Introduction
Cell migration is a fundamental cellular behavior involved in developmental and physiological processes including germline, craniofacial, and cardiac development, angiogenesis and wound healing, and pathogenesis such as cancer metastasis (Rørth, 2009; Scarpa and Mayor, 2016). In complex dynamic multicellular environments, cells integrate biochemical and mechanical cues to guide their migration. Some migration specialists, like neutrophils, navigate complex environments as single cells (Wang et al., 2020). Conversely, many developmental, homeostatic, and pathogenic morphogenetic events involve the coordinated movements of cellular collectives, as observed during neural crest migration in chick, lateral line migration in zebrafish, and border cell migration in the
Migratory collectives typically exist on a continuum with varying degrees of cell-cell contact and polarity (Capuana et al., 2020; Mayor and Etienne-Manneville, 2016). In minimally differentiated groups, individual cells move as autonomous units, while adjusting directionality and speed relative to their neighbors (Szabó et al., 2006). At the other extreme of collective organization, cells are integrated into supracellular arrangements, with marked front-to-back specialization and continuity of cytoskeletal structures between neighboring cells, ensuring mechanical coupling (reviewed in Shellard and Mayor, 2019). Such collective polarity implies communication between cells to coordinate subcellular processes.
Numerous studies uncovered mechanisms underlying collective organization, such as contact inhibition of locomotion (CIL) (Mayor and Etienne-Manneville, 2016; Ebnet et al., 2018) and leader-mediated inhibition of protrusive activity in follower cells (Cai et al., 2014; Serwane et al., 2017). Ultimately, both biochemical and mechanical properties of migratory collectives contribute to successful tissue morphogenesis. While many biochemical aspects of cell migration have been investigated, measurement of in vivo mechanical forces involved in morphogenetic cell migration has been a challenge (Campàs et al., 2014). To understand the mechanics of collective locomotion, in vitro techniques such as traction force microscopy were developed and used to correlate forces with movement and cytoskeletal dynamics (Danuser and Waterman-Storer, 2003). In more complex embryo settings, the distribution of mechanical forces can be inferred from imaging datasets, combined with available direct measurements of membrane tension (Campàs et al., 2014; Veldhuis et al., 2017; Godard et al., 2020). As a complement to biophysical measurements, computational modeling offers a powerful option to reverse-engineer forces from observed cell shape and enable in silico predictions that can be compared to experimental observations (Godard et al., 2020; Sherrard et al., 2010). There is a rich inventory of modeling approaches, from simple conceptual models of cells as point-like persistent walkers interacting with distance-dependent forces (Méhes and Vicsek, 2014), to detailed continuous or discrete models of interacting cells as distributed mechanical objects with complex rheology and free boundaries (Winkler et al., 2019; Buttenschön and Edelstein-Keshet, 2020; Alert and Trepat, 2020).
We use the cardiogenic lineage of the tunicate
Figure 1.
Model of force distribution in migrating trunk ventral cell (TVC) pairs.
(A) Diagram of
Figure 1—figure supplement 1.
In silico analysis of evolution of single-cell shape and two-cell cohesion under differing force distribution.
(A) Typical cell shapes for protrusive and retractive forces distributed within different ranges. (B) Unstable deformation of cell front resulting from focusing the protrusive force in the narrow layer near the flat substrate. (C) Detachment of the trailer from the leader resulting from failure to increase retractive forces in the trailer. (D) Elongation of the leading cell when using the force distribution associated with a single migratory cell. (E) Abnormal cell pair shape produced by loss of protrusive force in trailer and retractive force in leader.
Figure 1—figure supplement 2.
Sphericity of leader and trailer cells.
Sphericity is measured using automated Bitplane Imaris function and calculated as the ratio of surface area of sphere with volume equal to that of a cell being analyzed to the actual surface area of the cell. VL, volume of leader cell; VS, volume of sphere that is equivalent to the volume of leader cell; SA, surface area. Table shows individual sphericity values for matched leader/trailer cells.
Figure 1—figure supplement 3.
Myosin distribution at the cell-cell junction.
(A) Micrograph at left shows a dorsal view of a leader/trailer cell pair with leader oriented to the right. Dashed lines show positions of line scans of fluorescence intensity (a.u.) taken in the green (
Here, we model TVC shape and behavior using the Cellular Potts Model (CPM) (Thüroff et al., 2019; Rens and Edelstein-Keshet, 2019; Fortuna et al., 2020). In the CPM framework, each cell is a shifting shape described by a sum of mechanical energies of cell-substratum and cell-cell adhesions, surface tension and hydrostatic pressure, and protrusion and retraction forces (Figure 1A, bottom panel). These energies effectively correspond to realistic cytoskeleton-generated forces (Rens and Edelstein-Keshet, 2019; Sherrard et al., 2010). The cell boundaries fluctuate, mimicking random force and movement on subcellular scale, and shape changes minimizing the total energy are accepted. This results in evolving, collectively moving cells (Videos 1 and 2). CPM is advantageous in modeling the TVC pair as it allows us to reproduce both the detailed evolving 3D shapes of motile cells and the deformation of tissues surrounding these cells over a reasonable computational time (Thüroff et al., 2019; Rens and Edelstein-Keshet, 2019; Fortuna et al., 2020) – one of the more challenging tasks for detailed force-balance models in 3D (Wu et al., 2018).
Video 1.
In silico model of a single migrating trunk ventral cell (TVC).
Video 2.
In silico model of trunk ventral cell (TVC) pair (leader in blue, trailer in red) migrating along a surface.
