bead volumes measured with 3D confocal reconstruction. We find that the precision of the volume measurement with 3D confocal reconstruction is high, exhibiting an error between 8.7 and 14% depending on the bead size (Fig. S3 c). Together these results indicate that the volume measurement based on 3D confocal reconstruction is reliable. Hence, in the rest of the experiments, we used 3D confocal reconstruction to measure cell volume. We observe striking differences in cell morphology, spread area, and cell height on different substrates. As shown in previous experiments (40), on stiff substrate, 3T3 cells are well spread with large lamellipodia (Fig. 1 a) and many stress fibers (Fig. 1 b). In contrast, cells cultured on soft substrate are typically rounded, barely spread, and show very few stress fibers (Fig. 1, a and b). The average spread area of living 3T3 cells increases from 400 to 1200 mm2 as the substrate stiffness increases (Fig. 1 c, blue line), which is in agreement with previous studies (6,8). We also find that the cell height decreases remarkably with the increase of substrate stiffness (Fig. 1 d). Surprisingly, the increase in substrate stiffness leads to a >50% cell volume decrease, from 3500 to 1500 mm3 (Fig. 1 e, blue line). Also, the cell volume approaches a constant value beyond a substrate stiffness of 2.2 MPa. We find a similar cell volume decrease in other cell types, such as Hela and MCF7 cells (Fig. S6 a), indicating that this volume decrease is quite universal across different species of cells. This is consistent with a recent study (41). However, there is also another experiment showing the opposite result, i.e., that the cell volume of fixed cells increases with substrate stiffness (42). We infer that the contradictory results might result from the fixation of cells. During immuno-staining, cells are usually fixed with paraformaldehyde. Therefore, it is vital to ascertain how this treatment affects the cell volume. After 3T3 cells were fixed with 4% paraformaldehyde (Fig. 1 b), not only the spread area but also the cell volume increases with substrate stiffness (Fig. 1, c and e, green lines). On soft substrate, the cell volume of fixed cells is much smaller than the cell volume of living cells, whereas on stiff substrate, the cell volumes of fixed and living cells are not significantly different (Fig. 1 e, green line). These results show that the fixation of cells with paraformaldehyde leads to remarkable cell shrinkage for cells cultured on soft substrate.

Cell volume decreases dramatically during dynamic cell spreading From Fig. 1, c and e, we can see that the bigger the spread area is, the smaller the cell volume becomes. Therefore, we speculate that cell volume may decrease during cell spreading. To verify this hypothesis, we examine the timedependent changes in cell volume when 3T3 fibroblast cells gradually spread onto plastic petri dishes. As the cell spreads out, the cell height decreases while the spread area increases with time (Fig. 1 g). Amazingly, as illustrated in Fig. 1 h, cell volume decreases by >40% during the first 150 min of cell spreading and approaches a steady value (
1600 mm3) during the late stage of cell spreading. Increasing available spread area reduces cell volume Since we have shown that the cell volume is closely related to the spread area (Fig. 1), we wonder whether the spread area alone is sufficient to regulate the cell volume. To control the available spread area, we fabricate adhesive islands that are coated with fibronectin and surrounded by non-adhesive regions (Figs. 2 a and S7). 3T3 cells are cultured on circular adhesive islands with various sizes (Fig. 2 b, dashed circles). As shown in Fig. 2 c, when the island radius is smaller than a critical value (
22 mm), the cell volume decreases by >40%, from 3000 to 1600 mm3, with the increase of island radius. At the same time, the cell height decreases (Fig. 2 d) as the spread area increases (Fig. 2 c). Due to the constraint of the adhesive islands, the spread area of cells is equal to the island area when the islands are small (Fig. 2 c). In contrast, when the island radius is bigger than the critical value, the cell volume, spread area and cell height remain constant as the island radius increases. This is because when the adhesive islands are too big, cells cannot spread all over the island (Fig. 2 b, right). Therefore, these variables do not change with island radius any more (Fig. 2, c and d). The critical island radius, rc , can be defined as the equivalent pffiffiffiffiffiffiffiffiffiaverage adhesion radius of unrestricted cells, i.e., rc ¼ A=p, where A is the adhesion area of unrestricted cells. Cell volume decreases as the adhesion energy density increases Besides the available spread area, the adhesion energy density is another parameter that can regulate the spread area of cells. Therefore, it’s interesting to probe how the adhesion energy density affects cell volume. To manipulate the adhesion energy density, we fabricate a micropatterned substrate with adhesive square regions separated by non-adhesive regions, or vice versa (Fig. 2 e). The effective adhesion energy density of the substrate, Geff , is proportional to the ratio of adhesive area to the total surface area, i.e., Aa =At .

