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# Mechanical interactions among followers determine the emergence of leaders in migrating epithelial cell collectives

## Abstract

Regulating the emergence of leaders is a central aspect of collective cell migration, but the underlying mechanisms remain ambiguous. Here we show that the selective emergence of leader cells at the epithelial wound-margin depends on the dynamics of the follower cells and is spatially limited by the length-scale of collective force transduction. Owing to the dynamic heterogeneity of the monolayer, cells behind the prospective leaders manifest locally increased traction and monolayer stresses much before these leaders display any phenotypic traits. Followers, in turn, pull on the future leaders to elect them to their fate. Once formed, the territory of a leader can extend only to the length up-to which forces are correlated, which is similar to the length up-to which leader cells can transmit forces. These findings provide mechanobiological insight into the hierarchy in cell collectives during epithelial wound healing.

## Introduction

To understand how leader cells emerge, here we have studied mechano-biological aspects of epithelial wound healing resolved in time and space. Using traction force and monolayer stress microscopy, we find that the leader cells at the wound-margin are effectively selected by the mechanical interactions of the follower cells located behind the leading edge. We demonstrate that the followers mechanically pull on the future leader, aiding in their polarization and protrusion. Combining experimental data with theoretical modeling, we are able to show that the territory of a leader extends only to the length up to which forces are correlated in the monolayer, which is similar to the length up to which leader cells can transmit forces. This finding, therefore, provides a mechanism for the formation of leader cells during collective cell migration, wherein we place mechanical interactions between the cells as the central player that determines when and where a leader cell would emerge.

## Results

Next, to understand the possible implications of the local increase in traction and tensile stresses on leader cell formation, we examined different microscopic mechanobiological traits of the individual cells including cell shape and aspect ratio, before the commencement of migration process. Relevantly, even a fully confluent epithelium can exist in two distinct structural states: jammed (solid-like) and unjammed (fluid-like) as explained by dynamic heterogeneity of the monolayer24,25,26. Moreover, as elucidated in normal and asthmatic bronchial epithelia, an unjammed monolayer displays considerably higher cell-matrix traction than a jammed one25. Further, a non-dimensional shape index (q) measuring the ratio of the perimeter to square root of the projected cross-sectional area (q=P/√A) of the individual cells can capture the specific state of the cells. Jammed cells were characterized with q < 3.81 and unjammed cells with q > 3.8124,25. In order to probe if the increase in traction stresses are associated with the possibility of local unjamming within a pre-migratory monolayer, we computed the shape index (q) for each individual cell. Indeed, follower cells behind the prospective leader cells displayed higher shape index than other cells within the same depth, at both temporal phases (Fig. 1c–f). Taken together, these results indicated a systematic elevation of tensile stresses and unjamming-like transitions of the cells immediately behind the prospective leader already in pre-migratory monolayer, though confirmation of true unjamming transition would ideally require further characterization of force fluctuations and perimeter elasticity. Since in an epithelial monolayer, the tensile stress is transmitted across the cell–cell junctions and is exclusively balanced by the cell–cell adhesive stress24, these results also implicated a local increase in the cell–cell junctional stresses between future leaders and corresponding follower cells.

