To simulate the various EMT-like scenarios, we generated a 2D agent-based model of proliferating pseudostratified epithelium (Fig. 1a, b) derived from our previously established model29. Briefly, in the model, each cell is abstracted to a nucleus attached to a set of dynamic springs that represent the viscoelastic properties of the cell. These springs are terminated by an apical point a and a basal point b. Apical points of adjacent cells are linked to one another by a contractile spring representing cell–cell adhesion. Basal points are attached to a simplified matrix represented by a straight non-deformable line. Basal points can only move along that line and cannot swap positions. Each nucleus (N) is made of two spheres: a hard core at the center and a soft core at the periphery. Hard cores cannot overlap, while soft cores can but are subjected to a repulsion force. This allows us to account for the deformation of nuclei that occurs at high density in pseudostratified epithelia without having to model actual changes in nuclear shape29. To maintain the stereotypical straight cell shape observed in pseudostratified epithelia, there is a straightness spring that imposes a flat 180° angle between the apical point, nucleus, and basal point of each cell. Cells proliferate following a simplified cell cycle (Fig. 1b) with passive springs in G1, S, and early G2 phases. During late G2 and mitotic (M) phases, the apical spring contracts to bring the nucleus to the apical side by generating pre-mitotic rapid apical movements (PRAM) driving interkinetic nuclear movements (INM) of nuclei. A complete description of the model is provided in Supplementary Information.Fig. 1: Presentation of the computational model.a Diagram representing the simulated cells with the various dynamic springs controlling cell–cell adhesion (apical-to-apical, red, connecting adjacent apical points, shown as red dots), cell–matrix adhesions (nucleus-to-basal spring, black, connecting basal points to the basal line, shown as black dots), the viscoelastic-like properties of the cell body (apical-to-nucleus and nucleus-to-basal springs, black), the alignment of the apical point, nucleus and basal point (straightness spring, green). b Overview of the simplified cell cycle implemented in the model. The apical-to-nucleus spring contracts in active G2 and M phases, the hard core of the nucleus increases in M phase. c Table of computational events used to simulate EMT-like scenarios throughout the study. Note that P is a secondary event as it can only occur if B happened. d, h Initial organization of the tissue at t0 for individual cell simulations (d) and group simulations (h). The EMT-like cell is marked in red. e–g, i Diagrams depicting the three types of outcome that were monitored during simulations, examples are shown for single cell simulations (e–g) and groups (i) with loss of apical adhesion (A). INM interkinetic movements, M mitosis, PRAM pre-mitotic rapid apical movements.In this study, we define four computational EMT-like events named A, B, S, and P as follows (Fig. 1c). A is the loss of apical adhesion. When A occurs, a cell detaches its apical point from its neighbors. The neighbors heal the local “wound” by creating a new apical-apical bound. B is the detachment of the basal point from the basal line. When B occurs, the basal point can be displaced within the whole 2D plane of the model. By default, after detachment, basal points and nucleus-to-basal springs remain passive. A seek-and-grab behavior of basal points can be further implemented and is called P for protrusion. P is a secondary event that can only occur if B happened. If P occurs, the basal spring actively extends until it reaches the area beneath the basal line. When it does, the basal point attaches and pulls, generating a traction force on the nucleus via the nucleus-to-basal spring. This means that in the model, the matrix is represented as a substrate but not as a physical obstacle. The basal points of cells can adhere to the basal line as well as the area underneath it and apply force. However, cells do not experience confinement. The relaxation of the straightness spring is called S and no longer imposes that apical and basal points, and the nucleus be positioned along a straight line. Biologically, this can be interpreted mostly in two ways: (i) a mild relaxation of apicobasal polarity and (ii) as a loss of stiffness. Indeed, after the relaxation of the straightness spring, a cell offers less resistance to lateral pressure (e.g., local crowding, moving nuclei due to INM). Finally, INM can be turned ON or OFF in EMT cells or in control cells.To assess the impact of simulated scenarios, we monitored three main outputs: (i) apical and (ii) basal extrusions, which respectively correspond to the nucleus of a cell being located beyond the apical domain or the basal line of the epithelium, and (iii) basal positioning (Fig. 1d–i). In this last situation, a cell still has its nucleus within the confines of the epithelium but it is located basally with respect to the mean position of the other nuclei in the tissue. This is a relevant factor since it has been shown that, in the case of chick neural crest cell delamination, 90% of the delaminating cells had their nuclei located basally within the hour preceding extrusion20. A perfect physiological situation (e.g., neural crest delamination) would be 100% of basal extrusion and 0% of apical extrusion. Apical extrusion is considered a failure, as cells extruding on the apical side would die due to a lack of survival signals and would not be able to access the extracellular matrix to migrate.The time scale of the model was previously calibrated using cell cycle length and the normal growth of the chick neuroepithelium29. Hereafter, the