The directed migration of epithelial cell collectives through coordinated movements is key to many physiological and pathological processes and is increasingly well understood at the level of large confluent monolayers. Numerous migration processes rely on the migration of small groups of polarized epithelial clusters and their responses to external geometries. However, the interplay of cell-cell interactions and external boundaries in small cell clusters remain poorly understood. To tackle this, we used micropatterned stripes to investigate the migration of small epithelial clusters with well-defined geometries. Here we show that their migration efficiency is strongly dependent on the contact geometry, and in particular whether cell-cell contacts are parallel or perpendicular to the direction of migration. By systematically screening possible interaction mechanisms in a minimal active matter model, we show that a combination of velocity and polarity alignment with contact inhibition of locomotion captures the experimental data, which we then validated via force and intracellular stress measurements, as well as perturbations. Altogether, our results highlight the importance of geometry in defining the migration properties of cell clusters, providing a conceptual framework to extract interaction rules from how active systems interact with physical boundaries.
Article
Geometry-driven migration efficiency of minimal cell clusters
https://doi.org/10.21203/rs.3.rs-1867690/v1
This work is licensed under a CC BY 4.0 License
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published 19 Jun, 2024
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Collective cell migration is a fundamental process in many physiological and pathological events, such as wound healing1, cancer metastasis2 3 4 and morphogenesis5 6 7. Although the migration behavior and mechanisms of large-scale epithelial sheets has been under intense investigation in the past decades both in vivo6 and in vitro8 9, a number of physiologically relevant examples involve instead small clusters migrating with complex geometries and boundary conditions10 11. For instance, in vivo experiments in Drosophila indicated that the migration of small groups of few cells of approximately 20 µm in border cell migration of Drosophila to larger groups of approximately 100 µm in the posterior lateral line primordium of zebrafish6 12. In addition, highly polarized and persistent locomoting tumoral clusters of up to 8 cells were observed in patients with epithelial-originating cancers or carcinomas2 13 and in mesenchymal and epithelial cancer explants originating from various organs3 14.
The migration of epithelial clusters requires front-rear polarization at the single-cell level through the formation of cryptic lamellipodia15 and the establishment of a large-scale coupling between cells through axial and lateral intercellular adhesive interactions8 16 17 18. Different interaction rules have been proposed to describe the mechanisms underlying collective migration in large epithelial tissues, such as polarity alignment (PA), velocity alignment (VA), stress-polarity coupling (SPC) and contact inhibition of locomotion (CIL)19 20 21 22 23 24 25. From an active matter perspective, many of these possible interaction types give very similar predictions for the collective behavior of large monolayers26 making it hard to test each of them rigorously. Studying the behavior of small clusters of cells and their response to well-defined geometrical boundary conditions could give key insights in the regulation of collective motion through cell-cell interactions. However, deciphering their individual role in the migration of small epithelial clusters remains challenging both theoretically and experimentally.
To tackle this, we designed a set of experiments to systematically vary the size and aspect ratio of small epithelial cell clusters by placing a fish scale containing primary epithelial tissues on flat substrates functionalized with adhesive microstripes of fibronectin of various widths (Fig. 1a). After few hours of explant culture, a large tissue of primary epithelial keratocytes grew over the micropatterns and formed fingers of cells that broke down into epithelial clusters of varying dimensions. We first concentrated on 15 µm wide microstripes, as it allows to form one-dimensional epithelial trains that lack lateral intercellular interactions (Fig. 1b). We exploited the variability of cell train geometries to study whether the length of these minimal epithelial clusters can affect their migration speed (Fig. 1c).
