Active Matter Workshop 2020

Active Matter Workshop 2020

VENUE:
Meiji University (Nakano Campus)
DATE:
10 - 11 January, 2020

1

Active Matter Workshop 2020

Organiser
共同利用・共同研究拠点

明治大学

先端数理科学インスティテュート（MIMS）現象数理学拠点
MEXT Joint Usage/Research Center Meiji University"Center for Mathematical Modeling and Applications" (CMMA)

Organisation committee
江端宏之（九州大学） Hiroyuki Ebata (Kyushu Univ.)

北畑裕之（千葉大学） Hiroyuki Kitahata (Chiba Univ.)

末松 J. 信彦（明治大学） Nobuhiko J. Suematsu (Meiji Univ.)
多羅間充輔（京都大学） Mitsusuke Tarama (Kyoto Univ.)
山口智彦（明治大学） Tomohiko Yamaguchi (Meiji Univ.)

Contact
email: active2020@googlegroups.com

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Active Matter Workshop 2020

Program2020/1/10 Fri.
9:30 - 10:00
10:00 - 10:10
10:10 - 10:50
10:50 - 11:00
11:00 - 11:20
11:20 - 11:40

11:40 - 12:00

Registration
Opening M. Tarama“How adhesive cells crawl by regulating their active force”
FL M. Iwamoto“Mechanism of Crawling Locomotion in Gastropods”
Break
CT S. Komura“Non-equilibrium probability flux of a thermally driven micromachine”
CT K. Era
“Autonomous three-sphere microswimmers driven by coupled internal
oscillations”
CT F. Fadda“Hydrodynamics of sedimenting squirmers with rotlet dipole”

12:00 - 13:30

Group photo
Lunch

13:30 - 13:50

CT D. Nishiguchi“Novel boundary conditions and topological dynamics of bacterial
turbulence”
CT K. Sone
“Anomalous topological active matter”
CT H. Matsuyama“Emergence of Hyperuniform state at Generalized Active OrnsteinUhlenbeck Particle System”
Break
PL M. Turner“Collective thinking in collective motion”
CT K. Nagai“Collective motion of C. elegans”
Break
CT S. Yasuda“Kinetic transport simulation of chemotactic bacteria”
CT F. Tsumori“Locomotion of soft robot by applied magnetic field”
CT E. Gauquelin“Emergence of large scale propagative signals during epithelial cell
migration”
CT S. Schnyder“Spontaneous spatiotemporal ordering of shape oscillations enhancescell migration”
Break

13:50 - 14:10
14:10 - 14:30

14:30 - 14:40
14:40 - 15:20
15:20 - 15:40
15:40 - 16:00
16:00 - 16:20
16:20 - 16:40
16:40 - 17:00

17:00 - 17:20

17:20 - 17:30

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Active Matter Workshop 2020

17:30 - 17:50

17:50 - 18:30
19:00 -

CT T. Shibata“Polar pattern formation induced by contact following locomotion in a
multicellular system”
FL S. Sawai“Crawling morphology and collective migration in amoeboid cells”
Banquet2020/1/11 Sat.
10:00 - 10:20
10:20 - 10:40
10:40 - 11:00

11:00 - 11:20
11:20 - 11:30
11:30 - 12:10

CT H. Ebata“Self-replicating pattern driven by granular segregation”
CT R. Kurita“Active hole generation in an ionic liquid droplet into a binary solvent”
CT M. Okada“Relationships between spontaneous deformation and fission of an oil
droplet on a surfactant aqueous solution”
CT K. Yasuda“State cycle model of biological nanomachines”
Break
FL Y. Iwadate“Rigidity sensing for directional migration in fast crawling cell”

12:10 - 13:40

Lunch

13:40 - 14:20

FL J. J. Molina“Modeling the mechanosensitive response of crawling cells”
FL P. Sens
“A scallop theorem for crawling cells”
Closing

14:20 - 15:00
15:00 - 15:10===========
Presentation time
PL: Plenary lectures [40 min each, including discussions]
FL: Focused lectures [40 min each, including discussions]
CT: Contributed talks [15 min presentation + 5 min discussions for each]4Active Matter Workshop 2020

