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Dynamics of epithelial monolayers has recently been interpreted in terms of a jamming or rigidity transition. How cells control such phase transitions is, however, unknown. Here we show that RAB5A, a key endocytic protein, is sufficient to induce large-scale, coordinated motility over tens of cells and ballistic motion in otherwise kinetically-arrested monolayers. This is linked to increased traction forces and to the extension of cell protrusions, which align with local velocity. Molecularly, impairing endocytosis, macropinocytosis or increasing fluid efflux abrogates RAB5A-induced collective motility. A simple model based on mechanical junctional tension and an active cell reorientation mechanism for the velocity of self-propelled cells identifies regimes of monolayer dynamics that explain endocytic reawakening of locomotion in terms of a combination of large-scale directed migration and local unjamming. These changes in multicellular dynamics enable collectives to migrate under physical constraints and may be exploited by tumors for interstitial dissemination.
Collective cell migration is essential for tissue morphogenesis during development and repair and for tumor dissemination1. Most aspects of multicellular migration are ruled by the physical interactions that cells establish among each other and with their environment. For example, during collective migration within confluent monolayers, cell sheets flow like a fluid yet remain fixed and solid-like at short time scales, with the motion of each cell constrained by the cell crowding due to its neighbours2–4. As cell density rises, neighbouring cells restrict the motion of each cell, forcing them to move in groups, surprisingly similar to what is observed in systems of inert particles that undergo a jamming or rigidity transition at large density4–7. However, while the transition in inert systems invariably occurs at a critical particle packing ϕc8, epithelial monolayers display limited density fluctuations. Therefore, material parameters that encodes cell properties such as cell–cell adhesion and cortical tension, rather than density alone, have been proposed to govern the rigidity transition in cell monolayers5, 6, 9–11. However, the general validity of this theoretical framework remains to be investigated. Even less understood are the molecular determinants and cellular processes that regulate multicellular dynamics by impacting on physical properties.
A cellular process that influences cellular and multicellular motility strategies is membrane trafficking12, 13. Here, we report that perturbation of endocytosis by altering the levels of its master regulator RAB5A14, 15 is sufficient to reawaken the motility of jammed epithelial monolayers. RAB5A causes large, anisotropic and spatially correlated motility streams by globally enhancing endosomal trafficking and macropinocytic internalization. These variations impact on junctional tension, topology and dynamics of junctional proteins facilitating coherent cell motion over long distances. RAB5A further promotes the extension of protrusions aligned to the local velocity of migratory cohorts. RAB5A-induced reawakening of motility is associated with a growing length scale, precluding an understanding of monolayer dynamics simply in terms of an increase in local rearrangements. A self-propelled Voronoi model that includes an active cell reorientation mechanism accounts for RAB5A-induced multicellular dynamics. The model identifies a motility regime that we define as flowing liquid, where local and long-range collective motility coexist. As a consequence of these emerging material properties, RAB5A-monolayers are not only efficient in directed locomotion during wound closure or epiboly gastrulation movement in zebrafish development, but also display a high degree of plasticity that allows them to migrate under physical constraints typical of interstitial tissues architecture. These properties may be exploited in tumorigenic settings to escape the intrinsic motility-suppressive environment of jammed epithelial tissues.
To test the role of endocytic trafficking on collective epithelial locomotion, we perturbed the levels of RAB5A by generating doxycycline-inducible, RAB5A-expressing populations of human mammary epithelial MCF-10A cells (Supplementary Fig. 1a). These cells form polarized monolayers and upon reaching confluence, display a typical collective locomotion mode characterized by the emergence of large-scale, coordinated motility streams, involving tens of cells. As cells keep on dividing, density increases causing a near complete kinetic arrest akin to a jamming or rigidity transition5, 16 (Supplementary Fig. 1b, Supplementary Movie 1). Unexpectedly, under these latter conditions, elevation of RAB5A reawakened motility of kinetically-arrested monolayer by promoting large and heterogeneous multicellular streams (Fig. 1a and Supplementary Movies 2-3). RAB5A expression had marginal effect on the rate of cell division of confluent monolayers (Supplementary Fig. 1c), and collective motility was unperturbed by inhibition of cell division (Supplementary Fig. 1d and Supplementary Movie 4). Large scale, collective locomotion was also induced by expression of RAB5A in jammed keratinocyte monolayers (Supplementary Fig. 1e and Supplementary Movie 5) and oncogenically-transformed MCF-10A variants, MCF10.DCIS.com (not shown). Finally, RAB5A-expression did not alter the migration of individual MCF-10A cells in random migration assays (Fig. 1b and Supplementary Movie 6). Thus, RAB5A effects on motility are emergent properties of cell collectives that elicit reawakening of locomotion of kinetically-arrested, jammed epithelia.