timings mentioned for simulations correspond to the equivalent biological time. All simulations run for 6 h to allow the epithelium to reach a steady state before EMT-like events start being implemented. To avoid all simulated events to occur simultaneously and allow for various order of events, there is a 6 to 24 h window of opportunity for EMT events to occur which is represented as a faint yellow area on each graph with a given output as a function of time. The simulations then run for an extra 30 h (54 h of total simulation time) so that the consequences of the events can be monitored. This schedule is in agreement with the time frame of chicken head and trunk neural crest cell delamination10. By default, and unless otherwise stated, all control cells in the tissue undergo INM while INM in EMT cells is on or off as indicated in the figures. All settings of sEMtor corresponding to each simulation of the study are in Supplementary Table 1.One-event EMT-like scenarios in individual cells or groups, with or without INMTo assess the impact of EMT-like events, we started by simulating one event (A, B, or S) in one EMT cell with INM on. A leads to apical extrusion of some cells during the permissive EMT period (Fig. 2a, gray curve), and this proportion no longer increases after the end of the EMT time window (Supplementary Movie 1 and Fig. 2a, gray curve plateaus after 24 h). This suggests that cells that extrude apically are in a specific situation at the time of A. Indeed, these cells have their nuclei located apically when A occurs (Fig. S1). A also leads to a progressive increase in basal positioning (Fig. 2b, gray curve). Very few of these cells eventually extrude basally (Fig. 2c, gray curve). By contrast, B has no immediate effect but progressively leads to apical extrusion (Fig. 2a, black curve). Finally, S is not sufficient to promote extrusion on either side or basal positioning of nuclei in the tissue (Fig. 2a–c, dotted line, overlapping with the X-axis). Simulating the same scenarios in a cluster of 11 cells (Fig. 2d–f) leads to the same outcomes with a slight increase in the apical (Fig. 2d) and basal (Fig. 2f) extrusion rates (Supplementary Movies 1, 2).Fig. 2: Rates of apical and basal extrusion in one-event EMT-like scenarios.a–l Rates of apical/basal extrusion and basal positioning after simulating one EMT-like event in cells with interkinetic movements (a–f) either individually (a–c) or in groups (d–f) or in cells without interkinetic movements (g–l) either individually (g–i) or in groups (j–l). The EMT-like events are loss of apical adhesion (A, gray lines), loss of basal adhesion (B, black lines), and loss of straightness (S, dotted lines). Data for control cells with no EMT-like event are plotted in green. The yellow area on each graph represents the time window of opportunity for EMT-like events to occur (see main text). Each simulation n = 500 for individual cells, n = 50 for groups of 11 cells. All graphs from panels a to l have the same X and Y axes scales, as labeled in a. Note that A (b, e) or loss of INM (h, k) leads to basal positioning while a combination of B and loss of INM leads to basal extrusion (i–l). m, n Scatter plots of rates of apical (Y-axis) and basal (X-axis) extrusion at t_final for scenarios with A (m) or B (n). Note that loss of INM (going from closed to open symbols) has more impact than passing from individual cells to groups (going from circles to squares). Also note that loss of INM has more impact when combined with B than with A. Source data are provided as a Source Data file.Next, to examine the role of INM, we repeated the same simulations without INM in the EMT cells (Fig. 2g–l and Supplementary Movie 3). In individual cells, canceling INM has dramatic effects. It reduces apical extrusion rates (Fig. 2g) and is sufficient to favor basal positioning, even when no other event is taking place (Fig. 2h, green curve). Interestingly, the loss of INM synergizes with the other events to increase basal extrusion, mildly in association with A (Fig. 2i, gray curve), dramatically in association B (Fig. 2i, black curve). The same simulations in groups (Fig. 2j–l) show the same trends for extrusion. Thus, loss of INM promotes basal positioning and basal extrusion.Since A or B lead to extrusion on either side, to better compare the relative efficiency of each scenario, we plotted the apical and basal extrusion rates at t_final as scatter plots (Fig. 2m, n). In the case of A with INM (Fig. 2m) going from a single cell (closed circle) to a group (closed square) increases both apical and basal extrusion rates. By contrast, in the absence of INM, going from a single cell (open circle) to a group (open square) slightly improves the efficiency with less apical and more basal extrusion. In the case of B (Fig. 2n), the main effect is seen when turning off INM. While no basal extrusion is observed in cells performing B with INM (closed circle and square), turning off INM (open circle and square) acts as a switch that reduces apical extrusion and dramatically enhances basal extrusion when B occurs.INM prevents basal positioning of nuclei cells autonomously by bringing nuclei apically at each round of G2/M. However, it also favors apical crowding29 and thus might act non-cell autonomously to promote basal positioning of nuclei outside of the G2/M phases. If this is correct, canceling INM in normal cells should reduce the rates of basal positioning and basal extrusion of EMT cells. Thus, we repeated simulations corresponding to Fig. 2g–l but this time without INM in both EMT and control cells (Fig. S2). Indeed, the rates of basal positioning and basal extrusion of EMT cells were dramatically reduced after INM was canceled in normal cells. These data indicate that INM in normal cells can