Contact enhancement of locomotion in spreading cell colonies

1.9 MB·

by  Joseph d'Alessandro

Contact enhancement of locomotion in
spreading cell colonies
Joseph d’Alessandro∗†,‡ Alexandre Solon§, Yoshinori Hayakawa¶, Christophe Anjard†,
Fran¸cois Detcheverry†, Jean-Paul Rieu† and Charlotte Rivi`ere∗†
The dispersal of cells from an initially constrained location is a crucial aspect of many
physiological phenomena ranging from morphogenesis to tumour spreading. In such
processes, the way cell-cell interactions impact the motion of single cells, and in turn
the collective dynamics, remains unclear. Here, the spreading of micro-patterned
colonies of non-cohesive cells is fully characterized from the complete set of individual
trajectories. It shows that contact interactions, chemically mediated interactions and
7
1 cell proliferation each dominates the dispersal process on different time scales. From
0
data analysis and simulation of an active particle model, we demonstrate that contact
2
interactions act to speed up the early population spreading by promoting individual

n
cells to a state of higher persistence, which constitutes an as-yet unreported contact
a
J enhancement of locomotion. Our findings suggest that the current modeling paradigm

5 of memoryless interacting active particles may need to be extended to account for the

possibility of internal states and history-dependent behaviour of motile cells.
]
h
p
- U indescriptionsbasedontheFisher-Kolmogorov-
o nderstanding how cell assemblies regulate
i Petrovski-Piskunov (FKPP) equation7,8. How-
b theirmotilityisamajorchallengeofcurrentbio-
s. physics.1 Indeed, collective effects in the motion ever, the assumption of non-interacting cells
c is often unwarranted9,10, as several types of
of cells play a crucial role in vivo in processes
si such as wound healing2, tumour progression3 or cell-cell interactions affecting the collective dy-
y namics have been uncovered experimentally. A
h morphogenesis4. In understanding the often in-
firstclassinvolveslong-rangeinteractions,which
p
tricate relationship between the behaviours at
[ may be mediated by a chemical11,12 as in quo-
the cellular level and the population scale, two
rum sensing, or by the substrate13. A second
1
basic questions arise: how do cell-cell interac-
v class includes short-range contact interactions:
5 tions alter the properties of individual cell mo-
volume exclusion, cell-cell adhesion or contact
2 tion? How do they impact the population dy-
2 inhibition of locomotion (CIL)14, which acts to
namics?
1 change the direction of motion of a cell upon
0
contact with another cell.
. The trajectory of a cell crawling on a surface is
1
0 akin to a correlated random walk characterized
Despite their local nature, contact interactions
7 by a persistence time beyond which the motion
1 have proven essential to the collective behaviour
becomes diffusive5,6. In the absence of interac-
: of cells, at least for dense assemblies with den-
v tions, thiswouldleadonlongtimetosimpledif-
i sity near close-packing. On the edge of a dense
X fusion dynamics at the colony level, as captured
colony, CIL15 or excluded volume16 combined
r
a ∗<To whom correspondence should be addressed. E- with a density gradient acts to bias the mo-
mail: joseph.d’[email protected],charlotte.riviere@univ- tion towards free space10,17,18, hence facilitating
lyon1.fr> the spreading of the colony9,16,19. This effect
†InstitutLumi`ereMati`ere,CNRSUMR5306,Univer-
is further reinforced by the tension created by
sit´e Claude Bernard Lyon 1, Universit´e de Lyon, Lyon,
leader cells through adherens junctions17,20. In
69622 Villeurbanne Cedex, France
‡Current adress: Institut Jacques Monod (IJM), the bulk of a tissue, force transmission through
CNRS UMR 7592 et Universit´e Paris Diderot, 75013 adherens junctions21,22 (but also nematic align-
Paris, France ment23,24 or simple volume exclusion25) can
§Department of Physics, Massachusetts Institute of
lead to coordinated motion over several cell
Technology, Cambridge, MA 02139, USA
¶CenterforInformationTechnologyinEducation,To- sizes and induce active jamming and glassy be-
hoku University, Sendai 980-8578, Japan haviour26,27,28. The slowing down of tissue dy-
1
namics is especially clear in cell systems domi- about 40h the density saturates at a carrying
nated by CIL15, which reduces the cell persis- capacity ρ ≈ 5−8×105cell/cm2 (Fig. 1c).
max
tence29 or effective speed30.