As reported for individual keratocytes27, cell trains were highly polarized, persistent and compacted (Supplementary Movies S1 and S2). Indeed, cell trains were characterized by an area proportional to the number of cells but significantly lower than the sum of the individual cell areas (Extended Data Fig. 1a). In addition, we found that keratocytes extended cryptic lamellipodia under the cell body in front of them28 (Extended Data Fig. 1b), which have been shown to be involved in polarization and cell sheet movement15. We then tracked the migration of cell trains of different lengths (2≤L≤10 cells) to determine whether their migration speed was modulated by the number (L) of constitutive cells (Fig. 1d). Interestingly, the projected areas of these cell trains were constant over time regardless their length, demonstrating that they moved as a cohesive and single unit (Extended Data Fig. 1c). Our findings showed that the migration speed of cell trains of different lengths was similar to the speed of individual cells on 15 µm wide microstripes27 and did not depend on the number of cells that composed the train (Fig. 1e). This suggests that intercellular axial contacts - defined as front to rear cell contacts in the direction of migration - do not influence global migration efficiency, which is in stark contrast to the much lower cell velocities of tissue-level cell migration (characterized by both axial and lateral contacts, Extended Data Figs. 1d-f). These findings also contrast with the classic view that cells far from the leading edge would behave as less migratory “follower” cells, as this would theoretically predict a decrease of global velocity with the train length L (with a 1/L trend, see Fig. 1f), instead suggesting a model where all cells are equally polarized (Fig. 1f). To confirm this, we used the mitochondrial potential membrane as a readout of the cell polarization. Indeed, it was shown that cell polarization requires increased cellular energy29 and that the mitochondrial activity promotes cell migration by supporting membrane protrusion and modulating F-actin polymerization30. Stationary and unpolarized keratocytes exhibited a rounded shape and a low MitoTracker (MT) intensity that increased immediately with their polarization (Fig. 1g, Extended Data Figs. 2a-b and Supplementary Movie S3). Interestingly, all cells within migrating cell trains of different lengths showed a large MT signal (Fig. 1h), reflecting a high level of mitochondrial activity that we found to be constant over time during the migration (Extended Data Fig. 2c). In addition, our results indicated a linear correlation between MT intensity and cell train areas (Fig. 1i), independent of the train length. Altogether, these findings indicate that all members of cell trains are metabolically active, polarized and contribute to the migration process, driving length-independent collective motion of cell trains.
We next sought to investigate the role of lateral adhesive interactions in collective migration, that were missing in one-dimensional cell trains. To this aim, we examined larger clusters of primary epithelial cells that formed on 30, 45 and 100 µm wide microstripes from an explant (Fig. 2a). The epithelial tissues grew on FN microstripes and fragmented in epithelial clusters of controlled widths (Fig. 2b) that were composed of compacted cells with cryptic lamellipodia (Extended Data Figs. 3a), as observed in the primary epithelial tissue (Extended Data Fig. 3b). Time-lapse experiments indicated that these migrating epithelial clusters of various widths were highly persistent (Supplementary Movies S4 and S5). The constituent cells of these clusters exhibited directed motion along the main axis of the microstripes (Fig. 2c), suggesting that the relative cell position within the cluster was maintained during the whole migration process, regardless the cluster width. Strikingly, widening the cell cluster to 30 µm, 45 µm and 100 µm strongly decreased the migrating velocity from 8.1±3.9 µm/min (n=59) for cell trains on 15 µm to 3.3±1.2 µm/min (n=51) on 30 µm, 2.5±0.8 µm/min (n=118) on 45 µm and 2.2±0.8 µm/min (n=64) on 100 µm (Fig. 2d), slowly converging towards the migration speed of large-scale epithelial tissues (1.4±0.4 µm/min, Extended Data Fig. 1g). This was unlikely to be due to neighbor-driven confinement as we found similar cellular densities within the different epithelial cluster sizes (Fig. 2e). Altogether, these findings suggests that lateral cell-cell adhesive interactions have drastically different consequence – compared to axial interactions – in collective cell migration.
To shed light on the role of the cell-cell adhesions in this behavior, we induced chemical disruption of cell-cell junctions with triethylene glycol diamine tetraacetic acid (EGTA) (Extended Data Figs. 4a-b)31. After EGTA treatment, we observed a fragmentation of all epithelial clusters into individual cells. Interestingly, EGTA treatments performed on 30 µm wide clusters and primary tissues induced a speed up of the cells, whereas the cell migration speed remained constant after EGTA treatment on single cells and 15 µm wide clusters (Extended Data Fig. 4c). Altogether, these data argue that the establishment of an increasing number of lateral, but not axial, contacts decreases migration speed during collective migration.