influence basal extrusion of EMT cells in a non-cell autonomous manner.Two-event EMT-like scenarios in individual cells or groups, with or without INMNext, we simulated two-event EMT scenarios in individual cells or groups. For simplicity, we plotted only the rate of apical and basal extrusion in Fig. 3 (Fig. 3a–d). Rates of basal positioning are provided in Fig. S3. In individual cells, S had no major effect when coupled with A or B (Fig. 3a, b, black and gray curves) compared to A or B alone. By contrast, coupling A and B lowered apical extrusion and increased the rate of basal extrusion (Fig. 3a, b, brown curves) compared to A. Performing the same simulations in groups (Fig. 3c, d), increased further the rate of basal extrusion. If the same two-event scenarios are now implemented in cells where INM are canceled (Fig. 3e–h), efficiency is further improved with less apical and more basal extrusion. This is especially true for the scenarios in which B occurs but not A. Interestingly, the combination of loss of INM and B (Fig. 2i–l, black curves) is more efficient at promoting basal extrusion than coupling A and B in any order (Fig. 3f–h, brown curves).Fig. 3: Rates of apical and basal extrusion in two-event EMT-like scenarios.a–h Rates of apical/basal extrusion after simulating two EMT-like events in cells with interkinetic movements (a–d) either individually (a, b) or in groups (c, d) or in cells without interkinetic movements (e–h) either individually (e, f) or in groups (g, h). The EMT-like scenarios are AS (gray lines), SA (gray dotted line), BS (black line), SB (black dotted line), AB (brown line), and BA (brown dotted line). The yellow area on each graph represents the time window of opportunity for EMT-like events to occur. Each simulation n = 500 for individual cells, n = 50 for groups of 11 cells. All graphs from panels a–h have the same X and Y axes, as labeled in (a). Note that loss of INM reduces apical extrusion and increases basal extrusion for all scenarios. i–k Scatter plots of rates of apical (Y-axis) and basal (X-axis) extrusion at t_final for scenarios with A but not B (AS/SA, i), with B but not A (BS/SB, j), with A and B (AB/BA, k). Note that, in the absence of INM (open symbols), the occurrence of both A and B does not have a cumulative effect on the rate of basal extrusion. Without INM (open symbols), scenarios with A and B lead to more extrusion than with A alone but less than with B alone. Source data are provided as a Source Data file.Plotting the final extrusion rates as scatter plots (Fig. 3i–k), better shows the various trends. In particular, we note that AB scenarios are less sensitive to loss of INM and the size of the EMT population (Fig. 3k) than scenarios in which A or B occur separately (Fig. 3i–j). These plots also help to appreciate the modulating effect of S as in scenarios where S happens after A showing a slight increase of basal extrusion. Finally, these data also indicate that A partially cancels the effect of losing INM. Indeed, the loss of INM in the AB scenarios has a less dramatic effect than in scenarios with only B. In a cell with no attachment to the apical surface, INM can no longer bring the nucleus apically, and thus, performing INM or not becomes less relevant.Three-event EMT-like scenarios in individual cells or groups, with or without INMFollowing the same logic, we ran three-event scenarios with A, B, and S in various orders: with INM, in individual cells (Fig. 4a, b) or groups (Fig. 4c, d); without INM in individual cells (Fig. 4e, f) or groups (Fig. 4g, h). Rates of apical and basal extrusions are in Fig. 4, and rates of basal positioning are shown in Fig. S3. Interestingly, the scenarios in which A occurs before B and is the first event (Fig. 4a–h, brown curves) are systematically above all other scenarios in all tested conditions. It should be noted here that it is true for both apical and basal extrusions indicating that this order of event favors extrusion in general and not basal extrusion in particular.Fig. 4: Rates of apical and basal extrusion in three-event EMT-like scenarios.a–j Rates of apical/basal extrusion after simulating three EMT-like events in cells with interkinetic movements (a–d) either individually (a, b) or in groups (c, d) or in cells without interkinetic movements (e–h) either individually (e, f) or in groups (g, h). The EMT-like scenarios are starting with A (ABS, brown lines; ASB, brown dotted lines), starting with B (BAS, gray lines; BSA, gray dotted line) or starting with S (SAB, black lines; SBA, black dotted lines). The yellow area on each graph represents the time window of opportunity for EMT-like events to occur. Each simulation n = 500 for individual cells, n = 50 for groups of 11 cells. All graphs from panels a to h have the same X and Y axes, as labeled in (a). Note that loss of INM reduces apical extrusion and increases basal extrusion for all scenarios. i, j Scatter plots of rates of apical (Y-axis) and basal (X-axis) extrusion at t_final for scenarios with A before B (ABS, ASB, SAB, i) or with B before A (BAS, BSA, SBA, j). Note that the order of events seems to only have a moderate effect on the rates of apical or basal extrusion. k–m Rates of apical extrusion (k), basal positioning (l), and basal extrusion (m) of individual EMT cells in three-event EMT-like scenarios without INM with implementation of protrusive-like behavior (P); from 500 simulations. Note the reduction of apical extrusion in panel k compared to panel (e), and the increase of basal extrusion in panel m compared to panel (f). Rates of basal positioning in panel (l) should be compared to those in Fig. S3, panel g. Source data are provided as a Source Data file.Plotting the final extrusion rates as scatter plots (Fig. 4i, j), helps to better appreciate