Thespreadingof thecolony is foundto befaster
Here, we investigate collective cell migration at in the first few hours of the experiment. Us-
moderate density in assemblies lacking cell-cell ing the single cell trajectories obtained by au-
adhesion. Incontrasttothehigh-densityregime, tomated cell tracking, this observation can be
thisregionhasreceivedcomparativelymuchless relatedtotheaveragecellspeed(seeSupplemen-
attention so far. By studying the spreading tary Figure 1): After an initial increase, the cell
dynamics of micropatterned Dictyostelium dis- speed decreases until it reaches a low-motility
coideum cell colonies, we find that cell-cell con- plateau at t ≈ 10 h. This behaviour at long
tacts enhance the cell persistence, an effect that times is well explained by the overall regula-
we refer to as contact enhancement of locomo- tion of the motility through a secreted quorum-
tion(CEL).Thisphenomenonresultsinaspeed- sensing factor, which has been evidenced in our
up of the colony spreading upon increasing the group before11. Indeed, when repeating the
packing fraction and defines a novel kind of spreading experiments with a continuous per-
interaction, which, instead of acting instanta- fusion of fresh medium to rinse out secreted
neously as a physical force, modifies the internal molecules, the decrease in motility is suppressed
state of the moving agents and their subsequent and the colony instead rapidly reaches a high-
behaviour. motility plateau (see Supplementary Figure 1a).
Assoonastheperfusionstops,theconcentration
of quorum-sensing factors builds up and the cell
A highly controlled model of cell speed falls down.
colony
Collective effects on the short-
We used vegetative Dictyostelium discoideum
time spreading
(D.d.) cells, which are often considered as a
benchmark for the amoeboid motility of fast-
moving cells31,32,33. Moreover, they are espe- We now focus on the short-time spreading of
ciallyadaptedtostudytheroleofinteractionsin the colony. It strikingly reveals that the higher
the absence of strong cell-cell adhesion, as they the cell density, the faster the colony spreads
do not form such adhesions in nutrient-rich con- (Fig.2a-bandSupplementaryMovies2-3). This
ditions34. To experimentally mimic the disper- collective effect is seen on the density profiles
p
sal of cells from an initial location in a repro- or on the gyration radius, R = hr2i, which
g
ducible way, we constrained a controlled num- quantifies the size of the colony (see Fig. 2c–
ber of cells in a disk of diameter 320 µm, using e). To better characterise this effect, we com-
PDMS micro-stencils35,17 (Fig. 1a). Taking off pute the radial component v of the velocity of
r
themicro-stencil,weletthemmigratefreelyout- each cell, and average over the colony. We find
wards and image the colony for durations rang- that this averaged hv i exhibits a positive peak
r
ing from 8 h to 48 h (see snapshots in Fig. 1b around 100 min in the colonies with higher ini-
and Supplementary Movie 1). tial density N = 246 ± 66 (Fig. 2f and Sup-
0
plementary Figure 1). This implies that, in this
We caracterize the colony spreading both at the
time frame, cells move outward in average.
population and individual cell levels (Fig. 1c).
Makinguseofthecircularsymmetry,fieldquan- The existence of a non-vanishing radial velocity
tities such as the density (Fig. 1c) are aver- is not surprising in itself since it is the analogue,
aged over concentric rings and depend only on for self-propelled particles36, of an outward dif-
time t and the distance r from the centre of the fusive flux. However, one expects the peak to
colony. At short times, we first observe a de- be located at a time of the order of the persis-
crease of the density in the centre of the colony tence time of the particles (see Fig. 4), which is
as it spreads to invade free space. Then, on found around τ ∼ 5 min for D.d. cells in simi-
p
time scales of the order of the doubling time lar conditions11,37. On the contrary, the radial
β−1 ∼ 9 h, the density starts increasing uni- velocity peak happens here on a much longer
formly because of cell divisions. Finally, after time scale ∼ 100 min. It strongly suggests that
2
a b c
5
x 10
6
t=0 min
2) 4
−
m Time
(c 2 increases
ρ
0
0 200 400 600
r (µm)
t=150 min
Figure 1: A highly-controlled experimental set-up gives full access to colony spreading dynamics at
both individual and population scales.
