article: The ability of cells to coordinately migrate in groups is crucial to enable them to travel long distances during embryonic development, wound healing and tumorigenesis, but the fundamental mechanisms underlying intercellular coordination during collective cell migration remain elusive despite considerable research efforts. A novel analytical framework is introduced here to explicitly detect and quantify cell clusters that move coordinately in a monolayer. The analysis combines and associates vast amount of spatiotemporal data across multiple experiments into transparent quantitative measures to report the emergence of new modes of organized behavior during collective migration of tumor and epithelial cells in wound healing assays. First, we discovered the emergence of a wave of coordinated migration propagating backward from the wound front, which reflects formation of clusters of coordinately migrating cells that are generated further away from the wound edge and disintegrate close to the advancing front. This wave emerges in both normal and tumor cells, and is amplified by Met activation with hepatocyte growth factor/scatter factor. Second, Met activation was found to induce coinciding waves of cellular acceleration and stretching, which in turn trigger the emergence of a backward propagating wave of directional migration with about an hour phase lag. Assessments of the relations between the waves revealed that amplified coordinated migration is associated with the emergence of directional migration. Taken together, our data and simplified modeling-based assessments suggest that increased velocity leads to enhanced coordination: higher motility arises due to acceleration and stretching that seems to increase directionality by temporarily diminishing the velocity components orthogonal to the direction defined by the monolayer geometry. Spatial and temporal accumulation of directionality thus defines coordination. The findings offer new insight and suggest a basic cellular mechanism for long-term cell guidance and intercellular communication during collective cell migration.
  Collective cell migration plays an essential role during embryonic development, wound healing, tissue repair and cancer metastasis [1]–[4]. Directional migration and intercellular coordination are two cellular traits that play major roles in collective cell migration. It was previously demonstrated that collective cell migration relies mostly on a directional signal that stems from the moving cluster rather than from external cues [5], directionality might be correlated with metastatic potential [6], and is enhanced by growth factors [7]. Directionality and coordination are affected by substrate stiffness [8], topographic cues [9], cell density [10], and are linked to mechanical intercellular cooperation [11]–[13]. Vitorino et al. defined 3 modules for collective cell migration: motility, directionality and coordination, and classified genes that affect each of these modules [14]. Despite these vast research efforts, the physical mechanisms underlying intercellular coordination are still unknown. We present here a rigorous analytical framework to investigate the dynamic relations between different physical variables of migrating cells over time and space, which suggests new insights regarding the mechanisms that account for directionality and intercellular coordination. Capabilities of collective behaviors of cancer cells involve some modes of inter-cellular communication, social networking and cooperation between cells, which regulate dissemination, proliferation and colonization within the body [6], [15]–[19]. Revealing common and different cellular and molecular mechanisms that govern intercellular coordination of normal and cancer cells may lead to new therapeutic paradigms to target intracellular signaling processes and intercellular communication in cancer metastasis [20]. In vitro wound healing assays involve the partition of a cell monolayer into two separated segments by scratching. We studied the collective dynamics of such a monolayer, as these segments move towards each other to close the wound. As the wound edge advances, the cell monolayer is moving forward. Here we focus on global organization during collective cell migration of DA3 mammary tumor cells and MDCK normal epithelial cells and the effects of Met signaling activation by its ligand hepatocyte growth factor/scatter factor (HGF/SF), master regulators of cell motility in malignant and normal processes [21]–[24]. Growth factors play a central role in collective cell migration [7], [14], [25]. We choose to study HGF/SF-Met signaling effects on cell motility since: 1) it is a well characterized signaling pathway in different aspects of cell motility; 2) the molecular tools to study this pathway are well established enabling to effectively inhibit Met signaling [26]; 3) The relevance of this signaling pathway to cancer and especially metastasis [27], [28]. We previously established that HGF/SF induces in tumor (DA3) migrating cells a backward propagating wave of increased velocity that is associated with shape modification into larger and more elongated cells. This wave propagates from the wound edge backward into cells located farther away from the advancing front [29] (Supporting Text SI1 in Text S1, also shown for MDCK cells here). Here we reveal that collective cell migration is more intricate than was previously reported. We applied specially-designed analytical techniques to investigate the spatiotemporal dynamics of acceleration, cellular