1. Physics of Living Systems
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Polar pattern formation induced by contact following locomotion in a multicellular system

  1. Masayuki Hayakawa
  2. Tetsuya Hiraiwa
  3. Yuko Wada
  4. Hidekazu Kuwayama
  5. Tatsuo Shibata  Is a corresponding author
  1. Laboratory for Physical Biology, RIKEN Center for Biosystems Dynamics Research, Japan
  2. Mechanobiology Institute, National University of Singapore, Singapore
  3. Universal Biology Institute, University of Tokyo, Japan
  4. Faculty of Life and Environmental Sciences, University of Tsukuba, Tennodai, Japan
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Cite this article as: eLife 2020;9:e53609 doi: 10.7554/eLife.53609

Abstract

Biophysical mechanisms underlying collective cell migration of eukaryotic cells have been studied extensively in recent years. One mechanism that induces cells to correlate their motions is contact inhibition of locomotion, by which cells migrating away from the contact site. Here, we report that tail-following behavior at the contact site, termed contact following locomotion (CFL), can induce a non-trivial collective behavior in migrating cells. We show the emergence of a traveling band showing polar order in a mutant Dictyostelium cell that lacks chemotactic activity. We find that CFL is the cell–cell interaction underlying this phenomenon, enabling a theoretical description of how this traveling band forms. We further show that the polar order phase consists of subpopulations that exhibit characteristic transversal motions with respect to the direction of band propagation. These findings describe a novel mechanism of collective cell migration involving cell–cell interactions capable of inducing traveling band with polar order.

eLife digest

The cells of animals and many other living things are able to migrate together in groups. This collective cell migration plays crucial roles in many processes in animals such as forming organs and limbs, and healing wounds.

A soil-dwelling amoeba called Dictyostelium discoideum – or just Dicty for short – is commonly used as a model to study how groups of cells migrate collectively. Individual Dicty cells may live alone but sometimes many cells come together to form a larger mobile structure called a “slug”. Chemical signals coordinate how the cells collectively migrate to form the multicellular slug. Mutant Dicty cells that lack these chemical signal processes can still move together as a band that travels across a surface. This movement resembles a type of collective motion that has previously been observed in physics experiments using self-propelled particles. However, it remains unclear how this collective behavior works.

Hayakawa et al. have now combined genetics, cell biology and computational approaches to study how groups of the mutant Dicty cells migrate together. The experiments showed that the traveling band is dynamically maintained by cells joining or leaving, and that this turnover is caused by simple interactions between the cells known as “contact following locomotion”.

Contact following locomotion has been also reported in mammalian cells so the findings of Hayakawa et al. may aid research into how animals develop and how errors in cell migration may lead to diseases. Further studies are required to find out whether other cells showing contact following locomotion also travel in a band.

Introduction

The collective migration of eukaryotic cells plays crucial roles in processes such as wound healing, tumor progression, and morphogenesis, and has been the focus of extensive study (Haeger et al., 2015). The collective effects are typically associated with cell–cell interactions, such as long-range interaction mediated by secreted chemicals or short-range stable cohesive interaction mediated by adhesion molecules. However, the study of self-propelled particles in physics has revealed that motile elements which lack such activities may nonetheless give rise to dynamic collective motion, such as a traveling band (Chaté et al., 2008; Ginelli et al., 2010; Ohta and Yamanaka, 2014; Solon et al., 2015), mediated by a relatively simple transient short-range interaction, such as alignment interaction (Marchetti et al., 2013; Vicsek et al., 1995; Vicsek and Zafeiris, 2012). The emergence of such collective motions of self-propelled particles, such as formations of clusters and traveling bands, has been observed in a wide variety of systems, ranging from animal flocks (Ballerini et al., 2008), bacteria swarms (Wioland et al., 2013; Zhang et al., 2010), and cell assemblies (Szabó et al., 2006) to biopolymers and molecular motors (Butt et al., 2010; Schaller et al., 2010; Sumino et al., 2012). For cell assemblies of eukaryotic cells, higher order organized movements have been also reported for migrating cells confined in circular micropatterns (Doxzen et al., 2013; Segerer et al., 2015; Wan et al., 2011) or spheroids (Chin et al., 2018). For some of these systems, the connection between a macroscopic collective behavior and the microscopic dynamics of its constituents has been established. For the traveling band formation of biopolymers and molecular motors, local physical interactions among constituent elements effectively works as an alignment interaction, which induce the collective motion (Schaller et al., 2010; Sumino et al., 2012; Suzuki et al., 2015). In the case of eukaryotic cells, however, the connection between macroscopic traveling band formation (Kuwayama and Ishida, 2013) and microscopic short-range cell–cell interactions remains unclear. In particular, quantitative characterization of the traveling band formation and genetic analysis to reveal responsible cell-cell interaction have not been performed yet.

The social amoeba Dictyostelium discoideum is a model organism for the study of collective cell migration. The coordinated movement of cell population is achieved by individual chemotactic motion to the cAMP gradient, which is formed in a self-organized way. However, a mutant cell that lacks chemotactic activity to cAMP still exhibits an organized coordinated motion that is probably mediated by cell-cell contacts (Kuwayama and Ishida, 2013). Here, we demonstrate that this coordinated motion is a spontaneous polar order formation which phase-separates with a disordered background. We further show that this polar order formation is attributable to the tail-following behavior among the migrating cells, called contact following locomotion (CFL). We find that the polar ordered phase caused by CFL has an internal structure. An agent-based model with CFL further reveals that this internal structure is characteristic of the CFL-induced polar order formation. Thus, we establish the link between the collective behavior and the cell-cell interactions. Our findings open new possibilities that the concept of self-propelled particles contributes to the understanding of a highly orchestrated biological event of migrating cells in multicellular systems.

Results

Traveling band formation of non-chemotactic Dictyostelium cells

In the present study, we investigated collective cellular motion in a mutant strain of Dictyostelium discoideum, known as “KI cell,” which lacks all chemotactic activity (Kuwayama and Ishida, 2013; Kuwayama et al., 1993), and thus does not form a cell aggregate under starvation conditions. Wildtype Dictyostelium discoideum forms an aggregate as a result of chemotaxis mediated by a self-secreted extracellular chemoattractant. Under starvation conditions, KI cells spread on a non-nutrient agar plate show a segregation of cell density, which propagates as bands in around six hours (Kuwayama and Ishida, 2013), when the cell density is within a particular range (1.0×105 cells cm-2 to 4.0×105 cells cm-2) (Video 1). Initially, the traveling bands propagate in random directions with high orientational persistence. When two bands collide, they appear to pass through each other, retaining their shapes (Figure 1a left) (Kuwayama and Ishida, 2013). However, over time, the propagation directions gradually become aligned, probably due to weak reorientation of propagation direction as an effect of collisions. Finally, the bands are arranged almost periodically in space with a spatial interval of about 1 mm (Figure 1a right, b).

Figure 1 with 1 supplement see all
Segregation of cell density and formation of bands in non-chemotactic D. discoideum KI cell.

(a) The density profile of three time points with a time interval of 15 min indicated by color-coding (red t = 0 min, green 15 min, blue 30 min). Brighter color indicates higher density. Five (left) and 25 (right) hours after incubation. See also Video 1. (b) The intensity profile along the line indicated in (a), showing a periodic distribution of high-density regions. The inset shows a power spectrum of the intensity profile, indicating that the spatial interval was about 1 mm. (c) Time evolution of phase-contrast image of high-density region (dotted lines) at t = 2110, 3150, 4200 s, respectively. The time points correspond to that in Video 2. (d) High magnification images of low-density region (i) and high-density region (ii). Arrows indicate the migration directions of cells.