(a) Cartoon of the patterning technique. The cells are first deposited in a home-made well (brown)
on top of a PDMS stencil (light gray) made by soft-lithography techniques (top). After 45min of
adhesion, the well and the stencil are removed (centre), creating an initial circular pattern of 320 µm
in diameter (bottom), whose spreading is then followed by time-lapse microscopy. (b) Snapshots of
a colony with N = 245 cells initially at t = 0min (top) and t = 150min (bottom). Scale bars:
0
200µm. (c) Top: Evolution of the density profiles ρ(r,t) over 60h (from blue to red) for one colony
with initially N = 349 cells. All the curves are separated by a 2h interval. The first three curves
0
are drawn thicker to highlight the fast initial spreading of the colony. Bottom: Cell trajectories at
the edge of the initial spot, from t = 0min to t = 60min. Scale bar 100µm.
an unknown effect speeds up the spreading on Cell-cell contacts increase their
this longer time scale. Importantly, this effect
persistence
neither originates from cell division (it happens
on a time-scale much shorter than the doubling
time) nor from distant chemically-mediated in- Fromourdatasetoftrajectories,wefindthatthe
teractions arising from bulk soluble molecules short-time speed-up of colony spreading is con-
(see Supplementary Figure 1) or from deposited trolled by a transient increase in the persistence
trails (see Supplementary Figure 2). of the cells, the effect being more pronounced
the denser the initial colony. This statement, il-
lustrated by sample trajectories in Figure 3a-b
and Supplementary Figure 4, is motivated by a
body of quantitative measurements.
First, the cells appear more elongated, hence
Most interestingly, we find that the amplitude
more polarised, in denser colonies (Fig. 3a). It
of the peak in radial velocity strongly depends
is quantified by computing the cell contours’ ec-
on the number of cells in the colony (Fig. 2f).
centricity, which increases with density at early
Thus, thespreadingrateiscollectivelyincreased
times before relaxing to values corresponding to
through local interactions likely occurring when
more isotropic cell shapes (see Supplementary
cells are in contact. To understand this density-
Figure 3).
dependentspreadingdynamics,wenowturntoa
morerefinedanalysisofthemotionofindividual Second,weusedthecoefficientofmovementeffi-
cells. ciency (CME, see Methods) to estimate the per-
3
Figure 2: Density-dependent colony spreading.
The experiments are divided in three groups to study the effect of the initial cell number N . (a-b)
0
“Snapshots” of the colonies for two different groups N = 35±12 (blue, left, 208 cells in total) and
0
246±66 (red, right, 1229 cells in total), at t = 0 and t = 150min. The positions of all cells in
each group of experiments are represented as coloured points. The dashed circle denotes the edge of
the stencil. (c-d) Normalised density profiles for each group at t = 0 min (c) and t = 150 min (d).
p
(e) Gyration radius R = hr2i of the colonies as a function of time. (f) Radial velocity hv i as a
g r
function of time averaged over the colony (same colour code for every panel). The error bars are
the standard deviation (n = 6,8,5 experiments respectively for N = 35±12,N = 97±25,N =
0 0 0
246±66).
sistence of the trajectories with good time and tence time or because of a bimodal motion of
space accuracy. This quantity, for a given in- individual cells41,44,42. However, the first possi-
terrogation time ∆t, ranges from 0 for a mo- bility can be ruled out since the relative weights
tion with persistence time much smaller than c and c0 are not constant in time.
∆t to 1 for ballistic motion. From the spatio-
temporal evolution of the CME measured with
Thus, all experimental clues point to the fact
∆t = 5min, it is clear that the persistence in-
that each cell is able to increase its persis-
creases with density (Fig. 3c). This is especially
tence upon collision. For modeling simplicity,
pronounced at short times and near the periph-
although we cannot rule out completely a con-
ery of the colony, where the radial velocity map
tinuouschange, weconsidercellsthatswitchbe-
also exhibits high values (Fig. 3d).
tweentwomodesofmotion,amode1whithper-
Finally, another quantitative characterisation is sistence time is Dr1−1 and average duration τ1,
provided by the velocity direction autocorrela- and a mode 2 with Dr2 < Dr1 and τ2. We used
tion function C(t0 − t) = hu(t0)·u(t)i, where this model to fit all experimental data, as ex-
u is the direction of motion of a cell. The plained in the Supplementary Information, as-
simplest models of persistent motion (Ornstein- suming for simplicity that the mode of higher
Uhlenbeck, activeBrownianparticleorrun-and- persistence is ballistic (Dr2 = 0). Fig. 3e shows
tumble motion) all lead to an autocorrelation representative examples for this fitting proce-
function which decays exponentially over the dure. As an output, we obtain the estimates
persistence time. In contrast, our data is better Dr1−1 =2 min and τ2 =10 min (see Supple-
describedbyasumoftwoexponentials(Fig.3e): mentary Figure 5), and the fraction φ2(t) =
τ /(τ +τ ) of cells in mode 2 (Fig. 3f). Like
C(t) = ce−γt+c0e−γ0t. (1) 2 1 2
the radial velocity, φ (t) reaches a maximum at
2
Thisformcouldequallyarisebecauseoftwodis- around 100min, and exhibits an overall increase
tinct populations of cells with different persis- with density, showing that higher densities pro-
4
c d -1
v (µm.min )
CME (5 min) r
0 0.5 1 0 1 2
a b
b Cc d
600
= 35 400 m)
i µ
0 (
Nh 200 r
0
600
6
4 )
2 400 m
= µ
N i0 200 r (
h
0
0 200 400 0 200 400
t (min) t (min)
e f
0.4 1.4
hN i = 35 g
0.4 0 v
hN i = 97 0.3 v/ 1.2
0
0.3
hN i = 246 1
C(t)0.2 Sin0gle exp φ20.2 ME 1.1 h
C
0.1
0.1 / 1
E
M
0 C
0 10 20 0 200 400 -10 0 10
t (min) t (min) t-t (min)
col
Figure 3: Local interactions between cells lead to an increase in cell persistence.
