## Results

### Four-color live cell imaging of adhesion sites

A fundamental barrier in studying cell-matrix adhesion sites arises from their molecular heterogeneity and large number of components1,7,16. Coping with this barrier requires the monitoring of multiple components in individual adhesion sites17,22. We previously reported 5-color imaging of cell-matrix adhesion sites in fixed cells, achieved by combination of orthogonal immunofluorescence labelings, small molecules and tagging with fluorescent proteins17. Along this line, we recently achieved imaging of 10 different components in single focal adhesions using cyclic immunofluorescence imaging15 – a techniques in which fixed cells are subjected to serial cycles of immunolabeling, imaging and bleaching. While multiplexed imaging of adhesion sites in fixed cells uncovers their composition diversity, for studying dynamic patterns of molecular changes in focal adhesions it is essential to perform multiplexed imaging in live cells. Although a large palette of fluorescent proteins with different emission and excitation spectra is available23, combining them for multicolor imaging is strongly hampered by their spectral overlap19. Multispectral imaging and linear unmixing can provide a good solution for cases in which most of the labeled components do not overlap spatially within the cell and that the co-localized ones are present in comparable levels19,24,25,26. However in the case of focal adhesions, the components are localized in the same small structures and could have highly incomparable levels17,19. In such cases, spectral imaging and unmixing are sensitive to noise and prone to errors in quantifying the contribution of each fluorescent protein to the integrated measured spectra in each pixel19. Therefore, to achieve quantitative multicolor imaging of adhesion sites it is required to use a combination of fluorescent proteins that can be spectrally separated without unmixing.

To facilitate sensitive 4-color live cell imaging of focal adhesions, we selected an optimal genetic-tagging combination of four fluorescent proteins, based on their photostability and spectra – mTagBFP, mTFP, mCitrine and mKate (Supplementary Fig. S1). Although this combination maximizes the spectral separation, inevitable partial spectral overlaps between the four fluorescent proteins still exist. Sequential excitation and imaging of each fluorophore facilitates further the spectral separation, without reducing the desired acquisition rate of one image every two minutes. Still, to completely separate the signals of the four fluorescent proteins it is required to narrow down the range of wavelengths collected for each one, which reduces the signal-to-noise ratio19. To compensate for this, we used tandem repeats (TD) of three of the fluorescent proteins (TDmTagBFP, TDmTFP, TDmKate2), thereby increasing the total brightness of these labels (Supplementary Fig. S1). An undesirable side-effect of such brightness increase can be a higher bleed-through to the other channels. However, since the edges of the emission spectra decay steeply and non-linearly along the spectrum, it is possible to effectively omit such bleed-through by narrowing down slightly the range of wavelengths collected for each fluorophore (Supplementary Fig. S1). The gain of brightness increases the signal-to-noise ratio, thereby enabling quantitative imaging in live cells of four proteins in the same small structures, such as cell-matrix adhesion sites (Fig. 1).

### Heterogenous responses of focal adhesion components to ROCK perturbations

For studying the molecular diversity in the mechano-responsiveness of focal adhesions we focused on four key proteins, including: paxillin and FAK which are vertically located within focal adhesions close to the plasma membrane, in the integrin signaling layer27,28,29,30,31, vinculin which is located at a higher vertical distance at the force transduction layer28,32,33,34,35 and zyxin which is embedded at the actin modulation layer and has been depicted as a prominent mechano-responsive component13,14,28,36 (Fig. 1A,B). Acute inhibition of actomyosin contractility was achieved by addition of the ROCK inhibitor Y-2763221,37,38 and recovery of contractility was achieved by washout of the drug (Fig. 1A). To investigate how mechano-responsiveness of focal adhesions is modulated by previous force perturbations, we applied two sequential cycles of ROCK inhibition and recovery (Fig. 1A,C). As expected, focal adhesions gradually disassembled upon actomyosin inhibition and reassembled following the washout of the inhibitor (Fig. 1C). The adhesion sites that were quantified were verified to be indeed focal adhesions, based on their zyxin content (Supplementary Fig. S2) and disassembly in response to ROCK inhibition (Fig. 1C). Most focal adhesions disassembled to sub-detection level following each of the Y-27632 treatments, while others disassembled partially and thereby spanned throughout the experiment (Figs 1C and 2A). Hence, the obtained data enables comparing the dynamic response patterns of zyxin, FAK, vinculin and paxillin to actomyosin contractility perturbations among a large number of single focal adhesions in live cells.

