RESEARCH ARTICLE

Polar pattern formation induced bycontact following locomotion in a
multicellular system
Masayuki Hayakawa1, Tetsuya Hiraiwa2,3, Yuko Wada1, Hidekazu Kuwayama4,
Tatsuo Shibata1*
1

Laboratory for Physical Biology, RIKEN Center for Biosystems Dynamics Research,
Kobe, Japan; 2Mechanobiology Institute, National University of Singapore,
Singapore, Singapore; 3Universal Biology Institute, University of Tokyo, Tokyo,
Japan; 4Faculty of Life and Environmental Sciences, University of Tsukuba,
Tennodai, Ibaraki, Japan

Abstract Biophysical mechanisms underlying collective cell migration of eukaryotic cells havebeen studied extensively in recent years. One mechanism that induces cells to correlate theirmotions 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 polarorder 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.

*For correspondence:tatsuo.shibata@riken.jp
Competing interests: The
authors declare that nocompeting interests exist.
Funding: See page 16
Received: 14 November 2019
Accepted: 15 April 2020
Published: 30 April 2020
Reviewing editor: Tâm Mignot,
CNRS-Aix Marseille University,
FranceCopyright Hayakawa et al. This
article is distributed under theterms of the Creative Commons
Attribution License, which
permits unrestricted use andredistribution provided that theoriginal author and source arecredited.

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 byadhesion 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 andtraveling 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 thetraveling band formation of biopolymers and molecular motors, local physical interactions among

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eLife digest The cells of animals and many other living things are able to migrate together ingroups. 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 commonlyused 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 thiscollective behavior works.
Hayakawa et al. have now combined genetics, cell biology and computational approaches tostudy how groups of the mutant Dicty cells migrate together. The experiments showed that thetraveling band is dynamically maintained by cells joining or leaving, and that this turnover is causedby simple interactions between the cells known as “contact following locomotion”.
Contact following locomotion has been also reported in mammalian cells so the findings ofHayakawa 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.

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 cellcell 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 thatlacks 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 thiscoordinated motion is a spontaneous polar orderformation which phase-separates with a disordered background. We further show that thispolar order formation is attributable to the tailfollowing 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 modelwith CFL further reveals that this internal structure is characteristic of the CFL-induced polarorder formation. Thus, we establish the link
between the collective behavior and the cell-cellinteractions. Our findings open new possibilities
that the concept of self-propelled particles contributes to the understanding of a highly orchesVideo 1. Macroscopic observation of the propagating
trated biological event of migrating cells inbands. The video was taken every 15 min for 28.5 hr.
multicellular systems.
Video acceleration: 11400  real time.

https://elifesciences.org/articles/53609#video1

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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 selfsecreted 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 passthrough 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 reorientationof propagation direction as an effect of collisions. Finally, the bands are arranged almost periodicallyin space with a spatial interval of about 1 mm (Figure 1a right, b).
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 ahigh-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 ¼ 200 mm to 700 mm (N=10) (Figure 1—figure supplement 1b). In contrast,
the traveling speed hvb i ¼ 0:5  0:03 mm/s (N=10) was consistent among different bands, independent of size W (Figure 1—figure supplement 1b).

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 motionof 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 ¼ 0:38  0:14 m s 1and vout ¼ 0:30  0:16 m 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 apersistent motion proportional to t 2 , to a random motion proportional to t, which indicates that thismotion 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.

Propagation of cell density profile

Video 2. Microscopic observation of the propagating
bands. The video was taken every 15 s for 1.66 hr.
Video acceleration: 230  real time.
https://elifesciences.org/articles/53609#video2

Hayakawa et al. eLife 2020;9:e53609. DOI: https://doi.org/10.7554/eLife.53609

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 inthe band, and that the band is continuously
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(a)

(b)
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ii
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100 µm

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i

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50 µm

50 µm

Figure 1. Segregation of cell density and formation of bands in non-chemotactic D. discoideum KI cell. (a) The density profile of three time points witha 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 phaseFigure 1 continued on next page

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Figure 1 continued
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) Highmagnification images of low-density region (i) and high-density region (ii). Arrows indicate the migration directions of cells.
The online version of this article includes the following source data and figure supplement(s) for figure 1:
Source data 1. Statistics of traveling bands.
Figure supplement 1. Experimental setup and properties of traveling band.

disassembled at the back. Thus, it is the cell density profile that shows propagation as aband (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 aband (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, ’ðn; t Þ ¼ hvi ðtÞ=jvi ðt Þjii2LðnÞ , obtained from the instantaneous cell velocity vi ðt Þ, where LðnÞ is thenth domain along the direction of band propagation (see Materials and methods). In the high-density region that propagates as a band, ’ðn; t Þ reaches around 0.8, while ’ðn; t Þ 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 parameterof band was positively correlated with the width of band W (Figure 3b).