Abstracts5Active Matter Workshop 2020

Day 1
10 Jan., 2020
9:30 - 10:00 Registration
10:00 - 10:10 Opening (M. Tarama)
10:10 - 10:50 Focus lecture (M. Iwamoto)
11:00 - 12:00 Contributed talk (S. Komura)Contributed talk (K. Era)
Contributed talk (F. Fadda)
12:00 Group photo
13:30 - 14:30 Contributed talk (D. Nishiguchi)
Contributed talk (K. Sone)
Contributed talk (H. Matsuyama)
14:40 - 15:40 Plenary lecture (M. Turner)
Contributed talk (K. Nagai)
16:00 - 17:20 Contributed talk (S. Yasuda)
Contributed talk (F. Tsumori)Contributed talk (E. Gauquelin)
Contributed talk (S. Schnyder)
17:30 - 18:30 Contributed talk (T. Shibata)
Focus lecture (S. Sawai)

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Opening

Active Matter Workshop 2020

10:00 - 10:10

How adhesive cells crawl by regulating their active force
Mitsusuke Tarama
RIKEN Center for Biosystems Dynamics Research, Laboratory for Physical Biology

Active matter is able to spontaneously exhibit various dynamics by autonomously generated forces.
These active forces vanish in total due to the law of action and reaction. To achieve a net directional motion
under this force-free condition, symmetry breaking plays a fundamental role. This is well-known as Purcell’sscallop theorem in the case of microswimmers, such as bacteria and algae, that swim in an (almost) zero
Reynolds number fluid.
In contrast to these swimming microorganisms, there are many cells that crawl by adhering to a
substrate, the extracellular matrix, or other cells. A typical mechanism of cell crawling is thought of as acycle of four processes: 1) protrusion of the leading edge, 2) adhesion of the leading edge to the substrate, 3)de-adhesion of the trailing edge from the substrate, and 4) contraction of the trailing edge. We demonstrated
the importance of the temporal order of these four basic processes by introducing a simple model of acrawling cell composed of two elements connected by a viscoelastic spring [1]. The spring contains a linear
actuator that elongates and shrinks in time, representing the protrusion and contraction. Since the force
generated by the actuator acts on the two elements symmetrically, the force-free condition is satisfied. In
addition, the substrate friction characteristics switches between an adhered stick state and a de-adhered slip
state, modelling the adhesion and de-adhesion processes of the two elements. The phase shift between the
stick-slip transitions in the substrate friction breaks the symmetry, which enables the cell to achieve a net
migration.
The main components responsible for the active force generation are filamentous proteins and theassociated molecular motors, such as actin filaments and myosin motors, which are typically much smaller insize than cells. Thus, it is not straightforward to understand how such microscale proteins can self-organise
themselves to drive the cell and eventually lead to multicellular dynamics such as tissue formation andhomeostasis. There have been many studies on the chemical signaling that regulates the polymerisation ofactin monomers into actin filaments and the contraction of the actomyosin cortex both experimentally andtheoretically. On the other hand, their study from a mechanical viewpoint is less developed. We recently
developed a coarse-grained molecular dynamics simulation on the dynamics of the composite of actin
filaments and myosin motors, in particular studying the formation of the actomyosin cortex [2].

References
1. M. Tarama, R. Yamamoto, “Mechanics of cell crawling by means of force-free cyclic motion”, J. Phys.
Soc. Jpn. 87, 044803 (2018).
2. M. Tarama, T. Shibata, “In-silico experiment on the formation of actomyosin cortex”, in preparation.

7

Focus lecture

10:10 - 10:50

Active Matter Workshop 2020

Mechanism of Crawling Locomotion in Gastropods
Mayuko Iwamoto1,2, Ryo Kobayashi2,3, Daishin Ueyama2,41

Department of Mathematical Sciences, Shimane University, Japan
Meiji Institute for Advanced Study of Mathematical Sciences (MIMS), Japan3
Department of Mathematical and Life Sciences, Hiroshima University, Japan
4
Department of Mathematical Engineering, Faculty of Engineering, Musashino University, Japan
2