the variations induced by the order of events, population size (single vs group) and occurrence of INM. One striking observation is that scenarios with all events (ABS in any order and no INM), which might represent a complete EMT, are comparatively less efficient at producing basal extrusion than some associations such as B and no INM that might be considered as partial EMT scenarios from a biological stand point.Collectively, these simulations with one, two, or three events with or without INM show that: (1) more than one scenario can lead to basal extrusion, (2) there is no major group effect as the outcome of a given scenario can be seen in individual cells and does not dramatically change if simulated in a group of cells, (3) the position of the nucleus at the time of epithelial destabilization is a major factor of the directionality of extrusion, (4) when occurring in absence of INM, scenarios with B but not A are more efficient than scenarios with A and B, but when both events do occur the rate of extrusion is higher when A occurs before B.Importantly, we observed that none of the above scenarios recapitulates the biological situation observed during physiological EMT. In vivo, neural crest cells either leave the neuroepithelium via basal extrusion or remain in the dorsal neural tube. There is virtually no apical extrusion. The same observation is true for gastrulating mesoderm. By contrast, in the model, all scenarios tested so far lead to some degree of apical extrusion. This suggests that, biologically, something prevents apical extrusions from occurring and/or that something strongly biases extrusion towards the basal side such that apical extrusions of neural crest cells are rare. A second striking difference is the timing of extrusion. In the best case scenario (B without INM in an individual cell), the rate of basal extrusion after 54 h of simulated biological time only reaches 50% (Fig. 2i, gray curve). In vivo time-lapse imaging shows that neural crest cells usually take no more than a few hours to leave the neuroepithelium20,21.The basally oriented force generated by apical crowding of nuclei due to INM in normal cells is sufficient to displace nuclei of EMT cells basally if EMT cells have lost their own INM or performed A (as shown in Fig. 2b, h and Fig. S1). However, this is not enough to ensure a timely exit of cells. The dichotomy between modeling and biological data strongly suggests that an actual driving force is needed. The most obvious candidate for the task is a protrusive activity directed towards the basal compartment. It is known that neural crest cells upregulate multiple integrin subunits implicated in cell motility prior to extrusion30,31. In the model, protrusive activity is represented by P, a seek-and-grab behavior of the basal point that can only occur if B previously took place. We rerun the EMT scenarios with three events in an individual cell without INM and added P (Fig. 4k–m and Supplementary Movie 4). Adding P dramatically enhances the rate of basal extrusion and shortens the time between the start of EMT-like events and extrusion. Importantly, it also suppresses apical extrusion. Both trends are observed in group simulations as well (Supplementary Movie 4). Collectively, these data indicate that a timely basal exit requires a destabilization of the epithelial structure (B or AB) coupled with a basal positioning of the nuclei (i.e., loss of INM) and an actual driving force towards the basal compartment (P).Simulation of heterogeneous clusters of EMT cellsNext, we wondered if implementing heterogeneity, with neighboring cells performing different EMT-like scenarios, would affect the relative efficiency of the various scenarios. We performed simulations with groups of cells but, this time, we implemented a gambling routine at the onset of simulations that attributes random times of occurrence for A, B, and S for each cell of the group (see Supplementary Information). For all permutations of one, two, and three-event scenarios to be statistically possible, we set the probability of picking a time for each event to 70% and that of not picking a time to 30%. Random times are within the time window of opportunity of 6 to 24 h. Times for each event are set at the onset of simulation and, if cell division occurs prior to an event, daughter cells inherit the times of the mother cell.We simulate a group of EMT cells surrounded by control cells on each side. To make sure that each scenario is generated multiple times, we ran fifty thousand simulations. This was done with or without INM in EMT cells. We then plotted apical and basal extrusion rates of each scenario implemented in heterogeneous clusters and compared them with the efficiencies when done in individual cells or homogeneous groups (Fig. 5). With INM (Fig. 5a, b), for most scenarios, heterogeneity (black triangles) increases extrusion rates. This indicates that, in the context of EMT cells performing INM, heterogeneity increases epithelial destabilization, leading to more cells leaving the tissue on either side but does not create a directional bias. When INM is canceled in EMT cells, the effect of heterogeneity is weak. There is either no effect or slightly less extrusion, depending on the scenario (Fig. 5c, d). We also plotted the fold difference between extrusion rates going from single cell to homogeneous groups and from homogeneous to heterogeneous groups per scenario and globally (Fig. S4) to better appreciate the impact of critical mass and heterogeneity on extrusions. Some scenarios are heavily impacted by going from individual cells to groups such as SA, while others (e.g., BS, SB, BAS, BSA, SAB, and SBA) are sensitive to the heterogeneous context.Fig. 5: Impact of heterogeneity on the rates of apical and basal