By examining the distribution of forces required to recapitulate the shape of migrating TVCs in silico, we first predict the polarized distributions of protrusive activity, cell-matrix adhesion, and actomyosin contractility across cells, and test these predictions using in vivo observations and molecular perturbations. We propose that the leader and trailer cells form the simplest possible supracellular arrangement of a migratory collective. We hypothesize that this arrangement emerges from a leader-trailer mode of migration, which invokes polarized abilities to respond to extracellular guidance and mutual cell-cell attraction. Our model explains the preference for a linear arrangement of cells polarized in the direction of migration as this arrangement improves the persistence of migrating cells, which can presumably better buffer variations in migration cues. Finally, our model predicts that the linear arrangement of cardiopharyngeal progenitors allows them to distribute forces in a way that helps them deform the trunk endoderm and facilitates their migration despite the mechanical resistance exerted by the developing gut primordium.
Results
Polarized protrusive and retraction forces are distributed across a supracellular collective
Cell morphology reflects and conditions cellular behavior, inasmuch as both emerge from underlying mechanical forces (Figure 1A; Mogilner and Keren, 2009). From that standpoint, cell shape provides a phenomenological proxy to biophysical forces driving cellular behavior (Campàs et al., 2014; Maitre, 2017). In migrating collectives, leader cells typically adopt splayed morphologies with protrusive activity at the leading edge, while trailing cells display a tapered rear (Nabeshima et al., 1995). This organization is conspicuous in pairs of multipotent cardiopharyngeal progenitor cells (aka TVCs; Figure 1A) in the embryo of the tunicate
Figure 2.
Polarized matrix adhesion promotes adoption of leader/trailer cell state.
(A) Establishment of leader/trailer polarity as measured by the asymmetry that develops between leader and trailer sphericity as cells polarize in the direction of migration. Diagram depicts dorsal view of cells at stages when sphericity was calculated. Migratory cells are highlighted in green. L, leader; T, trailer; ATM, anterior tail muscle. Scatter plots show mean with standard error. Data were pooled from three biological replicates. Statistical significance tested using ANOVA followed by Bonferroni test to compare means. *p<0.05 (B) Simulation of decreasing extracellular matrix (ECM) adhesion in one cell (red) of a migrating cell pair. Cells are migrating to the right starting in a parallel orientation as shown in T = 100 Monte Carlo steps (mcs). Bar graphs show likelihood of either cell assuming the leader or trailer position in either control conditions (50/50 likelihood) or when adhesion in red cell is decreased. Standard error of proportion is shown, and statistical analysis of the proportions is done using Fisher’s exact test. (C) In vivo modulation of ECM adhesion using mosaic inheritance of the
Figure 2—figure supplement 1.
Acute reduction of extracellular matrix (ECM) adhesion in single cell (red) causes detachment of that cell from the underlying epidermis and recapitulates the phenotype observed in vivo (bottom right) with the detached cell positioned on top of the cell that maintains ECM adhesion.
Micrograph at the bottom right shows trunk ventral cell (TVC) pair expressing
We leveraged the TVCs’ simplicity and experimental tractability, combined with mathematical modeling, to simulate cell shape and behavior from first biophysical principles. We used a previously established experimental perturbation, whereby mosaic expression of a dominant-negative inhibitor of the secretory pathway (Sar1dn) stalls the migration of the transfected TVC while allowing the other cell to migrate on its own, and compare the shapes of single cells to those of cell pairs (Gline et al., 2015). Single migrating TVCs generally display morphologies intermediate to those of either leader or trailer, generating both a leading edge and a retracting rear end, thus producing overall shapes similar to migrating pairs (Figure 1B and C). We further quantified the similarity of cell shapes by comparing the aspect ratios, defined as the ratio between the length and width of the smallest rectangular bounding box that can enclose the cell or cell pair, of single migrating TVCs with TVC pairs. This comparison shows that both maintain similar overall shapes (Figure 1C), leading us to hypothesize that similar force distribution profiles may exist in both conditions.
CPM (Thüroff et al., 2019; Rens and Edelstein-Keshet, 2019; Fortuna et al., 2020) predicts that cell morphologies emerge from the mechanical energies of diverse force-generating processes distributed within each cell (Figure 1A, bottom panel). To explore the cell-autonomous mechanics responsible for the observed shapes of one- and two-cell systems that we can observe in vivo, we selected parameters characterizing the adhesion, cortex tension, and hydrostatic forces from general considerations that apply to most motile cells (see Materials and methods), and investigated the spatial distribution of protrusive and retractive forces that would best recapitulate observed cell shapes as indicated in Figure 1B. We first focused on the spatial-angular distribution of protrusive and retractive forces in single cells. By varying the width of the angular segment for retraction forces at the rear, we observed that narrowly focused retractive forces cause aberrant widening of the leading edge and fail to produce the tapered rear (Figure 1—figure supplement 1A, bottom row), suggesting that a broadly retracting trailing edge better accounts for the observed shapes of single cells.
In contrast, a wide protrusive force distribution widens and flattens the leading edge (Figure 1—figure supplement 1A), recapitulating the observed shapes (Figure 1B). In general, several combinations of protrusive and retractive force distributions produce cell shapes that qualitatively recapitulate observations (Figure 1B, Figure 1—figure supplement 1A). Simulations showed that the single-cell shape is faithfully reproduced if the retraction force is centripetal, radially converging to the cell center along the width and heights of the rear half of the cell. Similarly, protrusion force is centrifugal in the front half of the cell, diverging from the cell center (Figure 1D, Video 1). Other force distributions tested in the cell are discussed in Appendix 1. The polarized distributions of protrusive and retractile forces at the leading edge and trailing rear, respectively, are thus consistent with classic models of single-cell migration on two-dimensional substrates (Ridley et al., 2003).