Video 1
Macroscopic observation of the propagating bands.

The video was taken every 15 min for 28.5 hr. Video acceleration: 11400 × real time.

To determine the mechanism underlying this collective cellular motion, we conducted high-magnification observations. At around 16 hours after cells were spread on an agar plate, a punched-out section of the agar plate was placed upside down on the glass slide, such that the monolayer of cells was sandwiched between agar and glass (Figure 1—figure supplement 1a). These cells formed a high-density area that moved as a band in low-density area for long periods of time with high orientational persistence (Figure 1c, d and Video 2). Whereas the cells in high-density area are packed without extra space, and thus the cell density is similar across different samples (Figure 1—figure supplement 1c), the size W of the band along the propagation direction showed a broad distribution, ranging from W=200 µm to 700 µm (N=10) (Figure 1—figure supplement 1b). In contrast, the traveling speed vb=0.5±0.03 µm/s (N=10) was consistent among different bands, independent of size W (Figure 1—figure supplement 1b).

Video 2
Microscopic observation of the propagating bands.

The video was taken every 15 s for 1.66 hr. Video acceleration: 230 × real time.

Analysis of single cell trajectories

To study the relationship between these collective behaviors and the migration of individual cells, we next performed cell-tracking analysis. Cellular movements were recorded by tracing the motion of fluorescent microbeads that were incorporated into the cells by phagocytosis. Figure 2a shows typical trajectories of individual KI cells. The distribution of migration speeds indicates that cell migration speed inside the band is slightly faster than that outside the band (Figure 2b). The average migration speeds of individual cells inside and outside the band were vin=0.38±0.14 μm s-1 and vout=0.30±0.16 μm s-1, respectively. The migration direction of the cells inside the band was distributed around the direction of band propagation (176.2 degrees, Figure 2c), although the fluctuation around the average direction is relatively large (standard deviation was 42.7 degrees). In contrast, the migration direction outside the band was distributed almost uniformly (Figure 2c). The mean squared displacement (MSD) inside the band was proportional to t2 for more than 103 s (Figure 2d). In contrast, the MSD outside the band exhibited a transition at around 100 s. from a persistent motion proportional to t2, to a random motion proportional to t, which indicates that this motion can be described as a persistent random motion with no preferred direction (Figure 2d). This observed directional randomness reflects the effects of cellular collisions, as well as its intrinsic nature of single cells. In sum, cells inside the band exhibit directionally persistent motions, whereas cells outside move randomly.

Analysis of single cell migrations inside and outside the band.

(a) Trajectories of single cells inside (red) and outside (black) the band taken every 15 s. These trajectories were taken from the data shown in Figure 1c. (b,c) The distributions of the migration speed (b) and migration direction (c) inside (pink) and outside (blue) the band shown in Figure 1c. The number of trajectories analyzed is N=35. In Figure 1c, the average of migration direction inside the band (pink) was 176.2 degrees and the standard deviation was 42.7 degrees. (d) Mean squared displacement (MSD) of cell motions inside the band (red), before entering the band (green) and after leaving the band (blue) (e) Scatter plot of the band speed vw against the cell speed vin within the band. The number of bands investigated is N=10. Trajectory data and traveling band position are available in Figure 2—source datas 1 and 2. Source data for (e) is available in Figure 1—source data 1. (f) Spatiotemporal plot of trajectories shown in a. The x coordinates of trajectories (horizontal axis) are plotted against time (vertical axis). The front and back of traveling band are shown by dotted lines.

Propagation of cell density profile

We then compared the average cell speed inside the band vin and the band propagation speed vb, (Figure 2e), and found that the band propagates faster than the cell migration speed for all samples investigated. This implies turnover of cells in the band, and that the band is continuously assembled at the front of the band and disassembled at the back. Thus, it is the cell density profile that shows propagation as a band (Kuwayama and Ishida, 2013). Such turnover of cells is also evident from the individual trajectories shown in Figure 2a and f, where the trajectories started in a low-density region entered a band (high-density region) at its front, and then left the band from its back.

Analysis of multicellular movement reveals polar order formation

To quantitatively characterize the multicellular movement, we introduce the local polar order parameter, φn,t=vit/vitin, obtained from the instantaneous cell velocity vi(t), where n is the nth domain along the direction of band propagation (see Materials and methods). In the high-density region that propagates as a band, φn,t reaches around 0.8, while φn,t in the low-density area remained below 0.4 (Figure 3a). Thus, the high-density region is polar-ordered phase, which propagates in the low-density disordered phase. The polar order parameter of the band showed intersample variability, and was distributed from 0.6 to 0.85 (Figure 3b). We found that the order parameter of band was positively correlated with the width of band W  (Figure 3b).

Figure 3 with 4 supplements see all
Analysis of heterogeneity within the ordered phase.

(a) Spatial profile of the local polar order parameter (solid lines) and the number of beads in the intervals (dotted lines) in Figure 1c. (b) Scatter plot of band width against polar order parameter within the band region. The number of bands studied is N=10. (c) Optical flow images in the front region of a band t=405 (top) and within the band t=1083 (bottom). See also Video 3. (d) Kymograph of the optical flow image along the line PQ shown in (c) (top). The arrows indicate the average velocity of band vb and the average cell speed vin. (e) Size-dependent squared local order parameter plotted against the area S for the data shown in (c). (f) Probability distribution function (pdf) of the migration direction within the band region obtained by averaging the pdfs of the sequential 150 frames in Video 3. The pdfs (i)-(iv) are obtained in the regions (i)-(iv) in (c) (bottom), respectively. Average pdf is shown by the black line (the mean is 178.1 degrees and the standard deviation is 31.2 degrees). (g) Snapshot of simulation result showing a polar ordered phase as a propagating band in the background of disordered phase. The color code indicates the migration direction of individual particle as shown in (c). See also Video 8. (h) Magnification of squared area shown in g. The size of area (20x20) is comparable to the whole area shown in (c). Each arrow indicates the direction of polarity. (i) Probability distribution function of the migration direction within the band region in the simulation (red, green and blue lines). For the choice of ROI, see Materials and methods. Average pdf is shown by the black line. Source data for (b) is available in Figure 1—source data 1.

Internal structure in the polar ordered region

The polar order phase is not completely homogeneous with respect to migration direction, but exhibits heterogeneity; this is related to the underlying assembly mechanism. This heterogeneity can be visualized in the velocity field obtained by optical flow, in which the direction of cell migration can be distinguished by color (Figure 3c and Video 3). The size-dependent squared local order parameter φl2(s) (see Materials and methods) shows a logarithmic decay with area S (Figure 3e), indicating that this heterogeneity is not spatially uncorrelated. Within the band (Figure 3c bottom), the migration direction was widely distributed from about 145 to 210 degrees (a black line in Figure 3f; the mean is 178.1 degrees and the standard deviation is 31.2 degrees). The probability density functions (pdf) of the migration direction obtained for the four regions (Figure 3c bottom (i–iv)) show peaks at different directions (Figure 3f), indicating the presence of two subpopulations; one in which the migration direction is ~160 degrees (regions (ii) and (iv)) and another in which it is ~190 degrees (regions (i) and (iii)). These two subpopulations are also recognized in Figure 3c (bottom) as the regions with dark blue and light green colors, respectively, forming stripes. These two types of stripes extend perpendicular to the direction of band propagation, and are alternately arranged. The typical width of the stripe was around 125 μm, as determined by the analysis of autocorrelation function (Figure 3—figure supplement 1a). The kymograph in Figure 3d shows the temporal evolution of the velocity field along the line PQ in Figure 3c, indicating that the stripes (light green and dark blue) are almost immobile, suggesting that the same cells experience the two stripes sequentially. In a reference frame co-moving with the band, cells move from the front to the end, since the speed of traveling band is faster than the speed of cells (Figure 2e, see also Figure 3—figure supplement 1b). During this relative motion of cells from the front to the end of a band, they move downward in a stripe, and then enter the next stripe moving upward direction (Figure 3—figure supplement 1b).

