Quantifying cellular forces and biomechanical properties by correlative micropillar traction force and Brillouin microscopy

: Cells sense and respond to external physical forces and substrate rigidity by regulating their cell shape, internal cytoskeletal tension, and stiﬀness. Here we show that the combination of micropillar traction force and noncontact Brillouin microscopy provides access to cell-generated forces and intracellular mechanical properties at optical resolution. Actin-rich cytoplasmic domains of 3T3 ﬁbroblasts showed signiﬁcantly higher Brillouin shifts, indicating a potential increase in stiﬀness when adhering on ﬁbronectin-coated glass compared to soft PDMS micropillars. Our ﬁndings demonstrate the complementarity of micropillar traction force and Brillouin microscopy to better understand the relation between cell force generation and the intracellular mechanical properties.

into continuum substrates [27]. These include (i) the capability to calculate displacements by exploiting the undeflected pillar positions in the patterned (e.g. hexagonal) grid, without the need for a reference image and (ii) the simpler and less computationally intensive force calculation due to the discrete adhesive surface (i.e. deflections of a given pillar only depend on the force applied to that pillar). However, compared to continuum substrates, such discrete adhesive surface affects the morphology of cell-ECM adhesions and the ability to reproduce the wide variations in stiffness found in in vivo tissues due to the restricted stiffness range (approximately one order of magnitude).
Brillouin microscopy is an emerging approach showing increasing biological interest because it enables an all-optical, label-free and three-dimensional assessment of the subcellular biomechanical properties at a submicron resolution [28,29]. In Brillouin imaging, a sample is scanned while a narrowband laser source probes point-by-point the spontaneous thermally-activated acoustic waves that locally propagate in the medium at the acoustic velocity [30]. A high-resolution (sub-GHz) spectrometer is thus used to analyze the spectrum of the scattered light [31,32]. The latter contains an elastic (Rayleigh) peak of the same frequency as the illumination laser beam, and two sidebands referred to as the Stokes and Anti-Stokes Brillouin peaks thinly shifted by few GHz from the central peak [33]. The frequency and the linewidth of the Brillouin peaks are directly related to the high-frequency complex Longitudinal modulus (M), which is indicative of the viscoelastic properties of the material analyzed [34]. Recently, water content has been shown to dominate shifts in the Brillouin frequency of highly hydrated (>90%) gels [35], as expected by the compressibility nature of the longitudinal modulus [36]. Such a scenario is however rather unrealistic in biological samples where water content is significantly lower (<70%) and naturally contribute to the overall stiffness of the material investigated [37].
The noncontact, label-free and high-resolution capabilities of Brillouin microscopy have stimulated a wide range of applications, including the assessment of the cellular mechanical properties and their response to external stimuli [38][39][40][41], the mapping of the spinal cord stiffness in zebrafish larvae [42] and the investigation of the Alzheimer's plaque viscoelasticity [43]. Moreover, Brillouin microscopy holds promise to become a potential diagnostic instrument for diseases such as atherosclerosis [44], keratoconus [45], cancer [46], meningitis [47] and amyotrophic lateral sclerosis [48,49]. To this aim, significant research efforts have also focused on the instrumental advancement to achieve a high spectral contrast [38,50,51] and extinction ratio [52,53], as well as to decrease the data acquisition time [54,55], which are key ingredients to enable in-vivo measurements of living biosystems.

Cell biology
3T3 fibroblasts were cultured in high-glucose Dulbecco's Modified Eagle's Medium (DMEM) supplemented with 10% calf serum (Thermo Scientific), 2 mM glutamine and 100 µg/ml penicillin/streptomycin. Cells were seeded at single cell density directly on the micropillar array or on a glass (#1.5) bottom 35 mm dish (Ibidi). Cells were allowed to spread for 24 hours before fixation in 4% Paraformaldehyde for 15 minutes. After membrane permeabilization with 0.1% Triton-X (Sigma) for 10 minutes followed by a blocking step with 1% bovine serum albumin (BSA, Sigma) in PBS for 1 hour, actin filaments and nuclei were stained with Alexa-Fluor 532-conjugated Phalloidin and DAPI (Life Technologies), respectively. Micropillar arrays were subsequently inverted onto glass (#1.5) bottom 35 mm dish (Ibidi) with imprinted 50 µm cell location grid and immersed in PBS. Glass weights were used to prevent the arrays from floating.  ) was used to collect the fluorescence signal emitted by the micropillars and therefore to measure the cellular adhesion forces from the pillar displacements [21]. The same sample was then moved to the Brillouin imaging setup ('SETUP 2') where the scattered signal was collected in a backscattering geometry and delivered to the background-deflection (BD) spectrometer. This is a single-stage VIPA spectrometer integrating a diffraction mask (DM) to deflect the elastic background signal from the dispersion axis [48]. (B) Sensitivity histogram of the Brillouin setup. N=1000 spectra were acquired on a PDMS sample. System sensitivity was evaluated to be σ = 0.025 GHz.