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Availlable spread area

Effective adhesion energy density Γ eff < 0.5Γi

e

a

a

non-adhesive region

non-adhesive region

adhesive region

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50μm

Γ eff = Γi

b

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unrestricted

Γ eff = Γi (1 −

a=2μm, b=4μm

a2 ) b2

a=1μm, b=4μm

a=2μm, b=5μm

6.25%

16%

a=2μm, b=3μm

a=3μm, b=5μm

a=2μm, b=4μm

a=2μm, b=5μm

64%

75%

84%

25%

a=3μm, b=5μm

36%

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44% Top view

25μm

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25μ 25μ 25 25μm 5μm

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a2 b2

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FIGURE 2 Cell volume decreases with the available spread area (a–d) and the effective adhesion energy density (e–h). (a) The available spread area is controlled via adhesive islands. (b) Snapshots of 3T3 fibroblast cells constrained in circular adhesive islands (dashed circles) with various radii. Scale bars, 10 mm. (c and d) The cell volume, spread area, and cell height for different-sized adhesive islands (n ¼ 13
17). The magenta and blue curves (with square or circle symbols) are experimental measurements, whereas the black curves are the theoretical results found by solving the 17 coupled differential-algebraic equations in Theoretical Model. The label ‘‘inf’’ represents the unrestricted cells. (e) Schematic of how to adjust the effective adhesion energy density, Geff , of substrate. Square regions with length a and center distance b are fabricated under the constraint a2 =b2 < 0:5. The effective adhesion density is adjusted by the ratio of adhesion area to total surface area, Aa =At , according to Geff ¼ Gi a2 =b2 or Geff ¼ Gi ð1  a2 =b2 Þ, where Gi is the adhesion energy density of the adhesive regions. Therefore, we use the ratio Aa =At to represent the effective adhesion energy density. (f) Snapshots of 3T3 fibroblast cells cultured on substrates of varying Aa =At (various values of a and b). Scale bars, 20 mm. (g and h) The cell volume, spread area, and cell height as a function of the ratio of adhesive area to non-adhesive area Aa =At (n ¼ 11
14). Error bars represent the standard deviations. To see this figure in color, go online.

Therefore, we can control the effective adhesion energy density at the mesoscopic scale by adjusting the square size, a, and the center-to-center distance, b, between the

680 Biophysical Journal 114, 675–687, February 6, 2018

two neighboring squares (Fig. 2 e). And we use the ratio Aa =At to represent the effective adhesion energy density, Geff , in Fig. 2, g and h.

Substrate Properties Tune Cell Volume −x ) + 1520.4 375.65

y = 14.07 exp(

substrate stiffness dynamic spreading available spread area adhesion energy density suspension cells drug treatments exponential fitting

b

−x ) + 5.04 369.2 substrate stiffness dynamic spreading available spread area adhesion energy density suspension cells drug treatments exponential fitting

minimum volume

minimum height

are minimal cell volume and cell height (Fig. 3, a and b, dashed lines) when the spread area is big enough. This minimal cell volume may be limited by the dry mass of the cell. We also find that the cell stiffness decreases with cell volume (Fig. S8), which is consistent with previous studies showing that cells exposed to hypertonic solutions are smaller and stiffer (18,19).

We find, on the substrate with high adhesion energy density, that 3T3 cells are well spread and show broad lamellipodia (Fig. 2 f). In contrast, when the effective adhesion energy density is small, cells are more rounded and characterized with long filopodia. As shown in Fig. 2, g and h, the spread area increases linearly with the effective adhesion energy density, whereas the cell volume and cell height decrease linearly with the effective adhesion energy density. Remarkably, the cell volume can decrease by >40%, from 2900 mm to 1500 mm3 (Fig. 2 g).

The cell-substrate interaction squeezes water and ions out Since transport of water and ions plays an important role in cellular volume regulation (32,43), we speculate that it might also contribute to the volume decrease of adherent cells. Therefore, we examine the effects of inhibiting ion transporters on cell volume of adherent cells cultured on glass. Among the tested inhibitors, the inhibition of Naþ/Kþ antiporters by ouabain (Oua), or the inhibition of Naþ/Hþ antiporters by ethylisopropylamiloride (EIPA), significantly hinders cell volume decrease, whereas inhibition of chloride channels by disodium salt hydrate or bumetanide (Bum) does not show a notable influence on cell volume (Figs. 4 a and S9).