Video 3
Propagating band with overlaying the coloring based on the optical flow analysis.

The video was taken every 3 s for 39.5 min. Video acceleration: 151 × real time.

We also tested if the similar behavior can be seen in the single cell trajectories analyzed in Figure 2. As shown in Figure 3—figure supplement 4, although the density of tracked cell is quite sparse, we found that the migration directions indicated by colors also exhibit heterogeneity with light green and dark blue (Figure 3—figure supplement 4a). The temporal average of migration direction at a given x position indicates that the direction is distributed from about 150 to 210 degrees (Figure 3—figure supplement 4b), which is consistent with the optical flow analysis (Figure 3f). Furthermore, the trajectories move through regions with different colors, implying that cells change their migration direction following the flow direction in the regions (Figure 3—figure supplement 4a). From the trajectories used in Figure 3—figure supplement 4a, the cell migration speed in the x-direction was 0.28±0.09 μm/s , while the width of stripes was estimated to be around 50 to 100 μm. Thus, the time scale that cells pass across a stripe is about 200-400 s, if the stripe is almost immobile as we have shown above. The time interval that cells travel across the traveling band is obtained as 1120 s. Thus, cells pass several different stripes during the time interval that cells stay in the traveling band. These analyses illustrate that the polar order phase possesses an internal structure with respect to the migration direction.

Contact following locomotion is the cell-cell interaction that induces polar pattern formation

The formation of a polar-ordered phase with an internal structure is ultimately related to the microscopic interactions between individual cells, which are short-ranged. In the low-density region, cells are not completely isolated, but rather are often associated with each other, migrating in single files (Figure 4a and Video 4). This tail-following behavior has been described for wild-type Dictyostelium cells within aggregation streams (Dormann et al., 2002). We call this behavior 'contact following locomotion' (CFL). In low-density assay, when two cells collide, they either form CFL (Figure 4b and Video 5) or not (Figure 4—figure supplement 1a). To quantitatively characterize CFL, we measured the duration of cell–cell contact after two cells collide. During the formation of CFL, the typical cell-to-cell distance is given by da=24 μm. We measured the time interval during which the distance is less than da from the time series of the distance between two cells (Figure 4—figure supplement 1b). As shown in Figure 4c, in half of the cases, cell–cell contact persists for more than 300 s. To determine whether cells that form contacts for >300 s exhibit CFL or side-by-side behavior, we measured the average angle a of the angles a1 and a2, which are the angles of the velocity vectors v1 and v2 with respect to the vector connecting the two cell centers d, respectively (Figure 4d). In almost 60% of all cases, the angle a is 0–30 degrees (Figure 4e) that corresponds to CFL.

Figure 4 with 1 supplement see all
Contact following locomotion responsible for band propagation.

(a) Snapshot of the contact following locomotion. See also Video 4. (b) Representative time evolution of collision of two cells. Colored arrows represent the same cell. See also Video 5. (c) Histogram of the duration of two cell contacts for KI cell (control). (d) Schematic of angle a1 (a2), which is the angle of the velocity vector v1 (v2) with respect to the vector d connecting two cell centers. Then, the angle a is obtained as the angular average of a1 and a2, that is Acosa=cosa1+cosa2/2,Asina=sina1+sina2/2. (e) Histogram of the angle a for the KI cells that contact each other for >300 s. (f) Histogram of the duration of two cell contacts for the tgrb1 null mutant. Source data for (c) and (f) are available in Figure 4—source datas 1 and 2.

Video 4
Migration of the KI cells in the low-density region.

The video was taken every 15 s for 2 hr. Video acceleration: 378 × real time.

Video 5
A binary collision of the KI cells in the low-density assay.

The video was cropped from the video of the low-density assay with a length of 10.25 min. Video acceleration: 153 × real time.

To determine whether CFL is responsible for the collective behavior of KI cells, we sought a mutant cell that lacks CFL activity. A knockout mutant that fails to express the cell–cell adhesion molecule TgrB1 exhibits reduced CFL activity (Fujimori et al., 2019). TgrB1 is known to mediate cell–cell adhesion via a heterophilic interaction with its partner TgrC1 (Hirose et al., 2011; Hirose et al., 2015; Li et al., 2015; Fujimori et al., 2019). We first assessed whether the tgrB1 null mutant forms propagating bands. As in the control case, under starvation conditions, we spread the tgrB1 null mutant cells on a non-nutrient agar plate at a cell density of 2.0 to 3.0×105 cells cm-2 (see Materials and methods). However, neither segregation of cell density nor propagating bands appeared (Videos 6 and 7).

Video 6
Macroscopic observation of the population of tgrb1 null mutant.

The video was taken every 15 min for 28.5 hr. Video acceleration: 11400 × real time.

Video 7
Microscopic observation of the population of tgrb1 null mutant.

The video was taken every 15 s for 1.25 hr. Video acceleration: 225 × real time.

We then quantitatively characterized the formation of cell–cell contacts. We found that in 80% of all cases, cell–cell contact is disrupted before 300 s (Figure 4f), and that only 10% of cells established CFL (Figure 4—figure supplement 1d). In particular, in half of all cases, the cell–cell distance becomes larger than da in 120 s, indicating that these cells failed to establish cell–cell contact. Thus, our analyses illustrate that in the tgrb1 null mutant, CFL is nearly absent. Since TgrB1 is a protein that can mediate cell-cell adhesion as well as contact-dependent signaling, it is reasonable that the tgrB1 null mutant cell does not show CFL. This analysis suggests that the reduced ability to perform CFL can be linked to the defect of tgrB1 mutant in the formation of traveling band formation, although we cannot exclude other effect that could explain the phenotype of this mutant. For instance, if there are some changes in the locomotive activity of individual cell due to the mutation of tgrB1, it could also affect the formation of traveling band. Thus, we next compared the locomotive activities between control cells and tgrB1 null mutants. The velocity auto-correlation functions C(Δt) of the isolated single cells showed similar behaviors (Figure 4—figure supplement 1c), indicating that locomotive activities were comparable between KI cells and the tgrB1 null mutant cells. The above analyses suggest that the difference in the cellular scale behavior between control KI cell and tgrb1 mutant cell is the ability of CFL, and we thus conclude that CFL is essential for the segregation of cell density and the formation of propagating bands.