extrusion.a, b Rates of apical (a) and basal (b) extrusions per EMT-like scenarios with interkinetic movements implemented in individual cells (open circles), homogeneous groups (brown cross), and heterogeneous groups (black triangle). Note that triangles are above the other symbols for both apical and basal extrusion rates for nearly all scenarios indicating that heterogeneity increases overall extrusion rates. c, d Rates of apical (c) and basal (d) extrusion per EMT-like scenarios without interkinetic movements implemented in individual cells (open circles), homogeneous groups (brown cross), and heterogeneous groups (black triangle). Note that in the absence of INM, heterogeneity has little to no effect. e, f Rates of apical (e) and basal (f) extrusion per EMT-like scenarios under various heterogeneous conditions: all EMT-like cells with INM (black triangles), none of the EMT-like cells with INM (open black triangles), 50% of EMT-like cells with INM, 50% without INM (open downward brown triangles), EMT-like cells with 50% chance of having INM and 50% chance of making protrusions (gray diamond). Note that P dramatically increases the rate of basal extrusion while reducing apical extrusion. g Scatter plot of the mean rates of apical and basal extrusion across all scenarios for the four heterogeneous conditions presented in panels e, f. Source data are provided as a Source Data file.To further increase heterogeneity, we allowed cells to choose to perform INM or not during the gambling phase. This generates populations with 50% of the EMT cells with INM and 50% without. We then compared extrusion rates encompassing all scenarios for this simulation with those of the heterogeneous clusters with or without INM in EMT cells (Fig. 5e–g). Interestingly, going from all cells with or without INM to a 50–50% situation mostly modulates apical extrusion without affecting the overall efficiency of basal extrusion (Fig. 5g). Finally, we introduced P in the gambling session. To account for the increased number of possible scenarios, we ran a hundred thousand simulations. All scenarios with P are extremely efficient at performing basal extrusion and preventing apical extrusion (Fig. 5e–g, gray diamonds).To further explore the data from the heterogeneous simulations, we ranked all scenarios per efficiency of basal extrusion, binning them per time of occurrence of each EMT-like event and per position of their nucleus at the onset of EMT (Supplementary Data 1). We noticed some interesting trends. As expected, scenarios with P top the list with a hundred percent efficiency of basal extrusion. This includes partial EMT-like scenarios with one or two events only. More interesting, among the most efficient scenarios without P, we find cells undergoing almost any scenario but sharing the common fact that their nuclei were near the basal side when EMT-like events were initiated. This reinforces the notion that nuclear positioning biases the directionality of extrusion.In order to assess the relative impact of the different events, we ran correlation analyses between the rate of apical or basal extrusion and the following parameters: (i) the occurrence of the events (A, B, S, P), (ii) the position of the nucleus at the onset of simulation, the onset of EMT or when A, B, S or P occur, (iii) the timing of events, and (iv) the time interval between the first EMT event and the last (for scenarios including at least two events). We used the data from the most heterogeneous situation in which EMT cells can perform any scenario with a 50% chance of performing INM, and a 50% chance of P (Fig. 6). These analyses reveal that P is the only event whose occurrence is negatively correlated with apical extrusion and positively correlated with basal extrusion. In addition, the position of the nucleus when the first EMT-like event occurs (y_emt), when A, B, or S occur (y_A/B/S) is systematically correlated with extrusion. More precisely, y_emt, y_A, y_B, and y_S are negatively correlated with basal extrusion meaning that the lowest values of y (basal positions of nuclei) favor basal extrusion while higher values of y (apical nuclei) favor apical extrusion. This is true even for events whose overall occurrence is not correlated (e.g., A, S) with either extrusion. This means that performing A in itself does not strongly favor basal extrusion, but performing A while the nucleus is basal strongly correlates with basal extrusion. For scenarios with B and P, the position of the nucleus (y_P) no longer correlates with extrusion. The protrusion generates a basally oriented driving force that bypasses the effect of the nucleus position. This global trend is true even if the correlation between y_emt and extrusion is plotted per scenario (Fig. 6c, d). Finally, the timing of the different events (t_A, t_B, t_S) and the duration of the EMT-like scenarios (Δt_emt) are not correlated with extrusion. In both INM and non-INM cells, the trend is similar, with the noticeable exception of the position of the nucleus at the initiation of the simulation (y_init) that goes from not being correlated (INM cells) to being negatively correlated with basal extrusion (no INM cells). This is due to the fact that in cells with INM, the initial position of the nucleus is not correlated to its position at the time of EMT because INM changes the nucleus position over time. While in cells without INM, the nucleus is statistically more likely to be basal, thus the weak negative correlation between y_init and basal extrusion in EMT cells without INM.Fig. 6: Correlation analyses between the occurrence/timing of events or nuclei position and the rates of apical and basal extrusion in heterogeneous simulations.a, b Correlation factor for a given parameters/event and apical (a) or basal (b) extrusion