The observation of length-independent but width-dependent collective motion suggests an intricate interplay of cell-cell interactions with the cell cluster geometry. From a theoretical perspective, various interaction types have been proposed in the context of collective migration26, but it is unclear which interactions are required to capture the migration dynamics of small confined epithelial clusters. To disentangle the role of these interactions, we developed a minimal theoretical model of confined cell clusters. Based on our observations that cells in trains and clusters are polarized and exhibit few cellular re-arrangements and density variations, we modelled cells as polar particles exerting active migration forces in a direction of polarity (defined in our system by the orientation of the lamellipodia), with each cell connected to its neighbors j by elastic links (adhesions). This model is described by the non-dimensionalized equation 
Importantly, this model allows cell velocities 
and polarities 
that are not necessarily equal, due to cell-cell mechanical interactions. The evolution of the cell polarity can then be generally modelled as 
where the first term describes the spontaneous polarization of single cells, and is 
Gaussian white noise (see Supplementary Theory Note for details)32.
The general interaction term 
subsumes many possible cell-cell interactions that could give rise to the intricate collective dynamics of confined cell clusters observed here (Fig. 2f). Two classes of interactions that have been particularly studied are neighboring cells either aligning or anti-aligning relative to each other20 26 33. Indeed, in our system, two-cell collision experiments can show both alignment (Extended Data Fig. 5a) and anti-alignment (Extended Data Fig. 5b) depending on the initial configuration34 35. Theoretically, on the one hand, alignment is motivated by the tendency of cells to “flock” in the same direction, which can be described by i) alignment of the polarity of each individual cell to match its own velocity (velocity alignment, VA)24 26 36 and ii) direct polarity alignment (PA) between neighbors, in analogy to spins in magnetism37 38. On the other hand, a number of cell types have been shown to anti-align to counter-act the forces exerted by their neighbors, either due to i) stress-polarity coupling (SPC) where cells exert polarity forces opposite to stress applied on their cell-cell contacts32 18 39 or ii) contact inhibition of locomotion (CIL), which tends to direct polarity away from cell-cell contacts21 23 40. We enumerate all possible couplings allowed by symmetry within our minimal model and show that they correspond to each of these categories (Supplementary Theory Note). This motivates a key question: could several distinct interaction types interplay to generate the observed nontrivial coupling to cluster geometry?
We thus proceeded to simulate clusters with varying cluster lengths and widths, under each of the possible combinations of interaction types. Generically, alignment interactions (PA or VA) lead to geometry-independent speed with all cells moving together in a specific direction, while anti-alignment interactions (SPC or CIL) induce rapidly decreasing speed with increasing length and width as clusters tend to develop a bidirectional polarity pattern (Fig 2g, Supplementary Movie S6). However, we reasoned that combining different mechanisms – to give rise to alignment in the axial direction and anti-alignment in the lateral direction – could be a promising avenue to explain our data. Interestingly, the screen of different computational models revealed that pair-wise combinations of interactions could still not qualitatively capture our observations (Supplementary Theory Note, Supplementary Movie S7), but that the combination of VA, PA, and CIL represents the minimal interactions necessary to reproduce length-independent, but width-dependent migration (Fig. 2h). Qualitatively, this combination of interactions causes length-independent aligned cell motion in the axial direction, while the presence of boundaries along the lateral direction renders such an aligned state impossible, allowing lateral anti-alignment to develop, driven by the tendency from CIL of boundary cells to polarize outwards (Fig. 2g). Here, velocity and polarity alignment play distinct roles: while VA breaks the symmetry between axial and lateral directions, as non-zero global velocities cannot arise in the lateral direction; and PA propagates the CIL-driven laterally outwards-pointing polarity into the bulk. This causes a re-orientation of polarity at the detriment of “productive” motion which can only occur in the axial direction. In the case where VA and CIL have similar magnitudes, this interplay of geometry and interactions then gives rise to the observed trends of speed independent of length but decreasing with width (Figs. 2h,i, Supplementary Movie S8).