### Diverse compositional changes in focal adhesions in response to ROCK perturbations

We asked whether the observed variability in the response extents of zyxin, FAK, vinculin and paxillin to ROCK reflects different changes in the compositions of focal adhesions. To resolve and visualize compositional changes from multicolor data it is important to consider all the labeled components simultaneously. Compositional imaging achieves this by clustering the pixels of multicolor images according to the similarity in the intensity ratios between the labeled components17. Here we extended compositional imaging to multicolor live cell data (see Methods) and thus resolved 7 distinguishable compositional signatures within the focal adhesions during their responses to ROCK perturbations (Fig. 3A,B). Visualizing the localization of these compositions in the cells revealed differential spatiotemporal organizations (Fig. 3C, Supplementary Fig. S4 and Supplementary Movies S1S5). Compositions which are enriched with zyxin (named A, B, C and E) get less abundant upon Y-27632 additions and more abundant upon washouts (Fig. 3B–E and Supplementary Movies S1S5). In contrast, compositions with low levels of zyxin (D, F and G) become more abundant upon Y-27632, while getting less abundant upon its first washout with the exception of composition F (Fig. 3B–E). Interestingly, while changes in the abundance of zyxin-rich compositions (A, B, C and E) were consistent among the two perturbation cycles, changes in the abundance of zyxin-low compositions (D, F and G) were not (Fig. 3D). This points toward a potential modulation of the focal adhesion mechano-responsiveness by past mechanical perturbations and depicts zyxin as a component which is less sensitive to such modulations.

### Weak correlations between the responses of focal adhesion components to ROCK perturbations

The observed variability in the responses of proteins to ROCK perturbations can be driven by spatial diversity in local external cues (e.g. different force levels), diversity in the internal composition of focal adhesions and biochemical or measurement noise15. Random noise is expected to lead to response extents which are uncorrelated between the proteins, while diversity in biological cues can give rise to correlated responses15. The pairwise correlations between the response extents of zyxin, FAK, vinculin and paxillin across focal adhesions were found to be significantly positive (Fig. 4A and Supplementary Fig. S7). Therefore the observed variability in the response extents is not dominated by random measurement noise or biochemical noise. Potential correlated noise between the imaging channels is also not expected to affect the derivations of response extents, as for these calculations the densities of proteins before and after perturbations were averaged over three sequential time points. Therefore the observed variability indicates, at least in part, biological diversity which is plausibly driven by variability of local cues.

While the correlations between protein responses to ROCK perturbations are significantly positive, the strengths of these correlations are moderate or weak, with average Pearson correlation coefficients ranging between 0.2–0.6 (Fig. 4A). Of note, the correlations between protein responses to the first addition of Y-27632 were stronger than the corresponding correlations upon the followup perturbations (Fig. 4A). Yet, this can reflect the overall stronger responses of the focal adhesions to the first perturbation. Pair-wise comparisons of the response extents of proteins indicate that they can be approximated to be either statistically independent or linearly related (Supplementary Fig. S7). Therefore, although different proteins may have different, nonlinear, response properties to force and other cues, the lack of strong correlations between their responses is unaccountable by deviation from linearity. Instead, the weak or moderate correlations between the responses of the proteins to ROCK perturbations suggest that additional multiple local and independent cues shape these responses differentially.

### Differential relations between the mechano-responsiveness of focal adhesion components and local cues

We next examined whether the response extents of zyxin, FAK, vinculin and paxillin to the ROCK perturbations correlate with the pre-perturbation size of focal adhesions. In focal adhesions which are bigger before perturbation, the response extents of the proteins to ROCK inhibition tend to be bigger, though with a moderate correlation strength (Fig. 4D). In comparison, the areas of focal adhesions before Y-27632 washout were more weakly correlated with the response extents of zyxin, FAK, vinculin and paxillin upon the washout (Fig. 4D). A possible explanation for this asymmetry is that in the presence of unperturbed actomyosin contractility, the area of focal adhesions is more governed by the applied mechanical force, therefore bigger focal adhesions are likely to experience a bigger decrease in force levels upon actomyosin inhibition. In contrast, after the actomyosin contractility is inhibited for sufficient time the remaining size of the disassembled focal adhesions is plausibly determined by other factors which are not indicative of the expected elevation in force upon contractility recovery.

All the aforementioned correlation analyses were performed by sampling a single time point after each perturbation. Importantly, the values of these correlations are expected to change along the experiment, hence altering also the patterns of correlations. Indeed, comparing the correlations obtained for 12 minutes versus 24 minutes after perturbations, between pre- and post- perturbation densities, shows that not only they get weaker with time, they also change their relative magnitudes (Supplementary Fig. S8A). An additional possible bias is that a larger range of response extents can provide higher Pearson correlation coefficients with another parameter, since it is less affected by a given noise level. However, the important features that remain robust are the presence of significant, though moderate, correlations between the compared parameters, and that these correlations are often nonuniform among proteins, perturbation types and perturbation cycles. Therefore, taken together, the correlation analyses suggest that multiple local cues are integrated to shape differentially the responses of zyxin, FAK, vinculin and paxillin to actomyosin contractility perturbations.