Collective locomotion depends on complex cell-cell interactions and communication occurring during the migration of epithelial sheets17. To characterize the phenotype induced by RAB5A in MCF-10A cells, we analysed movies by Cell Image Velocimetry (CIV)18 and Particle Image Velocimetry (PIV)19, focusing on the time window where the full availability of soluble (epidermal growth factor (EGF) enables locomotion (see Methods). We found that RAB5A expression robustly enhances cell coordination (Fig. 1c and Supplementary Movie 7). A simple indicator of the collective nature of cell motion is obtained by calculating the velocity correlation length Lcorr as the width of the correlation function of the (vectorial) velocity υ(x0) (see Methods). We observe a 20-fold increase of Lcorr from 55±5 μm (control) to 1.1±0.3 mm (RAB5A), which corresponds to about 50 cell diameters (Fig. 1d and Supplementary Movie 2). The directionality of collective motion is well captured by the order parameter 𝜓 (see Methods) that can vary in the range [0 to 1]: 𝜓 = 1 corresponds to a perfectly uniform velocity field, where all the cells move in the same direction and with the same speed, while 𝜓 0 is expected for a randomly oriented velocity field. While for the control 𝜓 always remains below 0.1, we observed a marked increase in 𝜓 for the RAB5A monolayer (Fig. 1e), in correspondence with a substantial increase of absolute motility, quantified by the root mean square velocity (Fig. 1a). We also quantified cellular motions using their mean square displacement (MSD) over a given time interval, Δt. For both control and RAB5A, the MSD exhibits for short times a quadratic scaling with Δt: MSD (u0Δt)2, which is indicative of a directed ballistic motion, although with dramatically different characteristic velocities (u0 =32 μm/h for RAB5A, u0=6 μm/h for the control). At later times, a transition to a diffusive-like regime characterized by a scaling exponent close to 1 is observed (Fig. 1f). An estimate of the persistence length Lpers, corresponding to the typical distance travelled by a cell with constant velocity before the direction of its motion becomes randomized, gives Lpers less than one cell diameter for control cells, while for RAB5A Lpers=650 µm, corresponding to more than 30 cell diameters (Fig. 1f).
Cell-cell coordination during collective locomotion is influenced by the strength and dynamics of cell-cell adhesion. We hypothesize that RAB5A may impinge on these junctional processes.
We initially investigated the distribution of the junctional marker E-cadherin. Our results showed that junctions of control cells were rather wavy. Conversely, RAB5A-cells displayed straight and compact junctions (Fig. 2a-b), and increased surface contact area (Fig. 2b). P-cadherin and the tight junctional markers ZO-1 also display similar RAB5A-induced topological alterations (Supplementary Fig. 2a). Thus, RAB5A might globally increase cell surface contacts and tension. Frequently, indeed, the straightening of junctions correlates with increase in junctional strength and tension20. Consistently, instantaneous recoil of cadherin clusters from the cut site (caused by two-photon laser nano-scissors) indicated that RAB5A-expression increased local junctional tension similar to the one observed after hypotonic stimulation, used as control21 (Fig. 2c and Supplementary Movie 8). RAB5A had no impact on actomyosin contractility measured by determining the levels of phosphorylated Myosin light chains (Fig. 2b), albeit RAB5A-induced motility was sensitive to blebbistatin (Supplementary Fig. 2c). Instead, RAB5A was found, by atomic force microscopy, to increase the overall monolayer rigidity to levels comparable to those obtained by hypotonic stimulation on control cells (Fig. 2d).
RAB5 is a master regulator of endocytic processes22. We therefore assessed whether elevation of RAB5A in MCF-10A enhances globally these processes and whether their perturbation, in turn, prevents RAB5A-induced reawakening of motility.
