posts, focusing on the posts' mean squared displacements (MSDs) to yield maps of the fluctuations and to identify those posts coupled to different components of the cytoskeleton, such as the stress fibers and the actomyosin cortex. Support Protocol 1 describes fabrication of the magnetic nanowires via electrodeposition in nanoporous templates. Support Protocol 2 describes how to configure the specific video acquisition software (Streampix) we employ for the magnetic rheology measurements. Note that Basic Protocols 4-6 are described in the context of special-purpose software written in Igor Pro (Wavemetrics) (available as online resource on Github). However, overviews of the principles involved are also provided should researchers wish to implement these protocols in other programming environments.

Basic protocol title: Fabrication of magnetic micropost arrays

This protocol describes how to use replica molding techniques to fabricate PDMS micropost arrays with magnetic Ni nanowires embedded in individual microposts. These nanowires have diameters of 350 nm, lengths of 5 µm, and average low-field magnetic moments µ = 0.15 pA m 2 , aligned along their long axes (Hultgren, Tanase, Chen, & Reich, 2004;Hultgren et al., 2005). This protocol assumes that the user can follow published protocols to make, or has access to, "master" versions of the arrays, which are typically made on silicon wafers by photolithographic techniques (Fu et al., 2010;Yang et al., 2011), and has followed published methods to cast "negative" PDMS molds of the desired micropost arrays (Tan et al., 2003;Yang et al., 2011). To make magnetic micropost arrays, magnetic Ni nanowires are positioned in the post forms (holes) in the negative molds and PDMS is cast around them, embedding the nanowires in the posts. The nanowires must be shorter than the length of the microposts or the magnetic microposts may be too stiff to bend in response to magnetic torques applied to the nanowires. The procedures described will yield approximately 1% of the posts containing magnetic nanowires for post arrays with1.8 µm post diameters and 4 µm center-to-center post spacing (Shi et al., 2019). Note that the magnetic microposts will be randomly distributed within the arrays. After the arrays are fabricated, they are removed from the molds in ethanol and dried using a critical point dryer to avoid collapsing the posts (Yang et al., 2011). The tips of the posts are functionalized with the extracellular matrix protein fibronectin via microcontact printing to promote adhesion of the cells to the micropost tips (Tan et al., 2003;Yang et al., 2011). Fibronectin works well for a variety of cell types, but other ECM proteins can be used if needed. The sides of the posts and the regions in between the posts are then blocked from cell adhesion by coating with Pluronics F-127. This is important as the conversion of micropost deflection to force depends on the cells' forces being restricted to the posts' tips (Fu et al., 2010;Tan et al., 2003). We note that nonmagnetic micropost arrays, produced via published protocols (Yang et al., 2011), are also used for some of the measurements described below.

1. Treat the molds with an oxygen plasma under a pressure of 450 mTorr at 100 W power for 90 s.

This is to enable functionalization of the mold surfaces in Step 2. It must be done before a mold is used for the first time and should be repeated every 3-5 times a mold is used.

2. Transfer the molds to a vacuum desiccator with a few drops of tridecafluoroctyltrichlorosilane on a glass cover slip. Pump to a rough vacuum and let stand overnight. This enables separation of the PDMS micropost arrays from the molds. This only needs to be done every 3-5 times a mold is used.

3. Select a pre-prepared solution of nanowires of the desired dimensions at a concentration of 10 6 /mL in ethanol.

The nanowires must be shorter than the length of the microposts or the magnetic microposts may be too stiff to bend in response to magnetic torques applied to the nanowires.

4. Sonicate the nanowire solution for 5 minutes.

5. Agitate the nanowire suspension in a vortex shaker for a few seconds.

The goal of these two steps is to break up any clumps of nanowires that may have formed due to magnetic attraction between the nanowires.

6. Arrange PDMS molds in a plastic petri dish (one mold per array desired).

7. Place rectangular-shaped rare-earth magnets under the petri dish, one under each of the molds.

The magnets should be placed flat with either their North or South poles pointing up. These magnets should remain under the molds until the molds have been filled with PDMS and are placed in the oven to be cured to keep the nanowires aligned vertically.

8. Pipette 30 μl of nanowire solution onto each mold.

The magnets underneath the molds will align the nanowires vertically in suspension and pull them into the holes in the mold that will form the microposts. If the nanowires are not aligned in this manner, they will not go into the post holes but will end up lying horizontally on the tops of the molds.

9. Wait for the solution to evaporate (20-30 min). This is to prevent to nanowires from flowing off the molds when the next drop is added.

10. Pipette another 30 μl of nanowire solution onto each of the molds and wait for it to evaporate.

11. Repeat until 180 μl of nanowire solution has been pipetted onto each mold. This should yield arrays with ~1% of the microposts containing nanowires.

12. Mix PDMS and curing agent in a 10:1 ratio in a Styrofoam cup.

Steps 12-15 can be done while waiting for the nanowire solution to evaporate from the molds . Prepare about 20 g of the PDMS mixture (e.g. use 20 g of PDMS and 2 g of curing agent.)

13. Stir the mixture with a spatula for about 3-4 minutes.

Stir until the bubbles disappear.

14. Pour the mixture into a 50 ml centrifuge tube and centrifuge for 5 minutes at 10 4 m/s 2 (5k rpm on the above system). This is to degas the PDMS to eliminate bubble formation that can lead to defects in the micropost structures.

15. Arrange cover glasses (one for each micropost array desired) on a plastic Petri dish and treat with ultraviolet (UV)/ozone for 7 minutes. This oxidizes the surface of the glass to promote bonding of PDMS to it.

16. Add a drop of PDMS onto each mold from Step 11.

The magnets should still be under the dish the molds are in.

17. Press a UV-treated cover glass onto each of the molds.

18. Degas the molds in a vacuum desiccator for 5 minutes.

19. Bake the molds at 65°C on a hot plate for 1 hour. This hardens the PDMS microposts sufficiently so that the nanowires do not move during subsequent processing.

Do not put the magnets in the curing oven.

21. Flip the molds over so the cover glasses are on the bottom.

22. Bake the dish with the cover glasses in a curing oven set to 70 °C overnight. This cures the PDMS. Make sure to keep the Petri dish level so the molds do not slide off the PDMS before it cures.

23. Remove the Petri dish and devices from the oven, allow to cool and add 100% ethanol to the dish until the cover glasses are completely immersed.

The molds do not need to be completely immersed.

24. Use tweezers to twist the molds off the cover glasses.

Keep the cover glasses with the MPAD arrays immersed in the ethanol during this process.

At this stage, the physical fabrication of the magnetic MPADs is complete. In subsequent handling, care must be taken not to damage the micropost arrays. In particular, arrays that are wet (e.g., in ethanol, water or PBS) must not be allowed to dry out as the surface tension of the drying front can knock down the microposts. A critical point dryer must be used to dry the arrays.

This procedure is described in (Yang et al., 2011).

26. Stamp fibronectin on the post tips via micro-contact printing and coat the non-stamped regions of the arrays with F127 Pluronic. This will promote cell adhesion to the post tips and prevent cell adhesion on the sides of the posts and other surfaces of the arrays. This is important as the conversion of post deflections to force depends on the assumption that cells are adherent only on the post tips. Procedures for these steps are described in (Yang et al., 2011).

27. Store fibronectin and Pluronic coated arrays in PBS until used.

Arrays should be used within 24 h after coating to avoid deterioration of the fibronectin coatings.

This protocol describes the fabrication of the nickel nanowires used to make the microposts magnetic. The nanowires are made by electrodeposition in nanoporous templates (Felton, 2009;Hultgren et al., 2005;Kramer, 2009;Rovner, 2013). The templates used are commercial 50 µm thick alumina filter membranes. These membranes have nominal pore diameters of 100 nm, but only have this diameter in a small region 3-5 µm thick near the bottom of the membrane. For most of their length, their diameter is 350 nm, which sets the diameter of the nanowires. The length of the nanowires is controlled by how much Ni is deposited into the pores. For the microposts described in this protocol, the desired nanowire length is 5 µm. (The deposition procedure typically allows the length to be controlled to ±10%.) A copper film is sputter-deposited onto the bottom side of the filter membranes to seal the ends of the pores in the template and serve as a working electrode for the electrodeposition. Note that thermal evaporation of Cu has been found to not seal the pores adequately. A thin layer of Cu is electrodeposited first to fill the narrow (100 nm diameter) end sections of the pores, and then Ni is deposited to produce the desired magnetic nanowires. The Cu is removed using a copper etchant and the template is dissolved in KOH to release the nanowires. The wires may be stored for extended periods in ethanol or isopropanol prior to use.

Alumina filter membranes, nominal pore size 100 nm, 60 µm thickness (Anodisc 47, Whatman Inc.) Copper sputter target Argon gas Acetone Isopropanol Cu plate, 0.25" thick, approx. 2.5" square DI water Copper electrodeposition solution: 125 g/L CuSO4 •5H2O, 30 g/L H3BO3, 20 g/L NaCl in DI water. Nickel electrodeposition solution: 514 g/L Ni(SO3NH2)2•4H2O, 20 g/L NiCl2•6H2O, 20 g/L H3BO3 in DI water. 0.5 M KOH solution in DI water Glass vials or glass test tubes Sputter deposition system Teflon electrodeposition chamber (cylinder with open bottom) Spring clamp Blow torch Pt counter electrode, consisting of Pt mesh attached to a Pt wire Ag/AgCl reference electrode (Bioanalytical Systems, Inc. MF-2052) Potentiostat (Princeton Applied Research, model 263A or equivalent) Computer to control potentiostat Single-edge razor blades Temperature controlled water bath (Neslab RTE-211, or equivalent) Sonicator (Branson 1510, or equivalent)

1. Clean alumina templates by rinsing in acetone and isopropanol.

2. Sputter deposit a layer of Cu 500 nm thick on the side of the alumina templates with the nominal pore diameter (the back side).