Empowered by our single-cell simulations, we turned to modeling polarized cell pairs. Although single TVC migration (Gline et al., 2015) suggests that individual TVCs are migration-competent and do not require a cell partner, computationally stitching two identical single-cell models failed to reproduce the polarized morphology of migrating pairs. Specifically, when simulated leader and trailer cells were endowed with equivalent protrusive activity, the width of the trailer front extended beyond the width of the leader posterior, a morphology not observed in control embryos (Figure 1E, yellow two-headed arrow). This also impacted collective polarity, causing the simulated trailer to leave its posterior position and travel side-by-side with the leader (Figure 1E). We quantified this phenomenon by calculating
Remarkably, we could reproduce this predicted behavior in vivo by using the TVC-specific minimal
Nevertheless, simulations that reduce protrusive activity in the trailer without increasing its retractile forces cause the leader to detach and move forward on its own, overcoming significant mutual adhesion between the two cells (Figure 1—figure supplement 1C). This suggests that some protrusive activity in the trailer is still required, and that, in paired TVCs, the cells exert equivalent forces, while coordinating their activities to distribute protrusive and retractile forces to the leader and trailer cells, respectively (Figure 1—figure supplement 1B–E).
Next, we sought to further probe the supracellular model using phenomenological observations. Notably, the best computational recapitulation of observed shapes was achieved with centripetal retractive forces dominating in the trailer, pulling the cell rear forward and down, while the centrifugal protrusive forces in the leader pushed the front forward (Figure 1B and D, Video 2). The morphology produced by this force distribution also reproduced the measured aspect ratio of the motile TVC pair and single cells (Figure 1C), as well as asymmetries of the leader and trailer as reported by the ratio of their sphericities in vivo compared to simulations (Figure 1B). This is reminiscent of the centripetal character of actomyosin contractility (Yam et al., 2007), which led us to analyze myosin distribution in migrating cell pairs. Consistent with the model’s prediction of a trailer-polarized retractile activity, we observe that iMyo-GFP, an intrabody that recognizes non-muscle myosin II through a conserved epitope (Chaigne et al., 2013; Hashimoto et al., 2015), accumulates at the rear of the trailer cell and is relatively depleted from the leader-trailer junction (Figure 1F, Figure 1—figure supplement 3), implying that the retraction in the trailer is dominant, while the retractive force in the leader is weak, lending further support to the hypothesis that TVC pairs migrate as a supracellular collective.
Taken together, our computational predictions and experimental observations support a model where pairs of multipotent cardiopharyngeal progenitors migrate as a polarized supracellular collective, with protrusive activity and myosin-based retraction distributed across leader and trailer cells, respectively.
Polarized cell-matrix adhesion contributes to leader/trailer states of migrating cells
Cell-matrix interactions and distribution of protrusive activity to the leading TVC result in the generation of a broad leading edge during the establishment of collective TVC polarity (Bernadskaya et al., 2019). The flattened leading edge of the leader lowers the cell's overall sphericity. Conditions that perturb cell-matrix adhesion often increase the sphericity of leading cells, suggesting that they fail to establish flattened protrusions at the leading edge (Bernadskaya et al., 2019). We compared the sphericity of the leader and trailer cells starting with TVC birth at developmental stage 19 prior to migration (Figure 2A). TVCs’ sphericities did not differ at stage 19, suggesting that they are born with equivalent shapes. Cell sphericities begin to differ significantly during migration, indicating establishment of leader/trailer polarity, adoption of distinct states (Figure 2A), and orientation in direction of migration. Collective TVC polarization is abolished by disruption of cell-matrix adhesion by misexpression of a dominant-negative version of the collagen receptor, Discoidin domain receptor (Ddrdn), which alters integrin-mediated cell-matrix adhesion and disrupts polarized Bmp-Smad signaling (Bernadskaya et al., 2019). This suggests that collective polarity and anisotropy of actin dynamics actively mature in response to extracellular cues and that leader/trailer selection can be biased based on the relative amount of cell-matrix adhesion experienced by the TVCs.
We previously showed that integrin ß1 (Intß1)- and Ddr-mediated signaling and cell-matrix adhesion to the basal lamina of the ventral trunk epidermis promote collective polarity and directional movement of TVC pairs (Bernadskaya et al., 2019; Figure 2A). Here, we harnessed the predictive power of our model to explore the consequences of varying the distribution and strength of cell-matrix adhesion forces across the cell pair in silico. We begin by simulating two cells side-by-side with the same protrusive/retractive force distribution, but with cell-matrix adhesion in one of the cells lower than the other. In order to focus on the cell-autonomous behaviors specific to the TVCs, we performed these simulations without modeling the overlying endoderm under which the cells move in vivo. In these conditions, the cell with reduced adhesion was more likely to assume the trailer position (Figure 2B). We tested this prediction in vivo using mosaic overexpression of the dominant negative forms of Intß1 and Ddr driven by the
Of note, one simulation of more acute reduction of cell
Our previous work has suggested that leading cells are more adhesive than trailer cells (Bernadskaya et al., 2019). To evaluate the distribution of adhesion-associated actin structure, we assayed the distribution of F-actin in leader/trailer cell pairs using Lifeact::GFP. The F-actin marker localized to the leading edge and an intracellular punctate pattern, suggesting association with adhesion complexed and/or intracellular vesicles (Figure 2D). Quantifications indicated that leader cells consistently contained more ventral Lifeact::GFP+ F-actin puncta than trailer cells, supporting the prediction that F-actin-rich adhesion complexes are enriched in leading cells during TVC migration (Figure 2D). Taken together, these results indicate that increased cell-matrix adhesion and protrusive activity are hallmarks of the leader cell state during collective cell migration.
Hierarchical guidance orients collective polarity in the direction of migration
From the above sections, a picture emerges whereby the supracellular organization of migrating pairs of cardiopharyngeal progenitors is characterized by leader-polarized protrusive activity and cell-matrix adhesion, and trailer-polarized deadhesion and myosin-driven retraction. Both experimental and simulated disruptions of this supracellular polarity alter directionality, marked by alignment of the leader-trailer axis with the direction of migration. However, the two cells are not arranged in a linear leader-trailer orientation at birth (Figure 3A), and previous observations indicated that either cell can assume a leader position, although single-cell lineage tracing indicates that the leader emerges from the most anterior cell in ~95% of embryos (Gline et al., 2015).
