The impact of jamming on boundaries of collectively moving weak-interacting cells

Collective cell migration is an important feature of wound healing, as well as embryonic and tumor development. The origin of collective cell migration is mainly intercellular interactions through effects such as a line tension preventing cells from detaching from the boundary. In contrast, in this study, we show for the first time that the formation of a constant cell front of a monolayer can also be maintained by the dynamics of the underlying migrating single cells. Ballistic motion enables the maintenance of the integrity of the sheet, while a slowed down dynamics and glass-like behavior cause jamming of cells at the front when two monolayers—even of the same cell type—meet. By employing a velocity autocorrelation function to investigate the cell dynamics in detail, we found a compressed exponential decay as described by the Kohlrausch–William–Watts function of the form , with 1.5 ⩽ β(t) ⩽ 1.8. This clearly shows that although migrating cells are an active, non-equilibrium system, the cell monolayer behaves in a glass-like way, which requires jamming as a part of intercellular interactions. Since it is the dynamics which determine the integrity of the cell sheet and its front for weakly interacting cells, it becomes evident why changes of the migratory behavior during epithelial to mesenchymal transition can result in the escape of single cells and metastasis.


Introduction
Collective cell migration is an important characteristic of morphogenesis, wound healing and the growth of a tumor front [1,2]. However, the origins of cooperative motion such as cell signaling processes and physical forces are still under debate and not fully understood [3][4][5][6][7]. The molecular and cellular mechanisms underlying collective cell migration require cell-cell cohesion, collective polarization and the coordination of cytoskeletal activities resulting in the generation of shear and traction forces within the monolayer [8][9][10]. This shear force can result in plithotaxis [8]. Classically, the integrity of the monolayer during migration is retained by cell-cell cohesion. It is therefore conceivable that epithelial to mesenchymal transition can only occur when single cells are capable of overcoming the boundary of the migrating monolayer. This concept was verified by studies in which single cells were able to escape an initially intact monolayer upon the addition of trypsin to the medium [11]. Chemicals such as trypsin down-regulate intercellular interactions and change the physical properties of the monolayer, especially the line tension, preventing cells from escaping the sheet. In contrast, fibroblast cells were shown not to migrate collectively; single cells detach from the monolayer and no smooth cell front is sustained [11,12].
Although intercellular interactions are important in maintaining the integrity of a migrating cell monolayer, the dynamic interplay between escaping single cells and the monolayer is also sufficient to maintain a constant cell front during collective cell migration. It was recently shown with a wound-healing-like assay that cells collectively migrating into free space move ballistically, while escaping single cells migrate randomly on long times [12]. This ballistic motion of the monolayer allows it to catch up with escaping single cells and a constant boundary and line tension during migration is observed.
The maintenance of a constant cell boundary is necessary for early stages of cancer when tumor cells remain within the growing host tumor and separate from the normal tissue surrounding it. In contrast to the described dynamically induced stabilization of boundaries [12], the differential adhesion hypothesis describes tissue demixing and boundary stabilization in three dimensions from a static force point of view [13]. Here cells and tissues exhibit a liquidlike behavior and are capable of demixing based on their mutual affinity [14,15], while cells of the same type prefer to cohere with each other instead of adhering to cells of another type. The adhesion difference between different cell types initiates cell sorting, which results in the separation of cells. The cell type with the lower surface tension envelopes the one with a higher surface tension. To this end, a constant cell boundary between both cell types is formed. There have been extensive experimental and theoretical studies [16] that demonstrated the importance of cell sorting through intercellular interactions and contractility in embryogenesis and cancer dissemination [17]. This three-dimensional (3D) cell sorting concept was extended to twodimensional (2D) cell monolayers [18][19][20]. In 2D, the adhesive difference between the cells and the substrate on which they migrate determines whether the cells form a monolayer or round up to form a 3D tissue. However, to what extent physical properties account for cell separation and their impact on collective cell migration remains an open question.