(a–d) Comparison of trajectory properties at low (hN i = 35, top row) and high (hN i = 246, bottom
0 0
row) initial densities. (a) Typical cell trajectory (plotted over 100 min), with “Start” denoting the
initial cell position, the white circle representing the border of the initial pattern and the arrows
pointing to collision events; (b) 64 examples of trajectories from t = 100min to t = 130min, picked
randomly over all cell trajectories; (c) spatio temporal dynamics of the CME with ∆t = 5 min and
(d) of the radial velocity v (the dashed lines represent the border of the initial colonies). (e) Velocity
r
direction autocorrelation function at t = 67−133min for various hN i (symbols, same colour code
0
for panels e and f) and fits using the expression detailed in Supplementary Information (solid lines)
with D−1 = 2min and τ = 10min. The thick black line represents the best single-exponential
r1 2
(‘Single exp’) fit for hN i = 246, which misses the experimental behaviour at both very short and
0
long times. (f) Proportion φ of cells in mode 2 as extracted from the fit of the correlation functions
2
(the lines are guides for the eye). The error bars represent the 95% confidence interval for the fit
parameter. (g–h) Normalised speed (g) and CME computed with ∆t = 5min (h) for cells undergoing
a single collision at t = t within a 30min interval. v (resp. CME), denote the basal speed (resp.
col
CME) before collision. The error bars show the SEM for the n = 464 pieces of trajectory from 232
collisions.
mote switching to the persistent mode. understood here as collisions or short-range in-
teractions – are the primary cause for the phe-
Because this enhancement of persistence is not
nomenon. Paralleling the CIL acronym, here-
chemically mediated (see Supplementary Figs. 1
after we refer to this effect as CEL, or contact
and 2) and depends strongly on the density
enhancement of locomotion. To confirm more
(Figs. 2 and 3), we conclude that contacts –
5
directly the existence of this phenomenon, we ration measured in the simulations are shown as
look at the statistics of cell-cell contacts. As de- a function of time in Fig. 4.
scribed in the Supplementary Information, we
First, we checked whether this simple interac-
retain only “clean” contacts (between cells un-
tionrulecouldyieldadensity-dependentspread-
dergoing no other collision for 15min before and
ing. Indeed, if we think of moving cells as
after). We compare the speed and CME of each
hard-core spheres undergoing a persistent ran-
single cell before and after collision and then
dom walk, the excluded-volume (EV) between
average over all available data (see Fig. 3g–h,
the cells gives rise to an outward pressure38.
and Suplementary Figures 10–12). Both com-
This effect is also present for Brownian hard
puted quantitites exhibit a significant transient
spheres, for which it can be taken into account
increase, demonstrating that CEL is indeed re-
by an effective diffusion coefficient increasing
sponsible for the density-dependent spreading
with concentration39. However, in the present
rate of the colonies. Note that the analysis of
experiments where cells are relatively sparse –
the angular scattering (see Supplementary Fig-
with packing fractions up to 0.3 – this pressure
ures8-9)showthatthecell-cellcontactshaveno
isnotexpectedtoplayanimportantroleandin-
aligning effect likely to promote collective mo-
deed, simulationsofEqs.(2)-(3)withonlyhard-
tion and to increase the spreading rate by itself.
corerepulsionexhibitnoeffectofdensity(Fig.4,
left).