RAB5A expression increased, as expected, the size and the number of EEA-1-positive early endosomes (Supplementary Fig. 3a). Using fluorescence recovery after photobleaching (FRAP) experiments, we further showed that RAB5A increases the mobility of membrane cargo, and most notably of GFP-E-cadherin (Fig. 3a), whose turnover is primarily mediated by endo/exocytic trafficking23 (Fig. 3a and Supplementary Movie 9). Furthermore, blockade of endocytosis by pharmacological inhibition of the pinchase dynamin with Dynasore24 impaired E-cadherin internalization (Supplementary Fig. 3b) and severely reduced velocity correlation, persistence length, and ballistic motility (Fig. 3b and Supplementary Movie 10).
RAB5 is also essential to control dynamin-independent internalization processes, including the intake of large macromolecules and fluids, through phagocytosis25 and macropinocytosis26. Consistently, elevation of RAB5A increased the intake of high-molecular weight dextran, used to track macropinocytosis (Supplementary Fig. 3c). This process was impaired by treatment with EIPA [5-(N-Ethyl-N-isopropyl)amiloride] an inhibitor of Na+/H+ exchangers that blocks macropinocytosis27 (Supplementary Fig. 3c). Remarkably, EIPA abrogated RAB5A-dependent collective locomotion and robustly decreased the mean velocity and velocity correlation length (Fig. 3c and Supplementary Movie 11).
Endocytic perturbations, besides affecting intracellular trafficking, may also alter fluid intake and membrane homeostasis, ultimately impacting on junctional topology and dynamics. If this scenario is correct, then altering these processes through alternative biophysical interventions might be sufficient to instigate collective locomotion and mimic the phenotype induced by RAB5A. To this end, we exposed monolayers to hypo- and hypertonic media. Remarkably, hypotonic treatment of control, jammed monolayers was sufficient to straighten junctions (Supplementary Fig. 4a), reawakened cell motility and increased velocity correlation and persistence length (Fig. 3d and Supplementary Movie 12). Conversely, the exposure to hypertonic media abrogated RAB5A-collective locomotion, which was, instead, enhanced by hypotonic stimulation (Fig. 3e and Supplementary Movie 13).
Thus, one mechanism through which RAB5A acts is by promoting global alterations in endocytic processes. These changes may, in turn, be critical to increase junctional tension and dynamics, and monolayer rigidity to promote RAB5A-induced long-range motility. Fluctuations in fluid intake and membrane tension may also be important here. However, hypotonic treatment reawakened the motility of jammed epithelia only 6-10 hours after the initial treatment (Fig. 3d and Supplementary Movie 12). Thus, changes in water influx, volume and membrane tension, which are rapid (within seconds or minutes) cell responses28, unlikely account for the effects on monolayer kinematics. Conversely, long exposure to hypotonic stimulation augmented internalization and turnover rate of E-cadherin (Supplementary Fig. 4b-c), endosome size21, and junctional topology (Supplementary Fig. 4a) and tension (Fig. 2c), mimicking the effects of RAB5A and indicating that global perturbation of endocytosis drives collective locomotion.
One striking feature of RAB5A-induced large-scale streaming flows is their persistent and ballistic motility, suggesting that individual cells must efficiently orient their motion with the local direction of migration. Actin-based, polarized protrusions are a proxy of cell-oriented locomotion. In monolayers, these protrusions extend underneath neighbouring cells and are called cryptic lamellipodia. By monitoring the dynamics of EGFP-LifeAct-expressing cells interspersed with non-fluorescent cells (Fig. 4a-b), we detected, only in RAB5A-monolayers, the formation of cryptic lamellipodia oriented along the motility direction of supra-cellular motility streams (Fig. 4b and Supplementary Movie 14). RAB5A-induced cryptic lamellipodia are RAC1-dependent, consistent with the role of RAB5A endo/exocytic cycles in spatially restricting RAC1 signalling for protrusions extension29. Indeed, a pharmacological inhibitor of RAC1 activation reduced cryptic lamellipodia formation (Fig. 4c and Supplementary Movie 15), and impaired the motility of RAB5A-monolayers (Fig. 4d and Supplementary Movie 16).