stretching (strain rate), directionality and coordination, and their associations and temporal order. We found that these quantities can exhibit wave-like phenomena, which move backward in respect to the monolayer' s moving direction - away from the wound edge. The wave' s profile is similar to a pulse: low acceleration is observed for the cells that are close to the edge, the acceleration increases for the cells that are behind them, and decreases again for cells that are farther away. The location of the maximal acceleration moves backward, i. e. , in a direction opposite to the motion of the monolayer itself. We refer to this phenomenon as backward propagating wave, and it is sketched in Fig. 1A. First, we discovered the emergence of a backward propagating wave of coordination. The wave reflects the formation of clusters of cells moving with coordinated trajectories. These clusters are measured by applying a region-growing segmentation algorithm that gradually merges adjacent trajectories to spatial clusters. Second, we show that HGF/SF treatment generates backward propagating waves of both cellular acceleration (escalating motility) and stretching (strain rate). We refer to these coinciding waves as a wave of acceleration and stretching. Thirdly, we uncover the emergence of a backward propagating wave of directionality, following the HGF/SF-induced wave of acceleration and stretching with an approximated one hour lag. The term ‘directionality’ is defined as the ratio between the cells' velocity towards the front, and the velocity parallel to the wound edge. Finally, we present the association between the waves of different cellular properties and suggest that the wave of directionality may be responsible for the amplified magnitude of the wave of coordination. Our data suggest that increased velocity leads to enhanced intercellular coordination: motility is increased due to acceleration and stretching that in turn increase directionality by temporarily diminishing the velocity components orthogonal to the overall direction defined by the monolayer geometry; accumulation of directionality over space and time thus defines coordination.
  The different physical properties of the moving cellular monolayer were measured and averaged spatiotemporally to describe the collective dynamics. To quantify each attribute, the cellular area in each image was discretized to patches or “agents” and their trajectories were tracked. It is important to note that no position-switching between these agents has been observed (also reported in [29]). Acceleration, strain rate and directionality were computed along the migration trajectories of each of the individual “agents”, as detailed below. Acceleration (increasing motility) was calculated as the change in the velocity along the trajectory (Fig. 1B), ; this local time-derivative was performed by computing the acceleration of the agent along its trajectory using the preceding and following time-frames. Strain rate is a measure for the local deformation of an object, typically caused by non-uniform force acting on the object which results in a non-uniform stretching. Strain rate was measured as the local spatial derivative of the speed, where x is the local migration direction of each agent. It was calculated as the difference between the velocities of the agents ahead and behind the agent of interest, according to its local direction. Assuming cellular cohesiveness and mass conservation, it is an implicit measure for cellular deformation rate [30], thus cell stretching was taken to be proportional to the strain rate along the trajectory (Fig. 1C). Directionality is defined as the absolute value of the ratio of the velocity component toward- and parallel- to the wound edge (Fig. 1D). The velocity components are measured with respect to the direction of the wound edge. Higher values of the ratio between the perpendicular and parallel components indicate that the motion is more directed towards the wound edge, while smaller values mean a “noisier” motion. Values lower than 1 mean that the dominant motion is parallel to the wound edge (not closing the wound), while values above 1 indicate a more efficient healing process as the directionality increase. Intercellular coordination is a measure of the collective migration, rather than a single cell' s. It is defined as the fraction of cells migrating in coordinated clusters within the monolayer. Explicit detection of these clusters was performed by applying image segmentation on a dense grid of trajectories, thus identifying and grouping similar trajectories of adjacent agents. It is important to note that directionality and coordination are not necessarily related: a pair of adjacent cells can move coordinately but with poor directionality, or migrate less coordinately with higher directionality (Fig. 1E). Full technical details on the measures that were used are given in Materials and Methods and in Supporting Text SI4 in Text S1. The results are organized as follows. Next, we present the emerged backward propagating waves of acceleration & stretching, directionality and coordination. Then, to assess the hypothesis that acceleration and strain rate lead to directionality that ultimately defines intercellular coordination, we apply spatiotemporal correlation analysis to reveal the temporal order between these waves. Further analysis revealed that HGF/SF induced coinciding waves of cellular acceleration and of cellular stretching (strain rate). Average acceleration and stretching were computed as functions of the distance from the wound edge. This was done by averaging over all the agents belonging to each of the parallel layers at different distances from the edge (more details in Supporting Text SI4 in Text S1). Figure 3 shows spatiotemporal maps (kymographs) of acceleration and strain rate for DA3 cells. Each element (t, d) in the map shows the average acceleration, over time interval Δt = 14. 