Cell volume is determined by spread area From the above experiments, we can see that the bigger the spread area is, the smaller the cell volume and cell height become. Strikingly, when all the data of living 3T3 cells are plotted in the same figure, we find that both the cell volume and cell height decay exponentially with the spread area (Fig. 3, a and b) no matter what method is used to decrease cell volume. Therefore, when cells adhere to substrate, their volume can be determined by the spread area. It should be noted that the cell volume of suspension cells is also on the exponential curve. Interestingly, there

*** ***

*** *** NS NS

2000

b

Ions channels Osmotic NS

1500

*** **

**

MT

NS

NS

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0

0

MT NS

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Cortex

Ions channels Osmotic

MT

20 ***

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*** *** *** ***

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5 0

Co nt

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Co ntr ol Ou a EIP A DI DS Bu m Hy po Hy pe Cy r toD La tA Be lb Y27 63 2 No c

Cell volume

3000

Cortex

ro O l ua EI PA DI DS Bu m Hy p Hy o p Cy er to D La tA B Y leb - 27 63 2 No c

Ions channels Osmotic

ro O l ua EI PA DI DS Bu m Hy po Hy p Cy er to D La tA B Y leb - 27 63 2 No c

a

FIGURE 3 Cell volume is determined by spread area. The cell volume (a) and cell height (b) decrease exponentially with spread area. The expression of the fitting curve is shown on top. Error bars represent the standard deviations (n ¼ 11
17). To see this figure in color, go online.

Co nt

y = 3000.5exp(

a

FIGURE 4 The volume decrease is due to the efflux of water and ions under increasing cortex contraction. The cell volume (a), spread area (b), and cell height (c) of cells adhered to glass when cells are treated with the Naþ/Kþ ATPase inhibitor ouabain (Oua; 20 mM, n ¼ 20), the Naþ/Hþ channel inhibitor (EIPA; 10 mM, n ¼ 16), the Cl channel inhibitor disodium salt hydrate (DIDS; 10 mM, n ¼ 11), the NaþKþ/2Cl channel inhibitor bumetanide (Bum; 40 mM, n ¼ 20), hypotonic shock (water, 50%, n ¼ 16) or hypertonic shock (PEG, 20%, n ¼ 20), inhibitors of the cortex system (cytochalasin D (CytoD; 5 mM, n ¼ 20), latrunculin A (Lat A; 1 mM, n ¼ 12), blebbistatin (Bleb; 20 mM, n ¼ 20), and Y-27632 (20 mM, n ¼ 20)), and the microtubule inhibitor nocodazole (Noc; 2.75 mM, n ¼ 12). *p < 0.05, **p < 0.01, ***p < 0.001, NS: non-significant difference. Data were analyzed by one-way analysis of variance. MT, microtubule. To see this figure in color, go online.

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water and ions is disturbed. Thus, we speculate that these drug treatments do affect cell volume and spread area themselves, but they do not affect the regulatory mechanism that couples cell volume and spread area. Thus, the relation between volume and spread area remains unchanged.

Interestingly, the hypotonic shock results in remarkable cell volume increase, whereas hypertonic shock by PEG does not show a detectable effect on cell volume (Fig. 4 a). This might be because the water inside the cells adhered to glass has already been squeezed out by 50% compared to the cells on soft substrates (Fig. 1), and this result further confirms our previous observation about the existence of the minimal cell volume (Fig. 3 a). These results suggest that the efflux of ions and waters leads to the volume decrease of adherent cells. Some studies have reported that cells spreading on glass can still decrease their volume after the hypertonic shocks (18,26), contrary to our observation. We speculate that this discrepancy may be due to different cell types or different experimental conditions. If cells do not have enough time to spread and reach the minimal cell volume before the osmotic shocks, they can still decrease their volume after the hypertonic shocks. It has been shown that cortical contraction may have a critical influence on cell volume (32,43). To test this idea, we examine the cell volume of 3T3 cells cultured on glass in the presence of various perturbations of the cell cortex. We find that when we treat cells with cytochalasin D or latrunculin A to depolymerize actin filaments, with blebbistatin to inhibit myosin II contraction, or with Y-27632 to inhibit ROCK activity, the cell volume of adherent cells significantly increases (Figs. 4 a and S9) and the cell spreading is blocked (Fig. 4 b). In contrast, the perturbation of microtubule dynamics by nocodazole does not affect the cell volume and spread area. Therefore, we conclude that cortical contraction is required for the volume decreases. After various drug treatments, the cell volume and cell height obey the same exponential decay with the spread area (Fig. 3 a, empty squares). The minimal cell volume and cell height are limited by the dry mass of the cell, and they should be the same for the same cell type no matter whether or not the cortical contraction or the transport of a