Mathematical modeling of polar pattern formation driven by contact following locomotion

The collective motion of KI cells induced by the CFL interaction can be modeled by an agent-based simulation (Hiraiwa, 2019). In the model, particle i at position ri  self-propels at a constant velocity v0 in the direction of its own polarity qi subjected to white Gaussian noise. Thus, without interactions, the particles exhibit a persistent random walk (Hiraiwa et al., 2014). The effect of CFL is introduced so that polarity qi orients to the location of the adjacent particle j, when particle i is located at the tail of particle j (parameterized by ζ). In addition to this effect, the particles interact with each other through volume exclusion interaction, adhesion, and the effect of polarity qi orienting toward the direction of its velocity vi=dri/dt (parameterized by α). For a fixed parameter set (α=0.4; see Materials and methods), without CFL (ζ=0), the collective behaviors did not form (Figure 3—figure supplement 2). In contrast, with CFL (ζ0.1), a polar-ordered phase appeared as a propagating band in the background of disordered phase (Figure 3g and Video 8). The speeds of the traveling band and particles within the band were 0.96 and 0.9, respectively, relative to the speed of isolated particles, indicating that the band is dynamic with assembly in the front and disassembly in the tail, consistent with our experimental results. From the spatial pattern shown in Figure 3gh, in which the migration direction is indicated by color code, heterogeneity in the migration direction is recognized within the polar-ordered phase. In the simulation, we studied the pdf of migration direction in regions, whose size is comparable to that in Figure 3c ((i)–(iv)), and found that the pdf exhibited peaks at different directions (Figure 3i), similar to our experimental results (Figure 3f). To determine whether this formation of internal structure is a characteristic of propagating bands induced by CFL, we studied a propagating band formed by increasing alignment effect α without CFL (ζ=0), and found that the pdfs of migration direction exhibit peaks at closely similar positions, indicating that the migration direction in the ordered phase is more homogeneous (Figure 3—figure supplement 3). Thus, the formation of internal structure appears to be a characteristic of the collective behavior induced by CFL. The size-dependent squared local order parameter φl2(s) (see Materials and methods) also shows the characteristic decay with a logarithmic dependence on area S (Figure 3e), as observed experimentally.

Video 8
Propagating band formation generated in the agent-based simulation.

The color code indicates the migration direction of individual particle as shown in Figure 3c. Arrows indicate the direction of polarity.

Discussion

In this study, we report that a mutant of Dictyostelium cell that lacks all chemotactic activity exhibits spontaneous segregation into polar ordered solitary band (Kuwayama and Ishida, 2013). This pattern formation is attributable to the cell-cell interaction called contact following locomotion (CFL) (Figure 4). The agent-based model that includes CFL reproduces the observed macroscopic behaviors (Figure 3g). Thus, we establish a link between the microscopic cell-cell interactions and the macroscopic polar pattern formation.

We showed that the width of band is distributed widely from W=200 µm to 700 µm (Figure 1—figure supplement 1b), and found the positive correlation between the width and the order parameter within the band (Figure 3b). The local cell density within the band is similar across different samples (Figure 1—figure supplement 1c), suggesting that the local cell density may not be a relevant factor for the increase in the order parameter. We speculate that if the correlation in the migration direction is gradually decorrelated from the front to the end of the band, bands with lower order parameters will be more prone to larger decorrelation in the migration direction. Consequently, we expect that the stronger the polar order, the wider the band width W.

One characteristic behavior of the present polar pattern formation is the formation of internal structure, which consists of subpopulations with transversal motions (Figure 3c, d, f. From the numerical simulation result, this formation of subpopulation was not seen in the model without CFL (Figure 3—figure supplement 3d, e). Thus, the internal structure is a characteristic of CFL induced polar pattern formation. A population of cells enters the band at its front with directional alignment induced by CFL in random direction. During the relative movement of these cells from the front to the end of band, the migration direction may not be dampened completely to the direction of band propagation probably due to the directional persistence induced by CFL. In this way, subpopulations with respect to the migration direction are formed when CFL is present. A full analysis of this mechanism remains to be a future topic.

In this paper, we mainly focused on the behavior of single solitary band. We studied the traveling band, which was well separated from other bands. Thus, all properties of single solitary band studied in this paper is independent of interaction between different bands. In some area, the traveling bands are arranged almost periodically in space with a spatial interval of about 1 mm (Figure 1b). How bands interact with each other to reach a periodic spacing and whether the interval is independent of band width W are to be investigated.

Wildtype Dictyostelium discoideum usually aggregates through chemotaxis to form a hemispherical mound with a central tip region that regulates the formation of slug-like multicellular structure (Williams, 2010). It has been suggested, however, that other mechanism also involves in the formation of aggregate, such as contact following (Dormann et al., 2002; Fujimori et al., 2019; Shaffer, 1962; Umeda and Inouye, 2002). In fact, whereas the KI cell alone does not form the multicellular structure, KI cells are able to spontaneously migrate to the central tip region transplanted from a wildtype slug and undergo normal morphogenesis and cell differentiation; this is not observed in mutant KI cells lacking TgrB1 (Kida et al., 2019), suggesting that TgrB1-dependent CFL without chemotaxis allows KI cells to spontaneously migrate in slug. Furthermore, in wildtype cells, the chemical guidance cue has been shown to cease during the multicellular phase, which suggests that an alternative mechanism induces collective cell migration in the multicellular body (Hashimura et al., 2019). We propose that polar order formation induced by CFL plays an important role in late-stage morphogenesis in this organism. Contact following locomotion, or chain migration, have been reported in other cell types (Li and Wang, 2018). The macroscopic behaviors reported in this paper may thus be found in other systems as well.

Materials and methods

Key resources table
Reagent type (species)
or resource
DesignationSource or referenceIdentifiersAdditional information
Cell line
(Dictyostelium discoideum)
KI-5National BioResource
Project Cellular
slime molds
NBRP ID: S00058Available in National
BioResource Project Cellular
slime molds
(https://nenkin.nbrp.jp)

Culture condition of KI mutant cells and cell density measurement

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1 mL of Klebsiella aerogenes suspended in 5LP medium (0.5% Lactose, 0.5% bactopeptone 211677, Optical density = 0.1) was spread on the 9 cm 5LP plate (0.5% Lactose, 0.5% bactopeptone 211677, 1.5% agar), 5LP medium dried, the non-chemotactic Dictyostelium discoideum, KI mutant cells were inoculated on the plate. The KI cells were incubated for about five days at 21°C. After cultivation, the KI cells and Klebsiella on the plate were collected with a phosphate buffer (PB). To remove the Klebsiella, the suspension was centrifuged and discard as much of the supernatant liquid as possible by aspiration, then clean PB was added. After repeating this process two times, the number of cells was counted using a hemacytometer.

Macroscopic observation of the traveling bands

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The washed KI cells were spread (cell density = 5.0 × 105 cells/cm2) on a 9 cm non-nutrient agar plate (1.5% agar) to cause starvation. After drying of the PB, the plate was scanned every 15 min using a film scanner (V850, EPSON). The brightness in scanner images is inversely correlated with cell density (Takeuchi et al., 2014). For Figure 1a and b, the original images were inverted with color that depends on time points.

Microscopic observation of the traveling bands

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The KI cells were spread (cell density = 2.0 to 3.0 × 105 cells/cm2) on the non-nutrient agar plate and incubated at 21°C for around 16 hr. A punched-out piece of the agar plate was placed upside down on the glass slide, and the travelling bands between the agar and glass was observed by phase contrast imaging. For Figures 1 and 2, 3a, b and 4, the images are taken every 15 s, using an inverted microscope (TiE, Nikon, Tokyo Japan) equipped with camera (iXon+, Andor Technology) and a 20x phase-contrast objective. For Figure 3c–f, the images are taken every 3 s, using an inverted microscope (TiE, Nikon, Tokyo Japan) equipped with camera (DS-Fi3, Nikon, Tokyo Japan) and a 20x phase-contrast objective.

Tracking analysis of individual KI cells

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For the tracking analysis shown in Figure 2 and Figure 3 and 1 μL of the PB including 3% fluorescent microbeads (ex:441, em:486, 1.0 μm, Polysciences, Inc) was spread at the same time with the KI cells. The trajectories of the microbeads were automatically tracked by using the ParticleTracker 2D, a plugin for Image J (National Institutes of Health, USA). To eliminate the trajectories of the microbeads that was not internalized by the KI cells, if |vcell| was slower than 0.25 μm/s for 300 s continuously, we excluded such trajectories.

