In this study, we investigate epithelial cell migration within 3D environments by introducing PDMS micropillars as adhesive obstacles with varying densities. Micropillar arrays are ideally suited to mimic various micro-environments, permitting us to address different length scales at which glassy dynamics emerge, ranging from individual cells to the absence of confinement. By comparing the collective migration dynamics of confluent cell sheets on surfaces with and without these micropillars, we seek to elucidate how 3D geometrical cues influence the coherence of collective motion. By varying the distance between the pillars, we identified a length scale at which collective motion drops substantially (<80 μm) compared to the non-confined reference. Vertex simulations that included attractive pillars at varying densities successfully predicted experimental findings. Our model shows that cells adhering to the pillars obstruct the movement of other cells, creating localized blockages. Away from these pillars, however, the cell layer remains fluid and largely unaffected by their presence. We also investigated the role of intercellular connectivity in epithelial mechanics by using cell lines with specific defects in tight junctions and adherens junctions, respectively4. By employing specific genetic mutants with altered intercellular junction mechanics resulting in different contractility4, in conjunction with substrates displaying regularly spaced pillars, we achieved a controlled perturbation of both cellular connectivity and geometric confinement. Albeit pillars are not found in vivo, our setup permits a quantitative analysis of how these mechanical factors influence key metrics of collective migration, including velocity profiles, mean squared displacements, spatial correlation lengths, and cluster formation.
Highly ordered arrays of micropillars were employed to impair the collective migration of Madin-Darby Canine Kidney II (MDCK II) epithelial cells. The pillars are designed to be taller than the cells to ensure a true 3D confinement and prevent cells from crawling on top. The spacing variation between the pillars allows for identifying a length scale at which collective migration is perturbed. The micropillars, made from polydimethylsiloxane (PDMS) and uniformly spaced, act as adhesive obstacles that mimic structural aspects of the extracellular environment regulating cell motility in vivo. Phase contrast microscopy images (Fig. 1a-f) show the spatial arrangement of micropillars (red circles) within the MDCK II monolayer. The images display a representative range of pillar densities, with wall-to-wall spacing varying from 20 to 150 μm. This allows us to systematically assess the effects of different length scales on cell migration. In addition, 3D surface topography images (Fig. 1g), obtained using a laser scanning microscope, illustrate the precise structural dimensions of the cylindrical micropillars confirming a consistent pillar height of 35 μm, as indicated by the color-coded height profile. The diameter of the pillars was chosen accordingly to ensure the mechanical stability of the high aspect ratio structures. Altogether, the pillars' cylindrical geometry and uniform height ensure that the physical barriers presented to the cells are consistent across the array, providing a reproducible platform for exploring the role of mechanical confinement in collective cell behavior. By varying the spacing of the micropillars, we can systematically probe how different degrees of confinement alter epithelial sheet organization, cell-cell junction integrity, and the transition between coordinated, collective movement and more diffusive, individual cell motility.
The presence of pillars changes a number of parameters associated with the transition of the cell layer from a motile, fluid-like one to a solid-like kinetically frozen one. Here we adhere to the terminology put forward by Fredberg and coworkers. We refer to caging if individual cells become increasingly confined by their neighbors due to crowding, limiting their ability to move freely. Jamming occurs when this confinement reaches a critical threshold, causing the collective motion of cells to slow down dramatically and transition from fluid-like behavior to a solid-like state, where rearrangements require large-scale cooperative movement.