Our model then makes a clear and experimentally testable prediction: the outward polarization induced by CIL at the boundary and propagated by PA causes a build-up of lateral inter-cellular stress, which should increase with increasing width. To test this key prediction, we performed traction force microscopy (TFM) experiments to quantify the orientation of the traction forces generated by cell clusters of different geometries. To separate axial (along the microstripe axis) and lateral (perpendicular to the microstripe axis) components of the traction stresses (Fig. 3a), we plotted tractions in a reference frame where the horizontal and vertical axes (x, y) correspond to length and width of the cell cluster, respectively. As shown in Fig. 3b, cell trains were characterized by a dipole of forces concentrated at both extremities of the cell train and directed inward toward the center of the train, implicating a strong intercellular coupling8. Interestingly, widening cell clusters to 45 and 100 µm led to the generation of more pronounced lateral traction forces. By calculating the strain energy as the dot product of the traction force with the displacement (Fig. 3c), we determined the individual contribution of axial (Ex) and lateral (Ey) components of the strain energy. In agreement with a dipole of forces, we found that cell trains on 15 µm wide microstripe exhibited a large axial component, which accounted for ~96.7% of the total strain energy (Fig. 3d) while the lateral component was negligible (~4.3%). Interestingly, the lateral component Ey increases with width, even leading to an inversion of the major strain energy component for 100 µm wide clusters, with Ey that represented ~27.1% and ~56.4% of the total strain energy for 45 and 100 µm wide clusters, respectively (Fig. 3d). As shown in Fig. 3e, widening cell clusters leads therefore to the inversion of the major strain energy component for 100 µm wide clusters. Taken together, these findings point toward a transition between axial and lateral contractile forces as a function of the cluster width, where the larger amount of traction forces in wider cell clusters is exerted normal to the direction of migration.
As traction forces must be balanced by internal forces transmitted within and between cells, we can infer the the spatio-temporal profile of the stress tensor within the monolayer using Monolayer Stress Microscopy (MSM), and thus calculate axial (σxx) and lateral (σyy) components of the internal stress field41 42. Our model indicated a very small amount of lateral stress in cell trains of 15 µm wide, which increased with the cluster widening (Fig. 4a). More quantitatively, our model – with parameters fully constrained based only on the speed variations as a function of cluster geometry (Fig. 2j) – successfully predicted a significant increase of the stress ratio σyy/σxx as a function of the cluster width (Fig. 4b), in agreement with MSM experiments conducted on 15, 45 and 100 µm wide clusters (Fig. 4c). The good agreement between our theoretical (Fig. 4b) and experimental (Fig. 4e) results highlight the role of the lateral stress component in wide epithelial cluster, as well as the cooperative role of several modes of cell-cell interaction to shape the collective migration and stress profile of small cell clusters.
This specific combination of several mechanisms with opposite effects on cell polarity raises the question of what functional consequences this could have, especially since they lead to substantial unproductive lateral stresses and thus slower collective migration. To address this question, we used our model to predict how various combinations of cell-cell interactions affect cluster behavior in response to more complex external environments. When subjected to environments with blind-ends, where cell clusters must abruptly change their polarization, we found that the repolarization behavior is strongly affected by the choice of cell-cell interactions considered in the model (Extended Data Figs. 6a-d, Supplementary Movie S9). Indeed, while VA and PA mechanisms lead to fast migration in simple straight geometries, they result in poor repolarization abilities, while, intuitively, CIL leads to slow moving clusters which however repolarize quickly when contact geometry changes. Interestingly, the parameter region that captured the experimental observations (intermediate values of all three interaction parameters), exhibits a seemingly optimal behavior with both fast straight migration and obstacle-driven repolarization (Extended Data Fig. 6d). Importantly, time-lapse experiments and quantitative cell trackings performed on epithelial clusters reaching the end of a FN stripe are in agreement with the theoretical prediction, showing fast and global repolarization of both cell trains and clusters (Extended Data Figs. 6e-j). Together, these findings strengthen the validity of the combination of VA+PA+CIL and point to a potential functional relevance of these interactions.
In summary, in this work we have combined a controlled in vitro micropattern approach, force measurement assays and theoretical modelling to dissect the role of contact geometry in migration behavior of small epithelial clusters. We found that not only the size of a cluster, but also its geometry and aspect ratio, was a crucial parameter in determining its migration efficiency, polarization, and state of mechanical stress. In particular, we found that axial contacts, established in the direction of cell migration, did not impede migration speed. In contrast, lateral contacts, perpendicular to the direction of cell migration, led to a build-up of lateral polarization, as evidenced by a reorientation of traction forces and monolayer stresses, and thus decreased the migration efficiency of larger cell clusters in proportion to their width. Interestingly, this displays a similar phenomenology, but at the very different length scale of multicellular systems, to how lateral confinement regulates the migration speed of individual cells27. Our findings are in line with the established importance of intercellular junctions to direct collective cell migration18 43, but reveal for the first time their different functional consequences on small cluster migration depending on their geometry relative to the direction of motion.
