Measuring (biological) materials mechanics with atomic force microscopy. 5. Traction force microscopy (cell traction forces)

Abstract Cells generate traction forces to probe the mechanical properties of the surroundings and maintain a basal equilibrium state of stress. Traction forces are also implicated in cell migration, adhesion and ECM remodeling, and alteration of these forces is often observed in pathologies such as cancer. Thus, analyzing the traction forces is important for studies of cell mechanics in cancer and metastasis. In this primer, the methodology for conducting two‐dimensional traction force microscopy (2D‐TFM) experiments is reported. As a practical example, we analyzed the traction forces generated by three human breast cancer cell lines of different metastatic potential: MCF10‐A, MCF‐7 and MDA‐MB‐231 cells, and studied the effects of actin cytoskeleton disruption on those traction forces. Contrary to what is often reported in literature, lower traction forces were observed in cells with higher metastatic potential (MDA‐MB‐231). Implications of substrate stiffness and concentration of extracellular matrix proteins in such findings are discussed in the text. Research Highlights Traction force microscopy (TFM) is suitable for studying and quantifying cell‐substrate and cell–cell forces. TFM is suitable for investigating the relationship between chemical to mechanical signal transduction and vice versa. TFM can be combined with classical indentation studies providing a compact picture of cell mechanics. TFM still needs new physico‐chemical (sample preparation) and computational approaches for more accurate data evaluation.