5 minutes (1 frame), (Figs. 3A and 3C) and the average strain rate (Figs. 3B and 3D), at time (t) for all the agents of a layer of width Δd = 12. 4 µm (10 pixels), located at a distance (d) from the wound edge. Consecutive time projections (columns) of the spatiotemporal maps for HGF/SF treatment further illustrate the wave-like dynamics of the acceleration and strain rate (Figs. 3E and 3F). Comparison between the collective migration in response to HGF/SF and the control reveals that the wave of acceleration and stretching is generated as a response to HGF/SF treatment, while in the control case the acceleration and strain-rates spread from the edge inwards in a smooth manner without a distinct wave front. Comparison between the time projections of the spatiotemporal maps for acceleration (Fig. 3E) and strain rate (Fig. 3F) reveals the accurate coinciding of the waves of increasing motility (acceleration) and stretching (strain rate). These waves propagate at roughly twice the speed of the advancing front edge, consistently with previously published results [31]. A wave of enhanced directionality emerges following the HGF/SF-induced wave of acceleration and stretching. Here the directionality is measured for each layer at a distance (d) at each time (t) from the wound edge by - the ratio between the average speed towards the wound edge and the average speed in the parallel direction. More specifically, and are the average perpendicular speed and the average of the absolute value of the parallel speed, respectively, of all the agents that belong to a layer at distance (d) and at time (t). Note that since cells do not move backward from the wound edge, . Figures 4A and 4C show kymographs of this directionality measure for DA3 cells. Consecutive time projections (columns) of the spatiotemporal maps further illustrate the wave-like dynamics of the directionality in response to HGF/SF (Figs. 4B and 4D). Comparison between the collective migration in response to HGF/SF and the control reveals that the directionality wave is generated as a response to HGF/SF treatment. We find the emergence of three waves of collective migration during the wound healing process: a wave of acceleration and stretching, a wave of directionality and a wave of coordination. To address the hypothesis that acceleration and strain rate lead to enhanced directionality and coordination we proceed by suggesting a simplified theoretical model demonstrating a possible mechanism that links cell stretching to directionality and by quantifying the associations between acceleration and strain rate, directionality and coordination waves. The waves described above and their associations also emerge, under the same conditions with striking similarity, during collective migration of MDCK epithelial cells (Fig. 7), the most common model system for 2D collective cell migration. Additional control experiments to demonstrate the specificity of the HGF/SF induced wave to Met signaling revealed that DA3 cells treated with either HGF/SF with Met inhibitor (PHA) or with Met inhibitor alone, have similar, though slightly reduced, characteristics compared to control cells (See Supporting Text SI3 in Text S1 for details). These results demonstrate that the HGF/SF-induced wave is specific to Met signaling, serving as a model system to study the effects of growth factor on collective cell migration.
  Both wound healing and cancer metastasis are complex processes that require cooperation among many cells to efficiently migrate while keeping the cell sheet intact. We found a new mode of collective migration, a backward propagating wave of coordination that is described as clusters of coordinately moving cells that are formed a substantial distance away from the wound edge and disintegrate closer to the advancing front. We also found that HGF/SF, as a growth factor model, plays an important role in generating an orchestrated wound healing process. A backward propagating wave of acceleration and cellular stretching (strain rate) is generated in response to HGF/SF. This wave leads to the emergence of a wave of enhanced directionality that eventually results in an amplified wave of coordination (Figs. 7A and 7B and 7C). Backward propagating waves of increased velocities [29], [31], [33] and strain rate [31] were previously reported in epithelial cells. Ng. et al demonstrated that front cells were more coordinated than cells farther from the cell front, general coordination increased with time, and a gradual rise in coordination was observed for distal cells [8]. Our analyses looked at dynamic relationships between several physical variables incorporated across many experiments over time and space to reveal new insights on mechanisms that account for intercellular coordination. Our data are consistent with the effect of FGF in a dose-dependent manner, suggesting that growth factors mainly affect directionality [14]. These effects are presumably mediated via stimulation of the shape and motility regulators such as alteration of the actin cytoskeleton by the Met/Gab1/Grb2 signaling pathway [34]. Based on these results we propose that directional migration results from