Comparison with minimal active
We then further implemented the effect of CIL
particle models that is, upon collision, cells actively reorient
away from the contact. To that end, we added
an angular repulsion to the equations of motion,
To support our experimental findings, we now
intheformofatorqueactingoncellsundergoing
investigate several minimal active particle mod-
a contact: ΓP H(kr −r k−σ )sin(θ −β )
els. Discarding other types of contact interac- j6=i j i r i ij
in equation (3), where β = arg(r −r ), H is
tions, we show that a collision-induced increase ij j i
the Heaviside step function implementing the fi-
in persistence is necessary and sufficient to ac-
nite radius of interaction and σ is the contact
count for the salient features of the short-time r
distance (see Methods). Qualitatively, one can
dynamics of the colony spreading.
imagine that by reorienting the direction of mo-
Let us consider self-propelled hard disks mov- tion of particles toward free space, active reori-
ing at a constant velocity v. In addition, the entation could explain the experimental data15.
direction of motion θ of a particle is subject to However, evenwithalargevalueΓ = 100 min−1
rotationaldiffusionwithcoefficientD . Themo- corresponding to quasi-instantaneous reorienta-
r
tion of the ith particle is thus governed by the tion, the density-dependent increase in average
following equations radial velocity and spreading rate is an order
of magnitude smaller than in the experiment
X
∂tri = vu(θi)+ fij(ri−rj) (2) (Fig. 4, centre). In addition, the (very limited)
j6=i peak in radial velocity appears at a very early
p
∂ θ = 2D η (t), (3) time,atoddswiththeexperimentalobservation.
t i r i
In both situations, the rotational diffusion was
where u(θi) = (cosθi,sinθi) and ηi is a delta- set to D−1 = 5 min to match the average per-
r
correlated Gaussian white noise with zero mean
sistence time of experimental trajectories.
andunitvariance. f isthestericrepellingforce
ij
exerted by particle j on particle i (see Methods Finally, guided by the experimental observa-
for more details). As such, Eqs. (2-3) describe tions, we tested a minimal model of CEL: After
theactiveBrownianparticle(ABP)model,well- eachcontact,twoparticlesinvolvedinacollision
studied as a minimal model of phase-separating enter a mode of high persistence (Fig. 4, right).
active particles30,38, and a suitable basis for the Forsimplicity,thespeediskeptconstantandthe
modelling of the persistent random motion of motion is taken to be ballistic in this high per-
cells. Consistently with the experiments, we sistence(mode2)state. Theparticlesthenrelax
takev = 5 µm.min−1 andinitiallyplacethepar- to the basal (mode 1) state at a rate λ = τ−1.
2 2
ticles in a disk of 320 µm in diameter. The re- We fix D−1 = 2 min and τ = 10min, as deter-
r1 2
sulting average radial velocity and radius of gy- mined from the fit of the experimental data (see
6
EV EV+CIL EV+CEL
N = 20
0
N = 50
0
N = 100
0
N = 200
0
N = 300
0

1) 1.5 400
−
n
mi m)
1 300
m. µ(
µ g
〉 ( 0.5 200R
vr
〈
0 100
0 200 400 0 200 400 0 200 400
t (min) t (min) t (min)
Figure 4: Spreading colonies in a particle-based model mimicking the experiments.
Radialvelocityhv i(dashedlines, leftaxes)andcolonyradiusR (solidlines, rightaxes)insimulated
r g
colonies with different numbers of particles N in the three models considered. The cartoons on the
0
top row illustrate the different contact rules: Excluded-volume only (EV, left), excluded-volume
and angular repulsion (EV+CIL, center), excluded-volume and contact enhancement of locomotion
(EV+CEL, right).
Fig. 3). The proportion φ of cells in the persis- colony by increasing the speed and the persis-
2
tent mode (shown in Supplementary Figure 6a) tence time of the cells motion. This contact en-
evolves with time in a density-dependent man- hancement of locomotionisfurthersupportedby
ner due to changes in the collision frequency. a simple active particle model reproducing the
main characteristics of the experimental data.
We find that this model captures well the collec-
tive spreading of the colony. Indeed, as shown
The phenomenon of “CEL” that we have de-
inFig.4, theamplitudeanddensity-dependence
scribed here seems a priori different from CIL,
of the peak in radial velocity, as well as the
which acts to change the direction of motion
faster increase of R at higher density, are well
g
of colliding cells. However, they are not mu-
captured. Overall, given the simplicity of the
tually exclusive (see Supplementary Figure 12)
model, the agreement between simulations and
andcouldevenshareacommonmicroscopicori-
experimentsappearssurprisinglygood(seeSup-
gin.Indeed, the current explanation for CIL is
plementaryMovies2–5foravisualcomparison).