| INTRODUCTION
Cells detect changes in both physical and chemical properties of the extracellular matrix (ECM) and alter their activity and gene expression in response, a process known as mechanotransduction (Humphries et al., 2019;Janmey et al., 2020;Martino et al., 2018). This process is mainly mediated by focal adhesions (FAs), groups of proteins, including integrins, which are situated in the membrane and connect ECM and actin cytoskeleton (Humphries et al., 2019;Martino et al., 2018;Mishra & Manavathi, 2021). Integrin clusters detect changes in the stiffness or tension of the ECM and recruit other proteins, generating biochemical signals and altering the mechanical state of the cell (Martino et al., 2018). Changes in the mechanical state of the cell include variations in the dynamics of the cytoskeleton, modulation of cell elasticity, and alteration of the contractile forces of the cell (Martino et al., 2018;Webster et al., 2014).
Cells generate contractile forces to probe the mechanical properties of the surroundings, while also keeping a basal equilibrium state of stress, which is known as tensional homeostasis (Boudou et al., 2019;Brown et al., 1998;Webster et al., 2014). Cells tend to keep the tensional homeostasis and readjust their contractile forces depending on the changes observed in their surroundings (Martino et al., 2018;Webster et al., 2014). Proteins present in FAs, including integrins, focal adhesion kinase (FAK), talin and vinculin, have mechanosensitive properties and participate in the regulation of the contractile forces and the tensional homeostasis by altering the state of the actin cytoskeleton (Boudou et al., 2019;Martino et al., 2018).
Besides maintaining tensional homeostasis, cellular traction forces are also important in cell migration (Lange & Fabry, 2013;Lauffenburger & Horwitz, 1996), adhesion (Pelham Jr. & Wang, 1997), and ECM remodeling (Bloom et al., 2008;Lemmon et al., 2009). Alteration of the traction forces of the cells is observed in diseases including cancer and metastasis. Higher traction forces are usually observed in cancer cells when compared with their healthy counterparts (Kraning-Rush et al., 2012;Li et al., 2017;Massalha & Weihs, 2017). Additionally, the effects of substrate stiffness and ECM ligand concentration in the traction forces of cancer cells have been studied, showing an increase in the traction forces of cells seeded on stiffer substrates and higher concentration of ECM ligands (Kraning-Rush et al., 2012;Massalha & Weihs, 2017;Shebanova & Hammer, 2012). Other studies focused on the cytoskeleton in the generation of the traction forces, either by disrupting different types of fibers with drugs (Kraning-Rush et al., 2011) or severing single stress fibers using lasers (Kumar et al., 2006). Thus, the study of cell traction forces can be of interest in the field of cell mechanics (and cell-substrate interactions), especially when related to the mechanics of cancer and metastasis, as well as cell migration.
Since the first evaluation of traction forces of cells by measuring the wrinkles generated by cells on thin layers of rubber (Harris et al., 1980), different techniques have been developed. Most of them constitute what is known as two-dimensional traction force microscopy (2D-TFM), a series of techniques based on flat elastic substrates whose surfaces are functionalized with particles or markers, allowing the detection of the deformations of the surface (Figure 1). The traction forces generated by the cells that are seeded on top of the substrate stress the surface, causing the displacement of the particles. This displacement is proportional to the applied stress. If the cells are removed (for example, using trypsin or sodium dodecyl sulfate-SDS), the stresses disappear, and the particles return to their F I G U R E 1 Diagram of 2D traction force microscopy (2D-TFM) experiments. In 2D-TFM experiments, cells are seeded on elastic substrates that contain fluorescent particles on the top. When cells attach and pull on the substrate they generate tractions on the substrate, displacing the particles from their original position. When the cells are removed (e.g., adding trypsin or sodium dodecyl sulfate, SDS), the particles return to their original position due to the elastic properties of the substrate. Thus, images of the particles are taken before and after removing the cells, and the changes in the position of the particles are determined by particle image velocimetry (PIV), generating maps of the deformations of the substrate. Fourier transform traction cytometry (FTTC) is later used to transform these maps into maps of the traction stresses produced by the cells on the substrate taking into account the stiffness of the substrate. original position. Therefore, taking a microscopy picture before and after removing the cells allows the determination of the deformations caused by the cells, using particle image velocimetry (PIV) Liberzon et al., 2021). The deformation field can later be transformed into a stress field (traction map) based on the mechanical properties of the substrate, in what is known as Fourier transform traction cytometry (FTTC) Butler et al., 2002).
Other methods based on patterns are reference-free (avoiding the need to remove the cells), and include those based on platforms of micropillar arrays (Han et al., 2016;Li et al., 2017) or fluorescent micropatterns printed on the surface of elastic substrates (Beussman et al., 2021;Ghagre et al., 2021). Also, in 2D-TFM, only the traction forces generated in the same plane as the surface are measured. To measure out-of-plane traction forces, a more complex methodology is required.
In this primer we report on the methodology for conducting 2D-TFM experiments. In particular, we describe the preparation and characterization of elastic substrates, and the acquisition and analysis of the traction force data. As a practical example, we compare the traction forces of three different breast cancer cell lines, MCF-10A, MCF-7 and MDA-MB-231 cells, and we also test the effects of actin cytoskeleton disruption on their traction forces.
The primer is intended for a fast and easy establishment of the technique in those laboratories that would like to include the analysis of traction forces as a routine technique to complement cell mechanics studies.