Figure 3.
Hierarchical organization of multicellular migratory clusters.
(A) Evolution of trunk ventral cell (TVC) polarization. Panels show in vivo-rendered images of cells at the indicated embryonic stages. Leader in blue, trailer in red, non-migratory anterior tail muscles (ATMs) in white. Spheres inside cells mark the center of mass, sphere to the right indicates direction of anterior migration. Angle theta between the axis of leader/trailer and direction of migration is indicated. (B) Three hypothesized polarization modes for two-cell migration. Independent: cells polarize independently in the signal direction and move with the same speed. Faster-slower: cells polarize independently in the signal direction, but one cell moves faster than the other. Leader-trailer: one cell (leader) follows the signal direction, while the other (trailer) polarizes in the direction of the leader’s center of mass. L, leader; T, trailer. (C) Establishment of alignment between the leader/trailer axis and direction of migration.
We analyzed the establishment of leader/trailer polarity from the initial time of TVC birth to full polarization and alignment with the direction of migration over four embryonic stages encompassing TVC migration (Hotta et al., 2007). Tracking
We sought to explore possible cell-autonomous mechanisms governing the establishment of collective leader-trailer polarity and its alignment with the migration path. We modeled three possible directional modes for the cell pair without including directional noise (Figure 3B): the independent mode, where the two cells have the same distributions of retractive and protrusive forces and their retractive-protrusive axes are aligned to the right, along the net directional signal from the surrounding tissue; the faster-slower mode, where the total retractive-protrusive force in one cell is scaled up compared to the other cell, thus making one cell faster than the other; and the leader-trailer mode, where the prospective leader’s retractive-protrusive axis is aligned with the external signal direction, while the prospective trailer’s retractive-protrusive axis is oriented toward the leader’s center of mass. In simulations, the two cells are initially placed side-by-side, with their retractive-protrusive axes orthogonal to the migration path (i.e.,
Video 3.
In silico modeling of cell position rearrangement of two migrating cells using the faster-slower mode of migration.
Video 4.
In silico modeling of cell position rearrangement of two migrating cells using the leader-trailer mode of migration.
The assumption that the basic rule of follower cells polarizing hierarchically towards leader cells predicts that cells should adopt a linear arrangement of leader and follower states even if the number of migrating cells was increased. To test this, we further probed the distinct migration modes by modeling three migrating cells (Figure 3E, diagram at top). In these simulations, each of the three cells adheres equally to the other two. The modes are similar to those for two cells (Figure 3B), with two adaptations: in the faster-slower mode, one cell is the fastest, another – the slowest, and the third moves with an intermediate speed; the leader-trailer mode becomes the leader-middle-trailer mode, in which the polarization axis of the leader is fixed to the external signal direction, the middle cell’s axis orients towards the leader’s center, and the trailer’s axis orients towards the middle cell’s center. To mirror the initial arrangement observed in vivo, we start three-cell simulations with individual cells distributed in a triangular pattern (Figure 3E, Videos 5 and 6). Similar to two-cell simulations, the independent mode failed to produce linear arrangements and the cells remained in triangular formation with no leader emerging, potentially due to the three-cell system minimizing the adhesive energy when each cell maintains contacts with the other two (Figure 3E). Although cells arranged more linearly under the faster-slower mode (Figure 3E, Video 5), they failed to align with the direction of migration for an extended period of time, only achieving the single-file arrangement towards the end of simulations (Figure 3E). The leader-middle-trailer mode was again the most effective at producing full polarization and linear order rapidly (Figure 3E, Video 6), suggesting that basic hierarchical rules of collective polarization can produce linear arrangements of cell groups containing variable numbers of cells. We tested this prediction in vivo, where ectopic FGF/M-Ras/Mek-driven induction within the
Video 5.
In silico modeling of cell position rearrangement of three migrating cells using the faster-slower mode of migration.
Video 6.
In silico modeling of cell position rearrangement of three migrating cells using the leader-trailer mode of migration.
Video 7.
In vivo conversion of anterior tail muscle (ATM) fate to trunk ventral cell (TVC) by misexpression of
B7.5 lineage. Nuclei are marked with
Video 8.
In vivo conversion of anterior tail muscle (ATM) fate to trunk ventral cell (TVC) by misexpression of
B7.5 lineage. Cell membranes are marked with
Since the ability to organize cell collectives requires maintenance of cell-cell junctions, we also investigated the effect of cell-cell adhesion strength on collective polarization. Multiple simulations varying the cell-cell adhesion energy in our basic model show that cell-cell adhesion strength does not affect the total displacement of cell pairs over long time intervals (Figure 3G, bottom right). However, increasing or decreasing cell-cell adhesion energy causes the cell-cell boundary area to increase or decrease, respectively (Figure 3G, top right, blue plot), which leads to a drastic misalignment of cells with the direction of migration beyond a cell-cell adhesion strength of 10 (relative energy units). This suggests that the extent of cell-cell adhesion may be regulated in vivo and that cells with high cell-cell adhesion will reorient their supracellular polarity away from the direction of migration.
Collective polarity fosters persistent directionality
Having characterized ground rules that govern collective arrangement of migrating cardiopharyngeal progenitors, we sought to explore the specific properties conferred by this supracellular organization. Unlike specialized motile cells, such as
Figure 4.
Migratory persistence of cell pairs and single cells.