Exact procedures to do this will depend on the details of the sputtering system used, but will typically be done in 5 mTorr of argon gas. In our system, a sputtering current of 50 mA and a deposition time of 25 min yielded the desired layer thickness. This layer should not be too thick to facilitate its removal at the end of the nanowire fabrication procedure. If this layer is too thick, Cu will adhere to the tips or the nanowires or the alumina will not be completely dissolved.

3. Rub one side of the Cu plate thoroughly with sandpaper to remove its surface oxide. This provides a clean surface to make good electrical contact with the Cu film on the template.

4. Rinse the Cu plate with DI water.

5. Place the filter template Cu-side down on the Cu plate.

6. Rinse a rubber o-ring with DI water and place it on the top of the filter template.

The o-ring should be sized to the diameter of the deposition chamber.

Teflon electrodeposition chamber on top of the o-ring, and clamp it to the Cu plate with a spring clamp. The electrodeposition chamber should have the form of a hollow cylinder, as the bottom is formed by the filter template and the Cu plate, which together serve as the working electrode. It is important that a good seal is formed by the o-ring so that with the filter template/Cu plate forming the bottom of the electrodeposition chamber, no liquid can leak out. A flange on the bottom end of the Teflon tube to allow mating to the spring clamp is helpful.

8. Rinse the chamber with DI water. 9. Fill the chamber with Cu electrodeposition solution.

10. Preclean the Pt counter electrode by placing it briefly in the flame of a blow torch and then washing it in DI water.

11. Insert an Ag/AgCl electrode in the deposition solution to serve as a reference electrode.

12. Connect the Pt electrode, Ag/AgCl reference electrode and the Cu plate to the potentiostat.

13. Deposit Cu to fill the bottom 3-5 µm of the pores, using a reference potential of -0.2 V.

For the diameter of our deposition chamber, approximately 1 Coulomb of copper deposits 1 µm in the pores. The goal is to just fill the bottom, thinner section of the pores.

14. Pour off the spent Cu deposition solution and rinse the deposition chamber and electrodes in DI water to remove any remaining electrolytes.

15. Fill the chamber with the Ni deposition solution.

16. Deposit Ni into the pores to the desired length of the nanowires, using a reference potential of -1 V.

For the microposts we typically use, the desired length is 5 µm. Note that in our deposition system, we find deposition rates of 2-3 C/µm of Ni in the pores. 17. Pour off the spent Ni deposition solution and rinse the deposition chamber and electrodes in DI water.

18. Remove the filter membrane from the apparatus.

19. Cut away the sections of the filter template that were not electrodeposited into with a razor blade.

20. Place the section of the filter membrane containing the nanowires in a Petri dish, Cu side up.

21. Rub the filter membrane with a Q-tip soaked in Cu etching solution to remove the Cu. Repeat until all traces of the Cu are gone. This process can take 20-30 min and will require the use of multiple Q-tips. The template should turn completely black when all the Cu is removed.

22. Place the template with the nanowires in a glass vial or test tube.

23. Fill the vial (or test tube) with 0.5 M KOH in water. KOH will dissolve the alumina of the filter membranes but will not affect the Ni nanowires.

24. Seal the vial with parafilm and place the vial in a water bath at 60 °C for 4-6 h or overnight.

25. Sonicate the vial and nanowire suspension for 10 min. This will help break up clumps of filter material and nanowires.

26. Place one or more rare earth magnets against the side of the vial for approx. 5 min. This will collect the nanowires by attracting them to the magnet. The magnet should immobilize the nanowires against the inside wall of the vial.

27. Decant the KOH solution and replace with fresh KOH solution, while keeping the magnet in place.

It is important that the magnet not move from its position on the side of the vial during these steps or nanowires may be lost when the solution is decanted. The magnet may be taped to the vial or a collar that holds the magnet and fits tightly around the vial may be constructed.

28. Reseal the vial with parafilm and place the vial in a water bath at 60 °C for another 4-6 h.

29. Sonicate the vial for 10 min and shake gently by hand.

30. Collect and immobilize the nanowires again by places one or more rare earth magnets against the side of the vial for approx. 5 min.

31. Decant the solution and replace with DI water to wash the nanowires.

32. Repeat steps 29-31 five times.

33. Collect and immobilize the nanowires again.

34. Decant the DI water and rinse the nanowires once in acetone.

35. Repeat step 30 and replace the acetone with ethanol.

The nanowires may be stored in ethanol for extended periods, up to at least several years, while still retaining their magnetic properties.

36. Inspect the nanowires after fabrication with an SEM or an optical microscope.

For optical imaging, nanowires can be prepared on a microscope slide by allowing a drop of ethanol containing nanowires to evaporate. The diameter of the nanowires cannot be resolved by standard optical microscopy, but the lengths of the wires can be assessed. For SEM imaging, evaporate a drop of ethanol containing nanowires on a conducting substrate. The nanowires should form rods of uniform diameter. We have found from analysis of SEM images that the average diameter of nanowires produced in these templates is 350 ± 4 nm (Tanase et al., 2005).

Basic protocol title: Data acquisition for cellular force fluctuations on non-magnetic micropost arrays

This protocol describes how to use video microscopy to measure the time-dependent displacements of microposts in contact with cells. The resulting data are of sufficient quality that the positions of the microposts can be measured with nanometer accuracy at up to 100 video frames per second, using the image analysis procedures described in Basic Protocol 4. This protocol is used for data acquisition for cellular force fluctuations on non-magnetic micropost arrays. Many of the steps described here are also needed for local cell rheology measurements with magnetic micropost arrays (Basic Protocol 3.) This protocol includes instructions for seeding and culturing cells on the micropost arrays prior to the measurements. These are of necessity somewhat generic and may have to be modified depending on the specific cell type used. Note that when imaging a cell, it is important to have the cell sufficiently centered in the field of view to have a border of at least 3-4 rows and columns of microposts that are not engaged with the cell surrounding the cell. Data from these "background" microposts are used in the data reduction (Basic Protocol 4) to compensate for any overall drift in the position of the array, and to determine the undeflected positions of the posts in contact with the cell. The data from the background posts also provide a measure of imaging noise in the system. Note that in this protocol as described there will be a free liquid-air interface from the cell culture medium the optical path. This has not proven to be a problem for experiments such as those described in (Shi et al., 2019;Shi et al., 2021). However, if needed it is possible to eliminate this potential source of noise in the post tracking by using a dish such as that described in Basic Protocol 3 that eliminates the liquid-air interface.

Micropost arrays, functionalized to promote cell adhesion on the post tips, as described in Basic Protocol 2. Cells in culture ready to be passaged Cell culture medium with serum, antibiotics etc., as needed, to culture cells under study. Disposable, sterile 5 ml and 1 ml pipettes (Falcon, ThermoFisher, etc.) 5% premixed CO2 gas

Biosafety cabinet (Labconco Purifier BSC Class II, or equivalent) Glass-bottomed P35 culture dishes (Thermo Scientific) Sterilized tweezers Pipettor (Falcon Express) Tissue culture incubator (Sanyo Model MCO-17A, or equivalent) Cell culture inspection microscope (Nikon TS-100, or equivalent) Inverted microscope (Nikon TE-2000E or equivalent) 10x, NA = 0.3 air objective (Nikon Plan Fluor) 40x, NA = 0.6, extra-long working distance air objective with correction collar (Nikon Plan Fluor). 100 W halogen illuminator long-working distance condenser with NA = 0.52. Ultraviolet (UV) (Edmund Optics #64-667) and infrared (Edmund Optics #47-303) filters Microscope enclosure incubator with on-stage environmental chamber (In Vivo Scientific, Inc. Model CH.HC5.SAT, or equivalent) Microscope stage heating plate (20/20 Technologies, Model TC-500, or equivalent) Computer equipped with hardware to support Norpix Streampix software and camera Norpix streampix software -(Version 5.16 or later) Gigabit ethernet camera (Allied Vision GX1050, or equivalent)

1. Prepare a suspension of cells in culture medium.

The procedure here should be identical to that followed for routine passaging of the cells. All steps should be carried out in a biosafety cabinet, using appropriate sterile techniques.

2. Preheat to 37 °C and add 2 ml of cell culture medium to a glass-bottomed P35 culture dish. This should be the regular medium used to culture the cells, i.e., including any serum and antibiotics, etc.

3. Transfer a MPAD array from PBS to the P35 dish with tweezers.

4. Pipette 200μL of cells in suspension at the desired concentration to the dish These above steps are the same as for routine passaging, but with cells transferred to the MPADs instead of to a new culture dish. The goal is to have a sufficiently sparse population of cells on the MPAD array so that individual, isolated cells can be measured. This step will have to be calibrated for each cell type to take into account each cell type's propensity to adhere to the microposts.