Crawling locomotion is the one of the most fundamental locomotion strategies
for various kinds of animals without legs, for example, slime, earthworm, slug, sea
hare and snake. Many gastropods who are called generally “univalve shell” also
realize crawling movement by propagations of muscular contraction waves along
their pedal on the ground. The muscular contraction waves are classified into
“direct wave” (Fig.1) and “retrograde wave” by the directions of body movement
and muscular waves. It had already reported that friction control against the groundis important for realization of crawling motion for gastropods in addition to
muscular waves, and the friction control would be realized by lifting up a part oftheir pedal or a viscoelasticity of the mucus covered their pedal.
We have constructed a simple mathematical model of spring-mass system
which captures essential factors of physical properties, i.e., the muscle and the
mucus [1]. Our numerical calculations have indicated that the locomotion
mechanism with mucus can achieve to move by crawling with both direct andretrograde waves, and the features of the mucus and muscle have an effect on the
choice of locomotion styles. Furthermore, it has indicated that the regions where
both locomotion styles are stable would exist in the region of a middle ofcontraction rate, and bifurcation phenomenon of locomotion styles as pitchfork
appears with respect to the rate [2].
Now we are focusing a relationship between locomotion styles andsurrounding environments. Loping (Fig. 2) is one of the specific locomotion
styles separated from the ordinary crawling motions by muscular
contraction waves [4]. In this presentation, we will introduce ourobservations on loping, and aim to build a mathematical model forunderstanding a mechanism of loping.

Fig. 1: Crawlinglocomotion of snail
by direct wave.

Acknowledgements
We would like to thank Prof. Akio Ishiguro and Prof. Takeshi Kano
(Tohoku University), Prof. Hitoshi Aonuma (Hokkaido University) for theuseful discussions. This study was supported by JSPS KAKENHI Grant
Number JP17H04826.
References
1. M. Iwamoto, D. Ueyama and R. Kobayashi: “The advantage of mucus
for adhesive locomotion in gastropods”, J. Theor. Biol., 353, 133-141(2014).
2. M. Iwamoto: “腹足類の這行運動に見る運動メカニズムと制御”,

Fig. 2: Loping in snail.
(a) loping on a road paved withasphalt, (b) sketch of loping [3].

JSIAM 応用数理 26-2, 14-21 (2016) in Japanese.
3. A. J. Carlson: “The Physiology of Locomotion in Gasteropods”, Biol.
Bull, 8(2), 85-92 (1905).
4. A. McKee, et al.: “Substrate Attributes Determine Gait in a Terrestrial Gastropod”, Biol. Bull, 224(1), 5361 (2013).

8

Contributed talkActive Matter Workshop 2020

11:00 - 11:20

Non-equilibrium probability flux of a thermally driven
micromachine
Shigeyuki Komura, Isamu Sou, Yuto Hosaka, and Kento Yasuda
Department of Chemistry, Graduate School of Science,
Tokyo Metropolitan University, Tokyo 192-0397, Japan

We discuss the non-equilibrium statistical mechanics of a thermally driven micromachine consisting of
three spheres and two harmonic springs as shown in Fig.1 [1]. We obtain the non-equilibrium steady state
probability distribution function of such a micromachine and calculate its probability flux in thecorresponding configuration space [2]. The resulting probability flux can be expressed in terms of afrequency matrix that is used to distinguish between a non-equilibrium steady state and a thermal
equilibrium state satisfying detailed balance. The frequency matrix is shown to be proportional to thetemperature difference between the spheres. We obtain a linear relation between the eigenvalue of thefrequency matrix and the average velocity of a thermally driven micromachine that can undergo a directedmotion in a viscous fluid. This relation is consistent with the scallop theorem for a deterministic three-spheremicroswimmer.

x1

K

T1
ζ1

x2

K

T2
ℓ

ζ2

x3
T3

ℓ

ζ3

Fig.1: Thermally driven elastic three-sphere micromachine.
References
1. Y. Hosaka, K. Yasuda, I. Sou, R. Okamoto, and S. Komura, “Thermally driven elastic micromachines”,
J. Phys. Soc. Jpn. 86, 113801 (2017).
2. I. Sou, Y. Hosaka, K. Yasuda, and S. Komura, “Non-equilibrium probability flux of a thermally driven
micromachine”, Phys. Rev. E 100, 022607 (2019).