We then investigated whether, beyond the aforementioned correlation, this local increase in traction and tensile stresses and the unjamming-like behavior among the follower cells has any causal relationship with the cells ahead of them becoming the leader cells. Our earlier research has elucidated that a tumor-suppressor protein, merlin, supports collective cell migration by regulating the polarization of a migration promoting molecule Rac1 and thereby governing the direction of the cell motility within a monolayer23. Incidentally, on depleting the expression level of merlin with a specific small interfering RNA (siRNA), the resultant cell phenotype appeared intrinsically more unjammed and less correlated with their neighbors than the control cells as characterized by particle image velocimetry (Supplementary Fig. 4). The inverse relation between unjamming and velocity correlation length was similar to previous study27. In contrast to wild-type cells, merlin-depleted cells stay perpetually in an unjammed-like state even in confluent condition (Supplementary Figs. 4, 5a). Merlin-depleted cells showed higher traction stresses as well as higher shape index than control cells (Supplementary Fig. 5a). Taking advantage of this property of merlin depletion, we then mixed fluorescently labeled merlin-depleted cells with unlabeled wild-type cells in 1:10 ratio and determined the probability of the emergence of a leader cell in front of any merlin-depleted cell groups (Supplementary Fig. 5b). The statistics took account of only those cases where the 2–6 layers behind the wound margin contained at least two merlin-depleted cells. We further excluded any merlin-depleted leader cell. For control experiments, a scrambled siRNA replaced merlin siRNA while other conditions remained unchanged. The results consequently revealed that the presence of relatively unjammed merlin-depleted cells increases the probability of a marginal cell ahead of them to become a leader cell (Supplementary Fig. 5c).

These experiments together revealed that local development of contractile stresses as shown by increased stresses in the monolayer and unjamming-like transition in the following layer as shown by the increased shape indices stimulate leader cell formation during collective migration of epithelial cells. They also implied that while the emergence of leader cells is itself an interfacial phenomenon18, the factor regulating it have a hitherto unknown non-interfacial or bulk component, originating from the dynamics of the cells located behind.

While introducing merlin-depleted cells introduces controlled variation in the cell dynamics, in a genetically homogeneous monolayer, peaks in stress landscape appear spontaneously in a stochastic manner. In fact, as depicted by monolayer stress microscopy and also described previously28, the stress distribution within the bulk epithelial monolayer manifests a rugged landscape with peaks and basins extending over several cell diameters (Fig. 2a). The landscape also evolves with time and thus reveals dynamic heterogeneity within the bulk monolayer, which is reminiscent of the spatially heterogeneous dynamics in dense colloidal suspension approaching glass transition26,29. Interestingly, the cellular shape index, q, also shows similar spontaneously emerging heterogeneity, and its value appears to be distributed on both sides of the transition point (q = 3.81) even in an apparently quiescent and packed epithelial monolayer25. Since the emergence of the leader cells was preceded by the appearance of high stress regions behind them (Fig. 1c), we presumed that the extent to which the stress propagates across the monolayer also described by the stress correlation length, FCL (Fig. 2a), should closely match the separation between adjacent leader cells at the wound margin (Fig. 2b). Conceptually, the characteristic length-scale of the spatial autocorrelation function, C(r), of the average normal stress, known as the force correlation length30 (Supplementary Fig. 10), indicates the average number of cells that could collectively integrate their forces through the cell-cell junctions28 and give rise to the observed ruggedness in the stress landscape (Fig. 2a). Indeed, the distribution of leader-to-leader (dLL) separation distance showed excellent correspondence with the distribution of force correlation length (FCL) (dLL = 162.4 ± 30.2 μm; FCL = 170.5 ± 38.7 μm; mean ± s.d.) in both MDCK and HaCaT cells (Fig. 2c). This result further validated that in a genetically homogeneous monolayer, the stochasticity in mechanical activity of the bulk monolayer indeed determines the apparently random emergence of leader cells at the interface.

With these results in view, we next examined to what extent the contribution from the mechanobiology of bulk monolayer can prevail when the monolayer is presented with a perturbation at the interface. To this end, we generated monolayers with highly curved beak-shaped regions, using a soft-lithography based patterning technique (Fig. 2e, Supplementary Fig. 6). These high curvature beaks lead to the generation of locally confined high tractions at the margin and thus, impose an interfacial bias in the force landscape towards leader cell generation20. By varying the spacing between two consecutive beaks, we controlled the length-scale of the interfacial bias. In spite of the imposition of interfacial bias, the final distribution of leader cell separation in patterned monolayers appeared very similar to that in non-patterned monolayer (dLL for non-patterned (unbiased): 162.4 ± 30.2 μm; 75 μm pattern: 143.3 ± 22.3 μm; 300 μm pattern: 166.2 ± 31.8 μm; mean ± s.d.; Fig. 2d, Supplementary movie 8). Together these results established the importance of the collective cellular dynamics in regulating the emergence of the leader cells at the interface and indicated that bulk-mechanobiological parameters such as the length-scale of force transduction could control the length-scale of leader cell emergence.