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 canbe 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 orderparameter ’2l ðsÞ (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 m, 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 (lightgreen 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).
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 withlight 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

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300

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Front ofthe band0.3
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vin [μm/s]

End of the band

100
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500 1000 1500

x [μm]
Figure 2. 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 bandshown 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 theband (blue) (e) Scatter plot of the band speed vw against the cell speed hvin i within the band. The number ofbands investigated is N ¼ 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 shownin a. The x coordinates of trajectories (horizontal axis) are plotted against time (vertical axis). The front and back oftraveling band are shown by dotted lines.
The online version of this article includes the following source data for figure 2:
Source data 1. Trajectory data of 35 cells in the experiment shown in Figure 1c.
Source data 2. Front and end positions of band as functions of time in the experiment shown in Figure 1c.

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 m=s , while the width of stripes was estimated to be around
50 to 100 m. Thus, the time scale that cells pass across a stripe is about 200-400 s, if the stripe isalmost immobile as we have shown above. The time interval that cells travel across the travelingband is obtained as 1120 s. Thus, cells pass several different stripes during the time interval that cells

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(c)

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t = 2110 s

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Physics of Living Systems

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Figure 3. 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 ¼ 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 hvb i and the average cell
speed hvin i. (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.
The online version of this article includes the following figure supplement(s) for figure 3:
Figure supplement 1. Internal structure within a traveling band.
Figure supplement 2. Phase diagram of the agent-based simulation for changes of CFL a and the alignment effect z.
Figure supplement 3. Analyses of heterogeneityin the numerical simulations.
Figure supplement 4. Analysis of internal structure from individual cell trajectories.

stay in the traveling band. These analyses illustrate that the polar order phase possesses an internal
structure with respect to the migration direction.

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Contact following locomotion isthe cell-cell interaction that induces
polar pattern formation
The formation of a polar-ordered phase with aninternal structure is ultimately related to themicroscopic interactions between individual cells,
which are short-ranged. In the low-density region,
cells are not completely isolated, but rather areoften associated with each other, migrating insingle files (Figure 4a and Video 4). This tail-following behavior has been described for wild-type
Dictyostelium
cells
withinaggregation
streams (Dormann et al., 2002). We call thisVideo 3. Propagating band with overlaying the
behavior ’contact following locomotion’ (CFL). In
coloring based on the optical flow analysis. The video
low-density assay, when two cells collide, they
was taken every 3 s for 39.5 min. Video acceleration:either form CFL (Figure 4b and Video 5) or not
151  real time.
(Figure 4—figure supplement 1a). To quantitahttps://elifesciences.org/articles/53609#video3
tively characterize CFL, we measured the duration of cell–cell contact after two cells collide.
During the formation of CFL, the typical cell-tocell distance is given by da ¼ 24 m. We measured the time interval during which the distance is lessthan 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.
To determine whether CFL is responsible for the collective behavior of KI cells, we sought amutant 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, understarvation conditions, we spread the tgrB1 nullmutant cells on a non-nutrient agar plate at a celldensityof
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).
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, thecell–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 isreasonable that the tgrB1 null mutant cell does
Video 4. Migration of the KI cells in the low-density
notshow CFL. This analysis suggests that theregion. The video was taken every 15 s for 2 hr. Video
reduced ability to perform CFL can be linked toacceleration: 378  real time.
the defect of tgrB1 mutant in the formation of
https://elifesciences.org/articles/53609#video4

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(a)

(b)
t = 150 s

t = 300 s

t = 450 s

t = 600 s(d)
0.4 N = 136
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0

a1

a2
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τ [sec](f)frequency

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N = 1560.2
0.1
06 0- 5 9120 11 9
1 80 179
2 40 2 39
-2 9
9
3 00
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0
0 -2
9
3 059
6 090

frequency

(e)

v1
v2

06 0- 59
12 0 11 9
1 80 17 9
2 40 2 39
-2 9
9
3 00
-

frequency(c)a [deg]τ [sec]Figure 4. 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) Schematicof 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
A cos a ¼ ðcos a1 þ cos a2 Þ=2; A sin a ¼ ðsin a1 þ sin a2 Þ=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.
The online version of this article includes the following source data and figure supplement(s) for figure 4:
Source data 1. Source data of duration of two cell contacts for KI cell shown in Figure 4c.
Source data 2. Source data duration of two cell contacts for tgrb1 mutant cell shown in Figure 4f.
Figure supplement 1. Collision analysis and locomotive activity of KI and tgrB1 mutant cells.

traveling band formation, although we cannot exclude other effect that could explain the phenotypeof 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 nextcompared the locomotive activities between control cells and tgrB1 null mutants. The velocity autocorrelation functions CðDt Þ of the isolated single cells showed similar behaviors (Figure 4—figure
supplement 1c), indicating that locomotive activities were comparable between KI cells and thetgrB1 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 isessential for the segregation of cell density and the formation of propagating bands.