9

Contributed talkActive Matter Workshop 2020

11:20 - 11:40

Autonomous three-sphere microswimmers driven by coupledinternal oscillations
Katsutomo Era1, Yuki Koyano2, Yuto Hosaka1, Hiroyuki Kitahata3, Shigeyuki Komura1
1

Department of Chemistry, Graduate School of Science, Tokyo Metropolitan University
2
Department of Physics, Tohoku University
3
Department of Physics, Chiba University

Microswimmers are small machines that swim in a fluid and they are expected to be used in microfluidics
and microsystems. Over the length scale of microswimmers, the fluid forces acting on them are dominated by
the frictional viscous forces. By transforming chemical energy into mechanical energy, however,microswimmers change their shape and move efficiently in viscous environments. According to Purcell's
scallop theorem, reciprocal body motion cannot be used for locomotion in a Newtonian fluid with low
Reynolds number. As one of the simplest models exhibiting nonreciprocal body motion, Najafi andGolestanian proposed a three-sphere swimmer (NG swimmer) [1], in which three in-line spheres are linked by
two arms of varying length.
In recent years, such a swimmer has been experimentally realized by using colloidal beads manipulated by
optical tweezers, or ferromagnetic particles at an air-water interface.
In this presentation, extending the mechanism of an elastic swimmer [2], we propose a new type of threesphere swimmer which can autonomously determine its average velocity. In order to implement such a control
mechanism, we introduce a coupling effect between the dynamics of the two natural lengths of an elastic
microswimmer following the idea of the synchronization phenomena in coupled oscillator systems.
Importantly, we find that the proposed microswimmer attains a finite steady state velocity in the long-time
limit without any external control. The chosen steady state velocity can be tuned by changing the coupling
parameter in the model. Moreover, we shall investigate the condition that a microswimmer can attain anautonomous locomotion and further perform the stability analysis of the synchronized states both numericallyand analytically.

Fig. 1 An autonomous elastic three-sphere microswimmer
in a viscous fluid characterized by the shear viscosity η.

References
1. A. Najafi and R. Golestanian.: “Simple swimmer at low Reynolds number: Three linked spheres”, Phys.
Rev. E, 69, 062901 (2004).
2. K. Yasuda, Y. Hosaka, M.Kuroda, R. Okamoto and S. Komura : “Elastic Three-Sphere Microswimmer
in a Viscous Fluid”, J. Phys. Soc. Jpn., 86, 093801 (2017).

10

Contributed talkActive Matter Workshop 2020

11:40 - 12:00

Hydrodynamics of sedimenting squirmers with rotlet dipole
Federico Fadda1, John J. Molina1, Ryoichi Yamamoto1
1Department of Chemical Engineering, Kyoto University, Kyoto 615-8510, JapanThe squirmer model is a theoretical model introduced to study microorganisms like algae andbacteria. It consists in a spherical particle whose self-propulsion is ensured by a surface velocity
field [1].
It is well established in literature that the presence of walls can strongly modify the motion of
microorganisms. The bacterium E. Coli, indeed, is known to perform clockwise trajectories near asolid boundary [2]. On the other hand the gravity force, ubiquitous in nature, represents anotherfactor that can affect the motion of microorganisms [3-4].
In this work, using the Smoothed Profile Method [5], we combine all of these features studying the
dynamics of a sedimenting squirmer under the effect of the gravity force, near a solid boundary
taking into account the rotlet dipole term [6].
Computing quantities like the stationary swimming velocity, the stable swimming height, thestationary orientation and curvature radius we are able to characterize the dynamics of the single
squirmer.
In case of neutral squirmers and pullers, the gravity causes both of them to sediment to the bottom
wall, arresting their motion and reorienting them in a direction perpendicular to the wall. Pushers,
instead, exhibit continuous motion with tilted direction.
When the rotlet dipole term is neglected and the “classic” squirmer model is considered, all of typesof squirmers swim in straight trajectory. When the rotlet dipole term is introduced, it causes a
deviation from the straight path in circular trajectories whose radius of curvature strongly depends
by the magnitude of the rotlet dipole term.
After studying the single squirmer, the collective dynamics of squirmers is considered.
Acknowledgements
F. Fadda warmly thanks Norihiro Oyama whereas R. Yamamoto thanks Holger Stark forenlightening and stimulating discussions.
This research is supported by the Japan Society for the promonition of Science (JSPS) KAKENHI(17H01083) grant, and the JSPS bilateral joint research projects.
References[1] M.J. Lighthill, Commun. Pure Appl. Math. 5, 109 (1952); J.R. Blake, J. Fluid Mech. 46, 199(1971).
[2] E. Lauga, W. R. DiLuzio, G.M. Whitesides and H.A. Stone, Biophys. J. 90, 400 (2006).
[3] F. Rühle, J. Blaschke, J.-T. Kuhr and H. Stark, New J. Phys. 20, 025003 (2018); J.-T. Kuhr, F.
Rühle and H. Stark, Soft Matter 15, 5685-5694 (2019).
[4] Z. Shen, A. Würger and J.S. Lintuvuori, Soft Matter 15, 15-8-1521 (2019); Z. Shen and J.S.
Lintuvuori, arXiv:1905.11332v1 (2019).
[5] J.J. Molina, Y. Nakayama and R. Yamamoto, Soft Matter 9, 4923 (2013); Y. Nakayama and R.
Yamamoto, Phys. Rev. E 71, 036707 (2005); Y. Nakayama and R. Yamamoto, Eur. Phys. J. E 26,
361-368 (2008).
[6] E. Lauga, Annu. Rev. Fluid Mech. 48, 105 (2016).
11