For the analysis shown in Figure 2, we used the trajectories longer than 1 hr. The number of trajectories analyzed in Figure 2b–d was N = 35 with 2044 time points for the cells inside of the band and 9095 time points for the cells outside of the band. For Figure 2e, we performed the same experiment for 10 times. The numbers of trajectories that last for more than 1 hr in the 10 samples were N = 35, 19, 34, 12, 13, 17, 19, 16, 18, 7.

The mean squared displacement (MSD)

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The MSD (Figure 2d) was calculated using the formula below.

MSDt=1N(T-t)i=1NtT-t{rit+t-rit}2,

where Δt, T, and N means a time interval, final time, and number of the trajectory, respectively.

Polar order parameter

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To obtain the local polar order parameter φn,t shown in Figure 3a, the picture shown in Figure 1c was divided into n sections with width Δx (µm), and the order parameter was calculated in each section at each time from the trajectories obtained by the tracking analysis. The local order parameter φ is defined as

φn,t= 1N(n)i (n)vi(t)vi(t),

where n is the set of cells that satisfy (n-1)ΔxxinΔx,N(n) is number of the cells in ℒ(n), vi and xi are the velocity and x-position of i-th fluorescent microbeads, respectively. In this study, n = 14 and Δx = 119 µm.

To obtain the order parameter φ of the traveling band used in Figure 3b, we first obtained φ in the band region at each time step. Then, we took average it over all time steps.

Optical flow analysis

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Optical flow analysis was performed based on the Gunnar-Farneback method using OpenCV library. In the optical flow analysis, the displacement of each pixel in the original pictures are characterized by coloring based on the HSV (‘hue’, ‘saturation’, ‘value’) representation. The ‘hue’ varies depending on angular variation of each pixel. In this study, a ‘saturation’ and ‘value’ of the processed images via optical flow was fixed to 150 and 255, respectively. The sequential images of the traveling band used for this analysis were taken every 3 s.

Size-dependent squared local order parameter

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To characterize the internal structures of the traveling band, the size-dependent squared local order parameter φl2S is introduced (Figure 3e). To obtain the size-dependent squared local order parameter, we first calculate the squared polar order parameter φl2S within a ROI of size S , which is defined as

φl2(S)=1S2x,yROIcosΘx,y2+x,yROIsinΘx,y2

where Θx,y=hue×(360/255) indicates the angular variation of the pixel at position (x,y). The value of hue was obtained from the optical flow analysis (Figure 3c). Then, φl2S is averaged over the entire area to obtain φl2S. If Θx,y is a random number without spatial correlation, as the increase of the area S, φl2S is expected to decay in proportion to S-1.

The plot of the temporal average of the migrating direction in the band

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Firstly, we divided the x-t plane into the lattice with the interval of 20 µm (for x axis) and 60 s (for t axis). We then collect trajectories that pass through each lattice. In each lattice, the angle of migration direction was averaged. The obtained average angle in each lattice is shown with the color indicated in the color bar. Then, the traveling band region in x-t plane was divided as shown in Figure 3—figure supplement 4b right. The temporal average of migration direction was taken at a given x position, which was plotted in Figure 3—figure supplement 4b left.

Autocorrelation function of transverse motion with respect to the band propagation direction

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Because the band show propagation in x-direction, autocorrelation function of transverse motion Csin is defined using y-component of motion as

Csin(x)=1Y(X-x)y=1Yx=1X-xsinΘ(x,y)sinΘ(x+x,y),

where x is pixel interval along the x-axis. Csin was plotted after that unit of x is converted to the length.

Preparation of tgrB1 null mutant cells

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The gene disruption construct for tgrB1 was synthesized by a polymerase chain reaction (PCR)-dependent technique (Kuwayama, 2002). Briefly, the 5-flanking region of the construct was amplified with two primers, 5-CAACAGGTGGAGACTTCGGG-3 and 5- GTAATCATGGTCATAGCTGTTTCCTGCAGGCCAGCAGTAATAGTTGGAG-3. The 3-flanking region of the construct was amplified with primers, 5- CACTGGCCGTCGTTTTACAACGTCGACGAGAACTGTTGATTCTGATGG-3 and 5- CTTGGTCCTGAACGAACTCC-3. The bsr cassette in the multicloning site of pUCBsr Bam (Adachi et al., 1994) was amplified using the primer pair 5-CTGCAGGAAACAGCTATGACCATGATTAC-3 and 5-GTCGACGTTGTAAAACGACGGCCAGTG-3, both of which are complementary to the two underlined regions, respectively. The three amplified fragments were subjected to fusion PCR that produced the required gene-targeting construct. The gene-targeting constructs were cloned using a TOPO TA cloning kit for sequencing (ThermoFisher Scintific MA, USA). The linear construct was amplified by PCR using the outermost primers up to 10 µg and transformed into KI-5 cells. The KO clones were selected by genomic PCR using the outermost primers. tgrB1 KO KI-5 cell (NBRP ID: S90519) is available in National BioResource Project Cellular slime molds (https://nenkin.nbrp.jp).

Culture condition and starvation treatment of tgrb1 mutant null cells

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The tgrb1 null cells were cultured in HL5 medium (1.43% Proteose Peptone 211684, 0.72% Yeast Extract212750, 1.43% Gulcose, 0.05% KH2PO4, 0.13% Na2HPO412H2O) at 21 degrees Celsius. After reaching confluent, cells on the bottom were peeled off and collected, then washed two times with a centrifuge and PB. Next, the tgrb1 null cells were transferred on the 1/3 SM plate (0.33% Gulcose, 0.33% bactopeptone 211677, 0.45% KH2PO4, 0.3% Na2HPO4, 1.5% agar) with Klebsiella suspension, and incubated for around two days at 21°C. After, through the wash and count, the tgrb1 null cells were spread on the non-nutrient agar plate, after which the plate was scanned every 15 min using the film scanner.

Characterization of the contact following locomotion

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The KI cells and tgrb1 null cells for the collision assay were scraped from the traveling bands and surface of the plate, respectively. The scraped cells were placed on the non-nutrient agar and sandwiched with the glass. After around one hour incubation at 21°C, binary collisions of two cells were observed by microscopy and recorded every 15 s. The motion of the cells was tracked manually using the Manual Tracking, a plugin of Image J. Here, collision was defined as the contact of pseudopods. We collected the data from three and four independent experiments for the KI cells and the tgrb1 null cells, respectively. The total numbers of collision events are 136 (KI cells), and 156 (tgrb1 null cells).

The velocity autocorrelation function

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Firstly, the migrations of the KI and tgrb1 null mutant cells were recorded every 20 s for 60 min. Here, to extract an intrinsic locomotive activity of the cells, interactions with other cells, wall, and etc. were eliminated. Using obtained trajectories of cells that migrate with the velocity v, the velocity autocorrelation function C(τ) was calculated. C(τ) is described with the form of

C(Δt)=1N(T-τ)i=1NtT-τ{vit+τ-vit}2,

where τ, t, T, and N means a time interval, time, final time, and number of the trajectory, respectively (Figure 4—figure supplement 1c).