These finding indicate that RAB5A monolayers might exert large traction forces onto the substrate during locomotion. To directly assess this possibility, we measured surface tractions of control and RAB5A monolayers using a novel confocal reference-free traction force microscopy (cTFM)30. We found that RAB5A monolayers exert significantly higher and more dynamic substrate tractions (Fig. 4e and Supplementary Fig. 5a) that moved with the flow tracking velocity fields (Supplementary Movie 17). We obtained higher traction forces of RAB5A than controls monolayers also by measuring the displacements of fluorescent beads embedded into polyacrylamide gel substrates31 (Supplementary Fig. 5b-c).
Thus, RAB5A promotes the extension of aligned cell protrusions in combination with increased and more dynamic substrate tractions, both of which combine to promote monolayer unjamming and collective motility.
Our data suggests that RAB5A-induced reawakening is the result of a complex interplay between changes in cell adhesion and cortical tension, which are both altered in RAB5A monolayers as a consequence of changes in endomembrane dynamics (Fig. 2–3). This is accompanied by the efficient alignment of cell protrusions and dynamic tractions to ignite multicellular directed migration (Fig. 4).
To elucidate how these different contributions combine in our experiments, we performed numerical simulations of monolayer dynamics. Our simulations are based on a self-propelled Voronoi (SPV) model with few basic ingredients. The first is a target shape index p0 that is the result of the competition between intracellular adhesion and cortical tension, recently introduced in the context of a vertex model6. The latter model was found to describe well the unjamming of bronchial epithelial layers5 even in the absence of intrinsic cell motility mechanisms. The second ingredient is a prescribed self-propulsive speed for each cell, as also proposed in a recent SPV model32. At variance with the latter model, where the cell polarity is described as a unit vector undergoing random rotational diffusion, we assume a Vicsek-like polar alignment mechanism between the polarization direction of neighbouring cells2. The alignment efficiency depends on the characteristic response time τ that each cell takes to actively align its polarity along the direction of its local velocity (Supplementary Fig. 8 in Supplementary Information, section Computational Model). A study of the phase diagram reveals four different regimes for the monolayer dynamics (Fig. 5a). When the response time τ is large, the system behaviour is mainly controlled by the target shape index p05, 32: for small values of p0 the monolayer is jammed; by contrast, for increasing p0 cell adhesion favours local cell rearrangements leading to unjamming, as previously described5. Changes in index p0 reflect monotonically on the average shape parameter q, defined as the ratio between cell perimeter and square root of the cell area. Jamming occurs when q=q*=3.815, 32.
If the response time τ is decreased in the presence of a non-negligible single-cell speed, large scale collective motility is observed in simulations that can either be identified as a flowing solid (for small p0, large correlation length in the absence of local cell rearrangements) or a flowing liquid (large p0, large correlation length in the presence of local cell rearrangements). The latter case, in which both local and collective motility are present, captures RAB5A phenotypes (Fig. 5b and Supplementary Movie 18). A slow, short-range correlated rearrangement dynamics without directed motion (Fig. 5c and Supplementary Movie 18) is instead compatible with the non-flowing liquid-like state of control monolayers. Our simulations suggest that RAB5A acts mainly to decrease response time τ, in agreement with the increased protrusive activity and more efficient stress transmission detected in our experiments.
Next, we verified experimentally a key topological feature of our model and use it to produce testable predictions. We first compared the time-dependence of the shape parameter q during reawakening of cell motility induced by RAB5A (Supplementary Movie 3). Notably, while q remains almost constant in time for the control, it increases in RAB5A monolayers during the first stages of reawakening (Fig. 5d-e), indicating that the shape parameter is the control parameter of the jamming transition also in the presence of self-propulsion and reorientation.
In light of this, the observed increase of q should also lead to a topological unjamming. To test this prediction, we compared the self-overlap order parameter Q and the four-point susceptibility χ4 (Methods and ref 5) of control and RAB5A monolayers. This comparison was performed by first removing the average displacement due to collective directed locomotion, when present (see Methods for details), which is instead captured by the order parameter ψ (Fig. 5f). Results showed that while control cells simply slow down in time, the local dynamics in RAB5A monolayers is characterized by faster rearrangements accompanied by a decreasing length-scale of dynamic heterogeneities (Fig. 5g-j).