Contributed talkActive Matter Workshop 2020

13:30 - 13:50

Novel boundary conditions and topological dynamics
of bacterial turbulence
Daiki Nishiguchi1, Andrey Sokolov2, Henning Reinken3,
Sebastian Heidenreich4, Markus Bär4, Sabine H.L. Klapp3, Igor Aranson5
1

Department of Physics, The University of Tokyo, Japan
Materials Science Division, Argonne National Laboratory, USA
3
Institute for Theoretical Physics, Technische Universität Berlin, Germany
4
Department of Mathematical Modelling and Data Analysis,
Physikalisch-Technische Bundesanstalt Braunschweig und Berlin Germany
4
Department of Biomedical Engineering, Chemistry and Mathematics, Pennsylvania State University, USA
2

Collective motion of swimming rod-shaped flagellated bacteria, such as Eschelichia coli and Bacillus
subtilis, emerges as a result of competition between excluded volume interaction and hydrodynamic
instability [1]. In usual situations, hydrodynamic instability leads to spatio-temporally chaotic collective
behavior only with local short-range orientational order, which is termed active turbulence. Such turbulent
behavior has been observed in many systems including bacteria, mammalian cell culture, active colloids [2],and reconstituted biofilament systems. Although such turbulent phases seem rather universal, many realistic
situations require ordered and/or robust motion of the moving elements as seen in collective cell migrations
during developmental processes of multicellular organisms. How can such orders arise from intrinsicallychaotic fluctuating phases?
To address this question, we have previously conducted systematic experiments of bacterial turbulence
under periodic constraints and reported that bacterial turbulence self-organizes in antiferromagnetic vortex
lattices between microscopic pillar arrays with periodicity comparable to its intrinsic correlation length [3].
Recently we have found that the pillars generate characteristic topological flow profiles around them
depending on their diameters. To explain the macroscopic emergent order and the topological properties ofbacterial turbulence, we have experimentally extracted new boundary conditions for continuum equations ofbacterial turbulence. By using these boundary conditions, we have succeeded in numerically reproducing allof our experimental findings both qualitatively and quantitatively [4]. By making use of our understandingon the topology of bacterial flow field, we can predict that bacterial turbulence can also self-organize in both
hexagonal-lattice and Kagome-lattice antiferromagnetic vortex order. This gives a new methodology totopologically control microbial systems.

(a) Vorticity of bacterial turbulence in square lattices. (b) Instantaneous flow. Scale bar: 50 µm
[1] D. Nishiguchi, K. H. Nagai, H. Chaté, M. Sano, Phys. Rev. E 95, 020601(R) (2017)[2] D. Nishiguchi, M. Sano, Phys. Rev. E, 92, 052309 (2015)[3] D. Nishiguchi, I.S. Aranson, A. Snezhko, A. Sokolov, Nat. Comm., 9, 4486 (2018)[4] H. Reinken, D. Nishiguchi, S, Heidenreich, et al., under review.

12Contributed talkActive Matter Workshop 2020

13:50 - 14:10

Anomalous topological active matter
Kazuki Sone1, Yuto Ashida11Department of Applied Physics, The University of Tokyo