(A) Left: simulation of migration persistence over time for single cell and the centroid of the cell pair. The shaded area shows the standard error. In the model, green arrows show the direction of active forces for each cell that is directionally biased but also fluctuates randomly. The leader cell is biased to the right, which is the direction of the external cue, and the trailer cell is biased to the leader cell. and are the angles between the green arrows and the right direction, and is the angle between the line connecting two cells and the right direction. The specific stochastic equation for is given in the Materials and methods section using the same angle notations. The diagram on top shows the relationship between displacement and track length and . (B) Comparison of tracks from simulations of either migrating cell pairs or single cells within the same simulation time. Shaded vertical lines represent mean final displacement. Graphs on the right show mean total displacement and mean total track length with standard error. Statistical analysis was performed using Student’s
We compared the final displacement of single TVCs in vivo to the total displacement of the leader TVC. In agreement with simulations, TVC pairs migrated further from the anterior ATM than single cells (Gline et al., 2015; Figure 4C). To test if this was due to the loss of persistence, as predicted by the above simulations, we compared the persistence of cell pairs by tracking the nuclei of leader and trailer cells in 4D datasets and compared to the migration paths of single TVCs (Figure 4D, Videos 9 and 10). In control conditions, the leader and trailer migrate with similar persistence; however, the migration paths of single TVCs were significantly less persistent than those of either leader or trailer cells, suggesting that in vivo, collective organization confers robust directionality to the migrating cells.
Video 9.
In vivo migration of a control trunk ventral cell (TVC) pair.
Nuclei are marked with
Video 10.
In vivo migration of a single trunk ventral cell (TVC), produced by misexpression of
Nuclei are marked with
In summary, both simulations and in vivo observations suggested that polarized cell pairs migrate with increased robustness to fluctuations in directionality compared to single cells.
Polarized cell pairs overcome mechanical resistance from the endoderm during migration
The above sections indicate that collective organization endows the TVCs with defined properties (e.g., persistence) that are intrinsic to cell pairs and determine the characteristics of their migration. However, TVCs migrate surrounded by embryonic tissues that canalize their behavior (Christiaen et al., 2008; Gline et al., 2015; Bernadskaya et al., 2019). Specifically, shortly after the onset of migration, the TVCs penetrate the extracellular space between the ventral trunk epidermis, which they use as stiff substrate, and the softer trunk endoderm, which locally deforms as TVCs progress anteriorly (Gline et al., 2015; Figure 5A). We reasoned that the trunk endoderm likely exerts mechanical resistance to the passage of the TVCs and hypothesized that this resistance may be better overcome by polarized cell pairs (Figure 5A and B). We predicted that when two cells migrate in a leader-trailer arrangement, the surface that the leader exposes to mechanical resistance is equivalent to that of a single cell, while the trailer pushes from the rear, therefore adding forward-bearing compression force to overcome endoderm resistance (Figure 5B).
Figure 5.
Supracellular cell pairs are more efficient at dispersing pressure from surrounding tissues.
(A) Micrographs of stage 23 embryos showing the endodermal pocket formed during trunk ventral cell (TVC) migration. Embryos are oriented with anterior to the right. Endodermal cells are marked with
To explore this argument, we added deformable endoderm cells to our model and simulated cell migration under varying endoderm stiffness, comparing the effects on migration speed. We simulate migration of one- and two-cell systems, tracking the simulated cells’ centers of mass with five simulations run per condition shown in Figure 5D. When modeling a softer endoderm, by modulating volume preservation and cortical tension parameters relative to those of the TVCs (see Appendix 1), polarized cell pairs perform best, whether in supracellular mode or equivalent force distribution, while side-by-side cells were the slowest, presumably because they expose a greater surface to mechanical resistance (Figure 5B and D). Notably, two equivalent cells moving in single file advanced marginally faster than the supracellular pair, suggesting that cell alignment itself is a key determinant of efficient migration under the soft tissue. When simulating a stiffer endoderm, the advantage of supracellular organization became more apparent. In these simulations, the supracellular collective migrated faster than other arrangements (Figure 5D). Notably, cells migrating side-by-side were slower than single cells with either endoderm stiffness (Figure 5D), which is consistent with the notion that a more extended surface of contact with the endoderm exposes them to greater mechanical resistance, while the smooth teardrop shape of single cells may be near optimal for lowering the resistive deformations of the endoderm. This suggests that the collective shape resulting from supracellular organization optimally minimizes mechanical resistance of the surrounding tissue to migration.
The predicted relative speeds of cells migrating under the endoderm are based on the simplest model, which assumes that the endoderm’s primary effect is mechanical resistance to deformation. In vivo, the interactions between TVCs and endoderm cells are likely more complex, involving indirect cell-cell signaling via extracellular deposition of collagen9-a1 by the endoderm (Bernadskaya et al., 2019). In summary, the combined in silico simulations and in vivo observations indicate that the collective organization of migrating cardiopharyngeal progenitors allows them to overcome mechanical resistance from the deforming endoderm and reach a typically mesodermal position between germ layers for cardiac organogenesis.
Discussion
Complex multicellular behaviors, including directed collective cell migration, emerge from the context-specific integration of universal dynamic processes, which operate at subcellular scale and are coordinated within and across cells (Bernadskaya and Christiaen, 2016). The sheer complexity of integrated cellular systems constrains direct experimental interrogations, but mathematical models and simulations provide a powerful complement to probe the relative biophysical contributions of subcellular processes to cellular behavior.
In this study, we used a mathematical model, built from first biophysical principles, to generate computational simulations and explore the morphodynamic space of motile cardiopharyngeal progenitor cell pairs of the tunicate
The above patterns of protrusive activity, cell-matrix adhesion, and contractility might seem trivial, considering the well-established organization of individual migrating cells. However, in the ‘supracell,’ the distribution of various cytoskeletal activities across all cells in a collective suggests the existence of mechanisms to ensure such ‘division of labor.’ This simple prediction implies multiple roles for the cell-cell contact, in addition to its anticipated low surface tension.