5. Inspect the culture dish with a microscope. When using a 10x objective focused on the top of the microposts, one should see between 10 -30 floating cells sparsely distributed across the field of view.

6. Incubate the cells on the MPADs overnight in a tissue culture incubator at 37 °C and at the CO2 level appropriate for the cells in use.

Check that the cells are well-spread and adhered on the arrays before proceeding to the next steps.

7. Remove air bubbles from under the MPAD using tweezers.

Lift the MPAD just off the bottom of the dish and press it back into place. This is necessary to keep the MPADs from sliding across the bottom of the dish.

1. Switch on the heating plate and stage incubator of the microscope and allow to equilibrate at 37 °C. 2. Put the environmental chamber onto the stage and connect it with air flow control unit.

3. Start flow of 5% premixed CO 2 with an influx of 200 cm 3 /min. 4. Transfer the dish with cells seeded on an MPAD to the microscope's incubator and place it in the environmental chamber.

5. Wait until the medium in the dish warms to 37 °C. This should take about 20 minutes.

6. Position the UV and infrared filters in the incident light path of the microscope (Fig. 2) and switch on the microscope's illuminator. Position the microscope's green interference filter (GIF) in the light path as well. This confines the illumination to visible wavelengths and allows high illumination intensities while avoiding damage to the cells through prolonged exposure. The GIF further optimizes the incident light in the region of best performance of typical white-light lenses.

7. Open the condenser aperture fully and make sure that there are no other optical elements, such as phase rings, in the light path through the condenser. This is to maximize spatial resolution when imaging the microposts.

8. Adjust the microscope for Kohler illumination. 9. Using a 10x objective, center the field of view on a cell.

10. Rotate the sample dish so that rows of posts (in the hexagonal grid) are aligned with the horizontal (x translation axis) of the microscope stage. (See Fig. 3) This is most easily done with a 10x objective. This is done because the analysis software needs the post arrays to be in this orientation, and one wants to minimize the amount of rotation of the images that needs to be done in the analysis software.

11. Switch to the 40x objective.

12. Switch on the camera in the Norpix software.

13. Focus the camera to the plane of the tips of the posts (See Fig. 3).

If needed, rotate the camera so that the horizontal rows of the posts are aligned with the x-axis of the camera's image. The circular outlines of the post tips should be sharp. Note that as this imaging mode is optimized to observe the post tips and not the cells, it can be somewhat difficult to see the precise outline of a cell. However, as shown in Fig. 3 the approximate outline can be discerned, and highly deflected posts near the cell's edges can also sometimes be seen.

14. Optimize the image quality using the objective's correction collar as needed. This adjustment may be needed to compensate for aberration as one is imaging through both the glass bottom of the culture dish and the cover slip on which the MPAD array is mounted.

15. Set the gain to 1 in Norpix to avoid amplifying camera noise, and set the exposure time (Live Adjustments > Grabber Properties > Exposure (μs)). Increase the illuminator intensity to maximize image intensity as much as possible without saturating the image.

One can examine the histogram of the current frame, loading Norpix's "histogram" module, and adjust the illuminator intensity until the high-intensity tail of the histogram just reaches the camera's maximum pixel intensity, (e.g., 255 for an 8-bit image) (Fig. 4). This should correspond to the bright spots at the centers of the posts. For our system, we use an exposure time of 4.5 ms for recordings at 100 fps.

16. Record the cell at 100 fps for the desired time. In Norpix, these images are saved as lossless AVI files.

We typically image the cells for 30 minutes each, since the phenomena that we are interested in occur on that timescale. If the size of the resultant movies becomes a problem, the frame rate can be reduced but at the cost of a loss of time resolution and a more limited ability to account for background noise.

17. Change the field of view to center on another cell and repeat for as many cells as needed.

This protocol describes measurements of the local rheology of a cell by actuating a magnetic micropost with an AC magnetic field and recording the resulting motion of the post. For the Ni nanowires described here, this requires the ability to apply an AC magnetic field in the range of 10 mT to ensure linear response.

To enable robust measurement of the frequency dependent rheology, the system described operates from 0.1 Hz to over 100 Hz. It employs a dual magnetic tweezer (Fig. 5) to ensure that only one cell is exposed to the magnetic field at a time, but if this is not a consideration, then alternative approaches may be employed to generate the needed field. Detailed information on construction of such a magnetic tweezer system is provided in these publications: (Bose, Huang, Eyckmans, Chen, & Reich, 2018;Kramer, 2009;Lin, Kramer, Chen, & Reich, 2012;Zhao, Boudou, Wang, Chen, & Reich, 2014).

A block diagram of the magnetic actuation and video microscopy measurement system is shown in Fig. 6. A PC computer running the Streampix (Norpix, version 5.16) video acquisition software is equipped with a National Instruments (NI) DAQ card. To produce the AC magnetic field, sinusoidal voltage waves from the NI card provide programming voltages to a Kepco BOP AC power supply operating in current-control mode, which then provides current to drive a dual magnetic tweezer system mounted on an inverted microscope (green arrows). Hall sensors at the back end of the tweezers' cores monitor their magnetic field and the Hall voltages are read by the DAQ card and recorded by the PC (red arrow). The PC also controls a CCD camera on the microscope which records movies of the microposts' motion (black arrow).

To ensure the Hall voltages are measured simultaneously with the video frames, a digital pulse from the camera when a frame is captured is used to trigger the measurements of the Hall sensors by the NI card (yellow arrow).

Gibco CO2 independent culture media (Thermo Fisher Cat. #18045088) 5% Trypsin-EDTA (Corning) Phosphate-buffered saline solution (PBS) Biosafety cabinet (Labconco Purifier BSC Class II, or equivalent) Magnetic tweezers: two solenoids filled with iron cores, mounted on 3-axis micromanipulator stages. Sample dish with indented lid -custom-built. Details provided below. PDMS ring to seal sample dish. Details provided below. Computer configured to support Streampix software and equipped with National Instruments PCIe-6231 DAQ card. Norpix streampix software (Version 5.16 or later) Gigabit ethernet camera (Allied Vision GX1050, or equivalent) Kepco BOP 50-2M power supply. Hall sensors (Lakeshore HGT-2101) Inverted microscope (Nikon TE-2000E or equivalent) 10x, NA = 0.3 air objective (Nikon Plan Fluor) 40x, NA = 0.6, extra-long working distance air objective with correction collar (Nikon Plan Fluor). 100 W halogen illuminator long-working distance condenser with NA = 0.52. Ultraviolet (UV) (Edmund Optics #64-667) and infrared (Edmund Optics #47-303) filters Microscope enclosure incubator (In Vivo Scientific, Inc. Model CH.HC5.SAT, or equivalent) Microscope stage heating plate (20/20 Technologies, Model TC-500, or equivalent) Pipettes (200 and 20 µl) Vacuum grease UV cabinet (Model KT-16DC, Foshan Shunde South Electric Appliance Co., Ltd, or equivalent)

Further information on the sample dish used for cell rheology measurements. As shown in Fig. 5D and Fig. 7, a 50 mm diameter culture dish is fabricated out of acetal plastic. A standard square coverslip (22 mm width ´ 0.17 mm thick) (shown edge-on in Fig. 5D) is glued with PDMS into a cutout in the dish to allow optical access. A micropost substrate with adhered cells and mounted on a similar coverslip fits into the cutout on top of the first coverslip. An acetal lid (green in Fig. 5D) with a beveled top allows the magnetic tweezer tips (gray) to be brought within 1 mm of the cells without contacting the culture media (pink in Fig. 5D). The lid has a coverslip glued into it to allow illumination, and the culture media should completely fill the volume between the dish and the lid. The lid has four 2 mm diameter posts in a square pattern that fit into corresponding indentions in the dish to prevent motion of the lid. A PDMS ring (orange in Fig. 5D) covers the open area between the edge of the lid and the dish to reduce media evaporation. The PDMS ring may be cast in a suitably sized petri dish with a cylindrical insert (metal or plastic) to define the inner radius of the ring. The dish, lid and PDMS ring are shown separately in Fig. 7.

1. Configure the microscope for white light imaging of the magnetic microposts as described in Basic Protocol 2, Section 2.2, Steps 1-8.

2. Mount the dual magnetic tweezers onto the microscope. (Fig. 5) If the magnetic tweezer tips are rusty, use a grinding wheel or sandpaper to clean them. Then add a drop of PDMS and bake at 70 °C overnight. This will protect the tips from oxidation.

3. Pre-heat the system with the stage incubator to 37 °C. This will take approximately 4 hrs.

4. Set up the Streampix software as described in Support Protocol 2. This includes special-purpose modules to drive the magnetic tweezers.

5. Use a tweezer to add a drop of autoclaved vacuum grease at each corner of the custom glass-bottom dish. Place a magnetic AMPAD sample seeded with cells onto the glass bottom of the custom-built sample dish (Fig. 7) and ensure a firm contact between the glass bottom of the sample dish and AMPAD.

The grease prevents the AMPAD sample from moving during measurements.

Immediately add 1 mL of CO 2 -independent culture media into the dish and place the custom culture dish lid (Fig. 7) over the sample. This must be done quickly to ensure that the cells do not dry out. Make sure that the four posts on the bottom of the lid fit into the holes in the dish.