Topological materials including topological insulators have attracted much interest in condensed matterphysics. The topologically nontrivial systems exhibit unidirectional modes propagating along the edge of thesample. Such edge modes accompany a nonzero topological index calculated from the bulk mechanics,
which is known as the bulk-edge correspondence. The topological index is invariant under the continuous
deformation of the Hamiltonian, and thus guarantees that the edge modes exist robustly against disorder. The
most prototypical example is the quantum Hall effect observed under a strong magnetic field, where thequantized Hall conductance can be linked with the bulk topological invariant. Nowadays, similar phenomena
are observed without external magnetic fields (i.e., the quantum anomalous Hall effect) and in time-reversal
symmetric systems (i.e., the quantum spin Hall effect), which are considered as typical topological systems.
While conventional topological materials are studied in the electronic systems described by quantum
mechanics, recent researches have shown that classical systems can also exhibit topologically nontrivial
features. In classical systems, one can make the analogy between linearized dynamics and the Schrödinger
equation and thus can obtain the mathematically equivalent problems. The classical counterpart ofeigenstates in quantum mechanics is the natural oscillation modes of physical observables, such as densityand velocity. Therefore, a topological classical system exhibits robust unidirectional wave modes localized at
the edge of the system.
Here, we construct an active-matter counterpart of the quantum anomalous Hall effect [1]. Whileprevious studies must introduce intricate structures to realize the counterparts of the quantum Hall effect, ourmodel removes them and expands the possibility of experimental realizations and applications. In thispresentation, I will show some numerical results demonstrating the existence of a topological edge mode in
our active-matter model.

Fig.１： Topological active matter with a kagome-lattice structure [1].

Fig.２： Edge-localized topological sound mode in our model [1]. Its density-oscillation profile is presented.

References
1. K. Sone and Y. Ashida “Anomalous Topological Active Matter”, Phys. Rev. Lett. 123, 205502 (2019).

13

Contributed talkActive Matter Workshop 2020

14:10 - 14:30

Emergence of Hyperuniform state at Generalized Active
Ornstein-Uhlenbeck Particle System
Hiromichi Matsuyama1, Xia You, Takeshi Kawasaki, Kunimasa Miyazaki
1

Department of Physics, Nagoya University

Active Matter system features the emergence of the various collective behavior due to their selfpropelling force [1]. One of the most famous examples of collective behavior is Motility induced phaseseparation (MIPS). MIPS is resemble to liquid-vapor phase separation even when there is no attractive
interaction force and no alignment force. The long ranged density fluctuation is observed when MIPS takes
place [2].
Active Ornstein-Uhlenbeck Particle (AOUP) is one of the theoretical models for active matter [3]. Selfpropelled force of AOUP obeys Ornstein-Uhlenbeck process. Therefore, self-propelled force is basicallysame as the Non-Markov noise with a finite memory time !" . AOUP model also exhibits MIPS.
We have generalized AOUP model to add the finite memory time !# for particle interaction [4]. Our
new model which is called Generalized AOUP (GAOUP) has two memory time scales. This model enables
us to connect seamlessly the non-equilibrium AOUP model with non-Markov equilibrium Brownian motion.
Previous works pay attention only the two limited cases: !# → 0 (AOUP system) and !" = !# (equilibrium
underdamped Langevin system).
We have performed Brownian dynamics simulation of GAOUP system and found the MIPS emerges in
the !" > !# regime. In this regime, the static structure factor((*) develops a pronounced peak at small *’s. On the other
hand, we have found Hyperuniform state emerges in the!" < !# regime. Hyperuniformity is the phenomena which
the long-range density fluctuations of the system issuppressed [5]. This is opposite behavior of MIPS. In
previous work, it is known that hyperuniformity emerges
near the critical point of absorbing transition and Jamming
transition. The chiral active particle which undergoes
absorbing transition also shows hyperuniform state [6].
However, our GAOUP system does not undergo any phasetransition behavior. The Hyperuniform state is characterized Figure 1: The !" − !# phase diagram in GAOUP system.
by the behavior of ((*) near the original point. Our Red dots represent Hyperuniformity state. Blue and
GAOUP model shows ( (*) ∼ *..0 at small * ’s. This Purple dots represent MIPS state. Black line represents
equilibrium state. The value corresponds of color bar
exponent is not same as any of those previous work. In this thecorrespond to the exponent of ((*) near the originaltalk, I discuss about the feature of Hyperuniformity in point.
GAOUP system.

References
1. C. Bechinger et al: “Active particles in Complex and crowded environments”, Rev. Mod. Phys. 88,
045006 (2016).
2. Y. Fily and M. C. Marchetti: “Athermal Phase Separation of Self-Propelled Particles with no
Alignment”, Phys. Rev. Lett. 108, 235702 (2012).
3. É. Fodor et al: “How Far from Equilibrium Is Active Matter”, Phys. Rev. Lett. 117, 038103 (2016).
4. Xia You,  Active Ornstein-Uhlenbeck Particle
master thesis, Nagoya University
5. S. Toquato, “Hyperuniform states of matter”, Phys. Rep. 745, 1–95 (2018).
6. Q. Lei et al, Sci. Adv. 5, eaau7423 (2019).

