Nature Protocols: doi: /nprot Supplementary Figure 1

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1 Supplementary Figure 1 Photographs of the 3D-MTC device and the confocal fluorescence microscopy. I: The system consists of a Leica SP8-Confocal microscope (with an option of STED), a confocal PC, a 3D-MTC PC and a 3D-MTC; II to V: the steps of loading a cell-containing sample; VI: the current (magnetic field) control box for 3D-MTC.

2 Supplementary Figure 2 Schematic for the three-dimensional (3D) coils. (a) Schematic for the auto temperature controller of 3D coils. The auto temperature controller provides a low flow rate of 37 air to mitigate the potential local heating problem. (b) The size of 3D coils and stage. X and Y coils internal diameters are 4.1 cm and their external diameters are 6 cm; Z coils internal diameters are 5.1 cm and their external diameters are 7 cm. The coils thicknesses are 1 cm each. The stage top dimension are 16 cm x 11 cm x 0.5 cm, bottom dimensions are 15 cm x 10 cm x 0.5 cm. (c) Top view of the Z coils and dish. The diameter of the cell culture dish is 3.5 cm. In the top view, the lateral distance from the dish boundary to the Z coil is 0.8 cm.

3 Supplementary Figure 3 Displacement quantification method. (a) Flow chart of the image correlation method (ICM). (b) At each level the displacement field is estimated by using image A and image B. Image B is deformed by the displacement field calculated at the previous level. Succeeding levels have finer spatial resolution and smaller window size. Corr, calculation of cross-correlation; check, checkpoint; interp, interpolation 48. (c) GFP-H2B fluorescence image. Nucleus is outlined with a dashed line. (d) Displacement map image of the same nucleus.

4 Supplementary Figure 4 Nuclear H2B displacements influenced by stress directionality. A different cell from that in Fig. 4. From left to right: bright-field images of the cell, GFP-Histone 2B fluorescence images, and displacement map images of the same murine melanoma B16 cell. Nucleus is outlined with a dashed line. The thick white arrows point to the bead; the red arrows indicate direction of the bead displacement; the color bar indicates the displacement magnitude. (a) No applied stress (non-magnetized); (b) Magnetizing in Z axis and apply a 15 Pa torque (0.1Hz) in Y axis bright-field images; (c) Magnetizing in Z axis and apply a 15 Pa torque (0.1 Hz) in X axis bright-field images; (d) Magnetizing along Z axis and apply a 9 Pa along X axis and 12 Pa along Y axis (the resultant stress is 15 Pa and stress angle is 36.9 ). (e) Magnetizing along Z axis and apply a 10.6 Pa along X axis and 10.6 Pa along Y axis (the resultant stress is 15 Pa and stress angle is 45 ). (f) Magnetizing along Z axis and apply a 12 Pa along X axis and 9 Pa along Y axis (the resultant stress is 15 Pa and stress angle is 53.1 ). The white square in each displacement map is enlarged and presented on the right (the 4 th image in each row) to show the differences of the displacements between each loading direction (a-f) at the same loading magnitude. It is apparent that stress angles (loading directions) are important in resulting major differences in GFP-H2B displacements. The thin white arrow (150 nm) provides a scale for the magnitudes of the red arrows. Image acquisition time is 1 second per image. Scale bars, 7.5 µm. (g) Computed cell stiffnesses (complex moduli) for this cell at different forcing directions.at different forcing directions.

5 Supplementary Figure 5 H2B strains depend on force directions. This is the same cell as in Supplementary Fig. 4. The bulk strains and shear strains were computed from displacement maps of the nucleus in Supplementary Fig. 4. (a) Stress angle of 0. (b) Stress angle of (c) Stress angle of 45. (d) Stress angle of (e) Stress angle of 90. It is obvious that strain maps are different, with the 90 -stress angle generating highest strains.