To study the impact of adhesive differences on the stabilization of boundaries, we used the non-malignant epithelial cell line MCF-10A and the malignantly transformed epithelial cell line MCF-7. MCF-7 epithelial cells are expected to have weaker intercellular interactions in comparison with MCF-10A cells since the metastatic potential of the former should reduce their intercellular interactions [21,22]. Contrary to epithelial cells, fibroblasts in vivo do not form monolayers and have been shown in vitro to migrate diffusively upon the provision of free space. Therefore, we additionally employ NIH-3t3 fibroblasts to assess their migratory behavior. It is expected that the intercellular interactions between these cells should be very weak and the cells should not generally migrate collectively.
Glass-like effects were recently shown in collectively migrating cells [23]. However, these effects were employed for the center of a cell monolayer. This naturally raises the question: since a monolayer has a packing fraction of one, are jamming and glass-like effects occurring in a wound-healing-like assay? In this study, in contrast to a fibroblast monolayer in which cells do not migrate collectively, we find that glass-like effects occur in a migrating epithelial MCF-10A cell monolayer. Here the boundary of the monolayer was stable during migration due to ballistic motion of the underlying cells, while slowed down dynamics and jamming led to the formation of stable borders between two monolayers-even of the same cell type. We further characterized the collective dynamics by correlation functions, which could be fitted by compressed exponential functions of the Kohlrausch-William-Watts type. Thus, in contrast to the predictions of the differential adhesion hypothesis, jamming seems to stabilize the boundary even of weakly interacting cells within the monolayer when two counter propagating monolayers meet.
The MCF-7 cell line was bought from ATCC; it was cultured with Minimal Essential Medium Eagle's with L-glutamine and Earle's salt and was supplemented with sodium pyruvate, bovine insulin, non-essential amino acids, foetal bovine serum and penicillin/streptomycin. Epithelial cells generally migrate together since they strongly express cadherin proteins.
The NIH-3t3 fibroblast cell line was cultured in Dulbecco's Modified Eagle's Medium supplemented with 10% bovine calf serum. All the cell lines were cultured at 37 • C, with 5% CO 2 in an incubator, while media were changed every second day.

Phase contrast time lapse microscopy
For phase contrast microscopy migratory measurements, cells were washed with phosphate buffer saline, trypsinized, centrifugated and re-suspended in the culture medium. Cells were counted using a hemocytometer and seeded in an ibidi (München, Germany; product number: 80241) culture insert attached to a Nunc culture dish. The cells were allowed to attach, divide and form a monolayer by incubation at 37 • C with 5% CO 2 after which the insert was removed and the dish placed on an inverted microscope (DMIRB, Leica) containing a custom made heater kept at 37 • C and supplied with 5% CO 2 in air. A frame was taken every 5 min (using a Dalsa DS-21-02M30 CCD camera (Dalsa Corporation), 10× objective with NA 0.3 and a 0.5× C-mount) for the epithelial cells and every 2 min for the fibroblast cells. Each measurement lasted 48 h.

Mapping of displacement fields and spatial velocity distribution
To obtain the spatio-temporal velocity distribution, a mesh grid of distance 10 µm was defined on the cell monolayer images. At each grid point, a template pixel area (M) of size 20 × 20 µm 2 was cropped. M was overlaid and scanned through a larger search area (S) at the same grid point in the succeeding image. The size of S was 5 µm larger than M. A 2D-cross-correlation algorithm determined the pixel area in S that is most common with M. The cross-correlation was defined as where m and n are the position indices of each image point andM andS denote the average values of M and S. The position of maximum cross-correlation value in S defines the displacement vector of each grid point. This determines the movement of a cell within the monolayer from one image to the next and results in a discrete displacement vector field defined as where r (x(t), y(t)) = (x(t), y(t)). A 3D convolution kernel was used on the discrete displacement field interpolating to obtain the final flow field. This convolution kernel is a normalized Gaussian ranging ±2 frames in time with a variance of one frame. The spatial variance of the kernel was 20 µm. Furthermore, the convolution is only done for discrete displacements with a cross-correlation value above 0.7. The software is described in [24,25] in detail.