### Diverse patterns of responses to ROCK perturbations among single focal adhesions

Given the variable responses of zyxin, FAK, vinculin and paxillin to ROCK perturbations, and the overall moderate correlations between them, we sought to discriminate between two alternative options regarding the path of the occurring molecular changes. Such a path can be described as a trajectory in a multidimensional phase space, where each dimension corresponds to the level of one of the imaged components, indicating the levels of the four proteins along the experiment. The first possibility is that the molecular changes that occur in different focal adhesions follow different quantitative manifestations of qualitatively the same path trajectory. This possibility implies that certain qualitative features of the trajectory shape should be retained in all responding focal adhesions. The alternative possibility is that in different focal adhesions the trajectory of the molecular changes has a qualitatively different shape. The difference between the two options is fundamental, since the first one implies a fixed pattern of molecular changes while the second option allows for flexible patterns of molecular changes to occur in response to ROCK perturbations. Two-dimensional phase space diagrams, showing for individual focal adhesions the levels of two proteins versus each other along the experiment, capture illustratable projections of response paths, in all possible pairwise protein combinations (Fig. 5B and Supplementary Fig. S9). The average path of molecular changes reflects the observed average response properties, including the stronger response of zyxin to the ROCK perturbations (Fig. 5B, left). However inspecting the paths of molecular changes in single focal adhesions uncovered a variety of qualitative differences in their trajectories (Fig. 5B, right). Hence, these observations indicate directly that the patterns of molecular changes occurring in focal adhesions are flexible to a considerable extent.

We next compared the abundances of the response extent hierarchies among the various ROCK perturbations. The abundances of these hierarchies were found to be positively correlated between the two repeats of the same kind of perturbation (Supplementary Fig. S10C). Therefore, the first cycle of perturbations did not alter the relative sensitivities of zyxin, FAK, vinculin and paxillin to actomyosin contractility with respect to each other. The abundances of the fold response hierarchies upon Y-27632 addition are strongly negatively correlated with those upon washout (Supplementary Fig. S10C). Since fold density change is calculated as log (density after/before perturbation) for all perturbations, these strong negative correlations indicate that the opposing force perturbations only rarely lead to opposed hierarchies of response strengths. Instead, the tendency of a given protein to arise as a stronger responder is comparable for ROCK inhibition and recovery, as reflected also in the distribution of the strongest responders (Fig. 6B). Taken together, the results show that the hierarchy of zyxin, FAK, vinculin and paxillin response extents to ROCK perturbations, as well as the overall dynamic response pattern, are not conserved but instead significantly varying among single focal adhesions.

## Methods

### Cell culture and transfection

Rat embryonic fibroblasts (REF52; kindly provided by Joachim Spatz and Benjamin Geiger) were cultured in Dulbecco’s modified eagle’s medium (DMEM) containing 10% fetal bovine serum (Invitrogen, Carlsbad, CA, USA), 1% penicillin/streptomycin and 1% L-glutamine (PAN Biotech GmbH, Aidenbach, Germany) in a 5% CO2 humidified incubator at 37 °C. For live cell imaging, cells were plated with 400 μl DMEM in 8-well LabTek chamber slides (Thermo Fisher Scientific, Waltham, MA, USA) at a density of 104 cells per well and co-transfected the next day with a tandem (TD) monomeric Kate2 (TDmKate2-zyxin)40, mCitrine-FAK40, TDmTFP-vinculin and TDmTagBFP-paxillin (constructed by Kondaiah Moganti and Ruth Lambertz née Stricker, Max Planck Institute of Molecular Physiology, Dortmund, Germany) using Lipofectamine 2000 (11668-019, Invitrogen). Following transfection, cells were incubated for 24 hours prior imaging.