6 Supplementary Figure 6 Improved displacements quantification via 3D-MTC with STED. A living CHO cell was plated on collagen-1 coated dish overnight. A magnetizing field was applied along Z-axis and a twisting field was applied along X-axis (the short axis of the cell). The top panel is the data of GFP-H2B of the nucleus via a confocal microscope. The bottom panel is the data of the same cell under the same stress conditions quantified with a STED. Parameters for STED are: STED laser power (90 %) is 810 mw; the STED laser is CW (continuous wave) phase pattern; the excitation laser wavelength is 488nm; the STED depletion laser wavelength is 592 nm; scanning method is beam scanning. The scanning speed is 1000 Hz (1000 lines per sec). The 90 % STED power was estimated to be reduced to ~64.8 mw at the objective lens. (a) The GFP-H2B image of whole nucleus. The white box is the enlarged area. The top left of confocal image is the brightfield image of the same cell, the black dot is an RGD-coated magnetic bead. (b) Enlarged GFP-H2B images. (c) Full Width at Half Maximum (FWHM) of the fluorescence images. Confocal FWHM is 251 nm; STED FWHM is 118 nm. (d) Histograms of the fluorescence counts (with a Gaussian fit) at various FWHMs using confocal or STED. FWHM of confocal is ± 1.03 nm, of STED is ± 0.55 nm; mean ± s.e.m., 100 GFP-H2B spots were measured that were near the GFP-LacI spots next to the DHFR gene locus 19. P<0.001 when comparing FWHM of confocal with that of STED. (e) A 15-Pa stress was applied at 0.3 Hz and peak displacement map was computed (displacement). The white box is the enlarged area. (f) Enlarged displacement maps. The black arrow (150 nm) represents the scale for the displacement magnitude. Image acquisition time is 320 millisecond per image. Comparing the white box of H2B fluorescence via STED with that via confocal, one could see better spatial resolution of the GFP-H2B images. FWHM of the PSF is 118 nm, better than the ~185 nm resolution using the re-scan confocal microscopy 1. Comparing the white box of the displacement map via STED with that via confocal, improved displacements were also noticed. Several other cells showed similar trends.

7 Supplementary Figure 7 Lateral resolutions of confocal microscopy and STED. Full Width at Half Maximum (FWHM) of Point Spread Function (PSF) is defined as Lateral resolution. 0%, confocal fluorescence microscopy only; 30%, 30 % depletion laser power of 270 mw (reduced to ~21.6 mw at the objective lens); 60 %, 60 % depletion laser power of 540 mw (reduced to ~43.2 mw the objective lens); 90%, 90 % depletion laser power of 810 mw (reduced to ~64.8 mw at the objective lens). Mean + s.e.m.; n= 11 cells (each data point is an average value from multiple GFP-H2B measurements near the DHFR gene locus in a cell); the same cells were imaged by confocal microscopy first and then by STED. 3 independent experiments. P <0.001 between data from any two laser powers. The line is a fit from the inverse square root law.

8 Supplementary Figure 8 Nuclear H2B fluorescence images and displacement maps under different conditions. This cell is a representative cell in Supplementary Fig. 7. First row: brightfield images. White dashed lines are outlines of the nucleus. White arrow points to the magnetic bead. Second row: H2B fluorescence images. Note that the magnetic bead did not block the optical path because the bead was not in the optical path between the laser and the sample. Third row: H2B displacement maps when 15 Pa stress at Hz was applied. The pink arrow represents the magnitude and direction of the magnetic bead displacement. Bottom row: enlarged displacement maps corresponding to the white boxes above. (a) No-applied-stress (non-magnetized) confocal images. (b-e) Magnetizing in Z axis and applying a twisting field to induce 15 Pa stress at Hz along X-axis (the short axis of the cell); (b) image obtained with confocal microscopy. Full Width Half Maximum (FWHM) of the fluorescence image PSF is 279 nm; (c) image with 30% STED power (~21.6 mw). The FWHM is 198 nm; (d) image with 60% STED power (~43.2 mw). The FWHM is 157 nm; (e) image with 90% STED power (810 mw) (reduced to ~64.8 mw at the objective lens). The FWHM is 124 nm. Image acquisition time is 320 ms per image. Scale bars, 5 µm.