### Modifying the force correlation length

Subsequently, to test our hypothesis that force transduction determine the distance between the leader cells, we modulated the length-scale of force transduction by both chemical and physical methods. For chemical modification, we used the widely used pharmacological means of controlling the actomyosin contractility by treating the cells with a non-muscle myosin-II inhibitor, blebbistatin (5 μM), or a myosin-light-chain phosphatase inhibitor, calyculin A (1 nM). Blebbistatin reduced the contractile forces, while calyculin increased it. Then, as expected, blebbistatin treatment enhanced the ruggedness of the stress landscape and lowered the force correlation while calyculin treatment regularized the stress landscape and increased the correlation length (Fig. 3a, d), both in comparison to the control case. Remarkably, in each case, the force correlation length matched the corresponding leader-to-leader distance (Fig. 3a–c, Supplementary Fig. 8, Supplementary movie 9). HaCaT cells also showed similar trends of changes in leader-to-leader distance (Supplementary Fig. 7). Complementing the chemical perturbation, we also altered the force correlation length by physical means, by changing the stiffness of substrate over which the cells migrated (Fig. 3c, right panel). In this case, both force correlation length and leader-to-leader distance increased with increasing stiffness of the substrate (Fig. 3a–d). Together, these results confirmed systematic mechano-biological regulation of leader cell generation during collective migration of epithelial cells in wound closure, where a system-property emerging out from the bulk such as the force correlation length dictates the emergence of leader cells.

## Methods

### Cell culture

Madin-Darby canine kidney cells (MDCKII, Health Protection Agency) were cultured in minimal essential medium (MEM, Sigma) supplemented with 2 mM l-glutamine (Invitrogen), 10 U ml−1 penicillin, 10 μg ml−1 streptomycin (Pen Strep, Invitrogen), and 5% fetal bovine serum (FBS, Invitrogen). Human keratinocytes line (HaCaT, Cell Lines Service) were cultured in high glucose dulbecco’s modified eagle medium (DMEM, Gibco) supplemented with GlutaMaxTM, 10% FBS, 10 U ml−1 penicillin and 10 µg ml−1 streptomycin.

### Micro-patterning

Polydimethylsiloxane (PDMS) stencil masks with holes of defined shapes were fabricated in an adapted soft lithography process20,37. Briefly, desired shapes of monolayers were designed in a QCAD program and transferred on transparencies using a high-resolution printer (JD Phototools). In a clean room facility, SU-8/25 negative photoresist (MicroChem, Newton, MA, USA) was spin-coated on a 2″ silicon wafer to a final thickness of about 50 μm. The wafer was then baked on a hot plate for 5 min at 65 °C followed by a second baking for 15 min at 95 °C. The transparencies containing the “photographic negative” of the pattern to be transferred were used as masks to illuminate the wafer with UV light for 12 s in Mask Aligner MBJ4 (Suess MicroTec Lithography, Munich, Germany). To remove the unexposed photoresist, wafers were immersed in SU-8 Developer mr-Dev600 (Microresist Technology, Berlin, Germany). The prepared wafers containing the desired geometric pattern were then treated with 1 H,1 H,2 H,2H-Perfluorooctyl-trichlorosilane to reduce surface adhesiveness. A sandwich consisting of the patterned wafer, 0.5 ml of uncured PDMS, a piece of parafilm, a piece of paper and a glass slide was put into a custom made molding press to obtain uniform pressure distribution. PDMS was pressed against the wafer in order to create thin PDMS membrane containing holes of desired shapes. The assembly was put into a compartment dryer at 65 °C for 100 min to allow PDMS polymerization. To prevent cell adhesion, prepared stencil masks were incubated in a solution of Pluronic F-127 (Sigma Aldrich, 2% w/v in deionized water) for 30 min prior to use.