We explored the impact of varying pillar densities and distances on the dynamics of collective cell movement using optical flow techniques. By applying a tracking approach (detailed in the materials and methods section) to reconstruct example trajectories from pixels, we were able to determine the locations and velocities along a pixel's path. The velocities of cells over time were analyzed across different pillar densities (interpillar distances: 50 μm, 80 μm, 100 μm, 150 μm) and compared to a control group without pillars. At lower pillar densities, cells exhibited more collective, coordinated movements, while increasing the pillar density progressively obstructed the collective behavior, forcing the cells to navigate around the obstacles. Notably, micropillars with spacings of 5 μm, 10 μm, and 20 μm were excluded from quantitative analysis, as cells either grew on top of these pillars or the phase-contrast images lacked sufficient contrast for reliable algorithmic detection. As shown in Fig. 2a, the velocity of cells gradually decreases over time across all conditions, with the most significant reduction observed at higher pillar densities. As shown before, a general decline in migration speed can be attributed to increased cell density as the cell monolayer progressively enters a jammed state at higher density. Clearly and as expected, denser pillars impose greater constraints on cell motility. The spatial variation of averaged velocity as a function of distance from the nearest pillar is depicted in Fig. 2b. The velocity increases with distance from the pillars, indicating that cells experience less resistance and can move more freely as they are farther away from the obstacles. Therefore, we refer to the pillars as 'adhesive obstacles'. This adhesiveness likely arises from the tendency of MDCK II cells to adhere non-specifically to nearly any substrate, irrespective of its orientation. We also examined the mean squared displacement (MSD) calculated from the list of velocities (see material and methods) to identify deviations from Brownian motion and to estimate the caging size of the trapped cells. As shown in Fig. 2c, the MSD is plotted as a function of time for monolayers cultured in environments containing pillars of varying densities. Initially, the cells exhibit ballistic motion, which transitions into a shallower, subdiffusive regime at longer lag times. At longer timescales and small interpillar distances, the MSD displays a plateau-like behavior, characteristic of glassy dynamics, indicating that neighboring cells together with surrounding pillars impose spatial constraints that effectively confine the cells and limit their long-range motility. The two distinct scaling regimes in the log-log representation of the mean squared displacement (MSD) each follow a linear trend. The corresponding slopes, extracted from these linear regimes in the log-log plots, represent the power-law exponents (MSD ∝ τ) at short and long time scales, respectively (Fig. 2d, e). The slope of the MSD obtained from the first linear regime of the log-log plot allows us to deduce the type of diffusivity and cellular activity from the scaling exponent (α) for the different conditions at shorter time scales (Fig. 2d). An α value of 2 suggests linear movement, while α = 1 indicates Brownian motion, and smaller values imply enhanced interaction with neighboring cells or pillars, leading to subdiffusive motion. Superdiffusive motion is defined by 1 < α < 2 and is characteristic of self-propulsion and active matter systems. Typical values for MDCK II cells exceed 1.5 in the absence of obstacles indicative of active, directional cellular motion consuming chemical energy. At short times, the MSD exponent is almost unaffected by the presence of pillars unless a threshold of approximately 80 μm is undercut leading to a significant decrease in the MSD exponent α. The cellular response to spatial confinement intensifies at longer time scales Fig. 2e, as α decreases more markedly with reduced interpillar spacing. We also estimated the size of the confinement experienced by the cells (caging scale) from the intersection of the two linear regimes in the original MSD curves plotted on a log-log scale (Fig. 2c). The caging scale is the largest in the control group (no pillars), reporting only on the impact of neighboring cell clusters (Fig. S1). The size of the cage decreases non-linearly with increasing pillar density, indicating that cells are moving in a more confined space if pillars are denser. Again, a substantial drop in cage size was found below 80 μm interpillar distance. This behavior is also reflected in the spatial correlation length of cell movements (Fig. 2f). Higher pillar densities exhibit a faster decay in spatial correlation, implying that cell movements are more localized in these environments and force transmission is perturbed. The distribution of correlation lengths, shown in Fig. 2g, documents that the control group exhibits the longest-range correlations, with the correlation length decreasing as pillar density increases. Especially at interpillar distances below 80 μm, the drop in correlation is very pronounced (Fig. 2g, dotted vertical lines). Along the same lines, we identified cell clusters that are comprised of cells that move in similar directions. For this purpose, we segmented the cells and assigned their average optical flow angle (see material and methods). A representative image of cell clusters formed in the presence of pillars at a distance of 150 μm is provided in Fig. 2h. The corresponding distributions of average cluster sizes across different conditions (Fig. 2i) indicate that the control group, with no pillars, supports the formation of the largest clusters while increasing pillar density results in gradually decreasing cluster size being in line with the other findings of decreasing directed movements, correlation lengths, and cage sizes. Fig. S2 shows the time course of the enstrophy for wt-MDCK II cells, which is the squared vorticity. It represents a scalar quantity that mirrors the strength of the vorticity field. Based on the cell vorticity fields obtained from the optical flow data, we calculate the enstrophy per unit mass at space x and time t, where ω(x, t) is the vorticity. Here, it serves as a measure for the vortical energy of the turbulent structures occurring within the cell monolayer. We also investigated the change in average radius r = E/Ω, with E, the kinetic energy E = 0.5v(x, t) of the present vortices, an indication of coherent movement. Since classical turbulence is unlikely to occur at these length scales, an increase in enstrophy serves as a clear indicator of active matter behavior. Lin et al. observed that the energy spectra of mesoscale cell turbulence differ fundamentally from those of classical 2D Kolmogorov-Kraichnan turbulence. Regardless of the interpillar distance, both kinetic energy and enstrophy decrease over time as cell density increases. This behavior is characteristic of jamming, where collective cellular dynamics eventually come to a halt. Interestingly, enstrophy exhibits minimal variation across different samples, suggesting that vorticity is less influenced by the presence of pillars compared to velocity. Furthermore, the average radius decreases as pillar density increases.