From a theoretical perspective, we show that while different types of cell-cell interactions give rise to similar large-scale behavior 26, introducing anisotropic boundary conditions in small clusters allows us to distinguish them and infer the functional role of each interaction in cluster migration. Indeed, in the presence of boundary conditions, different interaction mechanisms cooperate in complex ways: contact-inhibition of locomotion (CIL) induces lateral polarization to slow down clusters, polarity alignment (PA) propagates the boundary information from CIL into the bulk; and velocity alignment (VA) breaks symmetry by inducing net polarization in the free axial direction. Thus, these interactions couple the bulk state of stress and polarization in cell clusters to specific boundary conditions. Other cell types such as MDCK have been shown to display flocking behavior experimentally when placed on a ring (periodic boundary conditions)18, while we find that they did not attain a global direction of polarization on open boundary conditions (Supplementary Movie S10), consistent with previous findings on large-scale monolayer expansion8 44. Interestingly, we found that our model (VA+PA+CIL) captures both of these behaviors (Supplementary Movie S11), showing more generically how the nature of boundary conditions shape cell cluster behaviors. In the future, it will be interesting to understand at molecular and biophysical level the basis for these interactions, whether they are transduced by similar or complementary pathways at the cell-cell contacts, as well as their conservation in other cellular types. This approach could further help advance our understanding of small cluster migration in vivo, for instance in the posterior lateral line primordium of zebrafish6 12 or in patients with epithelial-originating cancers or carcinomas 2 13.
PDMS-coated glass coverslips. Polydimethylsiloxane (PDMS) coated glass coverslips (170 µm thick) were fabricated by spin-coating, as previously described45. Briefly, PDMS was prepared from the commercially available Sylgard 184 silicone elastomer kit (Dow Corning, Midland, MI) by mixing the curing agent and the base (1:10 ratio) thoroughly for 2 min. The mixture was degassed, and spin-coated at 5000 rpm on clean 25 mm glass coverslips to obtain a thin PDMS layer of ~ 30 µm thick. The PDMS layer was then cured for 3 hours at 60°C, flushed with ethanol and exposed to UV illumination for 15 minutes. PDMS-coated glass coverslips were then stored in the dark at room temperature in a petri dish until use.
Microcontact Printing. PDMS stamps were used to create micropattern of fibronectin on PDMS-coated glass coverslips. A PDMS mixture (Sylgard 184, Dow Corning Midland, MI) was obtained by mixing the curing agent and the base (1:10 ratio) thoroughly for 2 min46. After degassing, the mixture was poured on microstructured silicon wafer which was previously functionalized with fluorosilane (tridecafluoro-1,1,2,2-tetrahydrooctyl-1-trichlorosilane, Gelest) vapors under vacuum to facilitate the removal of the PDMS layer (~ 1 cm thick). After curing overnight at 65°C, the PDMS block was peeled off and cut in stamps of approximately 1 cm2. PDMS stamps were washed in an ultrasonic bath with detergent solution (Decon 90, 5%) for 30 min at 35°C, then with isopropanol (70%) for 15 min at 20°C and the stamps were dried under a nitrogen flow A solution was then prepared by mixing 40 µL human fibronectin (Merck) and 960 µL of demineralized water. A volume of 100 µL of this solution was deposited on top of each stamp for 1 h at room temperature in the dark. After gently removing the solution, a PDMS stamp were dried under nitrogen flow and placed carefully in the center of a PDMS-coated glass coverslip for 15 seconds. PDMS stamps were then gently removed with tweezers and a Pluronic solution at 5 mg/mL was incubated for 5 min at room temperature to passivate non-printed areas. Microprinted PDMS-coated glass coverslips were rinsed three times with sterile PBS and dried under nitrogen flow.