Theoretical model Cellular volume and pressure regulation

To further probe the link between the substrate properties and cell volume, here we propose a theoretical model by considering cellular volume regulation, cell shape, surface tension, and the rigidity-sensing mechanism. Considering the transport of water and ions, the time evolutions of cell volume V and ion number n inside the cell are modeled as (43)

Πin Pin z

I

Close

T

θ0

θ0

membrane ligand-receptor bond

non-specific repulsion

separation l Substrate

II Extracellular Tension

Ion pump ATP

ADP+Pi

Extracellular

f

f

kb ks

Intracellular

MS channels

T

θ

Open

Tension

(2)

The cell shape is determined by the force-balance condition. The force condition along a section of cell radius r is

ra

MS channel

Extracellular

Intracellular

r

dn ¼ Aeff ðJout þ Jin Þ; dt

Cell shape, effective cell surface area, and cellular volume

Pout

θ0

(1)

where Aeff is the effective surface area without considering the adhesion area. Lp is the membrane permeability rate to water. DP ¼ Pin  Pout and DP ¼ Pin  Pout are the hydrostatic and osmotic pressure differences across the membrane, respectively (Fig. 5 a). Jout is the ion efflux due to the opening of mechanosensitive channels (Fig. 5 a, I), and Jin is the influx of ions through active pumps (Fig. 5 a, II). The detailed derivation of Jout and Jin are given in the Supporting Material.

b

Ions Membrane Actin Myosin MS channels Ion pumps Πout

dV ¼ Lp Aeff ðDP  DPÞ; dt

f

k1 =

kb k s kb + k s

rest length l1 < l

f'

f'

k2

rest length l2 > l

Intracellular

FIGURE 5 Schematic of the theoretical model. (a) The adherent cell is enclosed by the actomyosin cortical layer and cell membrane. The cell shape can be described by rðqÞ and zðqÞ, where q is the tangential angle. ra and q0 are the adhesion radius and contact angle, respectively. Pin and Pout are the osmotic pressure inside and outside the cell, and Pin and Pout are the hydrostatic pressure inside and outside the cell. Embedded in the membrane are several families of passive mechanosensitive (MS) channels (light blue ellipses) and active ion pumps (purple ellipses). (Inset I) The MS channels open under tension and then release ions. (Inset II) The ion pumps consume energy to actively transport ions across the cell membrane. (b) The connection between ligand-receptor bond and substrate is modeled as two springs in series with equivalent stiffness k1 and rest length l1 . kb is the stiffness of the ligand-receptor bond and ks is the stiffness of the substrate. The repulsive force between cell and substrate is also modeled as a compressive spring with stiffness k2 and rest length l2 . To see this figure in color, go online.

682 Biophysical Journal 114, 675–687, February 6, 2018

Substrate Properties Tune Cell Volume

DPpr 2 ¼ 2prT sin q;

(3)

where r is the cell radius, T is the surface tension, and q is the tangential angle (Fig. 5 a). In particular, at the adhesion surface, the force balance condition reduces to DPpra2 ¼ 2pra T sin q0 , where ra is the adhesion radius and q0 is the contact angle (Fig. 5 a). Based on these force-balance conditions, we obtain the radius of the cell as a function of the tangential angle rðqÞ ¼

sin q ra : sin q0

(4)

Combining Eq. 4 and dz=dr ¼ tan q, we can obtain dz=dq ¼ rðqÞ. Integrating z over q, we obtain zðqÞ ¼ ra cos q=sin q0 þ C, where C is an integral constant and can be determined by zðq0 Þ ¼ 0. Therefore, we get C ¼ ra =tan q0 . The cell shape found in experiment is nonaxisymmetric, but here we assume an axisymmetric cell shape to simplify the problem. It would be interesting in the future to consider a more sophisticated theory with a complicated cell shape. We can obtain the effective cell surface area and cellular Rp volume by integration as A ¼ 2prðqÞdz=sin q, and eff q0 Rp V ¼ q0 pr 2 ðqÞdz. In terms of adhesion radius ra and contact angle q0 , the effective surface area and cellular volume are Aeff ¼