| Preparation of elastic substrates for traction force microscopy
Elastic polydimethylsiloxane (PDMS) substrates with a Young's Modulus of approximately 9 kPa and 70 μm thickness on average (see below) were prepared following a modified protocol reported on the work by Teo et al. (2020) and Rheinlaender et al. (2021) (Figure 2).
Briefly, reagents A (elastomer) and B (curing agent) of the two-part PDMS rubber (DOWSIL CY 52-276, DOW Chemical Company) were mixed in a beaker, following a weight ratio of 1.2:1 (A:B), and then the mixture was sonicated for 10 min to remove gas bubbles. Approximately 100 μL (70 mg) of the mix were added on the center of 29 mm bottom-glass dishes (D29-20-1-N, Cellvis) and spin coated at 9 rps for 30 s. The PDMS substrates were then cured for 2 h at 80 C.
The stiffness of the PDMS substrate can be tuned by changing the ratio of reagents A and B, as stated in Teo et al. (2020) and Kenry et al. (2015). A mix containing reagents A and B in a weight ratio 1:1 should generate substrates with an apparent Young's modulus of about 20 kPa (Kenry et al., 2015), while further increasing the weight ratio in favor of reagent B increases the stiffness (e.g., a ratio of 1:1.2 produces substrates with a Young's modulus of about 40 kPa [Kenry et al., 2015]). Additionally, thicker substrates can be obtained by increasing the volume of PDMS mix added to the dish and decreasing the frequency and time of spin coating, or even removing the spin F I G U R E 2 Diagram showing the steps for the preparation of 2D traction force microscopy substrates. Polydimethylsiloxane (PDMS) elastomer and curing agent can be mixed in different proportions to produce elastic substrates with different stiffness. Spin coating of the PDMS mix generates flat substrates that are later covered with a thin layer of PDMS containing fluorescent microparticles. Before cell seeding, substrates must be coated with an extracellular matrix protein, such as fibronectin or collagen, and then sterilized with Pluronic. After seeding, cells are allowed to attach to the substrate for 24 h before staining the membrane, changing the medium to Leibovitz's-L15, and commencing image acquisition for traction force microscopy experiments. coating step if the volume added is high enough (approximately 300 μL). However, to generate flat surfaces, the parameters indicated above are recommended.
After curing, the surface of the substrates was coated with a thin layer of the same PDMS mix containing fluorescently labeled melamine resin microparticles (MF-FluoGreen-S1940, diameter 1.11 μm, SD 0.05 μm, microParticles GmbH). The powdered monodisperse microparticles were properly mixed with the PDMS (w/w ratio 1:100) in a beaker and sonicated for 10 min before applying 10 μL on top of the cured substrates and spin coating them at 80 rps for 40 seconds.
The substrates were then cured again for 2 h at 80 C and stored at room temperature (RT) in the dark until they were used for cell seeding.

| Characterization of the properties of the elastic substrates
Substrate thickness and Young's modulus are required for TFM algorithms (as explained below). To measure substrate thickness, a layer of small fluorescent nanoparticles (latex beads, 0.5 μm mean particle size, L5530, Sigma-Aldrich, Merck) was added on top of the bottom glass before preparation of the substrate. For this, bottom glass petri dishes were treated with 0.01% (w/v) poly-L-lysine solution (PLL, P6282, Sigma-Aldrich, Merck) for 30 min at room temperature, rinsed with milli-Q water and then treated with an aqueous suspension of the fluorescent nanoparticles diluted 1:1000 for 5 min. The suspension was then removed, and the dishes dried with a N 2 gun before preparing the substrates as stated above. The thickness was then measured in an inverted fluorescence microscope (Axio Observer Z1, Zeiss), by calculating the difference in distance in the Z axis between the bottom layer and the top layer of fluorescent particles. The mean thickness was 68 μm (SD ±10 μm), after measuring the thickness of four different substrates, in seven different points substrates (sample size, n, 28).
The Young's modulus (E) of the substrates was determined by atomic force microscopy (AFM), following the procedures indicated in Kenry et al. (2015). Thicker substrates (approximately 700 μm) were prepared by adding 300 μL of the usual PDMS mix (1.2:1 ratio) without spin coating, and then covered with a top layer of nanoparticles and cured as usual. AFM measurements were conducted in a JPK Nanowizard III (JPK instruments-Bruker). Tipless nitride cantilevers (MLCT-010, Bruker), with a nominal spring constant of k = 0.10 N/m and functionalized with a 20 μm diameter silica particle glued to the tip were used. The cantilevers were calibrated on glass covered with phosphate buffered saline (PBS, 1108.1, Carl Roth) before the measurements, and their spring constants were determined by the thermal fluctuation method (Hutter & Bechhoefer, 1993). The measurements were done in 1% (w/v) bovine serum albumin (BSA, A7906-10G, Sigma-Aldrich, Merck) dissolved in PBS. Force-vs-distance curves were obtained by indenting the surface of the substrates on different points. The tip was approached to the surface of the substrate at a speed of 250 nm/s, the motion recorded for 4 μm with an acquisition rate of 2048 Hz, and a contact setpoint of 5 nN was stablished. After contact, the tip was retracted at the same speed. Force curves were collected for six different substrates, prepared in three different batches; 15 different points per substrate were tested, each point indented three consecutive times (n = 267). Data was then analyzed using JPKSPM Data Processing software (JPK instruments-Bruker).
Force curves were processed to determine the baseline, contact point and indentation, and then Young's modulus (E) was determined by fitting the approach segment of the curves with the Hertz-Sneddon model, following Equation (1): where F is the force, R c indicates the radius of the particle glued to the tip of the cantilever (10 μm), ν is Poisson's ratio (set to 0.5 for incompressible materials) and δ is the indentation of the sample. The mean Young's modulus of the elastic substrates was determined to be 9378 Pa (SD ±792). (v/v) penicillin/streptomycin, 5% (v/v) horse serum (16050122, Gibco, Thermo-Fisher), 0.5 μg/mL hydrocortisone (H0888, Sigma-Aldrich, Merck), 10 μg/mL insulin (I1882, Sigma-Aldrich, Merck), 20 ng/mL epidermal growth factor (EGF, PHG0313, Gibco, Thermo-Fisher) and 100 ng/mL cholera toxin (C8052, Sigma-Aldrich, Merck). Cells were kept in incubators at 37 C with 5% CO 2 and 95% relative humidity until almost reaching confluence. 2.5 | Traction force microscope data analysis TFM data was analyzed using pyTFM 1.3.5, a Python package developed by Bauer et al. (2021) that can be used to determine force generation and stresses in single cells, cell colonies and cell monolayers.