Cell culture. Fish epithelial keratocytes were obtained from the scales of Central American cichlid (Hypsophrys Nicaraguensis)27 45. Scales were gently taken off the fish and placed in the center of a microprinted PDMS-coated glass coverslips and covered with a drop of 150 µL of culture medium. The culture medium was composed of Leibovitz’s L-15 medium (Thermo Fisher Scientific) supplemented with 10% fetal bovine serum (FBS, Capricorn), 1% penicillin/streptomycin (Westburg), 14.2 mM HEPES (Sigma Aldrich) and 30% deionized water were put on top of the scale. A glass coverslip of 22 mm in diameter was deposited on top of the scales and few drops of culture medium were added around the samples. Epithelial keratocytes were cultured in the dark at room temperature for 12 h.
Time-lapse imaging. Time-lapse microscopy experiments were carried out on a Nikon Ti-U inverted microscope (Nikon, Japan) equipped with a manual stage27 45. Differential Interference Contrast (DIC) images were taken every 3 min using a ×10, ×20 or ×40 objective and captured with a DS-Qi2 camera (Nikon, Japan) controlled with the NIS Elements Advanced Research 4.0 software (Nikon). Tracking of the cell clusters were performed with the Manual Tracking plugin on FIJI.
Drug treatment. EGTA (Sigma Aldrich) was added to the normal medium at a final concentration of 2 mM to partially chelate the calcium in the medium.
Mitochondrial membrane potential. The mitochondrial membrane potential was measured using 50 nM of the MitoTracker Red dye (Invitrogen) for 30 min at room temperature to allow dye equilibration across the plasma and inner mitochondrial membranes. For imaging, the medium containing the MitoTracker Red dye was replaced with fresh normal medium.
Immunofluorescence and confocal microscopy. Fish keratocytes were fixed and permeabilized with 4% paraformaldehyde and 0.2% Triton X-100 in PBS for 15 min at room temperature. The samples were then incubated with 1% BSA in PBS for 30 min at room temperature, followed by sequential incubation with primary and secondary antibodies diluted with 1% BSA in PBS for 45 min at 37°C. Images were collected in epifluorescence and confocal mode with a Nikon A1R HD25 motorized inverted microscope equipped with x20, x40, x60 Plan Apo (NA 1.45, oil immersion) and x100 Plan Apo silicone objectives and lasers that span the violet (405 and 440 nm), blue (457, 477, and 488 nm), green (514 and 543 nm), yellow-orange (568 and 594 nm), and red (633 and 647 nm) spectral regions. Epifluorescence images were recorded with a photometrics Prime 95B camera (Photometrics Tucson, AZ) using NIS Elements Advances Research 4.5 software (Nikon). Confocal images using small Z-depth increments (0.15 µm) were processed using NIS-Elements (Nikon, Advanced Research version 4.5).
Polyacrylamide hydrogels. Polyacrylamide gel substrates of 18 kPa were prepared as previously described47 48. Briefly, glass-bottom dishes (MatTek, 35 mm) were treated with a solution of 714 µL acetic acid (%), 714 µL of silane in 10 mL of ethanol (96%) for 20 min. After the removal of the solution, the dishes were rinsed twice with ethanol (96%) and dried under nitrogen flow. For 18 kPa gels, a solution of 0.65 mg of N-hydroxyethyl acrylamide (HEA) in 5 mL of PBS was prepared. 820 µL of this solution was mixed in a microcentrifuge tube (Eppendorf, 1.5 mL) with 100 µL bisacrylamide (2%), 80 µL acrylamide (40%) and 3 µL red fluorescent carboxylate-modified beads (0.2 µm, red 580/605, Life Technologies). Degas under vacuum for at least 20 min and then 0.5 µL of N,N,N’,N’-tetramethyl ethylenediamine (TEMED) with 5 µL of ammonium persulfate (APS) were added to initiate the polymerization. 25 µL of the solution was carefully put on each glass-bottom dishes and 18 mm glass coverslips (previously treated under corona) were placed on top of them. After 1 h polymerization under oxygen-free atmosphere, the coverslips were removed from the gels in hot water by using tweezers. PDMS stamps were then used to create micropattern of fibronectin on each gel. After washing the stamps in an ethanol solution (70%) for 15 min in an ultrasonic bath and drying under nitrogen flow, a Corona was used for 30 s to make them more hydrophilic. A solution was prepared by mixing 70 µL human plasma fibronectin (Merck), 20 µL green fibrinogen and 910 µL PBS. 100 µL of this solution was put on top of each stamp for 1 h at room temperature in the dark. After the removal of the solution, the stamps were dried under nitrogen flow and deposited carefully in the center of each gel. We pressed carefully on each corner of the stamp with tweezers to allow protein transfer. The printing process occurred overnight at 4°C in the dark. Stamps were then gently removed with PBS and gels were rinsed 3 times with PBS. Bovine serum albumin (BSA) solution (5 mg/mL) was then used for 4 hours at and 4°C to passivate areas without any protein on the gels followed by 3 rinses with PBS. Cells were then seeded on microprinted hydrogels.