14

Plenary lecture

Active Matter Workshop 2020

14:40 - 15:20

Collective thinking in collective motion
1

Matthew Turner1,2
Department of Physics and Centre for Complexity Science, University of Warwick, UK
2
Department of Chemical Engineering, University of Kyoto, Japan

Life requires movement. This is seen in individual cells, organisms and collections of organisms. The
purpose of motion is to enhance an organism’s fitness in an uncertain world. For example, the fitness
associated with a wound-healing skin cell is not directly related to its speed but rather to what its motion
contributes to the fitness of the organism that it repairs, given a risk of infection or mis-function.
I ask whether those of us interested in understanding the movement of animal swarms may have been too
ready to use “off-the-shelf” theoretical physics. For example, the prevailing assumption that all animalswarms are controlled by local interactions, like the spin models familiar in physics, has never been properly
tested. More physiologically plausible models, based directly on vision, are now becoming available [1,2].
Our recent work involves a “bottom-up” approach. Here, a fitness principle is used to derive thedynamics, rather than these being coded into the structure of a model at the outset. We study such a fitness
principle in which agents take actions that give them access to the greatest number of different (visual) statesof the world in the future [2]. They do this by first explicitly computing each state on a decision tree of their
future actions and then selecting the best branch/action in the present. Such “Future State Maximisation”(FSM) algorithms may provide fitness in an uncertain world for rather general reasons, giving more options
to choose between in the future. They are also naturally consistent with a propensity for energy
accumulation, providing more options; and risk avoidance, mitigating against option-poor outcomes. Finally,
we construct heuristics mimicking FSM could operate under animal cognition in real time. Such aninheritable heuristic trait may represent the first candidate for a “bottom-up” explanation of the emergence ofswarm behaviour in higher animals.

Fig.１： Agents, moving together in a swarm, decide how to move by using sensory input to inform a(heuristic) model of the future. They employ such a model to choose actions in the present that give themaccess to the maximum number of different states in the future. This generates remarkably realistic collective
dynamics (snapshot shown). We propose heuristics based on this principle that could operate under animal
cognition. Counter-intuitively, the collective motion of higher animals may be the most promising system inwhich to test these ideas, although they may also apply much more generally, even to single-celled organisms.

Acknowledgements
My talk incorporates the work of several dedicated PhD students, including D. Pearce, A. Miller, A. King
and, in particular here, H. Charlesworth.
References
1. D.J.G. Pearce, A.M. Miller, G. Rowlands and M.S. Turner: “The Role of Projection in the Control ofBird Flocks”, PNAS, 111, 10422 (2014).
2. H.J. Charlesworth and M.S. Turner: “Intrinsically motivated collective motion”, PNAS, 116, 15362(2019).

15

Contributed talkActive Matter Workshop 2020

15:20 - 15:40

Collective motion of C. elegans
Ken H. Nagai1, Hiroshi Ito2, Takuma Sugi3
1

Japan Advanced Institute of Science and Technology
2
Kyushu University
3
Shiga University of Medical Science

Ordered structures ubiquitously emerge in collective motions of self-propelled objects including birds
and fish. Using bacteria and motile cells on a substrate, it has been found that various animate collective
motions are governed by simple rules [1, 2]. In contrast to unicellular living organisms, unclear is what kindsof collective motion of animals can be described by simple descriptions like the Vicsek model, since animals
generically have little experimentally controllable parameters.
It is known that some kinds of nematode collectively form ordered structures in naturalenvironments. To reproduce the structures in a laboratory, we developed a new cultivation method of
Caenorhabditis elegans (C. elegans) with which the density of worms become much higher thanconventional methods. The highly concentrated worms formed dynamical networks on various substrates as
seen in Figure 1. The structure was kept dynamically agitated and transformed into a different network inaround 100 s.
C. elegans is one of model animals used in various fields of study; therefore, various methods toaffect the motility and various motility mutants are known. Utilizing the knowledges about C. elegans, weinvestigated the dependence of the dynamical network on various parameters such as the ambient humidity,
the density of the worms, and the motility characteristics which can genetically be modified.
Next, we formulated a minimal self-propelled multi-agent model which have two characteristics
which were found in isolated worm’s motility: long-time memory of rotation rate, and nematic alignment of
two worms after collision. The model reproduced the formation of the dynamical network of the worms. Not
only the formation but the dependences on various parameters were well reproduced by the simple model,
which indicates that the two characteristics mainly govern the collective motion of C. elegans [3].