cellular stretching forces, corresponding to the strain-rate. To test this hypothesis we devised a theoretical model demonstrating that stretch-rate can be transformed to a chemical directionality signal by its effect on binding/unbinding rates of cell-cell adhesion molecules. This phenomenon may be regulated by cellular inherent elasticity, cell-cell adhesions and self-propulsion. Notably, the shape deformation is consistent with previous studies linking directionality changes to RhoGTPases and cell morphology deformation: increase in RohGTPases leads to lamelliopodia-to-lobopodia transition (stretching) with enhanced directional and persistent motion [35]. Additional experimental effort will be made to validate this hypothesis in the collective migration setting. The coordination wave occurs in both DA3 and MDCK cell lines under different serum condition, more prominently in the presence of HGF/SF, implying that HGF/SF-Met signaling plays a major, but not exclusive, role in mediating this phenomenon. The association between directionality and coordination accords with the idea that cell-substrate traction is produced by polarized lamellipodia, which tend to polarize neighboring cells in the same direction, eventually forming long-range polarization and intercellular coordination [36]. The data may imply that even a weak directional cue is sufficient to promote a coordinated response that is transmitted to cells within the cell sheet; basal activation of Met or other tyrosine kinase signaling could induce a weak wave of directionality that can explain the observed results. We conclude that the wave of coordination is an intrinsic trait in collective cell migration that is amplified in the presence of HGF/SF, speculatively by progressive mechano-sensing cell-cell communication mechanisms. Isolated cells, or cells in small clusters respond to HGF/SF by rapid activation of cellular motility mechanisms [37] in an orderly manner; they spread, loose cell-cell adhesions, exhibit increased motility and spatial scattering [38]. Similar relations between cell-cell adhesions (which affect density), motility and intercellular coordination occur in confluent monolayers; Inhibition of cadherin-mediated cell–cell adhesions increased general motility but reduced directionality, persistence and intercellular coordination for confluent monolayers of MCF10A cells [8]. Increased monolayer density is associated with decreased motility and increased intercellular coordination, experimentally [10], [39]–[42], theoretically [43] and known to exist in other systems as well, such as bacterial populations [44]. It is well established that in response to HGF/SF, epithelial monolayers become sparser, maintain higher motility [29], and weaken cell–cell contacts [25]. Nevertheless, higher intercellular coordination was found here as response to HGF/SF (Fig. 8D). This observation may imply an alternative channel of mechanical intercellular communication [25], [45]. For example, a mechanism that is based on emerged collective sensing from individuals modulating their speed in response to local cues through social interaction with their peers [46] may explain our findings. We speculate that the wave of directionality has an important role in this phenomenon, and that increased motility coupled with a general directional cue introduced by the free edge is more prominent than the known density-motility-coordination intrinsic relations, thus leading to increased coordination. The enhanced coordinated motility induced by HGF/SF-Met resembles its effect on the induction of tubulogenesis, where increased cell-cell association is crucial for tubule formation [21], [47]. Other processes, such as epithelial plasticity, are also known to be common to development and cancer [48]. Thus, the enhanced waves of directionality and coordination found here might imply that even in tumor cells, HGF/SF-Met activate similar pathways to those activated during embryogenesis.
summary: The fundamental mechanisms underlying intercellular coordination during collective cell migration remain elusive despite considerable research efforts. We present a novel analytical framework that considers spatiotemporal dynamics across several traits. Our approach was applied to discover new modes of organized collective dynamics of cancer and normal cells. Following disruption of a cell monolayer, a propagating wave of coordinated migration emerges as clusters of coordinately moving cells are formed away from the wound and disintegrate near the advancing front. Activation of Met signal transduction by hepatocyte growth factor/scatter factor, master regulators of cell motility in malignant and normal processes, generates coinciding waves of cellular acceleration and stretching that propagate backward from the wound front and trigger a delayed wave of directional migration. Amplified coordination is intrinsically associated with enhanced directionality suggesting that even a weak directional cue is sufficient to promote a coordinated response that is transmitted to cells within the cell sheet. Our findings provide important novel insights on the basic cellular organization during collective cell migration and establish a mechanism of long-range cell guidance, intercellular coordination and pattern formation during monolayer wound healing.
keywords: physics
  cell motility
  cell biology
  biology and life sciences
  physical sciences
  computational biology
  biophysics
title: Propagating Waves of Directionality and Coordination Orchestrate Collective Cell Migration