### Microscopy

Multicolor live cell imaging was performed using a Zeiss LSM 510 Meta confocal microscope (Carl Zeiss, Jena, Germany) with a 40x water immersion objective and pre-warmed incubation chamber at 37 °C with 5% CO2. Before imaging, the growth media was replaced by imaging media (P04-01163, PAN Biotech, GmbH) supplemented with 10% fetal bovine serum. Multicolor imaging data was acquired by sequential excitation and detection of TDmKate2-zyxin (excitation at 561 nm and emission detection at 575–800 nm), mCitrine-FAK (excitation at 514 nm and detection at 530–565 nm), TDmTFP-vinculin (excitation at 458 nm and detection at 470–500 nm) and TDmTagBFP-paxillin (excitation at 405 nm and detection at 420–480 nm). At the indicated time points during the time lapse imaging, Y-27632 (Y0503, Sigma-Aldrich, St Louis, MO, USA) was added from a stock solution of 10 mM in water to give the final applied concentration of 100 μM, to inhibit ROCK and later washed out from the cells dish using imaging media (“washout”). The applied dose of Y-27632 facilitates an abrupt and synchronized inhibition of actomyosin contractility17,38,55,56,57,58, thereby enabling to compare the dynamics of proteins across different focal adhesions and cells. For chromatic aberrations correction, multicolor TetraSpeck 1 μm diameter beads (T14792, Invitrogen) were imaged using the same setup, but with a higher laser power to enhance the signal-to-noise ratio.

### Image preprocessing

The acquired multicolor live cell data consist of an array of images, Imgraw(c, t, p), where c = 1, …, 10 cell index, t = 1, …, n time frame and p = 1, …, 4 imaging channel. Chromatic aberrations were measured based on the multicolor TetraSpeck beads images and accordingly each image in Imgraw(c, t, p) was corrected with respect to its corresponding mCitrine channel image. The background intensity in each image was measured in a region outside cells and then subtracted from the whole image. Then bleaching was corrected by multiplying each image by a factor that keeps the total intensity of the corresponding protein in the corresponding cell constant along time. High-frequency spatial noise in these images was removed by low-pass mean filtration with a radius of one pixel. Then, low-frequency spatial background noise was removed by high-pass filtration in which the value of each pixel is subtracted by the mean intensity of the pixels within a 6 μm-wide box around it. Pixels with negative values were then set to zero. Lateral shifts between images of different time frames, due to minor movements of cell dish during acquisition and perturbations, were corrected by restoring the xy-shift in the pixels as estimated from the image registration of the reference (i.e. mCitrine) channel. For compositional imaging (Fig. 2), high-frequency noise was smoothed using the nsmooth algorithm59. For the analysis of single focal adhesions responding to two repeated perturbations (Figs 2A and 5) Kalman filtration was applied.

### Compositional imaging

Compositional imaging resolves and visualizes spatial and temporal differences in the molecular composition of intra-cellular structures17. Similar to ratio imaging between two proteins6,16, in compositional imaging the ratio between the levels of labeled and unlabeled copies of a component is an unknown constant which gets mathematically cancelled in the comparisons of compositions between time points or spatial positions17. For compositional imaging analysis pixels were pooled from the processed Imgpr(c, t, p) images of five cells, resulting in an array $$Px{l}^{all}(c,t,x,y,\vec{I})$$ where c = 1, …, 5 cells, t = 1, …, n time frames, x and y indicate the pixel position, and $$\vec{I}$$ is a vector containing the intensity levels in the four imaging channels in this pixel. Pixels outside focal adhesions with background intensity levels were removed by setting an intensity threshold for each protein in each cell and excluding those pixels that have for all proteins intensity values lower than the corresponding thresholds, resulting in a shorter list of pixels. To make the data comparable between cells and to give each protein an equal weight in the further analysis, the intensity values of each protein were then normalized by dividing them by the median value of all pixels with positive intensity values in the corresponding cell. Pixels with overall low intensity values were excluded by thresholding them based on the root of the sum of squared intensity values of the four proteins, $$\sqrt{({\rm{\Sigma }}{I}_{j}^{2})}$$. The composition stoichiometry of the four proteins in each pixel was then calculated by dividing the intensity value of each protein by $$\sqrt{({\rm{\Sigma }}{I}_{j}^{2})}$$, thereby obtaining its fractional intensity. The resulted array of pixels were then clustered by hierarchical clustering with spherical distance metric to group pixels with similar composition using a custom C++ program. The program implements the standard hierarchical agglomerative clustering algorithm but calculates the distance between points over the surface of a unit sphere. New points resulting from the merge of others are also calculated over such a surface, to maintain the stoichiometric normalization of the data. To enable clustering large datasets, the program does not store in memory the distance between points but calculate them on demand. This results in a longer calculation time which is mitigated by applying a parallel computing approach implemented using OpenMP. The obtained clustering dendrogram was partitioned interactively to a set of clusters which are consistent with its topology and exhibit distinct spatial or temporal profiles. These clusters were spatially visualized as compositional images by color-coding each pixel according to the cluster it belongs to.