### Migration experiments and Traction force microscopy

For performing collective cell migration in defined patterns, PDMS microstencils with patterned holes or ibidi cell culture inserts (80209) were allowed to stick onto the customized glass bottom dishes (5 cm diameter) coated with 10 μg ml−1 fibronectin unless otherwise specified. Cells were seeded into the dish and incubated in a cell-culture incubator for 1 h until they adhere onto the fibronectin-coated glass accessible through the holes of the microstencils. The unattached cells were then removed by replacing the media. The set up was incubated again overnight or until a confluent cell monolayer of around 3000 cells/mm2 is obtained after which, the PDMS stencil was removed to trigger collective migration. Migration experiments were carried out at 37 °C and in 5% CO2 environment either inside a stand-alone cell culture incubator, or within an incubator staged over the microscope.

Traction force microscopy was performed as described previously38. Briefly, glutaraldehyde activated glass bottom dishes (MatTek) were used to cast thin polyacrylamide (PAA) gel substrates (Young’s modulus of about 11 kPa) containing 0.5 μm fluorescent carboxylated polystyrene beads. These gel surfaces were then functionalized with sulphosuccinimidyl-6-(4′-azido-2′-nitrophenylamino) hexanoate (Sulfo-SANPAH, Thermo Scientific) and covalently coated with 0.5 mg ml−1 fibronectin (Sigma) to ensure cell attachment. A horizontal confinement was created on the functionalized PAA gels using thin PDMS blocks. Cells were seeded in the confined areas and grown until a confluent monolayer is obtained. Subsequently, confinement was released by lifting off the PDMS block and images for cells and beads were acquired as the cells migrated. After experiment, cells were trypsinized and resulting bead positions in relaxed state were obtained (i.e., reference images). The displaced images were aligned to correct for drift and compared to the reference image using particle image velocimetry to create a regular field of displacement vectors with a grid spacing of 5.44 μm. Displacement vectors were interpolated using cubic splines. From these vectors, traction stresses were reconstructed using regularized Fourier Transform Traction Cytometry39 with a regularization parameter chosen by Generalized Cross Validation40.

### Monolayer stress microscopy

Stresses within the monolayer were then calculated from the cell-substrate tractions using a force balance algorithm written in MATLAB (MathWorks) as described in our previous study23. Force correlation length was computed by characteristic length scale of the spatial autocorrelation function of the average normal stresses as formulated elsewhere. Briefly, the extent to which the force propagates across the monolayer was obtained by the characteristic length-scale of the spatial autocorrelation function, C(r), of the average normal stress, which is known as the force correlation length30. C(r), was calculated as:

$$C\left( r \right) = \frac{1}{{Nvar\left( {\sigma \!\! {\acute\ }} \right)}}\mathop {\sum }_{i,j = 1}^N \mathop {\sum }_{\left| {r_i - r_j} \right| = r} \delta \sigma \!\!{\acute\ }_i.\,\delta \sigma \!\!{\acute\ }_{j}$$

where $$\delta {\sigma \!\! {\acute\ }}_i$$ is the local deviation of the average normal stress at position ri from its spatial mean $$\sigma {\prime}_i$$ and $$\mathrm{var}\left( {\sigma {\prime}} \right)$$ is the variance of these deviations. Stress correlation length was determined as the point where the stress correlation function became negligible in value. For practical purposes, we took correlation length as the distance at which the correlation function was equal to 0.01

### siRNAs and transfection

Merlin siRNA was purchased from Qiagen (5′ CAAAGAGAGGGAGACAGCCTTGGAT -3′) and was transfected by reverse transfection using Lipofectamine 2000 (Invitrogen), as instructed by the manufacturer. The scrambled siRNA was purchased from Qiagen.