Modeling collective motion induced by contact following locomotion

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The collective motion of KI cells induced by the CFL interaction can be modeled by an agent-based simulation. In the model, self-propelled particle i at position ri  moves at a constant velocity v0 in the direction of its own polarity qi subjected to white Gaussian noise. Thus, without interactions, the particles exhibit persistent random walk (Hiraiwa et al., 2014). Collective motion can be modeled by assuming particle-particle interactions (Hiraiwa, 2019). We firstly assume that the particles interact with each other through volume exclusion (parameterized by β) and adhesion (parameterized by γ). We also assume the feature that the polarity of each particle orients to the direction of its velocity vi=dri/dt (parameterized by α); it is known that this assumption can effectively give rise to the alignment interaction between the particles when it is combined with the volume exclusion effect (Li and Sun, 2014). (Therefore, we simply refer to this feature as alignment effect in the main text.) As the main focus of this article, we incorporate CFL into this model by assuming the particle-particle interaction by which polarity qi orients to the location of the adjacent particle j when particle i is located at the tail of particle j (parameterized by ζ). The equation of motion for the particle i are then given by

(1) dridt=v0qi|qi|βjN(i)Rrjri|rjri|2+γjN(i)rjri|rjri|
(2) dqidt=Iqi(1|qi|2)+Ci+αvi|vi|+ξi

where the second and third terms on the right-hand side of Equation 1 are the effects of volume exclusion and adhesions, respectively. Here, 𝒩(i) is a set of particles that are contacting with the particle i, that is the particle j𝒩(i) satisfies |rj-ri|R. On the right hand side of Equation 2, the first term shows the self-polrization, the third term gives the effect that the polarity orients to the velocity direction vi/|vi|, the last term is white Gaussian noise with ξi=(0,0) and ξi(t)ξj(t')=σ2δijδ(t-t'), and the second term Ci describes the CFL, parameterized by ζ, given by

(3) Ci=ζ2jN(i)rjri|rjri|(1+qi|qi|rjri|rjri|).

Here, when the polarity of particle j, qj, and the vector from particles i to j, rj-ri, are in the same orientation, the maximum following effect is exerted on particle i to the direction of particle j. Such a situation is expected when particle i is located in the tail of particle j with respect to the polarity qj. In contrast, when particle i is located in the front of particle j, Ci almost vanishes. The simulation is implemented within a square box of size L with periodic boundary condition. For all simulations, we used fixed parameter values except ζ and α, given by v0=1.0,β=1.0,R=1.0,γ=1.20, and σ2=0.4. For I in Equation 2, we consider the situation where I is infinitely large, so that q was projected onto the unit vector q=1 for the numerical simulation. The density of particles per unit area ρ is given ρ=1. The number of particles n is n=80,000 (Figure 3g-i and Figure 3—figure supplement 3) and n=10,000 (Figure 3—figure supplement 2).

Histogram of migration direction in the numerical results

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Firstly, we selected only the ROIs in the vicinity of the band front in the following way: We define a ROI as being within the bands if the particle density is higher than 1.16, which corresponds to the 2D dense packing fraction of disks, ~0.91. Using this definition, we define the ROI as being vicinity of the band front if the ROI is within the band at the last Fana frames whereas it is out of the band at the frames between the last Fana+Fwait+Fout and the last Fana+Fwait. In other words, Fana means the number of frames to be analyzed and must be within the band, Fout means the number of frames to determine the band front (i.e. the frames in which the ROI must be still out of the band assuming that the band travels only in one direction), and Fwait means the number of the waiting frames (i.e. the frames which are not used at all) between these frame sets.

The results of this algorithm for CFL-induced (ζ=0.1, α=0.4) and alignment-induced (ζ=0.0, α=1.0) bands are shown in Figure 3—figure supplement 3a and b, respectively. Here, we used the following sets of the parameters for our analysis in this article: Fana=55, which corresponds to the time window in the analysis of experimental data. Fwait=76, with around which the band front can propagate across one ROI. Fout=5, which has been empirically determined. The duration between each frame is dt=0.2 in the unit of time of our numerical simulation.

Secondly, using these near-front ROIs, we calculate the histograms of migration direction (dri(t)/dt)/|dri(t)/dt| for each ROI using all the Fana frames (t) and the particles (i) in it at each frame. Then, we plot only the histograms for the ROIs which have the top eight and nine peak probability densities for CFL-induced and alignment-induced bands, respectively. The results are plotted in Figure 3—figure supplement 3c and d, respectively. One can find the clear difference in these histograms between the CFL-induced and alignment-induced bands. The peak position and height for the CFL-induced band have large varieties, whereas those for alignment-induced band are less distributed. Furthermore, the peaks for the CFL-induced band are much higher than those for alignment-induced band. Figure 3i of the main text and Figure 3—figure supplement 3e plot three typical histograms from Figure 3—figure supplement 3c and d, respectively.

References

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Decision letter

  1. Tâm Mignot
    Reviewing Editor; CNRS-Aix Marseille University, France
  2. Aleksandra M Walczak
    Senior Editor; École Normale Supérieure, France
  3. Tâm Mignot
    Reviewer; CNRS-Aix Marseille University, France
  4. Sander Tans
    Reviewer; AMOLF, Netherlands

In the interests of transparency, eLife publishes the most substantive revision requests and the accompanying author responses.

Acceptance summary:

This manuscript describes a new form of non-chemotactic behavior in the form of multicellular wave propagation in a Dictyostelium community. Multiscale analyses including cell tracking and theory describe a mechanism whereby the waves consist of cellular spatial densities that form as single cells penetrate and leave them by a process termed Contact Following Locomotion. While the biological function of this process is yet unclear, the observations reveal how complex and dynamic cellular patterns can form following simple cell-cell interactions.

Decision letter after peer review:

Thank you for submitting your article "Polar pattern formation induced by contact following locomotion in a multicellular system" for consideration by eLife. Your article has been reviewed by two peer reviewers, including Tâm Mignot as the Reviewing Editor and Reviewer #1, and the evaluation has been overseen by Aleksandra Walczak as the Senior Editor. The following individual involved in review of your submission has agreed to reveal their identity: Sander Tans (Reviewer #2).

The reviewers have discussed the reviews with one another and the Reviewing Editor has drafted this decision to help you prepare a revised submission.

This paper by Shibata et al. explores an intriguing phenomenon of periodic wave formation in Dictyostelium discoideum. Using a strain that cannot perform chemotaxis the authors discover a yet undescribed phenomenon where the cells spatially assemble at the mesoscale into high density waves of varying width and persistent directed motion. As it grows over time, this phenomenon propagates until the bands become arranged periodically at the scale of the entire cell community. The authors explore the cellular basis and genetic basis of this phenomenon and come up with the compelling conclusion that the bands form as cell penetrate the band front and escape at the back. Contrarily to the lower density areas, the bands are marked by a high level of polar order resulting from aligned opposite cell flows that move transversal to the wave movement direction. Genetic basis and computational modeling convincingly reveal that a known phenomenon called contact following locomotion (CFL), in which a cell tends to follow another cell upon direct contact, explains the formation and the propagation of the waves. The resulting picture is quite elegant and suggests that a mechanism for wave formation: cells become trapped in specific motile conformations as they enter high polar order regions and escape as the polar order collapses.

The emergent higher-order organization and locomotion that the authors describe has a number of complex and intriguing features, such as the traversal movements of individual cells, that translate in a non-intuitive way to the population level. While complex, the system is still rather clean in the sense that they do not display chemotactic communication. Hence, they are suited for the quantitative active-matter approach chosen by the authors. The paper continues from earlier work in 2013 where the banding phenomenon was also studied, and now provide a highly quantitative analysis. As such, the work has direct value within the active matter community, while the biological relevance of the effects is less direct, though not absent.

Essential revisions:

1) Although the authors get close to nailing an intuitive explanation, they often fall short, which was a bit frustrating. It is not presently clear how single cell movements correlate with the migration direction observed as internal structures in the polar ordered region? The individual cell trajectories, difference in speeds, etc, ultimately 'implies' a critical cell turnover at the band (which is supported by the model), but this is not experimentally demonstrated nor intuitively visualized how this would be central. For example, in the subsection “Analysis of single cell trajectories”, it is mentioned that the cells direction is distributed around the direction of band propagation, but the stripes within the bands extend perpendicular to the direction of propagation. Do the cells that enter these structures follow these flows for sustained period or do they escape quickly mostly traversing the bands? Subsection “Internal structure in the polar ordered region”: the cells are proposed to move inward in one stripe and then downward in the other. This appears contradictory with the single cell trajectory described. Please clarify this picture providing quantifications that cement it would provide a nice example of how something very non-intuitive then becomes transparent.