Traction force microscopy. Fluorescent beads of 200 nm in diameter were homogeneously added in the polyacrylamide solution before polymerization and their position was imaged over time with an IX83 inverted microscope equipped with a 632/22 excitation filter (incorporated in the Spectra-X light engine), a glass dichromatic mirror (Olympus), and FF01-692/40 − 25 (Semrock) emission filter. A reference image was obtained after the removal of cells by trypsinization. The 2D displacement field was computed using a custom PIV implementation in Matlab (MathWorks). Traction forces were computed by finite-thickness Fourier-transform traction microscopy as described previously44 49 50.
Monolayer stress microscopy. We employed the monolayer stress microscopy (MSM) method42 to quantify the spatial distribution of intracellular stress in cell clusters. This method is based on force equilibrium between cell-substrate tractions and cell-cell stresses. Implementation of MSM starts with the recovery of local tractions exerted by the monolayer upon its substrate. We consider a monolayer of contiguous cells which forms a uniform sheet that is flat and thin, meaning that, compared with the lateral span of the monolayer, its height is negligible. In that case, stresses within the monolayer and underlying tractions exerted by the monolayer upon its substrate are taken to be planar with no out-of-plane contributions. The stresses everywhere in the monolayers are then determined by terms arising from tractions and boundary conditions. Since the monolayer always remains in mechanical equilibrium, Newton’s laws demand that this force balance must be independent of material properties of the monolayer. MSM was implemented, as a custom-made software, in Python 3 using NumPy51, SciPy52, Matplotlib53, scikit-image54, pandas55, pyFFTW56, opencv57 and cython58.
Statistical analysis. Differences in means between groups were evaluated by two-tailed Student’s t-tests performed in Origin 8.5 (OriginLab, Northampton, MA). For multiple comparisons the differences were determined by using an analysis of variance (ANOVA) followed by Tukey post-hoc test. *p < 0.05, **p < 0.01, ***p < 0.001 and n.s. is not significant. Unless otherwise stated, all data are presented as mean ± standard deviation (s.d.).
Ethical compliance. The use of primary epithelial cells, keratocytes, harvested from the scale of hypsophrys nicaraguensis was done in accordance to European guidelines for animal experimentation and with the agreement of the local ethic committee of the University of Mons which has reviewed the procedure.
Data availability. The data that support the plots within this paper and other findings of this study are available from the corresponding authors upon request.
Acknowledgments
M.L., E.V. and S.G. acknowledges funding from FEDER Prostem Research Project no. 1510614 (Wallonia DG06), the F.R.S.-FNRS Epiforce Project no. T.0092.21 and the Interreg MAT(T)ISSE project, which is financially supported by Interreg France-Wallonie-Vlaanderen (Fonds Européen de Développement Régional, FEDER-ERDF). E.V. and Y.K. are financially supported by FRIA (F.R.S.-FNRS). This project was supported by the European Research Council under the European Union’s Horizon 2020 Research and Innovation Program Grant Agreements 851288 (to E.H) and the Marie Skłodowska-Curie grant agreement 797621 (to M.G.G.). D.B.B. is a NOMIS Fellow supported by the NOMIS Foundation, and performed this work in part at Aspen Center for Physics, which is supported by National Science Foundation grant PHY-1607611. X.T. and M.G.G. acknowledge support from The Generalitat de Catalunya (AGAUR SGR-2017-01602 to and the CERCA Programme), the Spanish Ministry for Science and Innovation MICCINN/FEDER (PGC2018-099645-B-I00), the European Research Council (Adv-883739), Fundació la Marató de TV3 (201903-30-31-32), the European Commission (H2020-FETPROACT-01-2016-731957), La Caixa Foundation, and by CIBER -Consorcio Centro de Investigación Biomédica en Red- (CB15/00153), Instituto de Salud Carlos III, Ministerio de Ciencia e Innovación. IBEC is recipient of a Severo Ochoa Award of Excellence from the MINECO.