rates at t_final, either with INM (gray circle), or without INM (pink circles). Correlation factors are plotted for the occurrence of a specific event (A, B, S, or P), the timing of a given event (t_A, t_B, t_S, t_P), the time interval between the first and last event of any EMT scenarios with more than one event (Δt_emt) and the position of a cell’s nucleus at the onset of simulation (t_init), the onset of EMT (y_emt) or when a given event occurs (t_A, y_B, y_S, y_P) across all relevant scenarios. For instance B occurs in the following scenarios B, BS, SB, AB, BA, ABS, ASB, BAS, BSA, SAB, and SBA with/without INM and with/without P but does not occur in A, S, AS, and SA. Thus, correlation analyses reflect the influence of B across all relevant scenarios. The same logic applies to all parameters tested. Note that the position of the nucleus is positively correlated with apical extrusion and negatively with basal extrusion. Also, note that P is highly positively correlated with basal extrusion and negatively with apical extrusion. c, d Correlation factor for the position of nuclei when the first emt event occurs (y_emt) and apical (c) or basal (d) extrusion per scenarios with or without INM, n = 500 for each simulation. Note that apical extrusion (c) is systematically positively correlated with nucleus position (apical) regardless of the scenario and INM status. By contrast, note, for instance, that basal extrusion and nucleus position (d) can show no correlation (scenarios with P) or display a strong negative correlation (scenarios with B but neither A nor P without INM). Source data are provided as a Source Data file.Overall, the simulations with heterogeneous populations and correlation analyses indicate that i) heterogeneity can act as a destabilization factor increasing extrusion rates on either side of the epithelium and further support the idea that ii) the position of the nucleus and protrusion heavily influence the directionality and timing of extrusion. Next, we decided to confront our in silico observations to the physiological EMT of neural crest cells or the destabilization of epithelial features in the neuroepithelium.Regulation of INM is looser in the neural crest domain than in the rest of the neural tubeSimulations indicate that the basal positioning of nuclei is crucial for basal extrusion. This is consistent with data from trunk neural crest cells suggesting that synchronizing EMT with the S-phase of the cell cycle represents a window of opportunity for cells to exit the neural tube while their nuclei are basal32. It is also in agreement with the observation that 90% of neural crest cells have their nuclei basally positioned in the hour preceding delamination20. Our simulations indicate that another way to increase the probability of having a basal nucleus is to cancel INM. Lack of tight regulation of INM leads to non-apical mitoses that can be easily observed by immunostaining on fixed samples. Previous data showing that non-apical mitoses are frequent in the trunk neural crest domain at the time of EMT suggests the absence of tight regulation of INM during this process33.We then wondered whether such non-apical mitoses were a consequence of EMT itself (e.g. apical detachment) or if they could be observed in the neural crest domain prior to EMT. To this end, we monitored the distribution of mitotic cells using phospho-histone H3 staining in cephalic and trunk neural crest regions prior to and during EMT (Fig. 7a, b). In pre-EMT neural crest cells at cephalic (Fig. 7c–e) and trunk levels (Fig. 7f–h), the rate of non-apical mitoses is higher than in the neuroepithelium (where no EMT occurs). Interestingly, the rate of non-apical mitoses in the neuroepithelium significantly drops from posterior to anterior regions (Fig. 7g), indicating that tight regulation of INM is progressively implemented as the neural tube develops. The neural crest domain follows an opposite trend with an increase of non-apical mitoses as EMT is initiated. Overall, these data indicate that a significant amount of non-apical mitoses is observed before the onset of EMT, showing that neural crest cells initially lack tight regulation of INM prior to EMT implementation and that EMT further increases the rate of non-apical mitoses. According to our simulations, this would favor basal positioning of nuclei, which may facilitate basal, rather than apical, extrusion of neural crest cells upon epithelial destabilization.Fig. 7: Neural crest territory has a high rate of non-apical mitoses before the onset of EMT.a, b Diagrams representing a transversal section of the neural tube and how we classified apical vs non-apical mitoses. A mitosis is considered apical (green) if there are no other nuclei in between that mitotic figure and the apical domain. It is considered non-apical (magenta) if at least one nucleus separates the mitotic nucleus from the apical side. c–h Quantification of non-apical mitoses, as a percentage per embryo, in neural crest cells and the adjacent neural tube at the level of pre-EMT cephalic neural crest cells (c–e) and at the levels of pre-EMT (neural tube facing presomitic mesoderm (psm), j), early EMT (i) and late EMT (h) trunk neural crest cells. The statistical tests used are two-tailed unpaired t-test with Welch’s correction (d, n = 7 embryos per condition, p = 0.0182), one-way ANOVA/Fisher’s LSD test (g, nembryos = 12 (pre-EMT/psm level, p = 0.9796), 6 (onset of EMT/−1 to-6 somites, p = 0.0002), 7 (EMT/−7to-12 somites, p < 0.0001); NTemt/NTpsm, p = 0.002). EMT epithelial-mesenchymal transition, pH3 phosphor-histone H3. Source data are provided as a Source Data file.Upregulation of integrins contributes to epithelial destabilizationOur simulations point to a critical role of protrusions to ensure a