2) The authors introduce the term Contact Following Locomotion, as if it is a major thing in the Abstract even, but CFL appears to be the same as the previously used term tail-following behavior/locomotion (e.g. subsection “Contact following locomotion is the cell-cell interaction that induces polar pattern formation”, first paragraph, where both are used almost interchangeably). Terminology should be conservative in the community to avoid confusions. Since the two are essentially the same, the same term should be used.

3) It is reasonable to suggest that the tgrB1 mutant fails to form waves because its ability to perform CFL is reduced. However due to possible pleiotropy of the tgrB1 mutation other indirect effects could explain why this mutant does not form the pattern. It is agreed that this result with tgrB1 is informative but it is not a definite genetic proof that CFL is responsible for band formation.

4) The authors noted another interesting observation, namely the transversal movement, which they do not aim to explain within the scope of this paper. At the very least, the authors should provide the best explanation they can.

5) Grammar, Abstract: paradigms do not induce. Also that phrase initially seemed logically wrong, with inhibition of locomotion leading to cells migrating away.

6) Introduction, first paragraph, there are other examples of eukaryotic systems in which contacts lead to higher order organized movement, while here the opposite is suggested. There was a study on migrating cells in circle shaped corrals, and also of rotations of various organoids.

7) Subsection “Internal structure in the polar ordered region”, penultimate sentence: please rephrase.

8) Do the simulations reproduce what is observed in Figure 4A?

9) Discussion, first sentence: novelty is suggested in that phrase but these findings were not demonstrated for the first time here.

10) Discussion, second paragraph: Is the notion that local cell density is not relevant supported by the model?

11) Discussion, third paragraph: 'not seen in the model without CFL'. Please refer to appropriate figure that backs this up. As a more general comment: please go through the paper, identify conclusions, and check if an additional reference to a figure would be helpful. There are other such occasions.

https://doi.org/10.7554/eLife.53609.sa1

Author response

Essential revisions:

1) Although the authors get close to nailing an intuitive explanation, they often fall short, which was a bit frustrating. It is not presently clear how single cell movements correlate with the migration direction observed as internal structures in the polar ordered region? The individual cell trajectories, difference in speeds, etc, ultimately 'implies' a critical cell turnover at the band (which is supported by the model), but this is not experimentally demonstrated nor intuitively visualized how this would be central.

To show the cell turnover more directly, we plot the cell trajectories in the x-t coordinate as shown in Figure 2F in the revised manuscript. The figure clearly indicates that cells enter the band at its front and leave the band at its back. This visualization suggests that what is propagating is the cell density profile rather than a group of particular cells, which is an essential property of this traveling band phenomenon.

For example, in the subsection “Analysis of single cell trajectories”, it is mentioned that the cells direction is distributed around the direction of band propagation, but the stripes within the bands extend perpendicular to the direction of propagation. Do the cells that enter these structures follow these flows for sustained period or do they escape quickly mostly traversing the bands? Subsection “Internal structure in the polar ordered region”: the cells are proposed to move inward in one stripe and then downward in the other. This appears contradictory with the single cell trajectory described. Please clarify this picture providing quantifications that cement it would provide a nice example of how something very non-intuitive then becomes transparent.

To clearly show how the analysis of single cell trajectories and the optical flow analysis are compatible, we first reevaluated the trajectories of individual cells used for the analysis shown in Figure 2, and found that the mean migration direction is 176.2 degrees and the standard deviation was 42.7 degrees (Figure 2C). From the optical flow analysis, we also plotted the distribution of migration direction in Figure 3F (black), where the mean and standard deviation of migration direction are 178 and 31 degrees, respectively. Thus, the standard deviations in the migration direction were comparable in these different analyses. These results consistently indicate that the cell migration direction within the traveling band shows a relatively large fluctuation. We also compared the histograms obtained from these two analyses, as shown in Author response image 1, indicating that the two histograms are quite similar to each other. We show the standard deviations in the migration direction in the two analyses in the revised manuscript.

Author response image 1

We next examine whether the internal structure found in the optical flow analysis shown in Figure 3C, D is also seen in the trajectories of individual cells. In Figure 3—figure supplement 4, which was newly added to the revised manuscript, the migration direction obtained from cell trajectories is indicated by color as a function of position x and time t. Cell trajectories are also shown by solid lines. The color-coded migration direction indicates the presence of heterogeneity with light green and dark blue regions, as in the case of Figure 3C, D. Each trajectory does not pass through the same color regions, but move through regions with different colors, implying that cells change their migration directions following the flow directions in the regions. The time interval that cells stay in a stripe structure can be quantitatively evaluated in Figure 3—figure supplement 4 in the revised manuscript. The cell migration speed in the x-direction was 0.28±0.09μm/s. Since the width of stripes was estimated to be around 50 to 100 μm (from the optical flow analysis the stripe width was estimate at 125 m as shown in Figure 3—figure supplement 1A), the time scale that cells pass across a stripe is about 200-400 s., if the stripe is almost immobile as we have shown in the main text. The time interval that cells travel across the traveling band is about 1120 s, in the case of Figure 3—figure supplement 1A. We therefore concluded that, while cells pass several different stripes during the time interval that cells stay in the traveling band, the cells stay in each stripe structure for sustained period of time. The analysis shown in Figure 3—figure supplement 4 and the optical flow analysis consistently indicate that there is an internal structure with respect to the migration direction within the traveling band region. We show this additional analysis in the revised manuscript.

2) The authors introduce the term Contact Following Locomotion, as if it is a major thing in the Abstract even, but CFL appears to be the same as the previously used term tail-following behavior/locomotion (e.g. subsection “Contact following locomotion is the cell-cell interaction that induces polar pattern formation”, first paragraph, where both are used almost interchangeably). Terminology should be conservative in the community to avoid confusions. Since the two are essentially the same, the same term should be used.

In the study of collective cell migration of Dictyostelium cells, “contact following” has been used to describe the property of the cells to follow the other cells in contact (Shaffer, 1962, Dormann et al., 2002, Umeda and Inouye, 2002, Fujimori et al., 2019). More recently, for the tail-following behavior found in a cultured mammalian epithelial cell, “contact following of locomotion (CFL)” have been proposed in (Li and Wang, 2018), since the behavior is similar to contact following of Dictyostelium cell. We decided to use “contact following locomotion (CFL)” following this recent work (Li and Wang, 2018) with minor modification for the grammatical issue. Because of these previous works, it would be appropriate to use “contact following locomotion (CFL)” in this paper. In the revised manuscript, we mention “contact following” in the study of Dictyostelium cells with references in Discussion.

3) It is reasonable to suggest that the tgrB1 mutant fails to form waves because its ability to perform CFL is reduced. However due to possible pleiotropy of the tgrB1 mutation other indirect effects could explain why this mutant does not form the pattern. It is agreed that this result with tgrB1 is informative but it is not a definite genetic proof that CFL is responsible for band formation.

We agree that several factors can affect the traveling band formation, such as cell-cell interactions, and locomotive activities of individual cells. As we have shown in the manuscript, the characteristic cell-cell interaction is the CFL, which is reduced in tgrB1 mutant. We also compare the locomotive activity between control and the mutant, and the velocity auto-correlation function exhibited a similar behavior. These analyses imply that the difference between KI cell and tgrB1 mutant cell is the ability of CFL. Therefore, CFL is a reasonable candidate of the cell-cell interaction that can explain the traveling band formation. Our mathematical model also supports this idea. Still, we cannot exclude other possibility that could explain the defect in the traveling band formation. We mention this point in the revised manuscript.