V ¼

2pra2 ð1 þ cos q0 Þ; sin2 q0

pra3 ð8 þ 9 cos q0  cos 3q0 Þ: 12 sin3 q0

(5)

(6)

Membrane stress and cortical stress

The stress of cell surface includes two parts, the active stress, sa , from the contraction of myosin motors and the membrane stress, sm , from the deformation of the membrane. We take an elastic deformation theory to describe the passive deformation of the membrane. Therefore, the constitutive law of membrane is sm ¼ Em ðA=A0  1Þ, where Em is the Young’s modulus of the cell membrane, A and A0 are the deformed and reference surface areas, respectively. The active contraction stress, sa , is directly proportional to the concentration of activated myosin, M, with sa ¼ smax M, where smax is the maximum active stress when all of the myosins are activated. The surface tension of the cell is T ¼ Tcortex þ Tm (34,35,44), where Tcortex is the cortical tension, and Tm is the membrane tension. We can define the surface stress, s, as sðhm þ hc Þ ¼ sa hc þ sm hm , where hm and hc are the thicknesses of the membrane and cortical layer, respectively.

Many experiments have indicated that cells exert stronger contraction force against stiffer substrates (6,45). It has also been shown that the Rho family of GTPases can regulate myosin contraction by controlling the activation of the myosin light chain (46,47). Rho can be activated by several guanine exchange factors that localize mainly at the plasma membrane (48). Therefore, the membrane stress can affect the activation of Rho. Furthermore, there is a feedback mechanism between membrane stress and cortical contraction (49). The membrane stress can change the cortical contraction by affecting the activation of Rho. In turn, the change of cortical contraction can regulate the membrane stress. The feedback loop between the active contraction force and the activated Rho can be described as (49) dR ¼ a1 Pðsm Þð1  RÞ  d1 R; dt

(7)

dM ¼ a2 ð1  MÞR  d2 M; dt

(8)

where R and M are the percentages of activated Rho and myosin; a1 and d1 are the activation and deactivation rates of Rho, respectively; and a2 and d2 are the myosin assembly and disassembly rates, respectively. Pðsm Þ is an activation function of Rho, which depends on the membrane stress, sm . We assume that Pðsm Þ ¼ 0 when sm < smc , Pðsm Þ ¼ ðsm  smc Þ=ðsms  smc Þ when smc < sm < sms , and Pðsm Þ ¼ 1 when sm > sms . smc is the critical membrane stress at which Rho activation starts and sms is the saturating stress at which all the Rho molecules are activated. The rigidity-sensing mechanism

To detect the mechanical properties of the substrate, adherent cells exert traction forces to the underlying substrate (50,51). When a tensile force is exerted on a ligand-receptor bond tethered to the substrate, both the ligand-receptor bond and the substrate are deformed simultaneously. Therefore, the connection between this bond and the substrate is modeled as two springs in series (52,53) (Fig. 5 b). kb and ks are the spring constants of the ligand-receptor bonds and the underlying substrate, respectively. ks is related to the Young’s modulus of substrate, Es , by (54) ks ¼

4pRc Es ; 7ð1 þ nÞð1  nÞ

(9)

where Rc is the radius of the contact area over which the ligand-receptor bond applies a force to the substrate and n is the Poisson’s ratio of the substrate. Since the springs are in series, the equivalent spring stiffness is k1 ¼ kb ks =ðkb þ ks Þ (Fig. 5 b). We further assume that the rest length of this equivalent spring is l1 .

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G ¼ shð1  cos q0 Þ;

The ligand-receptor bonds can repeatedly bind and unbind. The rate equation of the ligand-receptor bond density, rlr , is given by (55–57) drlr ¼ kon ðrr  rlr Þ  koff rlr ; dt

(10)

where rr is the total receptor density in the adhesion surface. kon and koff are the association and dissociation rates, respectively. We assume that the dissociation rate koff behaves like catch-slip bonds described by the classical two-pathway model (58–60), koff ¼ kc0 expð  ac f =kB TÞ þ ks0 expðas f =kB TÞ;