First and foremost, cell-cell adhesion must be strong enough to maintain the integrity of the collective and permit mechanical coupling, lest cells lose contact and migrate disjointly (Figure 1—figure supplement 1C). Conversely, the model predicts that excessive cell-cell adhesion antagonizes cell-matrix adhesion and disrupts collective polarity. Balancing cell-cell and cell-matrix adhesion may result from either mechanical interaction, as suggested by the model, and/or biochemical cross-talks, as observed in other systems (Martinez-Rico et al., 2010; Ramprasad et al., 2007). The coexistence and contributions of both cell-cell and cell-matrix adhesion to supracellular migration emphasize the hybrid nature of such multicellular systems, where cells adopt intermediate states on an epithelial-to-mesenchymal continuum (Friedl and Mayor, 2017; Bernadskaya and Christiaen, 2016; Lecaudey and Gilmour, 2006).
Close cellular contacts probably facilitate propagation of direct mechanical and biochemical interactions that underlie supracellular migration. We tentatively distinguish ‘information flows’ that propagate in either a back-to-front or a front-to-back fashion (Capuana et al., 2020; Mayor and Etienne-Manneville, 2016). For instance, similar to
TVCs’ collective polarity is marked by higher protrusive activity and cell-matrix adhesion in the leader, as indicated by experimental observations and model predictions (Christiaen et al., 2008). Mechanically, it is likely that adhesion complexes are established following lamellipodia formation and support traction forces, which complement rear-driven compression to propel the cells forward. It is conceivable that lower protrusive activity in the trailer limits the deployment of cell-matrix adhesion complexes. However, cell-matrix adhesion in the trailer is probably needed to anchor the cell and allow for its hydrostatic pressure to push the leader. Therefore, one must invoke mechanisms whereby the leader suppresses protrusive activity in the trailer, while permitting the establishment of trailer cell-matrix adhesion in its path. In
While future work combining biophysical modeling, force measurements, and/or inference from quantified cell shapes is needed to elucidate the mechanisms underlying supracellular organization in vivo, our model and experimental investigations uncover important consequences for directed migration: namely, persistence and mechanical interaction with surrounding tissues. Specifically, both computational simulations and live imaging indicated that the instantaneous directionality of single cells fluctuates more than that of cell pairs. In other words, polarized cell pairs are more persistent. It is possible that cell pairs are better at buffering the noise inherent to navigating a complex and changing environment, in part by distributing interactions over greater surfaces, and integrating guidance cues more accurately.
Finally, our observations indicate that supracellular organization determines the outcome of interactions with surrounding tissues during migration. We previously determined that TVC pairs migrate onto the extracellular matrix (ECM) associated with the basal lamina of the ventral trunk epidermis (Bernadskaya et al., 2019), which presumably offers a stiff substrate permitting traction forces. Of note, a specific collagen,
Resource availability
Lead contact
Further information and requests for resources and reagents should be directed to and will be fulfilled by the lead contact: Yelena Bernadskaya ([email protected]).
Data and code availability
The codes generated during this study are available on GitHub (Yue, 2021; https://github.com/HaicenYue/3D-simulation-of-TVCs.git copy archived at swh:1:rev:c8a79bc7822f295ab72edb8e3f7660c823c3699e).
Experimental model and subject details
Wild caught
Materials and methods
Key resources table
Reagent type (species) or resource | Designation | Source or reference | Identifiers | Additional information |
---|---|---|---|---|
Software, algorithm | https://github.com/HaicenYue/3D-simulation-of-TVCs.git | |||
Genetic reagent ( | Wild-caught | M-Rep, San Diego,CA | https://www.m-rep.com | |
Sequence-based reagent | RhoDFca-F | This paper | PCR primers | TGAAACTTGTATTGCGGCCGC |
Sequence-based reagent | RhoDFca-R | This paper | PCR primers | agacgtacgt |
Sequence-based reagent | iMyo::GFP – F | This paper | PCR primers | ACTTGTATTG |
Sequence-based reagent | iMyo::GFP – R | This paper | PCR Primers | gctgagcgcGAA |
Recombinant DNA reagent | pCESA: Mesp > hCD4::GFP (plasmid) | PMID:30610187 | B7.5 lineage specific GFP membrane marker | |
Recombinant DNA reagent | pCESA: Mesp > H2B::GFP (plasmid) | PMID:30610187 | B7.5 lineage specific GFP histone/nuclear marker | |
Recombinant DNA reagent | pCESA: Mesp > iMyo::GFP (plasmid) | This paper | B7.5 lineage specific GFP myosin intrabody | |
Recombinant DNA reagent | pCESA: Foxf > mCherry (plasmid) | PMID:30610187 | mCherry TVC-specific marker | |
Recombinant DNA reagent | pCESA: EfnB > hCD4::mCherry (plasmid) | PMID:30610187 | Epidermal mCherry membrane marker | |
Recombinant DNA reagent | pCESA: Mesp > 3xmKate2 (plasmid) | PMID:30610187 | B7.5 lineage specific mKate2 marker | |
Recombinant DNA reagent | pCESA: Nkx2−1> hCD4::GFP (plasmid) | PMID:30610187 | Endoderm specific GFP cell membrane marker | |
Recombinant DNA reagent | pCESA: Foxf>Sar1dn (plasmid) | PMID:25564651 | TVC-specific dominant negative Sar1 | |
Recombinant DNA reagent | pCESA: Foxf > Rhodfca (plasmid) | PMID:18535245 | TVC-specific constitutively active RhoD/F | |
Recombinant DNA reagent | pCESA: Mesp > LacZ (plasmid) | PMID:30610187 | B7.5 lineage specific LacZ loading control | |
Recombinant DNA reagent | pCESA: Foxf > Intβ1dn (plasmid) | PMID:30610187 | TVC-specific dominant negative Intβ1 | |
Recombinant DNA reagent | pCESA: Foxf > Rasca (plasmid) | PMID:18535245 | TVC-Specific constituitivley active Ras | |
Recombinant DNA reagent | pCESA: Foxf > Ddrdn (plasmid) | PMID:30610187 | TVC-specific dominant negative Ddr | |
Software, algorithm | FIJI | Schindelin et al., 2012 PMID:22743772 | RRID:SCR_002285 | |
Software, algorithm | Bitplane Imaris | Bitplane Imaris | ||
Software, algorithm | Prism 9 | https://www.graphpad.com/ | RRID:SCR_002798 |
Electroporation and transgene expression
Live imaging and TVC tracking