### Inhibition studies and Immunostainings

Blebbistatin, an inhibitor of myosin II, and calyculin A, a phosphatase inhibitor, were obtained from Sigma. Powders of these drugs were dissolved in DMSO (Sigma) to make the stock. Before removing the confinement, cells were treated with 5 μM blebbistatin and 1 nM calyculin A respectively in Opti-MEM reduced serum medium for 1 h at 37 °C in a 5% CO2 humidified incubator. During migration, Opti-MEM was replaced by MEM containing 5% FBS, 2mM l-glutamine and the respective inhibitor. For actin stainings, cells were fixed and permeabilized before adding Alexa fluor-488 labeled phalloidin (Thermo Fisher Scientific) for visualization of the actin cytoskeleton.

### Cell pulling experiment

A customized cell-pulling device was used to apply mechanical strain to an elastomeric PDMS substrate, onto which cells were later cultured, as also described previously23.The PDMS chamber for cell culture, was made by casting PDMS in a Plexiglas mold at an elastomer to crosslinker ratio of 10:1. The PDMS was cured for 2 h at 65 °C. The chamber was then peeled, sonicated in 70% ethanol and oxidized in an oxygen plasma environment for 1 min. This process coated a thin solid film of silica on top of the flexible PDMS membrane. A narrow trench was generated on the surface by scratching the silica-coated membrane with a micro-needle (tip size 20 μm) under an inverted table top microscope (Olympus CKX53). The PDMS chamber was then coated with 10 μg/ml fibronectin for 1 h at 37°C. Cells were then cultured until confluency on this fibronectin-coated membrane under confined conditions such that the trench is between 100 and 200 μm away from the cells (Fig. 5a). Next day, the confinement was released and cells were allowed to migrate until they have crossed the trench at several locations. The Cell-pulling experiment was then carried out by stretching the membrane unidirectionally with an impulse strain (25% per second). Cells were kept in the pulled condition for 2 min and are then relaxed. The PDMS membrane was immediately taken to the microscope for time lapse imaging.

### Modeling and simulation

The epithelial layer of height hc was modeled as a thin elastic layer of elasticity EC, Poisson’s ratio ν and an isotropic contraction stress σ0. The layer is further coupled to the underlying substrate elastically via springs of stiffness density Y31. The force balance equation results:

$$\sigma _{ij,j} - Yu_i = 0$$

Following constitutive relation, with a linearized strain $${\it{\epsilon }}_{ij} = \frac{1}{2}(u_{ij} + u_{ji})$$ was used:

$$\sigma _{ij} = 2\mu {\it{\epsilon }}_{ij} + \left( {\lambda {\it{\epsilon }}_{kk} + \sigma _0} \right)\delta _{ij}$$

with the two-dimensional Lame’ coefficients $$\lambda = \frac{{hE_cv}}{{1 -\,v^2}}$$ and

$$\mu = \frac{{hE_c}}{{2\left( {1 + v} \right)}}$$

We assumed a constant active stress σ0 throughout the cell layer, which leads to σ0,i = 0 within the cell layer. The active contraction manifests itself as the remaining stress normal to the exterior boundary of the layer and will be introduced via the boundary conditions. The force balance equation now simplifies to:

$$\sigma _{ij,j} = \lambda u_{k,ki} + \mu \left( {u_{i,jj} + u_{j,ij}} \right) = Yu_i$$