7. Seal the sample dish with a PDMS ring.

8. Raise the tips of the magnetic tweezers and slide the sample dish under the tweezer tips.

9. Using the 40x objective, adjust the focus of microscope until the top of the posts are in focus, rotate the sample dish so that rows of posts (in the hexagonal grid) are aligned horizontally (see Basic Protocol 2, Section 2.2, Step 10), and then raise the focal plane of the microscope by 1 mm above the tops of the posts.

10. Switch to the 4x objective and lower the tweezer tips until the they are in focus in the microscope.

11. Switch to the 10x objective. Adjust the lateral position of the tweezer tips until they are in the middle of the field of view and 500 µm apart.

12. Lower the tweezer tips by 200 µm.

This can be done by lowering the focal plane by 200 µm, and then adjusing the tweezer position until the tweezer tips are in focus. The goal is to have the tweezer tips just above the top of the indented section of the sample dish.

13. Switch back to the 40x objective.

14. Switch on the camera in the Norpix software.

15. Find a cell with one or more magnetic microposts underneath it.

Typically, magnetic microposts look like regular microposts, except that they are darker in color. Normally there will be defects in the MPADs, such as collapsed posts, and they can be used as landmarks to mark the position of the cell. If the MPAD arrays do not have fiducial marks then it is best to look for cells near the edges of the arrays, as this facilitates finding the cells' locations again in later stages of the protocol when the magnetic posts are re-measured after the cells have been removed.

16. Optimize the image quality and set the Norpix gain as described in Basic Protocol 2, Section 2.2, Steps 13-15. 17. Start the Kepco power supply and click on the "Record" button in Streampix. The software will drive the magnetic tweezer automatically and carry out measurements at a set of frequencies between 0.1 Hz and 135 Hz (0.1 Hz, 0.2 Hz, 0.5 Hz, 0.8 Hz, 1 Hz, 2 Hz, 4 Hz, 5 Hz, 8 Hz, 10 Hz, 20 Hz, 35 Hz, 55 Hz, 80 Hz, 95 Hz, 115Hz and 135 Hz). The movie taken at each frequency will be saved in a separate AVI file.

In our system, an AC current of 100 mA peak-to-peak from the Kepco power supply produces a magnetic field of 10 mT, which yields a torque of 1.5 nN•μm on a 5 µm magnetic nanowire and hence a ~250 pN effective force on the cell adherent to the magnetic post. This low force range serves to minimize the mechanical stimulation applied to the cells to remain in the regime of linear response. It is important to note that the driving current should not exceed the safe operating limits of the solenoids in the magnetic tweezers, to avoid any risk of burning them out, and therefore the hard current limits on the Kepco BOP should be preset manually following the manufacturer's manual. As the BOP should be operated in current-programming mode, make sure that the inductive voltage across the tweezers does not exceed the voltage compliance of the BOP at the highest frequencies studied.

18. After finishing recording, shut down the Kepco power supply, move the file(s) with the readout from Hall sensors into the same folder with the AVI files, and then repeat Steps 13 and 14 for additional cells as desired.

19. When finished with data acquisition, raise the tweezer tips and take out the sample dish.

20. Open the lid of the sample dish and rinse the MPAD array with 1 mL of PBS.

21. Add 1 mL of trypsin-EDTA preheated to 37 °C into the dish, and leave for 5 min to allow the cells to be removed from the microposts. Then pipette out the remaining solution inside the dish and refill with DI water at 37 °C.

22. Put the lid back on to the sample dish.

23. Repeat Steps 6 to 15 to measure again all the fields of view where cells were measured. This is to measure the magnetic microposts' rheology after the cells are removed. In Basic Protocol 5, this will be subtracted from the overall modulus (cell plus post) measured in step 6-15 to obtain the cell's modulus.

24. Clean the customized dish with ethanol, then put it in the UV cabinet for 30 min. This is to sterilize it for the next use.

Support Protocol 2: Configuring Steampix for magnetic rheology measurements.

This support protocol describes the procedures for setting up Streampix to load modules that drive the dual magnetic tweezers with varying frequency magnetic fields, measure Hall voltages from the tweezers and perform image acquisition simultaneously. It assumes one uses Streampix 5.16 to drive the camera on the microscope and that the user has access to our custom software modules. Once a video file is created, the driving module will run its "Start" command, and generate a sinusoidal wave composed of a signal frequency ranging from 0.1 Hz to 135 Hz, and a reference frequency at 7 Hz in the output channel of a NI DAQ card. Then, whenever an image frame gets recorded, the module will run its "Increment command", which will read the magnetic field from the Hall sensor. Finally, when the recording stops, the driving module will run its "Stop" command, which shut down both the input and output channel in the NI card. These 3 steps continue iteratively until all frequencies to be measured are covered.

1. Open Streampix (the camera driving software), load the module "VoltageoutNin_sync_DF" (Fig. 8), then under the "Tools" panel in Streampix click "reload saved script".

For first time users, under the "Tools" panel in Streampix click "Edit scripts", then under the module "streampixCore", under the event "On PostCreate AVI" insert the command "Start" from "Demo Module" to set up channels in the NI card to output a sinusoidal wave and take readout from the Hall sensors (Fig. 9). Under the event "On recording stopped," insert the command "Stop" to close the two channels mentioned above (Fig. 10). Under the event "On AVI image saved" insert the command "Increment" (Fig. 11) to record readout from the Hall sensors each time a frame is captured. Once all these are set, close the editing window, and click "Save Current Scripts" (Fig. 3), so that these settings can be reloaded the next time you run Streampix.

2. In "Streampix setting", in the "Auto Naming" panel, check "Auto naming new videos" (Fig. 12). Then under "Recording rate" panel, set to "Use a recording script" (Fig. 13), and load the script "synchronizedscript".

The recording script will iteratively record 17 videos, covering the frequency range from 0.1 Hz to 135 Hz. It will record for 180 s for frequencies under 1 Hz, 60 s for frequencies between 1 Hz and 10 Hz and 30 s for frequencies between 10 and 135 Hz. It will skip the frames in the first and last 30 s of the video, so that any transient response of the magnetic microposts when the driving frequency is changed will have time to damp out.

Basic protocol title: Data reduction: determining microposts' motion

The data acquisition of either non-magnetic or magnetic measurements results in videos of the microposts' motion at up to 100 fps for each cell measured. This protocol describes a procedure to reduce these raw data to obtain the position of the center of each micropost in each video frame to allow construction of position vs time traces for each post. This protocol uses a centroid-based particle tracking algorithm (Crocker & Grier, 1996) that is widely used in the microrheology literature. The custom version used, written in Igor Pro, takes advantage of the known underlying lattice of the posts. One begins by using a visual inspection of the first frame of the movie to define an initial mask that classifies the posts as either "cell posts" that are in contact with the cell, "background" posts that are not in contact with the cell, or "ignored" posts. The ignored posts are not analyzed, and should include broken or bent posts, and posts that may be under cells in the field of view other than the one to be analyzed. The distinction between cell posts and background posts is initially provisional and will be refined in subsequent stages of the analysis. Frame-to-frame drift is accounted for by measuring the average displacement in each frame relative to the first frame for all the background posts and subtracting this from each post's trajectory. To avoid including cell posts in the de-drifting calculation, it is thus better to err initially on the side of classifying posts near the cell as cell posts, rather than as background. At this point the posts' positions vs time are measured in camera pixels. The undeflected positions of the cell posts is then determined by interpolation based on the positions of the background posts in corresponding rows and columns of the post lattice. The undeflected positions are subtracted from the raw positions to yield the posts' deflections vs time for subsequent analysis. Note that long movies at high frame rates can be timeconsuming to process.

PC or Macintosh computer (e.g., Dell Precision Tower 5810) Igor Pro Software (Wavemetrics, Inc, version 8 or higher) Custom Igor Procedure Files (See Internet Resources)

Protocol steps with step annotations:

1. Launch Igor Pro, load the procedure file "Centroid_Fit_Main_V11.ipf", and compile it. This will load a number of other Igor Pro ".ipf" procedure files via "#include" statements.

2. Run the function GfitGridAllM() from the Igor Pro command line to open the main graphical user interface (GUI) (Fig. 14)

This GUI controls all the data reduction and analysis functions described in this paper.

3. Click the "Set Folder" button and choose the folder where the data video file to be analyzed is stored.

4. Click "Pick Input Movie" and load the video file to be analyzed. You will have to set the Data Files file type to "all files." 5. In the "Working Name" field, enter a new folder name the video name to use. This will create a folder with the name you enter, and results from all following analysis will be stored in there. Click "Accept".

It is best for this name be similar to the name of the video file to simplify record keeping.

6. Click the "Define Array and Mask" button to open the GUI (Fig. 15) for defining the set of microposts to be analyzed and setting up the initial mask classifying the posts as "cell-associated", "background" or "ignored" for subsequent analysis.

7. Click the "Initialize and Pick ROI" button and enter "0" in the pop-up panel (Fig. 16) to start a new analysis. Click "Continue."

Enter "1" if you are re-running a previous analysis. This will recall the positions of your ROI boundaries, but you will have to rotate the image again.

8. The "Input Parameters" GUI (Fig. 17A) and an image of the first frame of the movie should now be open. Rotate the image (positive for clockwise) so that the horizontal axis of the hexagonal grid of posts aligns with the horizontal axis of the image frame by entering an angle in the "Angle (degrees)" box and clicking "Rotate" to carry out the rotation. This is an incremental rotation from the current image orientation. Successive image rotations can be carried out as needed. Use the "Revert" button to return to the original unrotated orientation.