RAB5A-increase in monolayer motility predicts that deregulation of this protein may also influence the plastic motility behaviour of collective entities. We tested this prediction on directional migration in wound repair processes, migration into confined spaces, and on gastrula morphogenesis in zebrafish. Firstly, RAB5A-monolayers closed a wound two times faster than control cells (Fig. 6a and Supplementary Movie 19), whereas silencing of RAB5 genes impaired wound closure speed (Fig. 6a and Supplementary Movie 19). CIV analysis revealed that RAB5A enhanced angular velocity correlation length (Supplementary Fig. 6a and Movie 20), consistent with the increased cell coordination observed in unwounded monolayers (Fig. 1c-e). RAB5A accelerated wound closure also of oncogenic MCF10.DCIS.com cells33, and of immortalized HaCaT keratinocytes (Supplementary Fig. 6b-c). Higher magnification analysis of the wound-front cells further revealed that RAB5A-monolayers extended larger and more persistent protrusions than control cells (Fig. 6b and Supplementary Movie 21). We also detected cryptic lamellipodia coherently oriented toward the wound in RAB5A, but not in control cells located more than 10 cell rows behind the leading edge (Supplementary Fig. 6d and Supplementary Movie 22). We exploited these features to estimate indirectly the experimental orientational response time τ, which our numerical simulations predict to be significantly shorter for RAB5A cells. Firstly, we noticed that RAB5A monolayers are significantly faster in reaching maximum speed soon after wounding and in reorienting their angular velocity (Supplementary Fig. 7a). Secondly, kymograph analysis of wounded monolayers revealed that RAB5A cells move into the wound as highly correlated sheets with a directed velocity that remains constant even 40-50 cells away from the wound edge (Supplementary Fig. 7b). Thus, RAB5A cells are more efficient in long-range propagation of stresses, have reduced random rotational motion (noise) that leads to a reduction of reorientation time τ.
A multicellular tissue that has gained fluid-like properties might be optimally fitted to flows into confined channels, mimicking those encountered by normal and tumor cells disseminating into interstitial tissues34. To this end, we performed 2D migration assays of mammary monolayers using micro-fabricated PDMS channels of 25 µm width, which mimic the space between collagen interfaces observed in vivo34. Both control and RAB5A-MCF-10A monolayers crossed these channels moving in a collective fashion. However, RAB5A monolayers efficiently flowed, like streams, into these narrow slits resulting in much higher number of cells crossing the paths (Fig. 6c and Supplementary Movie 23).
The gastrulating embryo is an additional, striking example of directed, collective migration35. Gastrulation is initiated by spreading of meso- and endodermal (mesendodermal) cell sheets over the yolk cells, a process called epiboly. Epiboly is governed by the strength of cell-cell adhesion mediated by E-cadherin molecules and requires RAB5-dependent endosomal trafficking of this molecule36, 37. We therefore assessed whether ectopic expression of mammalian RAB5A accelerates epiboly. We injected one-cell-stage wild-type zebrafish embryos with control or human CFP-RAB5A mRNA and monitored epiboly progress between 3 and 8 h post fertilization. Epifluorescence analysis revealed that CFP-hRAB5A was readily expressed (Fig. 6d) and robustly accelerated the epiboly progress (Fig. 6d and Supplementary Movie 24).
We found that RAB5A controls a diverse set of collective motility processes in vitro and in vivo by re-awaking the directional, coordinated locomotion of jammed and kinetically-arrested monolayers. RAB5A exerts this function by promoting the formation of polarized, actin based, lamellipodia that generate traction forces, which can be efficiently transmitted at long ranges through enhanced junctional contact and stresses. The increased mechanical coupling also enables a cell to obtain directional guidance cues from their neighbours forcing adjacent cells to align their front-rear polarity, resulting in a positive feedback between polarity and net displacement. This, combined with increased dynamic of junctional E-cadherin to accommodate for cell neighbouring exchange, volume, density and strain fluctuations, collaboratively enable multicellular entities to acquire a fluid-like character. These alterations appear primarily to be the results of mechanical changes caused by global membrane trafficking perturbations. However, given the inextricable link between endocytocis and signalling, we cannot exclude that amplification and rewiring of specific biochemical pathways, particularly those emanating from EGF receptors, underpins some of the altered mechanical properties — a possibility that is currently under investigation. Importantly, these changes of plasticity promote the motility of otherwise jammed and glassy-like monolayers, leading to invasive, collective migration under physical confinement and accelerated multicellular directed migration during embryonic development.