To generate 4D datasets, embryos at 4.5 hpf FABA stage 15 were mounted on glass-bottom microwell Petri dishes (MatTek, part# P35G-1.5–20C) in artificial seawater. Plates were sealed by piping a border of vaseline and 5% (v/v) mineral oil (Sigma, #M841-100ml) and covered with a 22 × 22 Fisherbrand Cover Glass (#12-541-B). Embryos were imaged on a Leica inverted SP8 X Confocal microscope using the 40× water immersion lens at 512 × 512 resolution every 3.5 min for 4–5 hr. B7.5 lineage nuclei and epidermal cell membranes were visualized using
Image acquisition
All images were acquired using the Leica SP8 X WLL confocal microscope using the 63× glycerol immersion lens, NA = 1.44. Z-stacks of fixed embryos were acquired at the system optimized Z-step, 512 × 512 resolution, 600 Hz, and bidirectional scanning. Multiple HyD detectors were used to capture images at various wavelengths.
Quantification and statistical analysis
Morphometrics analysis
The membrane marker
Image preprocessing
All 3D stacks were imported and converted to Imaris format. Images were reoriented and cropped with the leader cell to the left. An automated Gaussian filter and background subtraction was applied to all images using the Imaris Batch module. Images were projected to 2D using Maximum Intensity Projection to reflect the dorsal view of the cells and exported as TIFFs for analysis in Fiji.
Aspect ratio calculation
2D projected images were imported into Fiji and converted to 8-bit format. A threshold was applied to each individual image, and empty spaces were filled using the Binary -> Fill Holes function. Resulting object was used to derive the aspect ratio using the Analyze Particles function. In simulation, black-and-white images were obtained using imbinarize function in MATLAB and then regionprop.BoundingBox function was used to get the minimal rectangle that enclose the object. Aspect ratio is the ratio between the width and length of this rectangle.
Myosin intensity analysis
Images were imported into Fiji. Using the freehand line function with a width of 10 units, a scan was performed on the leading edge of the leader cell, the cell-cell junction, and the membrane of the trailer cell using the membrane marker as a guide. The intensity of iMyoGFP and the membrane marker
Lifeact::GFP distribution analysis
The Cell function was used to segment leader and trailer cells with vesicle detection. The membrane marker
Statistical analysis and data representation
For all data comparing two samples of continuous variables, the Wilcoxon rank-sum test (also known as the Mann–Whitney test) was used. Categorical data were analyzed using Fisher’s exact test. Simulation data were analyzed using Student’s
Model
We use the CPM (Graner and Glazier, 1992) to simulate the movement of one or several cells on the substrate. The model is based on the minimization of the effective energy
In the CPM, the space is divided into pixels (in the model, the cell size is about pixels), and each pixel is assigned a spin . The spin is effectively an index that identifies which cell the pixel belongs to. A stochastic modified Metropolis algorithm (Cipra, 2018) was used to determine how the spin changes. At each step, the algorithm randomly selects a target site, , and a neighboring source site . If they belong to different cells, or to a cell and neighboring environment, the algorithm sets with probability, , which is determined by the Boltzmann acceptance function:
where is the change of the effective energy caused by this change of spin, and is an effective temperature parameter describing the amplitude of stochastic fluctuations of the cell boundary (Swat, 2012). We use for all the simulations in this paper. The key part of any specific CPM is the effective energy . In our model, we define as
Here, the first and the second terms represent the effects of the volume conservation and cell surface (cortex) contraction, respectively. Alternatively, the first term can be thought of as the effect of the hydrostatic pressure of the cytoplasm, and the second term – as the effect of the cell cortex tension. The third term represents the adhesion energy between the neighboring cells and between the cells and the ECM (also called substrate or ECM below). The last term is the effective potential energy related to the protrusive and retractive forces (with subscript and , respectively). is the pixel’s index, and is the cell’s or environment’s spin. Variables and are the volume and surface area of the cell , and is its target volume. Unlike in some variants of the CPM, we keep the target surface area equal to zero, so effectively the cortex is contractile for any area. The target volume is a parameter that we take to be equal to the volume of the cube of the characteristic cell size. Parameters and are the coefficients determining how tightly the volume is conserved and how great the cortex tension is, respectively. Parameter is the adhesion energy per unit area of the boundary between cells and (or between cell and ECM). Variable is the area of the boundary between cells or between one cell and the ECM. Essentially, the model’s first two terms tend to minimize the cell’s area while keeping its volume constant shaping the cell into a sphere. Adhesion terms, however, try to maximize the boundary areas, flattening the cells. The competition between these terms makes individual cell look like a dome on the substrate (this is how we choose relative strengths of the cortex tension and characteristic adhesion), and two cells – like two domes pressed into each other side-by-side. To make the cells move, we must add the forces pushing the cell front and pulling its rear. Note that those forces originate from the cytoskeleton inside the cells, and not in the environment surrounding the cells, so the force balances are implied. Specifically, the force of protrusion that pushes on the cell leading surface forward from inside is balanced by a reactive cytoskeletal pushing directed to the rear and applied to the firm adhesions between the ventral surface of the cell and ECM. Similarly, the force of retraction that pulls the cell rear forward from inside is also balanced by a reactive cytoskeletal pulling directed to the rear and applied to the firm adhesions between the ventral surface of the cell and ECM.