Author contributions
S.G. and E.V. conceived the project and S.G. supervised the project. E.V. developed minimal epithelial models and performed cell experiments, tracking and imaging. D.B.B. and E.H. developed the theoretical model, D.B.B. implemented and performed simulations. L.R., Y.K. and M.L. contributed to experiments. E.V., D.B.B., M.G.G., X.T., E.H. and S.G. analyzed data. The article was written by E.V., D.B.B., E.H. and S.G., read and corrected by all authors, who all contributed to the interpretation of the results.
Competing interests
The authors declare no competing interests.
There is NO Competing Interest.
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Supplementary Movie S5. Time-lapse sequence in DIC mode of polarized epithelial cluster that migrates on a 50 µm wide fibronectin micropattern. The scale bar is 25 µm.
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Movie S4
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Supplementary Movie S3. Time-lapse sequence in epifluorescence mode of epithelial keratocytes labelled with the MitoTracker (MT) Red dye. Cells were detached from the front edge of primary tissue growing from the fish scale. The fluorescence intensity of the dye was proportional to the mitochondrial membrane potential. Unpolarized and stationary cells showed a low MT fluorescence intensity, which increased immediately with their polarization and migratory state. Cells were digitized in 256 bits and the MT intensity was color-coded (from high to low: white, purple, red, orange, yellow, green, light blue and dark blue). The total duration time is 1 hour and 59 minutes.
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Supplementary Movie S1. Time-lapse sequence in DIC mode of a polarized one-dimensional cluster (7 polarized cells) that migrated on a 15 µm wide fibronectin micropattern. The scale bar is 10 µm.
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Supplementary Movie S2. Time-lapse sequence in DIC mode of a polarized one-dimensional cluster (10 polarized cells) that migrated on a 15 µm wide fibronectin micropattern. The scale bar is 10 µm.Movie S2
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Supplementary Movie S11. Animated simulations of the model combining velocity alignment, polarity alignment, and contact inhibition of locomotion (VA+PA+CIL), with parameters that capture the qualitative behavior of MDCK cell clusters. Top: microstripe (open boundary conditions). Bottom: microring (periodic boundary conditions). Green dots: cell positions, green lines: elastic links between cells, magenta arrows: polarities. Cells were initialized with random polarities.
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Movie S10
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Supplementary Movie S6. Animated simulations of the model with single interaction types; from top to bottom: polarity alignment (PA), velocity alignment (VA), stress-polarity coupling (SPC), contact inhibition of locomotion (CIL). Green dots: cell positions, green lines: elastic links between cells, magenta arrows: polarities. Cells were initialized with random polarities.
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Supplementary Movie S8. Animated simulations of the model combining velocity alignment, polarity alignment, and contact inhibition of locomotion (VA+PA+CIL). Green dots: cell positions, green lines: elastic links between cells, magenta arrows: polarities. Cells were initialized with random polarities. From top to bottom, systems with increasing width are shown, corresponding to n = 1,2,3,4 cells.
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Supplementary Movie S7. Animated simulations of the model with pair-wise combinations of interactions; from top to bottom: VA+SPC, PA+SPC, VA+CIL, PA+CIL. Green dots: cell positions, green lines: elastic links between cells, magenta arrows: polarities. Cells were initialized with random polarities.
- MovieS91.mpg
Supplementary Movie S9. Animated simulations of the repolarization behavior of model in a confined system with various interaction mechanisms. From top to bottom, the interaction mechanisms PA, VA, VA+CIL, VA+PA+CIL are shown. Green dots: cell positions, green lines: elastic links between cells, magenta arrows: polarities. Cells were initialized with random polarities.
- ExtendedDataVercruysseClusters202200716.pdf
Extended Data Figures
- Gabrielenrreportingsummary.pdf
Reporting Summary