| Cell culture and TFM sample preparation
The package was used as an add-on for the image annotation tool Clickpoints (Gerum et al., 2017). A full tutorial can be found in the following webpage: https://pytfm.readthedocs.io. Images from each experiment were loaded into Clickpoints, the images corresponding to the same field of view (cell membranes, particles before and after cell removal) stacked together, and then the global drift between images in the same stack was corrected. The deformation field was subsequently calculated using the particle image velocimetry (PIV) crosscorrelation algorithm (Liberzon et al., 2021), and the traction stresses were then determined using the Fourier traction transform cytometry (FTTC) method (Butler et al., 2002), both included in the software. all the experiments the substrates were assumed to have an equal stiffness of 9000 Pa (based on the measured stiffness, as indicated above) and a Poisson's ratio of 0.5. The height of the gel was determined as 70 μm, although we only analyzed single cells that are smaller than the thickness of the substrates, and therefore this correction term is unnecessary Trepat et al., 2009). Once the traction stresses field was calculated, a mask containing all the tractions that corresponded to each individual cell was drawn, the cell boundaries were drawn using a second mask, and the strain energy and contractility of the cells were determined.   (Kraning-Rush et al., 2012;Li et al., 2017;Massalha & Weihs, 2017;Rheinlaender et al., 2021;Shebanova & Hammer, 2012). MCF-7, on the other hand, is an epithelial human breast cancer cell line, tumorigenic but with low metastatic potential (Comsa et al., 2015), whose traction forces have also been studied previously (Li et al., 2017;Rheinlaender et al., 2021). MDA-MB-231 is a basal-like, triple negative human breast cancer cell line, with high metastatic potential, also employed in cancer cell mechanics and traction forces studies  Note: n indicates the number of cells analyzed (before removal of outliers). In each data set, the mean value ± standard deviation (SD) is shown.  Table 1. In general, cell area did not seem to be affected by the treatment with cytochalasin-D, except for MCF-10A cells, whose cell area incremented significantly after the cytochalasin-D treatment (Figure 4, 2406 versus 3976 μm 2 ).

| Statistical analysis and data presentation
Total force generation of the cells is defined by the strain energy, the total energy that the cells employed in deforming the substrate; this strain energy is calculated following equation where d ! and f ! are the deformation and the traction force vectors, respectively . Figure 5a shows Another parameter frequently shown in TFM analysis is the contractility of the cells, which is defined as the sum of the projections of all the traction forces towards the force epicenter .
While the strain energy measures the total force generation, the contractility measures the coordinated force generation. Figure 6 shows  Table 1 gives an overview of the main parameters that are relevant when using traction force microscopy.

DATA AVAILABILITY STATEMENT
The data that support the findings of this study are available from the corresponding author upon reasonable request.