The effects of pillar density and cellular adhesion to adjacent pillars are experimentally indistinguishable. Therefore, to investigate the role of attractive forces between obstacles and cells in impairing collective cell migration, we employed a modified active vertex model that additionally considers adhesion. The vertex model represents the cells of a confluent tissue as a tiling of space with polygons, where the vertices of these polygons serve as the fundamental degrees of freedom (Fig. 3a, b). This modeling approach has been widely used to provide theoretical insights into epithelial cell behavior. We hypothesize that cells located adjacent to the pillars experience an effective adhesion, which in turn contributes to the slowdown of the cell monolayer shown in 2b. A simple harmonic potential V(x) is used to model adhesion. Hence, its strength is solely controlled by the adhesion constant ∂V(x)/∂x = K. The model parameters were selected to ensure that, in the absence of pillars, the cells display active behavior consistent with experimental findings. In the simulation, this activity arises primarily from cell shape and self-propulsion. Cell shape is described using the shape index (), which captures the interplay between cell-cell adhesion and cortical tension. When the shape index exceeds a critical value (3.81), cell-cell adhesion becomes dominant and the energetic barrier for rearrangements between cell borders disappears, resulting in a transition to a fluid-like state. Adding self-propulsion further enhances this effect, driving the system into an active fluid regime. The spatial arrangement of pillars in the simulations was chosen to closely replicate the available free space in the corresponding experiments, allowing for direct comparison of simulated and observed cell behavior. In all simulations, the shape index was fixed at 3.8 and the velocity was maintained at 0.01 (see materials and methods). These values correspond to an active state of the system, showing the characteristic 'ballistic behavior' at short time scales and the absence of a pronounced plateau in the MSD-curves at intermediate scales. The corresponding MSD curves in the absence of pillars are shown in Fig. 3c (black, continuous line). We began by examining how adhesion strength influences collective migration in a setup where the centers of adjacent pillars are spaced two cell diameters apart mirroring the 50 μm configuration of our experiments. We find that as K increases, the plateaus in the MSD curves become more pronounced (Fig. 3c), i.e., the cells move more subdiffusive at longer time scales. At K = 1 the cell-pillar adhesion seems to dominate the forces on the cells, and we get a similar plateau as from the experimental curves at 50 μm (Fig. 2c). In the absence of adhesion, the cells barely detect the presence of the obstacles (Fig. S3). This indicates that while the mere presence of pillars is sufficient to hinder cell movement at the smallest interpillar distances, adhesion amplifies this effect by prolonging the cells' contact with the pillars.
After determining the conditions that best match the experimental data (K = 1), we examine the influence of pillar density on the mean squared displacement (MSD) by varying the pillar spacing to reflect experimental interpillar distances of 50 μm, 80 μm, and 100 μm. As the spacing between pillars decreases, the mean squared displacement (MSD) shows only minor changes, indicating that the fluidity of the cell monolayer remains largely preserved (Fig. 3d). At an interpillar distance of 50 μm, the MSD curve exhibits a pronounced plateau at longer time scales, consistent with experimental observations indicating that cells become confined. This plateau emerges when fewer than two cells can fit between adjacent pillars, effectively blocking the passage at the narrowest point and arresting movement of the monolayer. At larger spacings of 80 μm or more, cells are able to squeeze between pillars, and the monolayer retains its dynamic, active behavior.