that the protrusions driving the motion are in-
hibited in the contact region15,45. Other protru-
sions can thus develop elsewhere on the cell’s
Discussion
periphery, leading to a new direction of mo-
tion. We could hypothesize that, similarly, ei-
Westudiedthedynamicsofspreadingcoloniesof ther the inhibition of ruffling in the contact re-
D.d. cells. Using a micro-fabrication technique, gion or the stabilisation of the new protrusions
wewereabletoproduceinitialcolonieswithcon- reinforces the new polarity thereby increasing
trolled shape and number of cells. We showed the speed and persistence of the motion. An
that the long-time dynamics of the spreading is important difference between the two effects is
controlled by cell divisions and long-range in- that CEL involves memory while CIL is usu-
teractions through a quorum-sensing factor. On ally modeled as an “instantaneous” contact pro-
the contrary, these two effects are absent from cess46,47,48,49. The two could have different rel-
the short-time dynamics, thus allowing us to ative importances depending on the situation.
study the effect of cell-cell contacts. We found For example, in dense cell clusters, the reorien-
that cell contacts enhance the spreading of the tationinducedbyCILforcestheparticlesonthe
7
edgetomoveoutward4,47 whereas, aswesaw, in coatedonthemouldfor1minat750rpmtoatarget
thicknessof70µm. Thesquareswerecutandpeeled
sparsercoloniestheincreaseinpersistenceisthe
off. Usually a thin PDMS membrane obstructed the
dominating effect.
hole. It was then removed with a surgical blade un-
der the microscope at low magnification.
Theimportanceofcontactinteractionsin vivo is
not completely understood. CIL has been found
The square stencil was stuck on the ground of a
to play an important role in neural crest migra- 3.5cmwideculturedishandahomemadesmallplas-
tion4 and the loss of heterotypic CIL (between tic well was stuck on it using silicon seal. A droplet
different cell types) is thought to be crucial in of medium was deposited into the well and the sam-
theinvasionofhealthytissuesbycancercells3,50. ple was placed under vacuum for 15min to help the
medium enter the central hole of the stencil and wet
Similarly, CEL could be an advantage in invad-
the dish’s surface.
ing the surrounding environment efficiently, in
the case of a less cohesive group of cells. Such a The cell suspension was added in the well and the
situation can be encountered during the escape sample was placed in the incubator for 45min to let
of highly metastatic and invasive cancer cells, as thecellssedimentandadhere. Then,theplasticwell
and the stencil were removed with surgical tweez-
well as in cell morphogenesis and microbial dis-
ers. Last, the spreading colony was imaged using a
persal. Moregenerally, itshouldbenoticedthat
slightly defocused bright-field microscope (TE2000,
CELisreminiscentofescapemechanisms, found
Nikkon) at 10X magnification and a wide-field An-
in various organisms, whichinvolve atemporary
dor Zyla sCMOS camera. A time-lapse movie was
change of the motile behaviour and can lead to recordedforupto48husingMicroManagersoftware
surprising collective effects51. with a 20s time-interval, while the temperature was
kept constant at 22.5◦C.
Finally, the new type of interaction uncovered
For perfusion experiments, we designed a macroflu-
here opens questions for active matter. Indeed,
idic chamber by sealing the culture dish with an
it exemplifies the wide range of possible interac-
adapted cover containing an input and an output
tions between active particles, compared to the
tube. The former was linked to a 1L supply bottle
usual “physicist’s particles”, which can lead to
of fresh HL5 medium under controlled overpressure
a rich phenomenology. It opens the door to fur- (OB1controller,Elveflow)whilethelatterwaslinked
ther studies of interactions that act on an ad- to a disposal bottle. All the system was closed ster-
ditional internal degree of freedom, which could ilely. We used a flow rate of 100mL/h so that the
exhibit other interesting effects. chamber volume of about 10mL was completely re-
newed every 6 minutes. We were thus able to main-
METHODS tain a stable medium renewal over 9 hours.
Image processing
Cell culture
The cells’ positions were retrieved using home-
We used Dictyostelium discoideum cells from the
made ImageJ macros based on the ’Find
strain AX2. The cells were cultured on cell-
Maxima’ built-in function. Then the indi-
culture-treated Petri dishes (BD Falcon) in HL5
vidual trajectories were reconstructed with a
medium with glucose (Formedium) and kept in a
temperature-controlled incubator at 22.5◦C, with a squared-displacement minimization algorithm
doubling time β−1 ∼ 9h. Before every experiment, (http://site.physics.georgetown.edu/matlab/)
and the data analysed using homemade Matlab
the cells were detached from the dish, centrifuged
programs.
5min at 663g, harvested and resuspended at the
seeding density.