(11)

where f is the traction force exerted on each bond, kc0 and ks0 are the dissociation rates of the catch bond and slip bond when f ¼ 0, ac and as are the characteristic lengths of the catch bond and slip bond, respectively, kB is the Boltzmann constant, and T is the absolute temperature. The association rate kon is assumed to depend on the separation distance between the cell surface and substrate l (Fig. 5 b) as  2  0 (12) kon ¼ kon exp  ðl  l1 Þ l ; 0 where kon is the rate constant and l is the characteristic length scale measuring how fast bond association decays with increasing surface separation. Besides the ligand-receptor bonds, there generally exist non-specific repulsive forces between cells and substrates. For example, the electrostatic forces result from the glycocalyx layer (61). These glycocalyx molecules can be modeled as springs with stiffness k2 and rest length l2 , which is bigger than l1 (Fig. 5 b) (62). These glycocalyx repellers are assumed to be immobile, with a constant area density equal to rg . From the force equilibrium equation, rlr k1 ðl  l1 Þ þ rg k2 ðl  l2 Þ ¼ 0, we have the equilibrium separation

l ¼

rlr k1 l1 þ rg k2 l2 : rlr k1 þ rg k2

(13)

Therefore, the traction force, f, applied on each ligand-receptor bond is f ¼ k1 ðl  l1 Þ ¼

k1 k2 rg ðl2  l1 Þ : rlr k1 þ rg k2

(14)

Other studies have shown that the magnitude of this traction force is a function of substrate stiffness so that cells can sense the rigidity of substrate (63–65). The adhesion between cell and substrate can be described by the Young-Dupre equation,

684 Biophysical Journal 114, 675–687, February 6, 2018

(15)

where G is the adhesion energy density, q0 is the contact angle, and s and h are the stress and thickness, respectively, of the surface layers. The adhesion energy density, G, includes two parts, the chemical term, Gc , and the mechanical term, Gm , i.e., G ¼ Gc þ Gm (53,66). We assume that Gc is constant, whereas Gm comes from the elastic energy of the ligand-receptor bonds and the underlying substrate and therefore can vary with substrate stiffness. From the elastic energy of the springs, Gm can be given as 1 1 Gm ¼ rlr k1 ðl  l1 Þ2 þ rg k2 ðl  l2 Þ2 : 2 2

(16)

By using Eq. 13, Gm reduces to Gm ¼

1 k1 k2 rlr rg 2 ðl2  l1 Þ : 2 rlr k1 þ rg k2

(17)

We can obtain the theoretical results in Figs. 1 and 2 by solving the 17 coupled differential-algebraic equations of the Theoretical Model. Specifically, for the theoretical results in Figs. 1 and 2, we vary the corresponding control variables, such as the substrate stiffness, Es , in Eq. 9, ra in Eqs. 5 and 6, and G in Eq. 15. It can be seen that our theoretical results agree with the experimental measurements very well (Figs. 1 and 2, black curves). As shown in Fig. S10, the number of connective receptor-ligand bonds between cell and substrate increases with substrate stiffness, and the mechanical adhesion energy density, Gm , is bigger for stiffer substrate. As shown in Fig. 1 c, the cell spread area approaches a nonzero constant on very soft substrate, and the cell height is smaller than the diameter of suspension cells. This is because on very soft substrate, Gm is nearly zero (Fig. S10 b; Eq. 17), but the contribution of Gc still exists. Therefore, the spread area approaches a constant as the substrate stiffness goes to zero. DISCUSSION In summary, combining experiments and theory, we propose a mechanism for active cellular volume regulation induced by the mechanical and physical properties of substrate, such as substrate stiffness, available spread area, and effective adhesion energy density. As illustrated in Figs. 6 and S11, when these parameters increase, the spread area becomes larger. Thus, the traction forces between cell and substrate become bigger, which induces higher cortical tension. The increasing tension results in more open mechanosensitive channels and efflux of ions accompanied by efflux of water. Therefore, the stronger cell-substrate interaction squeezes more water and ions out so that the cell volume can decrease by >50%.