Force measurement on micropillar arrays
A hexagonal array of poly-di-methyl-siloxane (PDMS, Sylgard 184, Dow Corning) micropillars of 2 µm diameter, 4 µm center-to-center distance and with a height of 6.9 µm were produced using replica-molding from a silicon wafer (for details see [21]). The pillar arrays were flanked by integrated 50 µm high spacers to allow the inversion onto glass bottom dishes, without compromising the already limited working distance of a high-NA objective on an inverted microscope. The tops of the micropillars were coated with a mixture of Alexa Fluor 647-labeled and unlabeled fibronectin (1:5, Life Technologies) using micro-contact printing. The position of the pillar tops was observed by fluorescence confocal microscopy at 647 nm excitation (Fig. 1A) and determined down to 30 nm accuracy using custom software (Matlab, Mathworks). Forces were obtained by multiplying the pillar deflections by the array's characteristic spring constant (16.7 nN/m determined by finite element modeling) [21]. Such spring constant corresponds to an equivalent Young's modulus in continuous substrates of ∼ 11.6 kPa, calculated as proposed in [56]. Only pillars at the cell perimeter and with a deflection above a given threshold (∼50 nm) were considered for the calculation of the average force per pillar and total cellular forces. Such threshold was determined for each confocal image as the 75th percentile of the displacements of pillars outside the cell area (i.e. not bent by the cells).

Confocal microscopy
3T3 fibroblasts adherent on fibronectin-coated glass and soft PDMS micropillar arrays were imaged with an inverted Olympus IX83 microscope, equipped with an UPLSAPO 60XW/1.2 NA water immersion objective ( Fig. 2A-B). The collinear light beams from 405 nm, 546 nm, and 647 nm laser diode light sources were injected into the microscope via a FV1200 MPE laser scanning confocal device. The 2048×2048 pixel fluorescence images (51 nm pixel size) were collected in line sequential mode to reduce the cross-talk among the fluorescence channels.

Brillouin microscopy
After fluorescence imaging, the same cells were transferred to the Brillouin confocal microscope (Fig. 1A) to investigate their biomechanical properties. The Brillouin microscope is composed of a standard scanning confocal imaging setup working in a backscattering geometry [29] where cells are illuminated by a single longitudinal mode laser beam (λ=532 nm, Coherent Verdi).
The scattered light was collected by a microscope objective of NA=1.3 and a single mode fiber working as a confocal pinhole were used, providing a spatial resolution of ∼ 0.3x0.3x1.1 µm 3 and a flexible beam delivery to a single-stage Virtually Image Phased Array (VIPA) spectrometer. The latter integrates a rhomboidal-shaped diffraction mask to deflect the background elastic light from the dispersion axis, in turn providing a spectral contrast of ∼ 70 dB in a single-stage arrangement, as previously reported in [48]. Brillouin spectra were acquired at each scanning location across the cells and detected by a CCD camera (Photometrics Prime) with a data acquisition (dwell) time of 100 ms. The resulting spectral profiles were fitted by Lorentzian functions to evaluate the frequency shift, which is related to the real part of the Longitudinal compressive modulus M (i.e. a measure of stiffness). Preliminary measurements were performed to characterize the system sensitivity. To this aim, N=1000 Brillouin spectra of bulk PDMS were acquired and fitted using a Lorentzian function. Fig. 1B shows a histogram of the measured Brillouin shift counts, which gave a mean value of ν B = 6.237 GHz and a system sensitivity associated with the uncertainty of σ = 0.025 GHz.
Representative Brillouin images of 3T3 cells are shown in Fig. 2C-D. Normalized probability density functions (PDFs) of Brillouin shifts were calculated by pooling together the acquired Brillouin images and considering the sensitivity of the system (i.e. σ = 0.025 GHz) (Fig. 3). The highest peaks in Fig. 3A correspond to the contribution of PBS. To uncouple the buffer component from the cellular contribution, as shown in Fig. 3A, we performed a Gaussian fit (black dashed line) of the highest peak from glass (red solid line) and we defined the Gaussian mean plus its standard deviation as the Brillouin shift threshold (i.e. ν T B =7.466 GHz).