MCF-10A cells were a kind gift of Dr. Joan S. Brugge (Department of Cell Biology, Harvard Medical School, Boston) and were maintained in DMEM/F12 medium (Invitrogen) supplemented with 5% horse serum, 0.5 mg/ml hydrocortisone, 100 ng/ml cholera toxin, 10 μg/ml insulin and 20 ng/ml EGF (Soule, Maloney et al. 1990). MCF-10.DCIS.com cells were kindly provided by Dr. John F. Marshall (Barts Cancer Institute, Queen Mary University of London) and maintained in the same media of MCF-10A without cholera toxin. HaCat cells were purchased from CLS (#300493) and cultured in DMEM medium (Lonza) supplemented with 10% FBS and 4 mM L-Glutamine. All cell lines have been authenticated by cell fingerprinting and tested for mycoplasma contamination. Cells were grown at 37 °C in humidified atmosphere with 5% CO2. MCF-10A, HaCat and MCF-10.DCIS.com cells were infected with pSLIK-neo-EV (empty vector control) or pSLIK-neo-RAB5A lentiviruses and selected with the appropriate antibiotic to obtain stable inducible cell lines. Constitutive expression of LifeAct-EGFP or EGFP-H2B was achieved by lentiviral and retroviral infection of MCF-10A cells with EGFP-LifeAct- puro or pBABE- puro-EGFP-H2B vectors, respectively.
Cells were seeded in 6-well plate (1.5*106 cells/well) in complete medium and cultured until a uniform monolayer had formed. RAB5A expression was induced, were indicated, 16 hours before performing the experiment by adding fresh complete media supplemented with 2.5 μg/ml doxycycline to cells. At the time of recording fresh media containing EGF was added. The addition of 20 ng/ml of EGF is absolutely essential to enable cell locomotion. Consistently, the incubation of monolayers in the absence of EGF prevents the emergence of streaming motility (not shown). EGF-dependent, RAB5A-mediated reawakening of cell motility is invariably transient, occurring between 4-12 hours after EGF addition, with a peak in velocity centered around 6-8 hours. The subsequent velocity decay is likely caused by exhaustion of EGF. Comparable cell confluence were tested by differential interference contrast (DIC) imaging using a 10X objective and counting the number of nuclei/field. In the cell streaming assay, the medium was refreshed before starting imaging. In wound healing assays, the cell monolayer was scratched with a pipette tip and carefully washed with 1X PBS to remove floating cells and create a cell-free wound area. The closure of the wound was monitored by time-lapse microscopy. Olympus ScanR inverted microscope with 10X objective was used to take pictures every 5-10 minutes over a 24-96 hours period (as indicated in the figure legends). The assay was performed using an environmental microscope incubator set to 37°C and 5% CO2 perfusion. After cell induction, doxycycline was maintained in the media for the total duration of the time-lapse experiment. The percentage of area covered by cells (area coverage %) overtime and wound front speed were calculated with MatLab software. In the Mitomycin C experiment, 1 μg/ml inhibitor was added together with doxycycline in fresh media before starting imaging. For the wound healing assay performed on interfered cells, 2.5*105 cells/well were plated in a 6 well plate and interfered the day after with 1 nM of siRNAs, following the same conditions already described in the “RNA interference” section.
For plasma membrane tension perturbation by osmotic treatments, an equal volume of hypotonic buffer (H2O + 1 mM CaCl2 + 1 mM MgCl2) or hypertonic buffer (complete growth medium + 200 mM sucrose-containing complete growth medium; final concentration 100 mM) was added to the cells.