Boundary stabilization
To gain insight into the collective properties of migrating MCF-10A and MCF-7 epithelial cells, we performed a wound-healing-like assay in which both cell types were employed as monolayers, migrating in opposite directions towards each other. We first observed that MCF-10A and MCF-7 cell layers formed stable boundaries (figures 1(a) and (b)), and the MCF-10A monolayer migrated faster than the MCF-7 cell. Indeed, the MCF-7 monolayer was stationary and no dynamics of the sheet itself became visible. When the boundary of the MCF-10A monolayer met the MCF-7 borderline, no mixing between the monolayers was evident (figure 1(b), see supplementary data, movie 1 (available from stacks.iop.org/NJP/14/115012/mmedia)). The velocity (color coded in figure 1(c)) of the MCF-10A monolayer was spatially and temporally heterogeneous, while the displacement fields (white arrows in figure 1(c)) of the monolayer were uni-directional and indicated directed persistent (ballistic) motion during migration. To verify if the lack of mixing of both monolayers emanates from the jammed nature of the monolayer and the strong intercellular interactions between the cells and not from the differential adhesiveness of the two cell types as postulated by the differential adhesion hypothesis, we employed the same wound-healing-like assay, but with MCF-10A cells on both sides. Thus, two MCF-10A monolayers migrated towards each other, while imaging the interaction of the sheet fronts and the dynamics of single cells after the incidence of the two monolayers. As shown in figures 2(a) and (b), no mixing of cells originating from oppositely migrating MCF-10A monolayers was present and the cells remained within their initial cell sheet (supplementary movie 2, available from stacks.iop.org/NJP/14/115012/mmedia). The cell density within the monolayer on the left-hand side (figure 2(a)) was lower (5 × 10 3 cells cm −2 ) compared to the density on the right side (2 × 10 5 cells cm −2 ). This variation in density originated in different single cell dynamics: while in the lower cell density sheet, single cells could escape during migration, such single cell motion out of the sheet was not evident for the high-density layer. The spatial velocity distribution of both monolayers was identical to the distribution of MCF-10A cells as shown in figure 1(c); the displacement fields were unidirectional, thus indicating ballistic motions. Due to this directionality, both monolayers retained  a constant cell front on longer times because of the monolayer's ability to catch up with escaping single cells [12]. However, when both monolayers met, a transition from directed to random motion of the cells at the borderline of both sheets became evident (figure 2(c)). Cell migration was hampered and finally stopped. Therefore, the establishment of a defined cell boundary, when oppositely migrating cells met, was initiated by the jamming of cells within the monolayers.
To investigate the effect of the dynamics on the ability of the monolayer to form a constant cell front, we repeated the experiment by letting two sheets of NIH-3t3 fibroblast cells migrate into each other. As can be seen in figure 3, NIH-3t3 cells did not migrate as a monolayer with a constant cell front (see also supplementary movie 3, available from stacks.iop.org/NJP/14/115012/mmedia). Rather, single cells escaped from the monolayer and moved randomly in front of the sheet. In contrast to the epithelial cell monolayer, there was no global uni-directional motion of the fibroblasts within the monolayer in the direction of escaping single cells. Thus, the monolayer was not able to catch up with the escaping cells, and consequently, no boundary at the margin of the monolayer was developed.
Our investigations on MCF-10A and MCF-7 epithelial cells suggest that jamming of cells within a 2D sheet results in the establishment of boundaries during collective cell migration and prevents the mixing of the cells originating from different monolayers no matter the cell type.