timely and directional extrusion. Interestingly, α4 and α5 integrins are specifically upregulated in neural crest cells prior to delamination30,31. Their inhibition in neural crest cells leads to migration defects30,31,34,35, indicating that these integrin subunits are critical for neural crest motility. In addition, some neural crest cells end up located in the lumen of the neural tube, indicating apical extrusion. This shows that impairing interaction with the matrix leads neural crest cells undergoing EMT to randomly exit apically or basally. This reinforces the notion that protrusive activity contributes to the directionality of extrusion and not just migration post extrusion (see also discussion in ref. 36). Another striking observation from these studies is the timing of expression of α4 and α5 integrins which start being expressed several hours before any membrane extensions are described. Given that cell–cell and cell–matrix adhesion complexes tend to be spatially segregated and functionally antagonistic25,37,38, we wondered whether the early upregulation of α4 and α5 integrins could contribute to epithelial destabilization in addition to their role in motility.To test that, we generated expression vectors for chicken α4 and α5 integrins and overexpressed them in the neuroepithelium (Fig. 8). Twenty-four hours post electroporation, we analyzed the distribution of multiple apical and basal markers: atypical Protein Kinase C (aPKC), N-cadherin, Pericentriolar Material 1 (PCM1), Laminin, and Fibronectin. In embryos overexpressing a control membrane-bound GFP, no defects are observed for any of the markers (Fig. 8a, e and S5). By contrast, expressing either α4 or α5 or a combination of both was sufficient to lead to ectopic localization of apical and basal markers as well as driving cell extrusion into the lumen (Fig. 8b–k and S5). The overall morphology of the neural tube appears normal and no major rearrangements of cell such as rosettes are observed by contrast to what happens after expression of polarity protein Par322,33 or pro-EMT factors such as ets112. These data indicate that, in addition to their role in motility, the expression of specific integrin subunits can contribute to epithelial destabilization as part of EMT. However, if their expressions are not coupled to other events promoting the acquisition of front-rear polarity to ensure protrusive activity toward the basal compartment, such destabilization may lead to apical extrusion, as we observed.Fig. 8: Overexpressions of α4 and α5 Integrins lead to moderate apicobasal defects and apical extrusions.a–d Representative images for immunostaining on cryosections against atypical protein kinase C (aPKC) from embryos expressing membrane-GFP (a, n = 3), α4-Integrin (b, n = 14), α5-Integrin (c, n = 5) or a combination of α4 and α5 Integrins (d, n = 7). e–h Representative images for immunostaining on cryosections against Laminin from embryos expressing membrane-GFP (e, n = 3), α4-Integrin-GFP (f, n = 14), α5-Integrin-Cherry (g, n = 6) or a combination of both α4 and α5 Integrins (h, n = 7). Nuclei are stained with DAPI (gray), α4 and α5 are displayed in green and red, respectively. Immunostainings are shown in magenta (a, b, d, e–f, h) or in cyan (c, g). Arrows indicate examples of ectopic staining in the electroporated area. Arrowheads show examples of cells that performed apical extrusion. Scale bars in low magnification 80 µm, in zooms 50 µm. i, j Percentages of embryos with ectopic staining on the electroporated side per marker per experimental condition (i), across all markers per experimental condition (j). k Percentages of embryos with apical extrusion (cells located in the lumen). Embryos: α4 (n = 14), α5 (n = 9), α4 + α5 (n = 8). Representative images of embryos for fibronectin, pericentriolar material (PCM) 1, and N-cadherin are shown in Fig. S5. aPKC atypical protein kinase C. Source data are provided as a Source Data file.Along these lines, our simulations also point to the importance of detaching cells from the basal line, as simulations with B and no INM have a high rate of basal extrusion. Gaps in the basement membrane are often proposed as opportunities for cells to exit the epithelium, but their ability to specifically promote basal extrusion is unclear. We tested this in embryos by treating whole trunk explants with Dispase II to partially degrade fibronectin (see Methods). This leads to a reorganization of the matrix with gaps in the laminin surrounding the neural tube (Fig. S6). Interestingly, the neuroepithelium is disorganized with local buckling as previously observed with similar treatments at later stages or when affecting actomyosin29,39. It also leads to non-apical mitoses and protrusive activity on both sides of the epithelium, as well as local loss of N-cadherin and apical extrusion (Fig. S6). These data indicate that impairing interaction with the matrix contributes to epithelial destabilization and promotes extrusion but, similarly to the upregulation of integrins, is not sufficient to provide a basal bias.Cephalic neural crest cells are more heterogeneous than trunk NC cellsFinally, our simulations indicate that heterogeneity (the co-existence of multiple scenarios) favors destabilization and increases overall extrusion rates. Thus, one might expect regions of massive neural crest departure (mesencephalon) to be more heterogeneous than regions of progressive neural crest departure (trunk). Heterogeneity of neural crest populations has been observed at cephalic and trunk levels by single cell transcriptomics40,41,42,43 but this technique does not allow to assess spatial heterogeneity. Other techniques such as multiplex RNA detection on sections44 showed heterogeneity in terms of gene expression but given that the relationship