We introduce these forces through effective potential energies as follows. First, we define a polarity for each cell, which is quantified using the angle between the polarization direction and the positive-x direction, , as shown in Figure 4A. Then, the respective potential energies can be defined as
Here, is the Heaviside step function (equal to 1/0 for positive/negative values of argument, respectively). is the 3D position of a specific pixel. is the angle of vector , in which is the position of 2D projection of a specific pixel onto the x-y-plane, and is the 2D position of the centroid of the cell. is the polarity angle mentioned above and are the angular ranges of the protrusive and retractive forces, respectively. For example, if the protrusive force exists in the front half of the cell and the retractive force exists in the back half of the cell, then the angles are, , is the 3D distance between a specific pixel and the centroid of the cell and taking a gradient of it, results in the centripetal retractive and centrifugal protrusive forces. and define the amplitudes of the energy terms that are also strengths of the protrusive and retractive forces, respectively. is a constant parameter, while is constant in some simulations but is a function of angle () in others. Their values, as well as the values for and , and for all other model parameters, are listed in Appendix 1—table 1.
When investigating directionality and persistence of the cells’ trajectories, stochasticity is introduced to the polarity’s dynamics as follows:
where is the angle shown in Figure 3B and denotes a Wiener process (stochastic directional noise). The first term shows the tendency of the polarity to align with the external signal’s direction (the positive-x direction), and the second term shows the tendency to follow the other cell. For different polarization modes, and take different values. More specifically, for the independent mode and the faster-slower mode shown in Figure 3B (when the cells follow the environmental directional guidance independently), for both cells, while for the leader-trailer mode (when the trailing cell follows the leader instead of following the environmental guidance), for the leader and for the trailer.
It is worth mentioning that the exact absolute values of parameters in the energy function are not important as the dynamics of the system is determined by the ratio in which is a ‘temperature’ parameter without direct relation to the biological processes, and the ‘Monte Carlo step’ in the simulation is not directly related to an actual time scale. So, we only check whether the ratios of the model parameters are consistent with the experimentally estimated orders of magnitude of the biophysical parameters. Experimental estimates of the force generated over of the lamellipodial leading edge are and the total traction force exerted by the cell is (Gline et al., 2015 ; Mogilner and Oster, 2003). As the leading edge of the lamellipodia is only thick, while in our model we cannot generate very thin protrusions, we distribute the total forces generated by the lamellipodia almost uniformly to the whole front of the cell and use the protrusive force density assuming the height of the cell is (Figure 1A). Similarly, we distribute the total traction force uniformly to the back of the cell resulting in the retractive force density . Thus, the orders of magnitude of the protrusive and retractive forces are close, and we keep them close in the model. The energy of adhesion between the cell and the substrate is estimated as follows. Each integrin attachment complex has a force (Ananthakrishnan and Ehrlicher, 2007) associated with it. The size of an integrin-based adhesion complexes formed at cell contacts with the ECM is (Geiger et al., 2001), so we estimate the adhesion force densities as . Then, the ratio between the active forces and the adhesion forces is ˜10. In our model, the force strength parameters, and , are on the order of 10–100 in dimensionless units, and the adhesion strength parameter ranges from 0 to 20 in dimensionless units, which is consistent with the force ratios from the experimental measurements.
After the orders of magnitude of the protrusion, retraction and adhesion energies are chosen as described, the rest of the principal model parameters are chosen following the following logic. The cortex contractility parameter is chosen so that an individual non-motile cell has a shape close to that of a hemisphere; if this parameter is too small, the cell becomes a ‘pancake’; if too large – a ‘ball.’ The parameter regulating the tightness of the cell volume control, , is fine-tuned to avoid (1) freezing the cell shape – when this parameter has a value that is too great, most fluctuations of the cell shape get arrested, and (2) loosening the cell shape too much – when this parameter has a value that is too small, cell transiently becomes too small or too large that disagrees with the observations. The values of the parameters for the stochastic directionality experiment are chosen so that the persistence of the single cell predicted trajectories fit that of the observed trajectories. Finally, note that the parameters for the adhesion strength (J) are scaled as follows. We make this parameter a large positive number for the boundary between the two motile cells and endoderm (or for cell-free space boundary in simulations without endoderm); this corresponds to the ‘no adhesion’ regime. Then, the adhesion parameters for cell-cell and cell-ECM boundaries are smaller positive numbers. Thus, the energy in the system decreases when the relative areas of the cell-cell and cell-ECM boundaries increases, so those are the adhesive surfaces.
Note that the dynamics of the simulated cell is determined by the probability function of spin changes, which is defined by the exponential function with a cutoff at 1. This leads to a speed-force relation of an exponential form when the force is too small and is saturated when the force is too large. We avoid this artifact because the parameters we choose restrict our simulations to the regime where the speed-force relation is approximately linear.
Simulations were done using software CompuCell3D 3.7.8 (Swat, 2012). In Appendix 1 tables, we list all model parameters that are varied between different simulations, and in the Supporting information we explain the reasons for the variance. When we simulate the actively migrating cells in the presence of the endoderm that mechanically resists the deformations, we make the endodermal cells mechanically more passive than the migrating cells (their contractile tension is half that of the migrating cells) and vary the endodermal ‘tightness of the volume conservation’ parameter a few fold less and greater than that of the migrating cells, respectively.
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Abstract
Physiological and pathological morphogenetic events involve a wide array of collective movements, suggesting that multicellular arrangements confer biochemical and biomechanical properties contributing to tissue-scale organization. The
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