The dynamics of the monolayer seems to play a dominant role in establishing a permanent cell front in 2D monolayers. When the cells are strongly interacting, such that single cells cannot escape, there is a permanent cell boundary preventing the mixing up of cells when two cell fronts meet (figure 1). In contrast, for weakly interacting epithelial cells, where single cells can escape the monolayer, the interplay between the ballistic motion of the monolayer and the random motion of the escaping cells enables the monolayer to catch up with the escaping cell, thereby retaining a constant cell front. Thus, the impact of a line tension in maintaining the permanent cell front is minimal. For non-interacting cells such as fibroblast, collective migration was theoretically shown to be an emergent property of single cell motion [26]. Although non-interacting single cells move as persistent random walkers, at very high densities, collisions between the cells can initiate collective motion [26,27]. However, in a wound healing assay, the density reduces as single cells randomly move away from the monolayer and this prevents collective motion in non-interacting cells ( figure 3(c)). Our study therefore shows that in two dimensions, when cells move collectively with a constant cell front, their jammed nature prevents two oppositely migrating monolayer from mixing up.

Glass-like features in the wound healing assay
The observed jammed behavior of cells exhibits features typical of a glass-like system; similar to collective cell migration that displays glass-like features when the density of the monolayer increases [23,28]. However, the application of glass-like dynamics on cellular motion is complicated because of the soft and out-of-equilibrium nature of cells; e.g. the transition to a glass-like state when two cell monolayers meet could be slower than for hard spheres. Features typical of glassy systems include non-Arrhenius relaxation times and a slow and heterogeneous dynamics with increasing cell density. Additionally, heterogeneous dynamics, as described for glassy systems earlier [29][30][31], were already observed in our experiments at the interface of two monolayers as shown in figures 1(c) and 2(c). To investigate the glass-like nature in more detail, we studied the dynamics of the MCF-10A monolayer at a low (5 × 10 −3 cells cm −2 ) and a high (2 × 10 5 cells cm −2 ) cell density (figure 4).
For both cell densities of MCF-10A cells, initially isotropic displacement fields were observed, that is, cells moved randomly on short times (figures 4(a) and (b)) with an average velocity below 0.4 µm min −1 . The random dynamics originated from local single cell rearrangements within the sheet. Besides the short time isotropic dynamics of the cells, the integrity of the monolayer was retained through cell-cell coupling. Thus, the cell monolayer moved into the direction of free space on long times (figures 4(c) and (d)).
On long times and for both cell densities, the displacement fields gradually changed from an isotropic to a directed pattern (figures 4(c) and (d)) with cells moving super-diffusively or ballistically. Furthermore, the spatial variation in magnitude of the velocity increased with time and was generally greater for the low cell density ( figure 5(a)) in comparison to the high density ( figure 5(b)). This increase in the width of the velocity distribution with time at a low cell density (figures 4(d) and 5(a)) correlates with an increase in cell surface area, which might initiate a larger cell density fluctuation. The decrease in cell density initiated by cell spreading also led to single cells dissociating from the monolayer on very long times ( figure 4(c)). However, at higher cell density, cell dissociation was not observed. In contrast, we obtained a decreasing velocity gradient from the front of the sheet, where cells are more spread, to the back where cells are more crowded and less spread (figures 4(d) and 5(b)). For both cell densities, there was a spatially heterogeneous dynamics, which is typical of a glass-like system and emanates from the cooperative motion of cells, i.e. faster cells move together, while slower cells stick together.

Intramonolayer dynamics
The comparison of epithelial and fibroblast cell motion showed that a stable cell boundary cannot be maintained if cells move randomly as individual cells. To determine the collectivity in migration of MCF-10A cells, we calculated the spatial velocity autocorrelation at various times. The spatial velocity autocorrelation was defined as where v = (r (t + δt) − r (t)) / (δt) and r (t) defined in equation (2) is the position of a cell at some time (t) determined from equation (1). · · · is the mean of the velocity in the y-direction.  The velocity autocorrelation was best fitted by the Kohlrausch-William-Watts function of the form C(x) t = C 0 exp (− (x/x 0 (t)) β(t) ) (figures 6(a) and (b)). x 0 is the correlation length and β the compressing exponent. The mean of the compressing exponent β was 1.79 ± 0.14 for low cell density and 1.50 ± 0.24 at high cell density ( figure 6(d)). The small values of β at short times at high cell density emanate from noise induced by cell media flows. The correlation length increased from a cell's diameter on short times to a maximum of about 10 cell diameters at long times (figure 6(c)). The increase in correlation length with time could result from the fact that at short times, the monolayer is stationary. As time increases, marginal cells start moving and this movement unjams the monolayer, since crowding suppresses the translation of cells. When the monolayer is unjammed, sub-marginal cells start moving; thus, spatial correlation increases with time, since the unjamming process is time dependent.