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Video 5. A binary collision of the KI cells in the lowdensity assay. The video was cropped from the videoof the low-density assay with a length of 10.25 min.
Video acceleration: 153  real time.
https://elifesciences.org/articles/53609#video5Video 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.
https://elifesciences.org/articles/53609#video6

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 z). In addition to this effect, the particles interact with each otherthrough volume exclusion interaction, adhesion, and the effect of polarity qi orienting toward the
direction of its velocity vi ¼ dri =dt (parameterized by a). For a fixed parameter set (a ¼ 0:4; seeMaterials and methods), without CFL (z ¼ 0), the collective behaviors did not form (Figure 3—figure
supplement 2). In contrast, with CFL (z  0:1), a polar-ordered phase appeared as a propagating
band in the background of disordered phase (Figure 3g and Video 8). The speeds of the travelingband and particles within the band were 0.96 and 0.9, respectively, relative to the speed of isolatedparticles, 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 recognizedwithin the polar-ordered phase. In the simulation, we studied the pdf of migration direction inregions, 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 a without CFL (z ¼ 0), andfound that the pdfs of migration direction exhibit peaks at closely similar positions, indicating thatthe migration direction in the ordered phase is more homogeneous (Figure 3—figure supplement3). 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 ’2l ðsÞ (see Materials and methods) also shows the characteristic decay with a logarithmic dependence on area S (Figure 3e), as
observed experimentally.

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

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pattern formation is attributable to the cell-cellinteraction called contact following locomotion(CFL) (Figure 4). The agent-based model that
includes CFL reproduces the observed macroscopic behaviors (Figure 3g). Thus, we establish
Video 7. Microscopic observation of the population ofa link between the microscopic cell-cell interactgrb1 null mutant. The video was taken every 15 s fortions and the macroscopic polar pattern
1.25 hr. Video acceleration: 225  real time.
formation.
https://elifesciences.org/articles/53609#video7
We showed that the width of band is distributed widely from W ¼ 200 mm to 700 mm (Figure 1—figure supplement 1b), and found thepositive 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 supplement1c), suggesting that the local cell density may not be a relevant factor for the increase in the orderparameter. 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 tolarger decorrelation in the migration direction. Consequently, we expect that the stronger the polarorder, 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 thenumerical 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 bandpropagation 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 travelingband, 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 travelingbands are arranged almost periodically in spacewith a spatial interval of about 1 mm (Figure 1b).
How bands interact with each other to reach aperiodic 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 andInouye, 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 andundergo normal morphogenesis and cell differentiation; this is not observed in mutant KI cells
Video 8. Propagating band formation generated in the lacking TgrB1 (Kida et al., 2019), suggesting that
TgrB1-dependent CFL without chemotaxis allows
agent-based simulation. The color code indicates theKI cells to spontaneously migrate in slug. Furthermigration direction of individual particle as shown in
more, in wildtype cells, the chemical guidance
Figure 3c. Arrows indicate the direction of polarity.
https://elifesciences.org/articles/53609#video8
cue has been shown to cease during the

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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
Cell line(Dictyostelium discoideum)

Designation

Source or reference

Identifiers

Additional information

KI-5

National BioResource
Project Cellularslime molds

NBRP ID: S00058

Available in National
BioResource Project Cellularslime molds(https://nenkin.nbrp.jp)

Culture condition of KI mutant cells and cell density measurement
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, theKI 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 byaspiration, then clean PB was added. After repeating this process two times, the number of cells wascounted using a hemacytometer.

Macroscopic observation of the traveling bands
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 minusing a film scanner (V850, EPSON). The brightness in scanner images is inversely correlated withcell density (Takeuchi et al., 2014). For Figure 1a and b, the original images were inverted withcolor that depends on time points.

Microscopic observation of the traveling bands
The KI cells were spread (cell density = 2.0 to 3.0  105 cells/cm2) on the non-nutrient agar plateand 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 byphase 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
For the tracking analysis shown in Figure 2 and Figure 3 and 1 mL of the PB including 3% fluorescent
microbeads (ex:441, em:486, 1.0 mm, 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 mm/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 bandand 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.