Results and discussion
We measured in a correlative fashion the contractile forces and the intracellular mechanical properties of 3T3 fibroblast cells adherent on substrates of controlled stiffness (elastic micropillars and glass) and biochemical composition (i.e. fibronectin coating) (Fig. 1). Fig. 2 shows representative fluorescence confocal images of single cells adherent on an elastic micropillar substrate ( Fig. 2A) and a standard glass coverslip (Fig. 2B). The associated Brillouin images are shown in Fig. 2C-D. The micropillar deflections allowed us to quantify the forces exerted by 3T3 cells on a soft substrate ( Fig. 2A). The Brillouin images show a significant increase in the Brillouin frequency shifts ν B across the nucleus with respect to the cytoplasm, as previously reported [38,39]. Remarkably, the average ν B significantly increased from 7.51±0.05 GHz to 7.57±0.08 GHz (p<0.05) as a function of substrate stiffness (Fig. 2C-D).
To further exploit the subcellular resolution of the Brillouin microscope, we analyzed the distribution of ν B for adherent cells on soft micropillars and glass (solid blue and red lines in Fig. 3A, respectively). The highest peaks correspond to the contribution of the buffer content (i.e. PBS). We then calculated a threshold value (ν T B =7.466 GHz) above which the ν B values belonged to the subcellular components (see Methods in 2.4). It is interesting to note that the left tail in the distribution of ν B on soft micropillars corresponds to the Brillouin signal of the PDMS micropillars themselves, whose positions can be clearly detected (Fig. 2C). In we show the multimodal distributions of ν B after thresholding (i.e. across cells) (solid blue and red lines) and the results of a non-linear least-squares fit with three independent Gaussian components (light blue and red lines) (see Fig. 6 in the Appendix for the choice of such model). We focused our further analysis and discussion exclusively on the Gaussian mean values rather than on the amplitude and variance because we believe that the latter present higher dependency on the biological variability and sample size. The obtained parameters in Table 1 interestingly suggest the existence of three major subcellular components with characteristic ν B values.   Table 1. The choice of such model is clarified in Fig. 6 in the Appendix. Table 1. Parameters from a non-linear least squares fit with three independent Gaussian functions of the Brillouin shifts PDF reported in Fig. 3B. A * , µ * and σ * are the amplitude, mean and standard deviation (±95% CI) of the Gaussian functions. The p-values were obtained from a t-test for which the significance level was set to p-value<0.05 (N=5 cells and 6 cells for soft PDMS micropillars and glass, respectively). Tee et al. [4] have previously demonstrated that the cell cortical stiffness increases as a function of substrate stiffness. The cell cortical stiffness was measured by Atomic Force Microscopy (AFM) in regions far from lamellipodia and nucleus, obtaining an ensemble average over both cortical actin and stress fibers (if close enough to the dorsal cell surface). In light of these findings, we hypothesized that the intermediate Brillouin shift values that we introduced above refer to the contribution of actin stress fibers and therefore provide a measure of their mechanical properties.
To validate our hypothesis, we performed a high-resolution Brillouin line scan far from the nucleus crossing actin stress fibers, which were detected in a correlative fashion by fluorescence confocal imaging (dashed red line in Fig. 4). The actin stress fibers could not be spatially resolved by the Brillouin microscope due to a size that typically falls below 100 nm in diameter. Nevertheless, the Brillouin shift line profile had an effective (mean) value close to the intermediate ν B value of Table 1 (µ 2 =7.608±0.002 GHz, dashed grey line). In addition, it is interesting to note a decrease in the Brillouin shifts towards µ 1 (dashed grey line) at the two ends of the line profile, i.e. in the proximity of the lamellipodia. These results support our hypothesis that we could (i) identify the Brillouin shift component potentially associated with the actin stress fibers and (ii) indirectly quantify changes in the intracellular biomechanical properties as a function of substrate stiffness.  Table 1.
We further investigated the relation between the actin Brillouin shifts and the mechanical forces generated by 3T3 fibroblasts on soft PDMS micropillars (Fig. 5)

Conclusion
In this work, we showed a correlative combination of micropillar traction force microscopy and Brillouin imaging methods to quantify cellular forces and intracellular biomechanics as a function of substrate stiffness. The label-and contact-free nature of the Brillouin imaging approach allowed us to go beyond the limitations present in AFM assessments and to quantify the mechanical properties of actin stress fibers with unprecedented spatial resolution. A fully integrated and high-resolution fluorescence and Brillouin microscope with live cell imaging capabilities will grant us simultaneous access to fundamental biomechanical information to better understand cell mechanotransduction.