Controlling Cellular Volume via Mechanical and Physical Properties of Substrate  Kenan Xie, Yuehua Yang, Hongyuan Jiang  Biophysical Journal  Volume 114, Issue 3, Pages 675-687 (February 2018) DOI: 10.1016/j.bpj.2017.11.3785 Copyright © 2017 Biophysical Society Terms and Conditions

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 μm. (c–e) The spread area, cell height, and cell volume, respectively, as a function of substrate stiffness (n = 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, Γc, 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 μm. (g and h) The time-dependent changes of cell spread area and cell volume during dynamic cell spreading (n = 13∼15). Error bars represent the standard deviations. To see this figure in color, go online. Biophysical Journal 2018 114, 675-687DOI: (10.1016/j.bpj.2017.11.3785) Copyright © 2017 Biophysical Society Terms and Conditions

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 μm. (c and d) The cell volume, spread area, and cell height for different-sized adhesive islands (n = 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, Γeff, 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 Γeff=Γia2/b2 or Γeff=Γi(1−a2/b2), where Γi 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 μm. (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 = 11∼14). Error bars represent the standard deviations. To see this figure in color, go online. Biophysical Journal 2018 114, 675-687DOI: (10.1016/j.bpj.2017.11.3785) Copyright © 2017 Biophysical Society Terms and Conditions

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 = 11∼17). To see this figure in color, go online. Biophysical Journal 2018 114, 675-687DOI: (10.1016/j.bpj.2017.11.3785) Copyright © 2017 Biophysical Society Terms and Conditions

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 Na+/K+ ATPase inhibitor ouabain (Oua; 20 μM, n = 20), the Na+/H+ channel inhibitor (EIPA; 10 μM, n = 16), the Cl− channel inhibitor disodium salt hydrate (DIDS; 10 μM, n = 11), the Na+K+/2Cl− channel inhibitor bumetanide (Bum; 40 μM, n = 20), hypotonic shock (water, 50%, n = 16) or hypertonic shock (PEG, 20%, n = 20), inhibitors of the cortex system (cytochalasin D (CytoD; 5 μM, n = 20), latrunculin A (Lat A; 1 μM, n = 12), blebbistatin (Bleb; 20 μM, n = 20), and Y-27632 (20 μM, n = 20)), and the microtubule inhibitor nocodazole (Noc; 2.75 μM, n = 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. Biophysical Journal 2018 114, 675-687DOI: (10.1016/j.bpj.2017.11.3785) Copyright © 2017 Biophysical Society Terms and Conditions

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 r(θ) and z(θ), where θ is the tangential angle. ra and θ0 are the adhesion radius and contact angle, respectively. Πin and Πout 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. Biophysical Journal 2018 114, 675-687DOI: (10.1016/j.bpj.2017.11.3785) Copyright © 2017 Biophysical Society Terms and Conditions

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. Biophysical Journal 2018 114, 675-687DOI: (10.1016/j.bpj.2017.11.3785) Copyright © 2017 Biophysical Society Terms and Conditions