The increase of the correlation length with time agrees with studies on the collective motion of cells using Madin-Darby canine kidney (MDCK) cells with stronger intercellular coupling [10]. In this study, the correlation length also increased linearly with time for cells migrating on a poly-acrylamide gel, and the increase in correlation length with time was shown to correlate with increasing cell density. However, on a glass substrate, the correlation length decreased with increasing cell density (the cell density increases with time as a result of cell divisions). It should however be noted that, while the center of the monolayer was considered in the study using the MDCK cells, we performed a wound-healing-like assay on the glass substrate. By considering the center of the monolayer, the density of the system increases over time, which initiates swirls and dynamic arrest [23], causing changes in the spatial velocity  correlation. In contrast, in a wound-healing-like assay, a density gradient is established as the monolayer migrates [12]. Using the MDCK cells in a wound healing assay, the correlation length was found to be about 200 µm, after 5 h of migration [6]; this is of the same order of magnitude as compared to our study.
The compressed exponentials for the spatial correlation length, which we found for this actively spreading cell monolayer, are typical of passive nematic liquid crystals with correlated quenched disorder [32]. Such systems show long-range directional order and their temporal dynamics is similar to that of aging glassy colloids [33]. Moreover, compressed exponential relaxation times (β = 1.5) were observed in other soft matter systems such as colloidal gels [34,35] and clays [36], and charged colloids with stronger inter-particle interactions showed β > 1.5 [37]. This compressed exponential behavior was heuristically modeled in terms of ultraslow, large-length-scale ballistic motions of elastic deformations in response to a local and spatially heterogeneous stress source [34,38]. This is the same ballistic motion that we find in our cell monolayer, which might explain the compressed exponential correlation lengths in our system.

Discussion and conclusions
In this study, we have shown for the first time that the dynamical properties of cells play a crucial role in maintaining the establishment of a permanent cell front during collective migration and the prevention of cellular mixing from different monolayers. For cells with strong intercellular interactions, it is obvious that single cells cannot escape the monolayer and a boundary is formed, suppressing the mixing up of cells when counter-migrating monolayers meet. However, even for weakly interacting cells, dynamic effects contribute in retaining a constant cell front. The ballistic motion of weakly coupled cells within a monolayer allows the moving sheet to catch up with single escaping cells, since these cells lose their super-diffusive behavior and migrate randomly [12]. Thus, for weakly interacting cells such as MCF-10A epithelial cells, the boundary is retained by the combination of the intercellular interactions and dynamic effects.
Moreover, we have shown that the formation of a permanent migratory front also acts as a dynamically induced barrier of jammed cells. According to the differential adhesion hypothesis, cohesion differences between two cell types result in the formation of 3D spheroids [39,40] and demixing, while cells with lower cohesion forces and surface tension surround the other cell type [15,41,42]. Our investigations show for the first time that for a 2D cell sheet, differential adhesion and line tension differences originating from the fluid-like behavior of cells as described earlier [14,[43][44][45] are not a prerequisite for a stabilization of cell fronts. Since cells of the same type did not mix in our experiments, even an extended differential adhesion hypothesis [16] where the line tension is modulated by contractility cannot explain our findings. Here, dynamic effects in concert with intercellular interactions lead to jamming, which creates a line tension preventing single cells from escaping the cell monolayer and can act as a cell mixing suppressor by stabilizing the monolayer boundary. Since surface tension differences are expected not only to contribute to cellular behavior in three dimensions, but also in a 2D monolayer and especially at the interface of two monolayers, we show that other active physical properties can contribute to boundary stabilization besides passive line tension and adhesion forces.