between RNA and protein levels is poor45 it is difficult to predict whether detected heterogeneity at RNA levels reflects actual heterogeneity at protein level.To compare the heterogeneity of cephalic and trunk neural crest cells in terms of EMT effectors at the protein level, we performed immunostainings against tfap2α, snail2, and sox9, two by two (Fig. 9a–d). Snail2 and sox9 have been implicated in neural crest EMT17,18,46 and tfap2α is known to be upstream of both factors47. In addition, all three transcription factors are deemed part of the core neural crest regulatory cluster in chicken neural crest cells44. Interestingly, snail2 and sox9 only lead to partial epithelial destabilization when overexpressed alone but promote basal extrusion together48. Thus differential levels of these two proteins may indicate a diversity of phenotypes along the EMT spectrum.Fig. 9: Differential heterogeneity of cephalic and trunk neural crest cells.a–c Double immunostainings against TFAP2α and Snail2 (a), TFAP2α and Sox9 (b), Snail2 and Sox9 (c) on cryosections of cephalic neural crest cells (left columns) or trunk neural crest cells (right column). Scale bars, 50 µm on low magnifications and 25 µm on zooms. Yellow arrows indicate neural crest cells with high staining for both markers. Note that in cephalic regions, double-positive cells are scattered while they are basally located in the trunk region. d, e Scatter plots from double immunostainings, each channel was normalized to its maximum value. f Box and whisker plot of normalized fluorescence intensity values for each marker at head and trunk levels, n cells/embryos Head AP2 = 954/4, Trunk AP2 = 237/5, Head Sox9 = 2750/5, Trunk Sox9 = 465/7, Head Snail2 = 2745/5, Trunk Snail2 = 409/6. The coefficient of variation (CV) is indicated underneath each box plot. One-way ANOVA with uncorrected Fisher’s LSD, ****p < 0.0001, **p = 0.011. Source data are provided as a Source Data file.In cephalic regions, neural crest cells strongly expressing a couple of the above-mentioned markers (Fig. 9a–c, arrows) are scattered across the whole neural crest domain and intermingled with cells expressing mostly one or the other proteins. By contrast, in the trunk, neural crest cells strongly expressing either couple of markers (Fig. 9a–c, arrows) are concentrated in the most basal part of the neural crest domain. This indicates a higher degree of spatial heterogeneity in cephalic than in trunk neural crest cells. Further, scatter plots of normalized intensities for each pair of markers in head and trunk neural crest cells (Fig. 9e, f) show that cephalic neural crest cells display a wider range of staining intensities of all three markers. Indeed, scatter plots for trunk neural crest cells show that most cells have high expression levels for both proteins (top right corner). Intensities per marker are significantly different in the trunk and cephalic neural crest cells (Fig. 9f), and the coefficient of variation (CV) are systematically higher in cephalic than trunk neural crest cells (Fig. 9f). Altogether, these data indicate that the cephalic neural crest population is likely to be more heterogeneous than the trunk population. Thus, heterogeneity level correlates with delamination intensity in the neural crest domain, supporting the role of heterogeneity as a modulator of EMT efficiency.In conclusion, rather than a linear cascade of events leading to extrusion followed by cell migration (Fig. 10a), our simulated and biological data depict the cellular implementation of EMT as the result of an array of multiple inputs that can cooperate through various scenarios (Fig. 10b). This description better fits models of gene regulatory networks of EMT displaying multiple parallel pathways interconnected by feedback loops49,50,51. Importantly, key determinants of timely and directional extrusion appear to be the prepositioning of the nucleus and protrusive activity. Given that nucleus position is influenced by multiple inputs, heterogeneity can be seen as an emerging property of the system which may further boost epithelial destabilization. Finally, the importance of protrusive activity as an early event to bias the directionality of extrusion strongly suggests that all molecular effectors of the motility machinery may be early rather than late markers of EMT.Fig. 10: Timely and efficient basal extrusion downstream of EMT requires basal positioning of nuclei and protrusive activity.a Diagram representing the theoretical linear EMT cascade often used to describe EMT cell events in a logical manner. It starts with a module of epithelial destabilization leading to the extrusion of cells into the extracellular matrix underlying the basal side of the tissue and ends with the adaptation of the cells to the local environment, adopting a migratory phenotype. Migration is only possible if extrusion occurs towards the basal side. An important limitation of this model is that epithelial destabilization in itself does not provide directionality of extrusion and can theoretically lead to either apical or basal extrusion. b Diagram representing the alternative view of a nonlinear array of EMT cellular events. The module of epithelial destabilization contains multiple interdependent events. This allows for multiple scenarios to coexist to promote basal positioning of the nucleus, a key step favoring extrusion towards the basal side. In this model, loss of interkinetic movements and protrusive activity actively contribute to basal extrusion. This network of non-mandatory events supported by computational and biological data better fits the observed diversity of EMT scenarios, the documented heterogeneity of EMT cell populations, and the current models of transcriptional regulation of EMT by a gene regulatory network.