The rows of posts do not have to be exactly horizontal but should be within ±0.1 -0.2 degrees of horizontal. As the rotation operation may have uncontrolled effects on image quality, it is important to have the post arrays lined up with their rows close to horizontal when the data are acquired in Basic Protocols 2 and 3.

9. Define the region of the image around the target cell to be analyzed. This is a two-step process. Leave at least a onepost gap between the ROI and the edge of the frame. Reducing the size of the ROI to avoid analyzing too many background posts can speed up the analysis. However, it is very important to leave a "border" 2-3 posts wide at a minimum around the cell in all directions. This border of background posts will be used to define a grid to determine the undeflected positions of the posts in contact with the cell. This is needed to measure the absolute post deflections and hence the absolute values of the cellular traction forces.

10. Click "Done Drawing" in the GUI. The positions of the corners of the rectangle you drew should appear in the boxes labeled "XT" and "YT" and the red crosses in the image will move to the corners of the rectangle in the image. (Fig. 17B)

The positions of red crosses are what the program uses to define the post lattice and ROI so these now need to be refined.

11. Adjust the positions of the red crosses using the up-and down-arrows by the x-and y-position values in the GUI to center them on posts. All the crosses should end up within 2 pixels of a post center. First, if necessary, adjust the upper left red cross.

12. Next adjust the position of the upper right red cross to center it on a post in the same row as the upper left cross. Count the number of posts between the two upper crosses, including the posts under both crosses, and enter this number in the "# posts in horizontal dimension" box.

It is important that each corner of this rectangle be closely centered on a micropost (to within 2 pixels). If it is necessary to adjust the position and shape of the rectangle after it is drawn, click on the Arrow (selector tool) in the Igor drawing menu, click on the rectangle and adjust as needed. 17. Click Continue. In the image of the first frame a red cross should appear over each post in your RO (Fig. 19). This is the default identifier for a background post. The locations of these crosses will be used as the initial guesses for the positions of the centroids of the posts when fitting the first frame. If the crosses are not well reasonably lined up with the posts, you will have to go back to Step 6 and re-define the ROI and numbers of posts.

Check that you counted the right number of posts in each direction. If you have miscounted, the crosses in the middle of the image will be systematically out of registry with the posts.

18. Identify the cell-associated posts ("cell posts") by clicking the "Draw Cell Outline" button. Click on the Draw Mode button in the upper left of the image frame, select the Polygon tool and draw a polygon enclosing the cell (Fig. 20). When finished, click the "Done Drawing" button, and then in the pop-up window, enter 1 to identify all posts inside the polygon as cell posts. Click Continue.

All posts in the polygon should now be marked with green x's identifying them as cell posts. (Fig. 21)

19. Click "Add Ignored Posts", then click on any posts in the image frame that you do not want to analyze. This should include any posts that are missing or collapsed, plus any posts that are under cells other than the cell to be analyzed. When finished, click on the "Done Adding" button.

All ignored posts will be marked with purple hour-glass symbols (Fig. 21).

20. Adjust the mask further as needed using the "Add Cell Posts", "Add Empty Posts", and "Add Ignored Posts" buttons followed by clicking on the image frame to change posts to cell, background (empty), and ignored respectively, as needed. Click "Done Adding" after working with each post type.

As noted in the introduction to this protocol, since the background posts are used to do the frame-toframe de-drifting correction, to avoid including cell posts in this calculation, it is better to err initially on the side of classifying posts near the cell as cell posts, rather than as background.

Note that there are other buttons in this GUI that can be helpful here and at various stages in the analysis. "Hide Mask", "Replot" and "Reset Mask" carry out the corresponding operations on the mask. "Show Index" replaces the mask symbols with the index of each post in the various data storage arrays.

21. Click "Done" in the "SetMaskPanel" GUI (Fig. 21) and in "DefArr" GUI (Fig. 15) to finish defining the mask.

The locations of the points in the mask will be used as initial guesses for the post positions in the analysis of the post trajectories.

22. Click "Fit All Posts" in the main GUI (Fig 14) to start centroid fitting of all the posts' trajectories. In the pop-up window, enter the number of the first and last frames to be analyzed (Fig. 22). You can choose whether to have an image of each frame shown as it is analyzed. (Use this for diagnostic purposes, only as this will be slower). You can also choose to have the current frame number printed periodically to track progress as the analysis runs. The fit post centers will be stored in units of pixels in the 3D wave FitRes_XXX, where "XXX" is the string entered in the Working Name field. The Layer dimension is the frame number.

When running this initially it can be useful to analyze only the first few frames of a video to verify that the process is working and to estimate the run time before attempting to analyze a long movie For a 10 frames per second video of duration 30 min (18,000 frames) this step will take approximately 30 minutes on a Dell Precision Tower 5810 PC.

23. Click the "Calc_bgshift" button in the main GUI (Fig. 14) to correct for frame-to-frame background drift. For the initial analysis, choose "manual" in the pop-up window.

"Manual" will use the post identification mask defined in steps 16-21. If desired, this can be refined after the MSD analysis is done, using "automatic" mode, which uses the more accurate MSD-based identification of cell and background posts. This can be used to correct possible issues that may arise with the dedrifting computation if cell posts are erroneously identified as background posts in the manally-created mask. The automatic mode can only be run after both the Make Cell Mask and the Force Bifurcation operations are run, as it uses the mask wave generated in the latter procedure (See Basic Protocol 6.). One would then want to re-do Step 24 below and run through the analyses in Basic Protocol 6 again.

24. Click the "Calc Grid Center" button in the main GUI (Fig. 14) to calculate the undeflected positions of the posts. In the pop-up window enter same number of frames as you analyzed in Fit All Posts in

Step 22.

Basic protocol title: Data analysis: determining local rheology from magnetic microposts

This protocol extracts the frequency dependence of the cellular rheology from the motion of the magnetic microposts in response to AC magnetic fields. The centroid-based particle tracking algorithm (Crocker & Grier, 1996) used in Basic Protocol 4 is used again, but the software is modified to handle the sequence of recordings at different magnetic field frequencies that is generated in Basic Protocol 3. Then digital lock-in analysis is applied to extract the response of each post at the (variable) drive frequency f and the reference frequency fR. Magnetic posts are identified by their large response compared to non-magnetic background posts. To account for time-dependence in the amplitude of the response at the drive frequency, the signals are broken up into 10 s intervals, and the average of the ratios of the displacements x(f)/x(fR) are computed (see Commentary). The driving force is deduced from the magnitude of the magnetic fields and used to compute the modulus k(w). As this is the combined response of the cell plus the post itself, k(w) is also computed for data obtained after removing the cells (See Basic Protocol 3), and then the two results are subtracted to obtain k(w) for the cell alone.

PC or Macintosh computer (e.g., Dell Precision Tower 5810).

Igor Pro Software (Wavemetrics, Inc, version 8 or higher) Custom Igor Procedure Files (See Internet Resources)

1. Follow Steps 1 to 21 in Basic Protocol 4 to define the analysis ROI, the post types, and the initial guesses for the post positions. 2. Note that the "working name" must be the same as the file root of the movie files. E.g., if the filenames are TLBRc2_1.avi, TLBRc2_2.avi, etc, the working name must be TLBRc2.

Magnetic posts are not identified separately in these initial steps. They should be classified initially as cell posts.

3. Click "con fitAllPosts" to track the trajectories of all the microposts in at each of the 17 frequencies measured in Protocol 3. (Fig 24). As in Basic Protocol 4, In the pop-up window, you can choose whether to have an image of each frame shown as it is analyzed. (Use this for diagnostic purposes, only as this will be slower). You can also choose to have the measuring frequency and the current frame number printed periodically to track progress as the analysis runs. The fit post centers will be stored in units of pixels in the 3D wave FitRes_XXX_Nhz, where "XXX" is the string entered in the Working Name field and "N" is the frequency. The Layer dimension is the frame number.

4. Click "cont calc bgshift" to perform the background drift correction.

5. Click "cont double frequency" to perform the digital lock-in (DLI) calculation.

For measuring the deflection magnitude with magnetic field in the x direction, select "Magnitude" in "Value" and "X" in "direction" (Fig. 25A), and enter the proper reference frequency (by default It is 7 Hz). DLI results for movies acquired at all 17 frequencies will be computed, and a heatmap of the DLI results at 0.1 Hz will be generated (Fig. 26), with the color indicating the magnitude of each post's deflection amplitude at that frequency. To Examine the DLI results for a movie taken with a specific frequency, one can use the button "Double freq" (Fig 25B). This will require additional input for the driving frequency at which the movie was taken, and a DLI heatmap will be generated.

6. Confirm that the magnetic posts are present by checking the deflection magnitude from the Digital Lock-in result. Normally deflections of magnetic posts will be larger than 1 nm whereas the magnitude from a non-magnetic post is ~0.1 nm. 7. Click "Load posts DLI" to load all digital lock-in result.

If needed, navigate to the FILEROOT folder that holds all the results. 8. Click "Correct time variance" to calculate the frequency dependence of deflection magnitude after correcting for temporal variation based on reference frequency (Fig 5 .4). 9. Click "Load Hall sensor readout" to load all readout from hall sensor. 10. Click "Calc Hall sensor DLI" to perform digital lock-in calculation on magnetic field. 11. Click "Calc Modulus" to calculate k(w) for all detected magnetic posts.