9 Supplementary Figure 9 STED power did not induce magnetic bead displacement. From left to right: bright-field images of the cell, GFP-Histone 2B fluorescence images, displacement map images and enlarged displacement maps. Nucleus is outlined with a dashed line. The thick white arrows point to the magnetized bead; the pink dot indicates the magnitude and direction of the bead displacement (<5 nm, suggesting no additional displacements by STED); the color bar indicates the displacement magnitude. (a) No applied stress in confocal images. The FWHM is 236 nm; (b) the same nucleus in 90% STED power (~64.8 mw) images. The FWHM is 120 nm. Image acquisition time is 320 ms per image. Scale bars, 5 µm.

10 Supplementary Figure 10 System description of 3D-MTC with confocal fluorescence microscopy. The platform of interfacing 3D-Magnetic Twisting Cytometry (3D-MTC) with the confocal fluorescence microscopy (with an option of stimulated emission depletion (STED) nanoscopy) includes three parts: magnetic field generator subsystem, monitoring and analysis subsystem, and observing subsystem. Each subsystem includes hardware equipment, interface board, control interface program or analysis modules.

11 Supplementary Method Quantification of cell stiffness 1) Complex shear modulus is defined as the ratio of shear stress to shear strain and it apply to Eq. (1). G φ Where σ is shear stress, ε is shear strain. 2) Torque per unit bead volume (the specific torque, Γ s )is defined as shown in Eq. (2). (1) s C H (2) Where C is magnetic moment constant of the beads, which may differ from batch to batch, and thus should be calibrated in a viscous fluid of known viscosity for each batch of beads. In the current study, C is calibrated to be 2 Pa/Gauss. H is the magnetic field strength; the coil s strength is measured as 25 Gauss/100 turns of coil, then for 3D-MTC (which has 180 turns of coil for each coil), H = 0.25 Gauss 180 = 45 Gauss. Thus, Torque per unit bead volume(γs) Γ s = C H = 2 Pa/Gauss 45 Gauss = 90 Pa 3) The total torque is defined by Eq. (3), and F is the total shear force acting the bead surface; see Eq. (4) T F D (3) F 2 4 r (4) Where r is magnetic bead s radius, D is magnetic bead s diameter; in this study, D is 4.5 m. Thus, substitute Eq. (4) into Eq. (3), one gets Eq. (5) T σ 4 π 3 2 4π r r 2r Γs 3 (5) Hence we can obtain shear stress with Eq. (5) (one can see that shear stress differs from the specific torque by a factor of 6): s C H 6 6 (6) 4) Cell shear strain is defined as ε by Eq. (7). ε * d d r (7) Where d is the displacement of a magnetic bead. 5) From Eq. (1), Eq. (6), and Eq. (7), we get Eq. (8). σ C H d C H r G (8) ε 6 r 6 d Since the actual shear stress on the cell surface depends on the contact area between the bead and the cell surface, we introduce a, a parameter of the contact area: 1

12 G β G β C H r 6 d (9) For a 40% embedment of the bead, = 2 (see ref. 46 for determining that is based on bead-cell contact area). For example: displacement of the magnetic bead d = 300 nm; r = 2250 nm; C = 2 Pa/Gauss;H = 45 Gauss, one can calculate the complex shear modulus or cell stiffness: β C H r G 6 d = 2 2 Pa/Gauss 45 Gauss 2250 nm/ (6 300 nm) = 225 Pa Reference. 1. De Luca, G.M. et al. Re-scan confocal microscopy: scanning twice for better resolution. Biomed Opt Express. 4, (2013). 2