In two dimensions, it has to be taken into account that the additional cell-substrate interaction determines if the cells round up into a 3D tissue or spread on the substrate and migrate [46]. If the intercellular interactions are too weak compared to cell adhesion to the substrate, no intact monolayer can be formed, and cells migrate randomly and escape from their neighbors as observed for NIH-3t3 fibroblast cells [18,20]. Since the diffusive dynamics of these cells prevents jamming, no permanent cell front is formed and cells mix upon meeting another sheet of randomly moving cells.
The behavior of epithelial cells at the front when two monolayers meet can be described not only in terms of a transition from super-diffusive, directed motion to random motion, but also by considering glass-like features. Glass-like behavior such as the observed jammed nature of strongly interacting cells is characterized by heterogeneous dynamics, namely cells with higher velocity moving together at the cell front [10,23] and starting to jam as soon as the directed motion is hampered. Moreover, we observed that the correlation lengths increased with time and are fitted well by compressed exponential Kohlrausch-William-Watts functions, characteristic of aging glassy systems. The increased correlation length with time suggests that the dynamics is highly coordinated and spans several cell lengths.
Interestingly, our study suggests that glass-like dynamics and jamming surprisingly occur within the actively moving and deformable cell monolayer system. Generally, glassy behavior is described by cooling or crowding passive systems, while the underlying dynamics and nature of glassy systems are not well understood. We can only assume that cell divisions and migration acting as external heterogeneous stress sources simultaneously jam and shear [8,23,47] the monolayer, respectively. Cell migration-induced shear stresses are heterogeneously transmitted [8,9] through cell-cell couplings to neighboring cells, which are consequently deformed and aligned [6,48] over a long distance. Cell deformation pre-strains the cells, which thereby results in a slight stiffening of the entire monolayer. The stiffening enables a long-range transmission of shear forces through intercellular couplings. Long-ranged force transmissions culminate in collective cell motion, which consequently jams the monolayer.
The observed jamming and glass-like dynamics are expected not only to play a crucial role in embryologic development, but also in the progression of a tumor since it can be considered a developing tissue. Höckel employed the term ontogenetic anatomy which maps the human body from its embryological origin (anlage) and characterizes the compartments representing morphogenetic units in the adult [49,50]. Here the compartment boundaries are primary proliferation and migration suppressors. Höckel could clearly show that women with non-metastatic carcinomas of the uterine cervix originating in the Müllerian compartment have a reduced mortality from 20 to 4% when the total compartment is resected even without subsequent radiation or chemotherapy [49,51,52]. Following his compartment theory, cells of the primary tumor have the ability to spread and migrate freely within their initial ontogenetic compartment where the tumor originated because tumor cells and normal cells behave similarly. Only major changes of the tumor cells such as epithelial-mesenchymal transitions are a prerequisite of tumor progression beyond compartment borders and subsequently metastasis. Since within such a compartment, normal cells and tumor cells do not necessarily demix as proposed by the differential adhesion hypothesis, the question of what keeps the tumor cells inside their host compartments might similarly be answered as observed in our experiments: intercellular interactions and dynamic effects stabilize compartment boundaries, while jamming can further act as a proliferation suppressor [18][19][20] due to a lack of space and increased homeostatic pressure [53]. To this end, future studies will focus on the dynamics of cells not only in 2D, but in 3D systems. Droplet cultures can be employed to investigate the origin of mixing and demixing in correlation with surface tension differences to understand why cancer cells can gain the ability to leave the host tumor and metastasize. Nevertheless, since Wicki et al showed that upregulation of podoplanin-a small mucin-like protein-of cells at the tumor front promotes invasion in the absence of epithelial-mesenchymal transition by the formation of filopodia [54], it becomes evident that tumor progression might be mainly determined by the underlying dynamics of single cells within the entire system, even without major changes in cell-cell interaction.