In the output of "Calc Modulus", there will be plots of loss modulus, storage modulus and modulus magnitude vs frequency for different microposts. When double clicking on figures in Igor, the trace name will indicate the post number for each trajectory, which is correlated with the heatmap generated in Step 4. "Calc Modulus" will also generate a 3D wave called "modulus_w", with different columns corresponding to the post number and rows corresponding to the measured frequencies. The first layer stores magnitude of the modulus, the second layers store the phase. The third and fourth layers are store and loss modulus respectively. 12. Follow step 1-11 to calculate k post(w) for all detected magnetic posts after cells are removed. 13. Open up the the two Igor project for the same field of view with and without cells attached. Calculate the difference kcell(w) = k(w) -kpost(w) by subtracting the frequency dependence of modulus magnitude (data in the first layer of the modulus_w wave) of the same post in the two projects.

Usually, the field of view will be slightly different when measuring the modulus with or without cells. Therefore, the post numbers for magnetic posts in kcell(w) and kpost(w) might be different. One needs to view the DLI heatmap in Step 4 to find the magnetic posts in the two field of views.

Basic protocol title: Data analysis for force fluctuation measurements

Measurements with non-magnetic microposts result in time traces that record the mechanical fluctuations of the cell. These are conveniently characterized using the mean squared displacement (MSD) <Δr 2 (t)> = <(r(t+t) -r(t)) 2 >, where t is the lag time. The MSD typically shows a power law dependence MSD ~ t a over a range of lag times from roughly 1 to 100 seconds. A procedure is described to extract the MSD exponent a by first subtracting the background noise floor and then fitting the logarithmic time derivative of the resultant subtracted MSD. The MSD exponent can then be used for multiple forms of analysis. Background posts that are not connected to a cell typically show much smaller MSD exponents a then do posts that are connected to a cell, and so the criterion a < 0.2 provides a means to identify the background posts. For long measurement times (e.g., up to half an hour) cell motility can lead to microposts near the edge of the cell being connected to the cell only over a part of the measurement interval as the cell moves.

To identify such posts the MSD may be calculated for the first third and last third of each time trace and the requirement that the corresponding exponents a1 and a3 both be > 0.5 can be used to identify posts that are connected to the cell throughout the measurement interval. Only these posts are used in subsequent analysis (unless one is interested in tracking motility). Procedures are described to bifurcate the population of cell posts into sub-populations that are associated with stress fibers and those that are associated with the cortex based on the average traction force produced on the posts.

Igor Pro Software (Wavemetrics, Inc, version 8 or higher) PC or Macintosh computer ( e.g., Dell Precision Tower 5810) Custom Igor Procedure files (See Internet Resources)

1. In the main GUI panel (Fig. 14), click the "MSD" button to open a pop-up window for calculating MSD. (Fig. 27). Enter the video framerate (In frames/s). Set the spike removal flag to 0 initially. Click "Continue". This will calculate the MSD for the x-component of the motion only. The y-component is not analyzed. The MSD is calculated in units of nm 2 . This may take several minutes to run for long videos. Note: you must have a minimum of 500 frames for the MSD calculation to run. Spike removal deals with some aspects of noisy data by running a sliding window through the data set and detecting whether there are outlying points using the standard deviation of the points in the window. If the difference of a point from this sliding mean is 3 times larger than the standard deviation of the points in the 10 nearest frames (before and after), that point is smoothed by averaging.

2. As desired, the MSD results can be surveyed using "Plot-A-Lot". Choose "MSD" in the Print in Right Column dropdown menu.

Step 25 for further details on Plot-A-Lot.

3. When finished with the MSD analysis, click "Make Cell Mask MSD" in the main panel to identify posts associated with the cell based on the MSD exponent. (Fig. 28).

We normally use 1/3 of the entire video length to calculate the MSD exponent. For a 30 min. video of 10 frames per second, total frame number will be 18000, and 1/3 of that is 6000 frames. In "Enter threshold for slope", normally one can use 0.5 to make sure all posts categorized as cell posts are associated with the cell. Use 0.2 as the threshold below which posts are identified as background posts.

4. Click the "Force Bifurcation" button in the main panel and enter the post stiffness (in nN/µm) and the thresholds for identifying stress fiber and cortical-associated posts to run the code that identifies posts associated with the actomyosin cortex or with stress fibers (Fig. 29).

Click "MSD Heat Map" button, this will generate panel C-E as in Fig. 37, which are the heatmaps for the MSD exponent, MSD magnitude at τ = 10 s, and traction force map, respectively.

6. Click "MSD Scatter Plot" button, this will generate panel F and G in Fig. 37, which show the scatter plot of the MSD magnitude at τ = 10 s against MSD exponent and traction force magnitude, respectively.

Background Information:

Thanks to the development of microfabrication techniques and the ability to engineer the mechanical properties of substrate materials for cell culture, a variety of approaches have been developed to probe mechanotransduction in cells at various scales (Martino, Perestrelo, Vinarsky, Pagliari, & Forte, 2018;Mohammed et al., 2019). PDMS micropost array detectors (MPADs) are one of the important techniques that have been applied to measure cellular traction forces (du Roure et al., 2005;Geng & Wang, 2016;Tan et al., 2003;Wolfenson et al., 2016). By coating the microposts' tips with fibronectin or other suitable ECM proteins via microprinting, one can achieve controlled coupling between the posts' tips and the cytoskeleton via cellular focal adhesions. For small deflections, the deformation of the microposts in response to cellular traction forces can be modeled by beam bending theory, which provides a method to directly transform the microposts deflections from their resting positions into the cellular traction force field (Fu et al., 2010;Tan et al., 2003;Trepat et al., 2007). Further, embedding magnetic nanowires into the microposts provides an approach to apply mechanical perturbations to cells through these same focal adhesion linkages by magnetic actuation (Shi et al., 2019;Sniadecki et al., 2007;Sniadecki, Lamb, Liu, Chen, & Reich, 2008). Another widely used technique to probe cellular traction force is traction force microscopy (TFM), which employs flat substrates with embedded microbead tracers (Plotnikov et al., 2014). The cellular traction force field can be obtained from measuring the displacement field of the beads. Since the TFM tracers are affected non-locally by the cellular traction field, obtaining the traction forces in TFM is mathematically more complicated than the conversion between displacement and traction force for MPAD arrays. Both TFM and MPADs have their own advantages: TFM allows cells to grow on a continuous substrate of variable stiffness with high probe particle densities. MPADs form a lattice of independent force probes underneath the cell. The effective stiffness of the substrate can be varied by changing the geometry of the individual microposts (Fu et al., 2010). Of course, like all techniques that are based on cell culture in two dimensions, both TFM and MPADs cannot reproduce the 3D cellular environment. However, the challenges associated with 3D approaches to measuring cellular traction forces mean that the 2D techniques can be expected to continue to have utility for the foreseeable future.

The protocols described herein focus on applying active MPADS (AMPADs) (MPADs with embedded magnetic nanowires) to enable high-precision measurements of both cellular passive and active microrheology rather than the static traction force or cells' response under large-scale external mechanical perturbations (Sniadecki et al., 2007;Trepat et al., 2007). Microposts with magnetic nanowires are actuated by a dual magnetic tweezer system to measure local cellular rheology, while all the microposts serve as probes for measuring cellular fluctuations at high spatial and temporal resolution. Compared with other methodologies for performing cellular microrheology, AMPADs have the following advantages: first, compared with other active microrheology techniques, coating microposts tips with fibronectin enables controlled coupling of posts to cellular actomyosin network through focal adhesion; second, AMPADs provide an organized mapping of cytoskeletal fluctuations of different subcellular architectures with high spatial and temporal resolution. Moreover, compared with TFM, the independent nature of the micropost probes allows one to study their correlations, and the capability of embedding magnetic nanowires inside the microposts allows one to perform active and passive microrheology with the same system.

Basic Protocol 1. This protocol describes how to extend replica molding techniques for fabricating MPAD arrays (Fu et al., 2010;Yang et al., 2011) to embed magnetic Ni nanowires in individual microposts (Shi et al., 2019). The original work describing magnetic micropost array fabrication (Sniadecki et al., 2007;Sniadecki et al., 2008) used Co nanowires instead of Ni. While Co has a larger magnetic moment than Ni, and hence can in principle provide larger magnetic actuation forces on individual microposts, there are some issues associated with the use of Co that make Ni preferable. First, and most importantly, Co metal dissolves in culture media and is toxic to cells.

In the original work of Sniadecki et al., the larger micropost sizes used (4 µm diameter) enabled the nanowires to be sufficiently well encased in the PDMS posts to minimize such issues. Ni is not dissolved in culture media and is not measurably toxic in cell culture at the concentrations used in the experiments described here over the relevant exposure durations of a few days (Zhao, Boudou, Wang, Chen, & Reich, 2013). In addition, the magnetic properties of Co mean that Co nanowires do not form permanent magnets and so behave somewhat like superparamagnetic particles in a field perpendicular to their long axis (as one has here). As a result, microposts with Co nanowires can only be deflected in a single direction from their resting position, no matter whether the applied magnetic field changes sign (Sniadecki et al., 2007;Sniadecki et al., 2008). Ni nanowires, in contrast, are good permanent magnets, and so their actuation is bi-directional, following the direction of the applied field.