We showed that motile, confluent MDCK II cells largely ignore the presence of pillars unless the interpillar distance undercuts a threshold of approximately 80 μm. Below this threshold, the cells lose spatial correlation, slow down, and move more diffusively as if the cells are unconnected. To what extent does this resilience of confluent epithelial cells to the presence of obstacles depend on the integrity of intercellular junctions, and which junction is more important for collective migration? We used two cell lines to closely examine the impact of impaired cell-cell contacts on cellular dynamics under environmental constraints. The first was a double knockdown (dKD) MDCK II cell line where proteins from the tight junction complex (ZO-1/2) were knocked down. dKD cells display a special phenotype with increased apical contractility leading to very compact cells coexisting with larger outstretched ones. These highly contractile dKD cells exhibit weaker cell-cell adhesion and lower traction force. Consequently, dKD cells tend to form compact clusters of smaller cells at elevated density with reduced migratory capacity, displaying hallmark features of jamming. This cell line thus serves as a model for enhanced apical contractility. The second was an MDCK II cell line lacking the essential adherens junction protein, E-cadherin (Cdh1). MDCK-II cells express E-cadherin and kidney-specific K-cadherin. E-cadherin knockout reduces cell-cell adhesion but still yields confluent monolayers that look like wild-type cells in microscopy (similar cell size, no apical constriction). In contrast, ZO-1/ZO-2 double knockdown (dKD) cells show strong apical constriction with coexisting large and small cells, high apical tension, loss of motility, and jamming; they move poorly as a group and cluster into immobile islands in co-culture. We therefore use dKD cells as a model for contractility-driven impairment of collective migration, whereas E-cadherin KO cells show reduced connectivity without obvious migration defects. The data shown in Fig. 4a-e reveal significant differences in cluster size, correlation length, MSD exponent, caging scale, and velocity over time across these conditions:
The average cluster size (Fig. 4a) of cells moving in the same direction decreases monotonically with increasing pillar density for all three cell lines, with WT cells forming the largest clusters compared to dKD and Cdh1-KO-cells. This trend indicates that cluster size is affected by both impaired cell-cell junctions and the presence of pillars, leading to a reduced dynamic cell aggregation. Similarly, the correlation length (Fig. 4b) decreases as pillar density increases, with WT cells maintaining more long-range correlations than dKD and Cdh1-KO-cells, respectively. This suggests that environmental constraints and compromised cell-cell contacts impair the spatial organization of cell populations in a similar fashion.
The MSD exponents α (Fig. 4c) of both regimes decrease with pillar density for all cell lines. WT and Cdh1-KO cells both exhibit a higher α-value across all conditions compared to dKD cells, indicative of more directional movement. Considering that cells moving ballistically on a straight line with constant velocity in one direction would lead to an α-value of 2, any bending of the MSD-trajectory to circumvent obstacles or neighboring cells inevitably leads to smaller values. Diffusive motion lacking any active motion corresponds to α = 1. Both WT and Cdh1-KO cells migrate well above this limit on short scales indicative of directed motion persisting even in the presence of very dense pillars. Conversely, dKD cells are less active (less superdiffusive) and almost perform merely random walks with α ≈ 1 in the presence of low pillar distances. Along the same line, dKD cells also show more constrained motion than WT and Cdh1-KO cells, i.e., the cage size decreases with pillar densities (Fig. 4d). This suggests that compromised tight junctions and the accompanied higher apical contractility affect the cage size and motility more than the removal of E-cadherins. This observation goes hand in hand with the reported tendency of dKD cells to undergo phase separation into large outstretched cells coexisting with small, contractile ones that are almost immobile. Recently, we showed that dKD are less active as they generate smaller cell-substrate fluctuations than WT cells but produce higher cell-substrate interaction forces rendering them less motile.