For measurements of cryptic lamellipodia directionality, MCF-10A cells stably expressing EGFP-LifeAct were mixed in a 1:10 ratio with unlabeled cells and seeded in wound healing or cell streaming assays, as described before. Cell migration was monitored by time-lapse phase contrast and fluorescence microscopy. In the wound healing assay, images were collected at multiple stage positions in each time loop, including at the leading edge of the migrating cell sheet and about 10 cell rows behind the leading edge. Cryptic lamellipodia directionality was measured as the angle ϕ delimited by the direction of the single lamellipodium and the direction vector of locomotion of the collective pack: ϕ = 0° indicates that protrusions and group migration have the same direction; ϕ = 180°; indicates that protrusions and group migration have opposite direction. Each assay was done 5 times and at least 25 cells/condition were counted in each experiment. Where indicated, Dynasore (80 µM), EIPA (75 µM), NSC23766 (100 µM) and Blebbistatin (25 µM) were added 1 or 2 h before imaging.
Wound healing assay was performed by Ibidi Culture Inserts (Ibidi) to avoid debrides affecting the quality of the kymograph analysis. Inserts were placed in a 12-well plates and MCF-10A cells were plated in each chamber, 5*104 cells/chamber. 16 hours before starting the experiment, growing media was replaced with fresh complete media containing 2.5 μg/ml of doxycycline to induce RAB5A expression. A cell-free wound area was created by removal of the insert. Cell migration was monitored by Olympus Scan^R inverted microscope with 20X objective (with an additional 1.6x magnification lens).
Images from 10 positions/condition were recorded every 30 seconds over 1 hour period. To measure the dynamic of protrusive structures the Kymograph plugin of ImageJ software was used. Dynamic parameters measured from kymograph images were persistence time (Δt), protrusion rate (Δs1/Δt1) and retraction rate (Δs2/Δt2). The same time interval and ROI length were set in the analysis of each condition.
Cell Image Velocimetry (CIV) analysis of monolayer and wound healing time series was performed as previously described18, 38. Overlays of phase contrast images and colored migration direction were exported from the software. Uniform color indicates a homogeneous migration direction and thus high coherence between cells. Angular correlation during wound healing was quantified for each frame between cells at a distance of 100 µm.
Maps of the instantaneous cellular velocities were obtained by analysing time-lapse phase-contrast movies with a custom PIV software written in MatLab. The time interval between consecutive frames was 5 min or 10 min. The interrogation window was 32X32 pixels (pixel size 1.29 µm or 1.6 µm), with an overlap of 50% between adjacent windows. The number of cells comprised within one field-of-view (FOV) was typically 2500. For a given monolayer, time-lapse images from different (typically from 5 to 10) FOVs were simultaneously collected.
The instantaneous root mean square velocity υRMS(t) of a cell monolayer was computed as where is the mean square velocity within the j-th FOV, υ(j) (xn,t) is the instantaneous velocity at the n-th grid point xn of the j-th FOV, N is the number of grid points in one field-of-view and M is number of independent FOVs.
The instantaneous order parameter 𝜓(t) of a cell monolayer was computed as where M and are defined as above, is mean vectorial velocity within the j-th FOV and, as above, N is the number of grid points in one FOV. According to these definitions, we have 0 ≤ 𝜓(t) ≤ 1. In particular, 𝜓(t) = 1 only if, within each FOV, the velocity field is perfectly uniform, i.e. all the cells in the monolayer move with the same speed and in the same direction. On the contrary 𝜓(t) 0 is expected for a randomly oriented velocity field.
The vectorial velocity correlation functions were calculated as where cj is the azimuthal and temporal average of the non-normalized velocity correlation function within the j-th FOV, which is calculated as Here DFT and IDFT are, respectively, the direct and inverse two-dimensional Digital Fourier Transforms. Unless otherwise stated in the main text, the temporal average was always performed over the time window comprised between 4 and 12 hours from the beginning of the image acquisition. is the temporal average of the above defined performed over the same time window.
In order to estimate the velocity correlation function Lcorr, the velocity correlation functions CVV(r) were fitted with a stretched exponential function of the form f(r) = (1 − α)e−(r/Lcorr)γ + α. Here γ is a stretching exponent and α is an offset which is non-zero in presence of a collective migration of the monolayer.
Cellular trajectories rm(t) were calculated by numerical integration of the instantaneous velocity field as obtained from the PIV analysis (see Ref. 3 and references therein). For each FOV a number of trajectories roughly corresponding to the number of cells were computed.