In particular, the CME was defined as:
kr(t+ δt)−r(t− δt)k
CME (t)= 2 2 (4)
Sample preparation δt Rt+δ2t kv(t0)kdt0
t0=t−δt
2
A reusable mould on Si wafer comprising an array
of squares with circular pillars of height ∼ 150µm Simulations
and diameter 320µm in the centre was fabricated in
SU8photoresistusingclassicalsoftlithographytech-
Simulations were carried out by integrating the
niques and its surface was silanized to make it non-
adherent. PolyDiMethylSulfoxyde(PDMS,Corning) Langevin equations Eqs. (2-3) using a Euler integra-
mixedwithcuringagentata1:10massratiowasspin tion scheme with time steps ∆t = 10−3 min. The
8
hard-core repulsion between particles is modelled of the Royal Society, Interface / the Royal
by a Weeks-Chandler-Andersen potential V(r) = Society, 4, 1107–1117 (2007).
4h(cid:0)σ(cid:1)12−(cid:0)σ(cid:1)6i+1 if r < 21/6σ and 0 otherwise,
r r
[10] Marel, A.K. et al. Flow and Diffusion in
where σ =10µm is the particle diameter. We define
Channel-Guided Cell Migration. Biophys.
two particles as being in contact when their relative
J., 107, 1054–1064 (2014).
distance r < σ = 21/6σ. In the simulations with
r
CIL, the torque term is turned on only during the
[11] Gol´e,L.,Rivi`ere,C.,Hayakawa,Y.&Rieu,
contacts, when r < σ . In the simulation including
r J.P. A quorum-sensing factor in vegetative
CEL,acontacttriggersaballisticrunwhichlastsfor
Dictyostelium Discoideum cells revealed by
an exponentially distributed time with rate λ .
2 quantitativemigrationanalysis.PLoS ONE
6, 1–9 (2011).
References [12] Phillips, J. & Gomer, R. A secreted pro-
tein is an endogenous chemorepellant in
[1] Travis, J. Mysteries of the cell: Cell biol- Dictyostelium discoideum. Proc. Natl Acad.
ogy’s open cases. Science 334, 1051 (2011). Sci. USA, 109, 10990–10995 (2012).
[2] Friedl, P. & Gilmour, D. Collective cell mi-
[13] Angelini, T.E., Hannezo, E., Trepat, X.,
gration in morphogenesis, regeneration and
Fredberg,J.J.&Weitz,D.A.Cellmigration
cancer. Nat Rev Mol Cell Biol 10, 445–457
driven by cooperative substrate deforma-
(2009).
tion patterns. Phys. Rev. Lett. 104, 168104
(2010).
[3] Friedl, P. & Wolf, K. Tumour-cell invasion
and migration: diversity and escape mech-
[14] Abercrombie, M. & Heaysman, J.E. Ob-
anisms. Nature Reviews Cancer 3, 362-374
servations on the social behaviour of cells
(2003).
in tissue culture: I. Speed of movement of
chick heart fibroblasts in relation to their
[4] Carmona-Fontaine, C. et al. Contact inhi-
mutualcontacts.Experimental cell research
bition of locomotion in vivo controls neu-
5, 111–131 (1953).
ral crest directional migration. Nature 456,
7224 (2008).
[15] Mayor, R. & Carmona-Fontaine, C. Keep-
[5] Selmeczi, D. et al. Cell motility as random ing in touch with contact inhibition of loco-
motion: A review. European Physical Jour- motion. Trends in cell biology 20, 319–328
nal: Special Topics 157, 1–15 (2008). (2010).
[6] Li, L., Norrelkke, S.F. & Cox, E.C. Per- [16] Dyson,L.&Baker,R.E.Theimportanceof
sistent cell motion in the absence of exter- volume exclusion in modelling cellular mi-
nalsignals: Asearchstrategyforeukaryotic gration. J. Math. Biol. 71, 679–711 (2014).
cells. PLoS ONE, 3, 5 (2008).
[17] Serra-Picamal, X. et al. Mechanical waves
[7] Kolmogorov,A.,Petrovskii,I.&Piscounov, during tissue expansion. Nat. Phys. 8, 628–
N. A study of the diffusion equation with 634 (2012).
increaseintheamountofsubstance,andits
application to a biological problem. Math. [18] Nnetu, K.D., Knorr, M., Strehe, D., Zink,
Mech. 1, 1-âĂŞ25 (1937). M. & K¨as, J.A. Directed persistent mo-
tion maintains sheet integrity during multi-
[8] Simpson, M.J. et al. Quantifying the roles cellular spreading and migration. Soft Mat-
of cell motility and cell proliferation in a ter 8, 6913 (2012).
circular barrier assay. Journal of the Royal
Society, Interface / the Royal Society 10, [19] Yates, C.A., Parker, A. & Baker, R.E.
20130007 (2013). Incorporating pushing in exclusion-process
models of cell migration. Phys. Rev. E 91,
[9] Sengers, B.G., Please C.P. & Oreffo R.O.C.