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The mean squared displacement (MSD)The MSD (Figure 2d) was calculated using the formula below.
MSDðtÞ ¼

N X
T t
X
1
fri ðt þ t Þ
N ðT t Þ i¼1 t

ri ðtÞg2 ;where Dt, T, and N means a time interval, final time, and number of the trajectory, respectively.

Polar order parameter
To obtain the local polar order parameter ’ðn; t Þ shown in Figure 3a, the picture shown in Figure 1c
was divided into n sections with width Dx (mm), and the order parameter was calculated in each section at each time from the trajectories obtained by the tracking analysis. The local order parameter’ is defined as’ðn; tÞ ¼

1 X v i ðt Þ;
N ðnÞ i 2 LðnÞ jvi ðt Þj

where LðnÞ is the set of cells that satisfy ðn 1ÞDx  xi  nDx;N(n) is number of the cells in L(n), vi andxi are the velocity and x-position of i-th fluorescent microbeads, respectively. In this study, n = 14
and Dx = 119 mm.
To obtain the order parameter h’i of the traveling band used in Figure 3b, we first obtained ’ inthe band region at each time step. Then, we took average it over all time steps.

Optical flow analysis
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 characterizedby coloring based on the HSV (‘hue’, ‘saturation’, ‘value’) representation. The ‘hue’ varies dependingon 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
To characterize the internal structures of the traveling band, the size-dependent squared local orderparameter ’2l ðSÞ is introduced (Figure 3e). To obtain the size-dependent squared local orderparameter, we first calculate the squared polar order parameter ’2l ðSÞ within a ROI of size S , which
is defined as(2  X2 )X
12’l ðSÞ ¼ 2
cos Qð x; yÞ þ
sin Qð x; yÞSð x;yÞ2ROI
ð x;yÞ2ROI
where Qð x; yÞ ¼ hue  ð360=255Þ indicates the angular variation of the pixel at position ð x; yÞ. The valueof hue was obtained from the optical flow analysis (Figure 3c). Then, ’2l ðSÞ is averaged over theentire area to obtain’2l ðSÞ . If Qð x; yÞ is a random number without spatial correlation, as theincrease of the area S, ’2l ðSÞ is expected to decay in proportion to S 1 .

The plot of the temporal average of the migrating direction in the band
Firstly, we divided the x-t plane into the lattice with the interval of 20 mm (for x axis) and 60 s (for taxis). 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 agiven x position, which was plotted in Figure 3—figure supplement 4b left.

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Autocorrelation function of transverse motion with respect to the bandpropagation direction
Because the band show propagation in x-direction, autocorrelation function of transverse motion
Csin is defined using y-component of motion as
Csin ðxÞ ¼

Y X
X x
X
1
sinQð x; yÞsinQð x þ x; yÞ;Y ð X xÞ y¼1 x¼1

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

Preparation of tgrB1 null mutant cells
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- GTAATCATGGTCATAGCTG
TTTCCTGCAGGCCAGCAGTAATAGTTGGAG-3. The 3-flanking region of the construct was amplified with primers, 5- CACTGGCCGTCGTTTTACAACGTCGACGAGAACTGTTGATTCTGATGG-3 and5- CTTGGTCCTGAACGAACTCC-3. The bsr cassette in the multicloning site of pUCBsr Bam(Adachi et al., 1994) was amplified using the primer pair 5-CTGCAGGAAACAGCTATGACCATGA
TTAC-3 and 5-GTCGACGTTGTAAAACGACGGCCAGTG-3, both of which are complementary to thetwo 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 mg 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
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. Afterreaching confluent, cells on the bottom were peeled off and collected, then washed two times witha 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
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 wereobserved by microscopy and recorded every 15 s. The motion of the cells was tracked manuallyusing 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 thetgrb1 null cells, respectively. The total numbers of collision events are 136 (KI cells), and 156 (tgrb1
null cells).