Basic Protocol 2. To optimize imaging of the microposts for the particle tracking analysis this protocol employs imaging procedures that maximize both resolution and signal-to-noise while maintaining cell viability. Therefore, the microscope's condenser aperture is maximized to optimize resolution, and the Illumination intensity is adjusted to maximize intensity in the captured frames without saturating the camera. The camera's digital gain is turned off to minimize camera noise. To capture bright field movies at 100 frames per second, the exposure time is adjusted to 4.5 ms so that there is a gap in time between successive exposures to ensure that there is no correlation between neighboring fames. To account for possible phototoxicity effects on the cells due to high illumination intensity, ultraviolet and infrared filters are used to restrict the illumination's wavelength within the range of 425 nm < λ < 700 nm. The microscope's built in green interference filter is also used to further minimize photo damage. Because of the high sensitivity of the accuracy of the post tracking to focus drift and thermal fluctuations, an enclosure incubator and a stage-mounted heating plate are used to keep the culture dish and its surroundings at 37 °C. For long experimental runs that can encompass several hours on the microscope to record force fluctuations for multiple cells, an on-stage environmental control chamber is used and filled with 5% premixed CO2 gas to help maintain cell viability. It is also important to allow sample dishes with cells on MPADs to stabilize at 37 °C for 30 minutes in the enclosure incubator prior to imaging to minimize possible thermal fluctuations that can arise when transferring cell culture dishes from the culture incubator to the microscope stage.

Basic Protocol 3. In order to acquire accurate data for the frequency dependence of the local cellular rheology with magnetic nanowires embedded in microposts and a magnetic tweezer system such as we employ (Bose et al., 2018;Kramer, 2009;Lin et al., 2012;Zhao et al., 2014), it is necessary to address a number of experimental considerations. To minimize evaporation and thermal fluctuations, we describe a customized sample chamber that allows the tips of the magnetic tweezer poles to be brought within 2 mm of the AMPAD array without contacting the culture media (Shi et al., 2019). This chamber greatly improves cell viability and decreases fluctuational noise in the measurements. One uses a sinusoidal magnetic field that results in micropost deflections of only a few nanometers. This does not interrupt normal cellular activity and keeps the measurements in the linear regime. In order to account for the time variance in the deflection magnitude associated with cellular activity (Massiera et al., 2007), such as timedependent coupling of the posts to the cytoskeleton, the actuating magnetic field is composed of a superposition of two frequencies: one frequency varies from 0.1 Hz to 135 Hz to measure the frequency dependence of cellular stiffness, and the other is kept fixed (at 7 Hz in our case) to measure the time variance in deflection magnitude (Fig 30A) (Shi et al., 2019). As the microposts themselves have a frequency-dependent viscoelastic response, after measuring the magnetic microposts' motion with cells attached, cells are removed, and the same field of view is measured again. By analyzing the differences between the magnetic posts' response with and without cells attached, one can extract the modulus of the cellular cortex (See Protocol 5).

Basic Protocol 4. To determine the microposts' positions vs time from the raw data (movies), Basic Protocol 4 uses an implementation of a centroid-based particle tracking algorithm (Crocker & Grier, 1996) written in Igor Pro. Each frame is processed with a 2D Gaussian filter with size of 3 pixels, and an averaging filter with the size of microposts' diameter. The results from the averaging filter are subtracted from the results from the Gaussian filter, to obtain intermediate images with enhanced contrast and subtracted background (Fig, 31). A square mask centered at the initial guess position of microposts center with size slightly larger than the diameter of the microposts is created, and the center position is recalculated based on the intensity-weighted center of all pixels within the mask (centroid fitting). The mask is shifted towards the new fitted center by the closest integer number of pixels, and this process is repeated recursively until the difference between the center of the current mask and the fitted centroid is less than 0.5 pixel. To account for frame-to-frame drift, the average displacement in each frame relative to the first frame of the movie of all the background microposts (those not in contact with cells) is subtracted from each individual micropost's trajectory. The undeflected positions of posts in contact with cells is determined by interpolation based on the positions of the background posts in the corresponding rows and columns of the array (Sniadecki et al., 2008).

Basic Protocol 5. The amplitudes and phases of the magnetic microposts' response at the measurement frequency f and the reference frequency fR are found via digital lock-in analysis (Dixon & Wu, 1989) of the microposts' positions r(t) determined from the image sequences as described Basic Protocol 4.. Due to the finite exposure time, the AC amplitude extracted from the digital lock-in analysis is reduced in a frequency-dependent way due to its averaging effect, as shown in the formula below.

Suppose we have a sinusoidal signal written as 𝑓(𝑡) = 𝐴 cos 𝜔𝑡. In our case, A is the deflection magnitude of the magnetic micropost and ω is the angular frequency of the magnetic field. Considering that the finite exposure time will give the amplitude of f(t) averaged over the exposure window, then the recorded signal intensity 𝑆 at the n th frame recorded at frame rate Δt over a finite exposure time 𝑇 ! is:

Where 𝛼 = 𝜔𝑇 ! /2. Therefore, the amplitude is reduced by a prefactor *+, --and the phase is shifted by 𝛼.

Another phase shift arises from the fixed lag time 𝑡 ./0 between the camera exposure window and the sampling of the magnetic field by the DAQ card. For our system this is 𝑡 ./0 = 0.02 s as measured by imaging an LED driven by the DAQ card. Data at frequencies above the Nyquist frequency fNy = fS/2 = 50 Hz (fS = 100 Hz is the sampling frequency in our system) are measured via aliasing, i.e, at apparent frequencies 𝑓 1 . Notably, this procedure will introduce an additional phase shift, as shown below: Suppose a sinusoidal signal can be written as 𝐴 = cos(2 𝜋𝑓𝑡 + 𝜙), where 𝑓 is the measured frequency and 𝜙 is the phase shift. Since 𝑓 2 𝑡 = 𝑛 is the index of the frame captured by the camera, it is an integer. Then when 50 Hz < 𝑓 < 100 Hz

found that their MSD exponents α are mostly less than 0.5, and therefore we use this criterion to distinguish background from cell posts.

Since cells can migrate on microposts over the typical 30 min time course of experiments using this technique, this protocol includes a procedure to identify posts that are associated with the cell for the full measurement interval. The trajectory of each post is broken up into three equal segments (10 min for a 30 min video) and the MSD exponent is calculated for each segment over the lag time range of 5 -10 s as described above (where MSD and lag time follows a power law relationship). For analysis of cell associated posts, we only accepted those with both the first third and last third having α> 0.5. Examples of how this criterion is applied are shown in Fig. 39.

Making the magnetic micropost arrays:

1. Ensure proper density of nanowires. A solution with excessively high density may result in excess nanowires in the micropost array base (not in the posts themselves) which will hinder imaging, whereas too low density may cause difficulty in finding cells with associated magnetic microposts. 2. In the magnetic actuation experiments (Basic Protocol 5) it is important to be able to re-find the locations of cells after they have been removed in order to re-measure the magnetic microposts' motion without the cells attached. It is therefore desirable to have reference marks of some kind in the micropost arrays to aid this navigation. In arrays without such marks, it is usually best to work near the edge of the array and to use the small but inevitable number of missing or collapsed posts (Fig. 32) as navigation aids to locate the magnetic posts.

Cell seeding on the arrays 1. Seeding density should be done as described in the protocol, with sufficient cells seeded while not overlapping. 2. Cells should be well spread on the microposts. When appropriate substrate stiffnesses are chosen, one can generally find microposts at the cell's periphery that are visibly bent, which indicates good focal adhesion formation and mechanical contact between the cells and the microposts.

Obtaining high-quality images:

1. To ensure high precision in determining the posts' center localizations, the image quality is crucial. This protocol maximizes illuminator intensity without photo damage to the cells. A sample image is shown in Fig. 31A, where there is clear contrast between the microposts' tops and the background while ensuring that the microposts' tops are as bright as they can be without saturating the camera.

Common problems with the protocols, their causes, and potential solutions. Itemized in a 3-column table of Problem, Possible Cause, and Solution (see below for example).

Table I. Troubleshooting MPAD fabrication and data collection Problem Possible Cause Solution Microposts collapsed Microposts were allowed to dry, and forces from liquid evaporation caused posts to collapse. Avoid letting the microposts dry out after submerging in liquid. If microposts are already collapsed, one can submerge them in ethanol and sonicate for 30 minutes. No visible microposts with nanowires Nanowire solution density too low. Increase nanowire solution density and/or increase volume of nanowire solution. Nanowires inside base of MPAD array. Nanowire solution density too high. Decrease nanowire solution density and/or decrease volume of nanowire solution. Large drift/vibration when imaging cells on MPADs. Air bubbles underneath coverglass. Remove air bubbles underneath coverglass when load MPADs into dish. Focus drift over the time course of imaging. System not in equilibrium. Wait for ~ 30 min. before measuring the first cell.

Basic Protocol 1 should yield arrays of microposts with approximately 1% of the posts containing magnetic nanowires. An example of a portion of an array is shown in Fig. 32. The "magnetic posts" are not always easy to spot with an optical microscope, but frequently appear darker than the non-magnetic posts. Such a post is shown in the green circle in Fig. 32. Note that when the concentration of nanowires is too high, it can result in nanowires embedded in the base of the array between the microposts rather than within microposts. It can also be useful when initially fabricating magnetic post arrays to image selected arrays with scanning electron microscopy. The nanowires show up clearly and their presence can be verified by energy-dispersive x-ray (EDX) compositional analysis (Sniadecki et al., 2007;Sniadecki et al., 2008).