052711 (2015).
Experimental characterization and compu-
tational modelling of two-dimensional cell [20] Sepu´lveda, N. et al. Collective cell motion
spreading for skeletal regeneration. Journal in an epithelial sheet can be quantitatively
9
described by a stochastic interacting parti- [32] Friedl, P. & Wolf, K. Plasticity of cell mi-
clemodel.PLoS Comput. Biol.9, e1002944 gration: a multiscale tuning model. J. Cell
(2013). Biol. 188, 11–9 (2010).
[21] Petitjean, L. et al. Velocity fields in a col- [33] Levine, H. Learning Physics of Living Sys-
lectively migrating epithelium. Biophysical tems from Dictyostelium. Phys. Biol. 11,
J. 98, 1790–1800 (2010). 053011 (2014).
[22] Tambe, D.T. et al. Collective cell guid- [34] Coates,J.C.&Harwood,A.J.Cell-cellad-
ance by cooperative intercellular forces. hesion and signal transduction during Dic-
Nat. Mat. 10 469–475 (2011). tyostelium development. J. Cell Sci. 114,
4349-4358 (2001).
[23] Coburn, L., Cerone, L., Torney, C., Couzin,
I.D. & Neufeld, Z. Interactions lead to co- [35] Poujade, M. et al. Collective migration of
herent motion and enhanced chemotaxis an epithelial monolayer in response to a
of migrating Cells. Phys. Biol. 10, 046002 model wound. Proc. Natl Acad. Sci. USA
(2013). 104, 15988–15993 (2007).
[24] Duclos, G., Garcia, S., Yevick, H.G. & Sil- [36] Cates, M.E. & Tailleur, J. When are
berzan, P. Perfect nematic order in con- active Brownian particles and run-and-
fined monolayers of spindle-shaped cells. tumble particles equivalent? Consequences
Soft Matter 10, 2346 (2014). for Motility-induced Phase Separation. Eu-
rophys. Lett. 101, 20010 (2013).
[25] Londono C. et al. Nonautonomous contact
guidance signaling duringcollective cell mi- [37] Bosgraaf, L. & Van Haastert, P.J.M. The
gration. Proc. Natl Acad. Sci. USA 111 ordered extension of pseudopodia by amoe-
1807–1812 (2014). boid Cells in the absence of external cues.
PLoS ONE 4, 4 (2009).
[26] Angelini, T.E. et al. Glass-like dynamics of
collective cell migration. Proc. Natl Acad. [38] Solon, A.P. et al. Pressure and phase
Sci. USA 108, 4714–4719 (2011). equilibria in interacting active Brownian
spheres. Phys. Rev. Lett. 114, 198301
[27] Park,J.-A.et al.Unjammingandcellshape
(2015).
in the asthmatic airway epithelium. Nat.
Mat. 14, 1040–1049 (2015). [39] Bruna, M. & Chapman, S.J. Excluded-
volume effects in the diffusion of hard
[28] Garcia, S. et al. Physics of active jam-
spheres. Physical Review E 85, 011103
ming during collective cellular motion in a
(2012).
monolayer.Proc. Natl Acad. Sci. USA112,
15314–15319 (2015). [40] Peruani, F. & Morelli, L.G. Self-propelled
particles with fluctuating speed and direc-
[29] Vedel, S., Tay, S., Johnston, D.M., Bruus,
tion of motion in two dimensions. Phys.
H. & Quake, S.R. Migration of Cells in a
Rev. Lett. 99, 010602 (2007).
Social Context. Proc. Natl Acad. Sci. USA
110, 129-134 (2013). [41] Potdar, A.A., Jeon, J., Weaver, A.M.,
Quaranta, V. & Cummings, P.T. Hu-
[30] Fily, Y. & Marchetti, M.C. Athermal
man mammary epithelial cells exhibit a
Phase Separation of Self-Propelled Parti-
bimodal correlated random walk pattern.
cles with No Alignment. Phys. Rev. Lett.
PLoS ONE 5, e9636 (2010).
108, 235702 (2012).
[42] Metzner, C. et al. Superstatistical analy-
[31] Friedl, P., Borgmann, S. & Br¨ocker, E. B.
sis and modelling of heterogeneous random
Amoeboid leukocyte crawling through ex-
walks. Nat. Commun. 6, 7516 (2015).
tracellular matrix: lessons from the Dic-
tyostelium paradigm of cell movement. [43] Selmeczi, D. et al. Cell motility as persis-
Journal of Leukocyte Biology 70, 491-509 tent random motion: theories from experi-
(2001). ments. Biophys. J. 89, 912–931 (2005).
10