The temporal analysis of cell velocity Fig. 4e reveals that WT cells always maintain higher motility over time compared to dKD or Cdh1-KO cells across all pillar densities. The continuous lines in the graph represent the cells moving in the absence of pillars, while the dashed lines refer to cells facing pillars with an interpillar distance of 50 μm. With time, the velocity of WT cells decreases linearly, while Cdh1-KO cells initially show a more pronounced reduction in motility but eventually decelerate linearly as time passes. The presence of pillars reduces the overall velocity but does not alter its time course. Eventually, a baseline fluidity is reached that could be roughly identified as the detection limit of the algorithm, i.e., the monolayer enters the jammed state. dKD-cells start off with a strongly diminished velocity compared to WT and Cdh1-KO cells as they show early signs of jamming. The velocity decreases further with elapsed time but at reduced deceleration until the aforementioned baseline fluidity is reached. In the presence of pillars (dashed line), this baseline velocity is quickly reached, and eventually, the four curves converge. WT cells remain more mobile at this time point. Interestingly, the Cdh1-KO cells exhibit similar collective behavior to dKD cells in terms of spatial correlation and velocity at higher cell densities. However, they resemble WT cells more closely regarding activity (MSD exponent α) and cage size. Cdh1-KO cells display no obvious morphological phenotype in contrast to dKD-cells that separate into smaller contractile cells and larger out-stretched ones. Hence, enhanced contractility found in dKD cells stalls collective migration by entering a partially jammed state and at the same time renders the cells more susceptible to the presence of obstacles forcing them into diffusive motion and hence fosters loss of directionality and collectivity. Cdh1-KO cells are, however, showing unaltered superdiffusional migration but at much smaller speed than WT cells. The cells are still firmly connected to each other and do not show a sign of altered cell-substrate interaction, which might be the reason why the scaling of the MSD is almost unaffected compared to WT cells. Importantly, the absence of E-cadherins reduces spatial correlation, resulting in diminished velocity of the cells in the layer, highlighting the crucial role of adherens junctions in collective migration. Contractility, however, is unaltered in cdh1-KO cells, which preserved the directional motion of cells in contrast to dKD-cells that suffer from apical cringing. Figure S4 shows the temporal evolution of enstrophy for dKD cells compared to WT cells across various interpillar distances. Both enstrophy and average vortex radius are significantly lower in dKD cells than in WT cells, exhibiting a clear dependence on pillar density. Fig. S5 demonstrates that the loss of E-cadherin induces only minimal changes in the monolayer's dynamic behavior. E-cadherin KO cells (green) show a slight increase in enstrophy compared to WT cells (blue), while the average vortex radius is marginally reduced in the KO cells, exhibiting a dependence on pillar density. These reductions in enstrophy and vortex radius underscore the crucial role of E-cadherin in preserving coordinated collective motion and maintaining monolayer integrity.
All cell lines respond to the presence of obstacles in a similar manner, revealing the same universal scale at which collective motion breaks down. However, the presence of pillars has the greatest impact on the velocity of WT cells during the initial phases when the cell layer is highly mobile. Compromised cell-cell junctions render cells less susceptible to obstacles, likely due to the inherently reduced spatial correlation. Highly contractile cells such as dKD MDCK II cells become almost random walkers in the presence of dense pillars, while Cdh1-KO still move collectively with diminished but preserved directionality.
Representative fluorescence images (Fig. 4f-h) show differences in cell morphology and junctional integrity among the cell lines under control conditions (see materials and methods). WT cells (Fig. 4f) exhibit well-defined cell junctions and an intact nucleus, while dKD (Fig. 4g) and Cdh1-KO cells (Fig. 4h) show partially disrupted junctions and altered nuclear morphology. The images indicate the morphological differences between cell lines, linking the observed quantitative differences in cell dynamics to underlying structural changes. Fig. S6 presents orthogonal and top-down perspectives of dKD MDCK II cell monolayers constrained by micropillars. The top-down view (center) illustrates the arrangement of E-cadherin (magenta) at cell-cell junctions, alongside the widespread, punctate distribution of tight junction proteins (green) resulting from their knockdown, with nuclei marked in cyan. The orthogonal side views (right and bottom) verify that the cells remain confined to the substrate plane and do not extend over the micropillars.
Together, these results demonstrate that both the inherent characteristics of cell lines and the physical constraints significantly influence cellular behavior. We found that cellular migration is less impacted by the presence of pillars if the organization of the cell monolayer is already perturbed by impaired cell-cell junctions.
dKD cells display a rounder, more compact morphology than wild-type (WT) cells. In a vertex/tiling-based model this is naturally captured by the dimensionless shape index, which encodes the balance between cell-cell adhesion and cortical contractility through a preferred perimeter-to-area ratio. Operationally, controls tissue mechanics: there is a well-known rigidity transition near 3.81, below which confluent tissues behave solid-like (jammed) and above which they fluidize with frequent neighbor exchanges. To reflect the dKD phenotype, we reduce the shape index in the simulations from 3.8 (WT) to 3.7 (dKD). This lower value makes cells rounder (smaller preferred perimeter at fixed area) and places the system firmly in the jammed regime. As a result, cell rearrangements are suppressed, mean-squared displacements plateau, and the tissue exhibits reduced motility and more solid-like response-both inside and outside the micropillar array-consistent with our experiments. By contrast, depletion of Cdh1 weakens cell-cell adhesion and is expected to promote more fluid-like behavior at the monolayer scale. In our phenomenological mapping, we capture this by increasing the shape index to 3.85, shifting the system deeper into the fluid phase. In simulations this yields higher T1 rates, faster relaxation of shear deformations, larger and more persistent cell deformations, and enhanced collective mobility (see Fig. S7).