Basic Protocol 2. After incubation on the MPADs cells should spread and adhere to the posts and exert traction forces on them (Fig. 3). Observation of such forces has been widely discussed in the extensive literature on the measurement of quasi-static cellular traction forces with MPADs (Geng & Wang, 2016). In the imaging mode used here, details of the cells are not visible, but the outlines can usually be observed with practice, and if sufficient traction forces are being exerted by the cells, highly deflected posts near the edges of the cells can be seen, as shown in Fig. 3. The main output of this protocol is movies of the time dependence of the fluctuating cellular forces. The fluctuations in the microposts' positions are typically too small to observe by eye but are readily resolved with the image analysis techniques described in Basic Protocol 4.

Basic Protocol 3 will yield data for the motion of the magnetic microposts under AC actuation. For larger actuations this motion can be seen by eye (Supplementary Movie 1), but for local rheology measurements, the AC deflection amplitudes should be kept in the < 10 nm range to remain in the linear regime. Such deflections are too small to see by eye but are readily detected upon image analysis (See Fig. 26). Movies should be obtained both with cells attached to the posts, and after removal of the cells to enable subtraction of the contribution from the viscoelasticity of the posts themselves. To find the same region after cell removal, we use naming convention to indicate the approximate location of the ROI on the microposts array when cell is taken (for example, we name cell "TLTRc1" if the cell is taken at the top right corner of the top left quadrant of the microposts array) , then use nearby imperfections in the micropost array to fine-tune its location. Examples of such movies are provided in the SI.

Basic Protocol 4. The data reduction in this protocol proceeds in three stages. These are illustrated below using selections from output from the "PlotALot" function in the associated analysis code, which allows one to view the x and y components of the trajectories of the posts, as well as the microposts MSDs (after finishing MSD analysis in Basic Protocol 6). The initial centroid-based particle tracking analysis of the image sequences (the "FIt All Posts" function in the main GUI (Fig. 14)) yields the "raw" x and y positions of each post in each video frame in the pixel coordinates of the camera (Fig. 33). Note that the three background posts in Fig. 33 have very similar trajectories. This reflects the background "drift" motion of the array. The amplitude of this motion of ~0.1 pixels (12.5 nm) is comparable to the motion of the less active cell posts (e.g., Posts 277 and 278 in Fig. 33), which illustrates the need for the de-drifting procedure (the "Calc_bgshift" function). The result of the de-drifting, which subtracts the average displacement of the background posts relative to the first frame, is illustrated in Fig. 34. Note that the background posts' residual trajectories, with amplitudes of ~0.01 pixels (1.2 nm), are reduced by approximately a factor of 10 compared to the raw data. Finally, after subtracting each post's undeflected position from the trajectory (via the CalcGridCenter function), one obtains the deflection of each post vs time (Fig. 35) (still in pixels). These can be converted into distance from the measured array lattice constant, and into force if desired from the posts' effective spring constant for lateral deflections (Fu et al., 2010). An example of this conversion is shown for the xcomponent of the motion for one cell post and one background post from Figs. [33][34][35]. Note that analysis of the background data such as that in Fig. 35 yields information on the background noise for the cell posts in such measurements. In our studies, which include slight non-linearities in the mapping from physical location to centroided position, the de-drifted background post motion over 30 min observations was ~2-3 nm RMS when measured at 10 fps, which is very small compared to typical motion of cell-associated posts.

Basic Protocol 5. The oscillation of a magnetic post in response to the two-frequency sinusoidal driving magnetic field yields post motions such as that shown in Fig. 30A, where the oscillations at both frequencies can be seen over the experimental noise. Such oscillations show considerable time dependence in their amplitudes. An example of this time dependence is shown in Fig. 30B, which leads to significant noise in the measurements of the response x(w) (Fig. 30C, raw signal). It is important to note, however, that the amplitudes of the responses at the two frequencies are correlated in time, an effect which can be attributed to time dependence in the cell's coupling to the post (Massiera et al., 2007). Thus, significant reduction in the uncertainty of the frequency dependence of x(w) is obtained by the ratiometric analysis described above (Fig. 30C, ratio signal). The frequency dependent stiffness of the cell + post k(w) = F(w)/x(w) (Fig. 30D) is determined from x(w) and the magnetic force. The stiffness of the post alone K post(w) is determined by remeasuring the response of the post alone (Fig. 30D) and then the final result kcell(w) is determined from the difference in these two measurements (Fig. 30E).

Basic Protocol 6. The measurements of cellular fluctuations (Basic Protocols 2 and 4) yield time traces of the displacements of the microposts in contact with a cell, such as the examples shown in Fig. 36 and Fig. 37A. Such fluctuating motion is typically characterized in terms of its mean square displacement (MSD) <Δr 2 (t)> = <(r(t+t) -r(t)) 2 >, where t is the lag time. Examples of typical MSDs for individual posts are shown in Fig. 37B. These data display a noise floor at short t and then power-law behavior, with the MSD µ t a for 1-2 decades in t. This power law exponent is typically > 1, with larger values for posts near the periphery of the cell. To ensure sufficient data are available for the MSDs, one should only compute the MSDs for t up to ~1/5 of the video length. To measure the MSD exponent a for each post, the software in Protocol 6 first obtains a post's noise floor by fitting the MSD trace for t £ 1 s to the form , and then subtracts the constant C from the MSD traces to obtain the "subtracted MSD," MSDSub.

6 =>?(94: %#$ ) 6 =>? < , and averages between 5 s £ t £ 10 s to obtain a and its uncertainty (Fig. 38). The identification of posts that are associated with the cell throughout the measurement window by requiring that such posts show a > 0.5 for both the first and last third of their trajectories (based on the observation that background posts show a < 0.5), is illustrated in Fig. 39, which shows a background post for reference, two posts that are engaged with the cell for only part of the measurement, and one that is engaged with the cell throughout the measurement. The corresponding MSDs for the first and last thirds of the measurement illustrate the cut based on a.

A key output of this protocol is the production of spatial maps of the MSD exponent (Fig. 37C) and magnitude (Fig. 37D). The output of the Basic Protocol 6 software that identifies sets of posts that are associated with stress fibers and with the actomyosin cortex based on the posts' average traction force is illustrated in Fig. 37E-G. Here, for cells on microposts with spring constant k = 15.7 nN/µm ("M6"), we identify the posts as stress fiber associated if their average traction forces are larger than 5 nN, and as cortical posts if their maximum traction force are less than 2 nN. This bifurcation procedure provides clean data sets that can form the basis for subsequent analysis of the cytoskeletal dynamics. We have used such data to study cytoquake phenomena and other aspects of cytoskeletal fluctuations (Shi et al., 2019;Shi et al., 2021).

In Basic Protocol 1, embedding nanowires into micropost molds takes approximately 2-3 hrs. The majority of this time is waiting for the ethanol of the nanowire solution to evaporate. Casting PDMS in molds take 30 minutes to carry out, then overnight for the PDMS to bake. Fabrication of magnetic nanowires takes about 30 minutes to set up, and the electrodeposition takes 20-30 minutes. Extracting nanowires takes about 1 hr of the operator's time and 12-18 hr of wait time.

In Basic Protocol 2, cell seeding takes approximately 30 min. to carry out and overnight to allow the cells to adhere and spread on the posts. Imaging takes 10-20 minutes to set up the microscope and optimize imaging parameters and 30 minutes for settling to thermal equilibrium. The actual imaging time then depends on the length of the observation time desired. For half-hour observations per cell, it is typically possible to measure 7 to 8 cells from a single substrate in a single day.

In Basic Protocol 3, setting up the Streampix script takes about 15 minutes. Microscope setup (including setting up magnetic tweezers and optimizing image parameters) takes about 30 minutes. Each cell takes about 30 minutes to scan across all frequencies from 0.1 Hz to 135 Hz.

In Basic Protocol 4, setting up the grid for localizing microposts centroid and creating hand-drawn cell masks takes about 10 minutes for each cell. For 17 videos taken at 100 fps with range from 3 minutes to 30 s (following the recording script described in Basic Protocol 4) with ~1000 posts (30 x 30 grid, approximately the whole ROI of our CCD camera when using a 40x objective), it will takes 10 hrs to analyze on a Dell Precision Tower 5810 PC.

In Basic Protocol 5, digital lock-in calculations of all micropost trajectories across all frequencies take about 30 minutes. Calculating the rheology curve of magnetic microposts takes about 5 minutes.

In Basic Protocol 6, MSD calculations take about 1 hr on the aforementioned data (180,000 frame videos). Generating a mask of cell associated posts based on MSD exponents takes 30 minutes, and bifurcating cortical and stress fiber associated posts takes about 5 minutes. Figure 4 Sample histogram of image intensity after setting halogen illuminator lamp intensity in Streampix prior to data acquisition. The dish rests on a heating plate (g) and can be moved with the microscope's sample stage relative to the tweezer tips. (D) Schematic of the sample dish, showing the AMPAD sample location, the tweezer tips (gray), the acetal base (blue) and lid (green) of the dish, and the PDMS ring (yellow) that seals the space for culture media (pink). See text and Fig. 7 for further details. Panel C is reproduced from (Shi, 2020). Used by permission. Panel D is reproduced from (Shi et al., 2019).