Substrate Properties Tune Cell Volume Substrate stiffness Available spread area Adhesion energy density

Cell-substrate interaction

Cell volume

Cortical tension

Traction force

Increasing cortical tension results in more open MS channels.

ion tension

MS channels

tension

tension

close

Weak interaction

tension

open

Intermediate interaction

Cell volume

Strong interaction Cortical tension

Nucleus

Ions

Traction force

Membrane

Water

Cortical tension

Actin

MS channels

Ions efflux

Membrane-cortex linkers

Ion pumps

Water efflux

To some extent, the adhesion between cell and substrate is similar to the compression of cells by external forces (32), since both of them force the cell to contact the substrate. The strength of cell-substrate interaction is the counterpart of the amplitude of external forces. It has been predicted that the larger the external force is, the smaller the cell volume becomes due to the efflux of water and ions (43). Similarly, here we demonstrate that the stronger the cellsubstrate interaction is, the smaller the cell volume becomes (Fig. 6). Thus, we term this the ‘‘mechanism of adhesioninduced compression of cells.’’ This idea can also be applied to other systems. In fact, when porous vesicles are subjected to hypertonic shocks, water would flow out and this would induce the spreading of these vesicles (67). Experiment shows that if the cell volume does not decrease, the high tension can induce the rupture of red blood cells due to the strong adhesion between cell and substrate (68). The interior of cells is a very crowded environment and here we show that the adhesion of cells to substrate will make it much more crowded. Therefore, many cell functions and behaviors, such as protein folding, cell metabolic activities, gene expression, and cell mechanical properties, should be significantly influenced by the cell volume change since all of them greatly rely on the water content inside the cell. Therefore, it is of great interest and importance to understand how the cell volume is regulated by the mechanical properties of microenvironments. Our work highlights the importance of taking cell volume into account when interpreting the effects of substrate

FIGURE 6 Mechanism of adhesion-induced compression of cells. As the cell-substrate interaction (characterized by substrate stiffness, available spread area, and adhesion energy density) becomes stronger, the spread area becomes larger so that the traction force (purple arrows) and cortical tension (green arrows) increase. The higher cortical tension leads to more open mechanosensitive channels and squeezes water and ions out. As a result, the efflux of water and ions (blue and pink arrows) increases and the cell volume decreases. The magnitudes of all the forces are denoted by the thickness of the arrows. To see this figure in color, go online.

properties on cell functions. For instance, our findings have important implications for durotaxis and haptotaxis, where cells migrate on the substrate with heterogeneous stiffness or adhesion. We have already shown that the cell volume may decrease by >50% when the stiffness or the effective adhesion energy of substrates increases. Therefore, the volume changes induced by these heterogeneous mechanical properties may provide a driving force for these directed cell migrations, since the transport of water and ions is closely related to cell migration (25,27). The volume changes we found here are also accompanied by the changes in membrane area and membrane tension. Other studies have shown that the increase in membrane tension can reduce endocytosis and increase exocytosis (69–71). Thus, by regulating exocytosis and endocytosis, the changes in cell volume and membrane tension may further affect membrane trafficking. Exocytosis and endocytosis can further change cell volume, membrane area, and membrane tension (33). Thus, it is interesting to further study the influences of substrate properties on exocytosis and endocytosis, and the feedback of membrane trafficking on cell volume regulation. Our results also indicate the importance of cell volume regulation in rigidity sensing and cell-fate determination. It has been shown that the increase in substrate stiffness can lead to an increase in the cytoskeletal tension and then regulate the YAP/TAZ ratio (72). However, here we show that the changes in substrate properties are accompanied by dramatic cell volume changes, which implies that

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the properties of substrate may indirectly affect rigidity sensing or cell fate (7,9,10) through regulating the cell volume. Indeed, the cell volume may regulate the transcriptional rate of cells (21). Therefore, our research raises one critical question, how volume regulation affects various cell functions and directs cell fate, and further experimental explorations are needed to answer this question. SUPPORTING MATERIAL Supporting Materials and Methods, eleven figures and one table are available at http://www.biophysj.org/biophysj/supplemental/S0006-3495(17) 35047-6.

AUTHOR CONTRIBUTIONS K.X. and Y.Y. contributed equally to this study. H.J. initiated and supervised the project. Y.Y. and H.J. conceived the theory. K.X. performed experiments. All authors analyzed the data and wrote the manuscript.

ACKNOWLEDGMENTS This work was partially carried out at the University of Science and Technology of China Center for Micro and Nanoscale Research and Fabrication. This work was supported by the National Natural Science Foundation of China (grants 11472271 and 11622222), the Thousand Young Talents Program of China, Fundamental Research Funds for the Central Universities (grant WK2480000001), and the Strategic Priority Research Program of the Chinese Academy of Sciences (grant XDB22040403).

SUPPORTING CITATIONS References (73–80) appear in the Supporting Material.

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