Mean squared displacements (MSDs) of the cells were calculated as where the average was performed over all the trajectories and, unless otherwise stated in the main text, in the time window comprised between 4 and 12 hours after the beginning of the experiment. This time window corresponds to the transient acquisition of cell locomotion induced by the addition of fresh EGF to the media just before the beginning of time-lapse recording. Within this time frame, monolayer velocity peaks around 6-8 hours, and subsequently decays, likely, due to exhaustion of the motogenic factor. In order to estimate the persistence length Lpers of the cellular motion the MSD curves were fitted with a function of the form This expression describes a transition between a short-time ballistic-like scaling MSD(Δt)~(u0Δt)2, corresponding to rectilinear motion with a typical speed u0, and a long-time scaling MSD(Δt)~(u0LpersΔt), corresponding to a diffusive-like behaviour with an effective diffusion coefficient u0Lpers/4. Within this description the transition between the two regimes takes place for Δt ≈ 1/u0Lpers, i.e. after the cell has travelled with an approximately constant velocity over a distance ≈ Lpers. The simple expression adopted for 𝑔 captures the same short- and long-time asymptotic behaviours that are expected for a particle with non-negligible inertia performing a Brownian motion.
Substrate tractions were measured using cTFM with an interdisc spacing of 3 µm30. During the reference configuration reconstruction step the position of the outermost QD nanodiscs plus a region of 2 µm towards the inside was fixed. QD nanodiscs inside this fixed frame were then relaxed to original positions as described in Ref. 30. As the fixed QD nanodiscs themselves are distorted, displacement reconstruction is prone to errors close to the image border. Therefore, final traction analysis was restricted to data originating from an area >15 µm from the image border.
Custom MatLab code for wound healing analysis, Particle Image Velocimetry (PIV) and cellular trajectory calculations is available from the corresponding author on request. Code for the numerical SPV-based modelling of monolayer kinematics is available from the corresponding author upon request, and a detailed description of the model and the related code will also be published elsewhere. Code for Cell Image Velocimetry (CIV) and confocal traction force microscopy (cTMF) has been previously described and is available in Ref. 18 and 30, respectively.
The authors declare that the data supporting the findings of this study are available within the paper and its supplementary information files.
Work is supported by grants from the following agencies:
To GS: the Associazione Italiana per la Ricerca sul Cancro (AIRC #10168), MIUR (the Italian Ministry of University and Scientific Research), the Italian Ministry of Health, Ricerca Finalizzata (RF0235844): Worldwide Cancer Research (AICR- 14-0335); from the European Research Council (Advanced-ERC-#268836);
To RC and FG: the Italian Ministry of Education and Research, Futuro in Ricerca Project ANISOFT (RBFR125H0M).
To XT: Spanish Ministry of Economy and Competitiveness (BFU2012-38146), the Generalitat de Catalunya (2014-SGR-927), and the European Research Council (StG-CoG-616480 to XT)
CM was supported by Fondazione Umberto Veronesi; SC was supported by an AIRC fellowship. MB and TL were supported by funding from the ETH-grant ETH-12 15-1.
Competing financial interests
The authors declare no competing financial interests.
Author informationCM, SC designed and performed experiments, interpreted the data, generated all the cell biological and molecular biological tools and reagents; FG analyzed all time-lapse experiments, interpreted the data, designed the computational model; MB, TL performed traction force microscopy experiments, interpreted and analyzed data; QL designed and build micro-fabricated channels and performed AFM experiments; ML contributed to the development of the computational model and to its interpretation; AD, AP, EM and DPar. performed laser nano-scissor experiments of EGFP-E-cadherin and interpreted data migration data; EF performed IF experiments; DPoul. designed and interpreted CIV and cTFM experiments; OKH, WY executed the semi-automated tracking of cell shape and size; GdF performed zebrafish experiments; GVB performed EM analysis; MU performed traction force experiments, interpreted and analyzed data; XT designed traction forces experiment, helped developing the computational model and writing the paper; PM design analytical tools, interpreted collective migration experiments and help in developing computational model; AF, RC and GS designed the research, analyzed and interpreted the data and wrote the paper. Each author contributed to writing the paper.