4) The authors noted another interesting observation, namely the transversal movement, which they do not aim to explain within the scope of this paper. At the very least, the authors should provide the best explanation they can.

Although the complete analysis remains to be a future problem, we try to provide an explanation on the mechanism of transversal movement. We added the following sentences in the Discussion section:

“A population of cells enters the band at its front with directional alignment induced by CFL in random direction. During the relative movement of these cells from the front to the end of band, the migration direction may not be dampened completely to the direction of band propagation probably due to the directional persistence due to CFL. In this way, subpopulations with respect to the migration direction are formed when CFL is present. A full analysis of this mechanism remains to be a future topic.”

5) Grammar, Abstract: paradigms do not induce. Also that phrase initially seemed logically wrong, with inhibition of locomotion leading to cells migrating away.

We improved the sentence to avoid the grammatical problem. Whereas it is intuitively unobvious if the contact inhibition of locomotion (CIL) generates collective cell migration, CIL has been seen in the collective cell migration of neural crest cells (Carmona-Fontaine et al., 2008). It has been also shown theoretically that a correlated migration of cells can be induced by CIL (Hiraiwa, 2019). Thus, the phrase is not logically wrong.

6) Introduction, first paragraph, there are other examples of eukaryotic systems in which contacts lead to higher order organized movement, while here the opposite is suggested. There was a study on migrating cells in circle shaped corrals, and also of rotations of various organoids.

According to the reviewers’ suggestion, we mention the studies on the organized motion on circular micropatterns and spheroids in the Introduction of the revised manuscript. However, as far as we know, there is no report that establishes the connection between traveling band formation of eukaryotic cells and the microscopic cell-cell interactions that induce the traveling band formation. We mention this point more clearly in the first paragraph of Introduction.

7) Subsection “Internal structure in the polar ordered region”, penultimate sentence: please rephrase.

We have rephrased the sentence in this line. In particular, we explain the reason of why the cell moves from the front to the end of band in a reference frame co-moving with the band. The reason is that the speed of traveling band is faster than the speed of cells. Then, the transversal motion is explained during the relative motion of cells within the traveling band.

8) Do the simulations reproduce what is observed in Figure 4A?

For the same parameter values shown in Figure 3G, H, we performed a simulation with low cell density, as shown in Author response image 2. Contact following locomotion (CFL) can be seen between two to four cells. However, we found that the life-time of CFL in the simulation was shorter than that in the experiments. This is an aspect that the model cannot reproduce and is considered a future issue.

Author response image 2

9) Discussion, first sentence: novelty is suggested in that phrase but these findings were not demonstrated for the first time here.

We now refer the previous work by one of the authors in this sentence.

10) Discussion, second paragraph: Is the notion that local cell density is not relevant supported by the model?

We found that the width of band and the order parameter within the band exhibited a positive correlation (Figure 3B). Because the order parameter is expected to increase with the cell density in general, one possibility for the correlation between the width and the order parameter could be that the cell density increases with the band width. However, our data indicates the local cell density within the band is similar across different samples with different width (Figure 1—figure supplement 1C), indicating that the above hypothesis does not hold.

In the model, we changed the values of several parameters, such as the effect of CFL ζ, alignment effect α, and the cell density ρ of entire area. For these simulations, the cell density within the traveling band was almost constant (Author response image 3), supporting our experimental observation.

Author response image 3

In the simulations, the width of band depended on some parameters such as the strength of alignment effect α (Figure 3—figure supplement 2).Nevertheless, we should also note that the system size in our simulation may not be sufficiently large to see the change in the width of band systematically. It has been reported that, for the well-studied simple model of a motile element system, the polar order region is split into multiple sequential bands without much change in the band width as long as the system size is large enough (Solon et al., 2015). Thus, the system size may strongly affect the band width. Due to this complexity, it is difficult to strongly conclude that in our simulation the cell density is constant for bands with different width.

In addition to this, so far, we have not found a reason of why the band width shows such variation in the experiment and how it is correlated with the order parameter. In this respect, it is difficult for the simulation to reproduce the correlation between band width and the order parameter, and thus to test if the density is constant for different band width in the simulation.

11) Discussion, third paragraph: 'not seen in the model without CFL'. Please refer to appropriate figure that backs this up. As a more general comment: please go through the paper, identify conclusions, and check if an additional reference to a figure would be helpful. There are other such occasions.

We have added references to figures to the sentences throughout the paper.

https://doi.org/10.7554/eLife.53609.sa2

Article and author information

Author details

  1. Masayuki Hayakawa

    Laboratory for Physical Biology, RIKEN Center for Biosystems Dynamics Research, Kobe, Japan
    Contribution
    Conceptualization, Data curation, Formal analysis, Validation, Investigation, Methodology, Writing - original draft, Writing - review and editing
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0002-9245-9593
  2. Tetsuya Hiraiwa

    1. Mechanobiology Institute, National University of Singapore, Singapore, Singapore
    2. Universal Biology Institute, University of Tokyo, Tokyo, Japan
    Contribution
    Formal analysis, Funding acquisition, Investigation, Methodology, Writing - original draft, Writing - review and editing, Designed and performed the simulation
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0003-3221-345X
  3. Yuko Wada

    Laboratory for Physical Biology, RIKEN Center for Biosystems Dynamics Research, Kobe, Japan
    Contribution
    Investigation
    Competing interests
    No competing interests declared
  4. Hidekazu Kuwayama

    Faculty of Life and Environmental Sciences, University of Tsukuba, Tennodai, Ibaraki, Japan
    Contribution
    Resources, Supervision, Funding acquisition, Writing - original draft, Writing - review and editing
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0002-4362-0790
  5. Tatsuo Shibata

    Laboratory for Physical Biology, RIKEN Center for Biosystems Dynamics Research, Kobe, Japan
    Contribution
    Conceptualization, Data curation, Formal analysis, Supervision, Funding acquisition, Validation, Investigation, Methodology, Writing - original draft, Project administration, Writing - review and editing
    For correspondence
    tatsuo.shibata@riken.jp
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0002-9294-9998

Funding

Japan Society for the Promotion of Science (JP17J05667)

  • Masayuki Hayakawa

Japan Society for the Promotion of Science (JP16K17777)

  • Tetsuya Hiraiwa

Japan Society for the Promotion of Science (JP19K03764)

  • Tetsuya Hiraiwa

Japan Society for the Promotion of Science (JP26610129)

  • Hidekazu Kuwayama

RIKEN

  • Tatsuo Shibata

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

Acknowledgements

We are grateful to M Tarama, T Yamamoto and D Sipp for critical reading of this manuscript, and all member of Laboratory for Physical Biology for discussion. This work was supported by JSPS KAKENHI Grant Numbers JP17J05667 (to MH); JP16K17777 and JP19K03764 (to TH); and JP26610129 (to HK).

Senior Editor

  1. Aleksandra M Walczak, École Normale Supérieure, France

Reviewing Editor

  1. Tâm Mignot, CNRS-Aix Marseille University, France

Reviewers

  1. Tâm Mignot, CNRS-Aix Marseille University, France
  2. Sander Tans, AMOLF, Netherlands

Publication history

  1. Received: November 14, 2019
  2. Accepted: April 15, 2020
  3. Accepted Manuscript published: April 30, 2020 (version 1)
  4. Version of Record published: May 11, 2020 (version 2)
  5. Version of Record updated: May 14, 2020 (version 3)

Copyright

© 2020, Hayakawa et al.

This article is distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use and redistribution provided that the original author and source are credited.

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