With the three-dimensional incompressibility condition ν ≈ 0.5, we arrive at:

$$u_{k,ki} + \frac{1}{2}\left( {u_{i,jj} + u_{j,ij}} \right) = \frac{{{\boldsymbol{u}}_{\boldsymbol{i}}}}{{L_p^2}}$$, where LP is the localization length, $$L_P = \sqrt {\frac{{hE_c}}{{Y\left( {1 + v} \right)}}}$$ and can be interpreted as the length up to which a point force is transmitted. To distinguish the contributions from bulk and substrate parameters, the localization length is defined, as described previously32:

$$L_P = \sqrt {L_a^2 + L_s^2}$$

with localization length due to the action of focal adhesions

$$L_a = \sqrt {\frac{{E_ch_cLl_{c0}}}{{k_a}}}$$

and due to the substrate

$$L_s = \sqrt {\frac{{E_ch_cLl_{c0}}}{{\pi E_s\left( {\frac{1}{{h_s2\pi \left( {1 + v_s} \right)}} + \frac{1}{L}} \right)}}}$$

The localization length, LP was computed by using the default values for the cell layer (Supplementary Table 1), as described previously34,41. We used the finite element solver FEniCS to calculate the displacements of the monolayer subject to external stresses42. Leader cell formation was simulated by decoupling a part of the monolayer from the substrate, then pulling on it by the action of two Gaussian-shaped forces of width of a finite element mesh size, as approximation for two point forces, separated by the distance dLL. Afterwards the full layer was again connected elastically and allowed to contract isotropically. During simulations, Blebbistatin and Calyculin-A treatments were mimicked by modifying bulk parameters as described previously (supplementary table 2)43,44. The values of EC were used as estimates to find a localization length in the range of dLL. Relative horizontal displacement (XC – XB) and relative displacement of UC (UC/UL) were plotted as exponential functions of distance. To compute the spatial extent of followers, velocity fields were derived by means of optical flow and Euclidean distance was calculated by comparing the velocity of leader cells from follower cells.

### Statistical analysis

Statistical analysis was carried out in Prism. All the data underwent normality test in Prism. Statistical significance was calculated by Student’s t-test for data following normal distribution and by Mann–Whitney test for the non-normal data. All values were given as mean ± s.d. (standard deviation) or s.e.m. or shown as boxplots. P-values greater than 0.05 were considered to be statistically not significant.

### Data and code availability

Relevant data and codes are available from authors upon request.

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## Acknowledgements

Parts of the research leading to these results have received funding from the European Research Council/ ERC Grant Agreement No. 294852, SynAd. This work is also part of the MaxSynBio consortium, which is jointly funded by the Federal Ministry of Education and Research of Germany and the Max Planck Society. Support was also granted from the Gottfried-Wilhelm-Leibniz Award of the German Science Foundation (DFG). J.P.S. is the Weston Visiting Professor at the Weizmann Institute of Science. J.P.S. and U.S.S. are members of the cluster of excellence CellNetworks at Heidelberg University. We acknowledge support from the Max Planck Society.

## Author information

Authors

### Contributions

T.D. and J.P.S. conceived the project. M.V., T.D. and J.P.S. designed experiments. M.V. performed all experiments except the elasticity experiments and experiments with HaCaT cells, which were performed by J.D.R. Theoretical model was contributed by D.P. and U.S.S. M.V., D.P., U.S.S., T.D. and J.P.S. analyzed and interpreted experimental data. T.D., D.P., and U.S.S., developed computational tools for traction force and monolayer stress analysis. J.P.S., T.D. and U.S.S. supervised the project. T.D., M.V. and J.P.S. developed and wrote the manuscript with help from D.P. and U.S.S. All authors discussed and commented on the manuscript.

### Corresponding authors

Correspondence to Tamal Das or Joachim P. Spatz.

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### Competing interests

The authors declare no competing interests.

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Vishwakarma, M., Di Russo, J., Probst, D. et al. Mechanical interactions among followers determine the emergence of leaders in migrating epithelial cell collectives. Nat Commun 9, 3469 (2018). https://doi.org/10.1038/s41467-018-05927-6

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