The velocity autocorrelation function
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, andetc. were eliminated. Using obtained trajectories of cells that migrate with the velocity v, the velocity
autocorrelation function Cðt Þ was calculated. Cðt Þ is described with the form ofCðDt Þ ¼

1
N ðT

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N X
T t
X
fvi ðt þ t Þt Þ i¼1

vi ðt Þg2 ;t

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where t , 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
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 byassuming particle-particle interactions (Hiraiwa, 2019). We firstly assume that the particles interact
with each other through volume exclusion (parameterized by b) and adhesion (parameterized by g).
We also assume the feature that the polarity of each particle orients to the direction of its velocity
vi ¼ dri =dt (parameterized by a); 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 andSun, 2014). (Therefore, we simply refer to this feature as alignment effect in the main text.) As themain 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 locatedat the tail of particle j (parameterized by z). The equation of motion for the particle i are then given
by
X
X
r r
rj ri
qi
dri
b
R jr j r ij2 þ g(1)
dt ¼ v0 jqi j
jrj ri jjij2NðiÞ

dqi
dt ¼ Iqi1j2NðiÞ

jqi j2 þ Ci þ a jvvii j þ i(2)where the second and third terms on the right-hand side of Equation 1 are the effects of volume
exclusion and adhesions, respectively. Here, NðiÞ is a set of particles that are contacting with the particle i, that is the particle j 2 NðiÞ satisfies jrj ri j  R. On the right hand side of Equation 2, the firstterm shows the self-polrization, the third term gives the effect that the polarity orients to the velocity
direction vi =jvi j, the last term is white Gaussian noise with hi i ¼ ð0; 0Þ and i ðt Þ  j ðt 0 Þ ¼ s2 dij dðt t 0 Þ,
and the second term Ci describes the CFL, parameterized by z, given by


X
rj ri
rj ri
qi
1
þ

Ci ¼ 2z(3)
jqi j jrj ri j :r rj2NðiÞ j j i jHere, when the polarity of particle j, qj , and the vector from particles i to j, rj ri , are in the sameorientation, the maximum following effect is exerted on particle i to the direction of particle j. Sucha 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, weused fixed parameter values except z and a, given by v0 ¼ 1:0;b ¼ 1:0;R ¼ 1:0;g ¼ 1:20; and s2 ¼ 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 jqj ¼ 1 for the numerical simulation. The density of particles per unit area  is given
 ¼ 1. The number of particles n is n ¼ 80; 000 (Figure 3g-i and Figure 3—figure supplement 3) andn ¼ 10; 000 (Figure 3—figure supplement 2).

Histogram of migration direction in the numerical results
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 the2D dense packing fraction of disks, ~0.91. Using this definition, we define the ROI as being vicinityof 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 þ Fwait þ Fout and the last Fana þ 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 assumingthat 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.

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The results of this algorithm for CFL-induced (z ¼ 0:1; a ¼ 0:4) and alignment-induced(z ¼ 0:0; a ¼ 1:0) bands are shown in Figure 3—figure supplement 3a and b, respectively. Here, weused the following sets of the parameters for our analysis in this article: Fana ¼ 55, which corresponds
to the time window in the analysis of experimental data. Fwait ¼ 76, with around which the band front
can propagate across one ROI. Fout ¼ 5, which has been empirically determined. The duration
between each frame is dt ¼ 0:2 in the unit of time of our numerical simulation.
Secondly, using these near-front ROIs, we calculate the histograms of migration directionðdri ðtÞ=dtÞ=jdri ðtÞ=dtj for each ROI using all the Fana frames ðtÞ and the particles ðiÞ in it at eachframe. 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 plottedin 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 lessdistributed. 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.

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); andJP26610129 (to HK).

Additional information
Funding
FunderGrant reference number

AuthorJapan 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 thedecision to submit the work for publication.
Author contributions
Masayuki Hayakawa, Conceptualization, Data curation, Formal analysis, Validation, Investigation,
Methodology, Writing - original draft, Writing - review and editing; Tetsuya Hiraiwa, Formal analysis,
Funding acquisition, Investigation, Methodology, Writing - original draft, Writing - review and editing, Designed and performed the simulation; Yuko Wada, Investigation; Hidekazu Kuwayama,
Resources, Supervision, Funding acquisition, Writing - original draft, Writing - review and editing;
Tatsuo Shibata, Conceptualization, Data curation, Formal analysis, Supervision, Funding acquisition,
Validation, Investigation, Methodology, Writing - original draft, Project administration, Writing review and editing
Author ORCIDs
Masayuki Hayakawa
https://orcid.org/0000-0002-9245-9593
Tetsuya Hiraiwa
https://orcid.org/0000-0003-3221-345X

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Hidekazu Kuwayama
https://orcid.org/0000-0002-4362-0790
Tatsuo Shibata
https://orcid.org/0000-0002-9294-9998
Decision letter and Author response
Decision letter https://doi.org/10.7554/eLife.53609.sa1
Author response https://doi.org/10.7554/eLife.53609.sa2

Additional files
Supplementary files. Transparent reporting form
Data availability
All data generated or analysed during this study are included in the manuscript and supporting files.
Source data files have been provided for Figure 1, 2, 3 and 4.

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