Figure 1: Dynamical network formed by a large number of C. elegans
on a glass plate. The scale bar corresponds to 2 mm.
References
1. Y. Sumino, K. H. Nagai, Y. Shitaka, D. Tanaka, K. Yoshikawa, and K. Oiwa, Nature, 483, 448-452(2012).
2. D. Nishiguchi, K. H. Nagai, H. Chaté, and M. Sano, Phys. Rev. E, 95(2), 20601 (2017).
3. T. Sugi, H. Ito, M. Nishimura, and K. H. Nagai, Nat. Commun., 10, 683 (2019).

16

Contributed talkActive Matter Workshop 2020

16:00 - 16:20

Kinetic transport simulation of chemotactic bacteria
Shugo YASUDA1
1

Graduate School of Simulation Studies, University of Hyogo, Kobe 650-0047, Japan

Collective dynamics of autonomous agents such as bacteria swarm and fish school have long been an active
research area in natural sciences. Nowadays, it also draws great attention from engineering researchers dueto the emergence of autonomous technologies such as swarm robotics and intelligent materials.
Simulation technology for the collective dynamics of autonomous agents may play an important role inelucidation of the complex natural phenomena and innovative development of the cutting-edge technologies.
This talk concerns a novel computational approach to the collective dynamics of chemotactic bacteria basedon a Boltzmann type transport equation, say a kinetic chemotaxis equation. The kinetic chemotaxis
equation1-3 and its novel stochastic numerical method4 are introduced. Traveling band and colony patternformation of chemotactic bacteria are investigated focusing on the multiscale mechanics behind thecollective dynamics5,6. Simulation results are also compared to some experimental and theoretical results.

Acknowledgements
This talk is financially supported by Japan Society for the Promotion of Science under the KAKENHI grant
No 17H01083.
References
1. R. Erban and H.G. Othmer: “From individual to collective behavior in bacterial chemotaxis”, SIAM J.
Appl. Math. 65, 361 (2004).
2. B. Perthame, Transport Equations in Biology (Basel: Birkhäuser, 2007).
3. B. Perthame, W. Sun, M. Tang, and S. Yasuda: “Multiple asymptotics of kinetic equations with internal
states”, Math Models Methods Appl Sci, (in print). (arXiv:1907.11043)
4. S. Yasuda: “Monte Carlo simulation for kinetic chemotaxis model: an application to the traveling
population wave”, J. Comput. Phys. 330, 1022 (2017).
5. V. Calvez, B. Perthame, and S. Yasuda: “Traveling wave and aggregation in a flux-limited Keller-Segelmodel”, Kinet. Relat. Mod. 11, 891 (2018).
6. B. Perthame and S. Yasuda: “Stiff-response-induced instability for chemotactic bacteria and flux-limited
Keller-Segel equation”, Nonlinearity 31, 4065 (2018).

17

Contributed talkActive Matter Workshop 2020

16:20 - 16:40

Locomotion of soft robot by applied magnetic field
TSUMORI Fujio and MAEDA Kazuki

Dept. Mechanical Engineering, Kyushu University, JAPANIn this work, authors propose a simple system to realize bio-mimic motion using a soft material
dispersed with magnetic particles. The developed elastic body with magnetic elements could be actuated by
an applied magnetic field.
Schematic image of the proposed actuator is shown in Fig. 1. A rubber magnet sheet, which is a mixtureof rubber and magnetic particles, is magnetized by an applied magnetic field (Figs. 1a, b). The sheet is cut
into block elements (Fig. 1c), and these magnetic elements are embedded in a silicone structure (Fig. 1d).
Figure 2 shows an example of a fabricated worm-type soft robot actuated under a rotating magnetic field.
The structure had 8 magnetic elements, which were arranged with their magnetized orientation changed by
90 degrees to the neighbors. As a result, the structure generated wavy motion, and propagation of this wave
caused simple crawling locomotion in a gap between 2 parallel walls.
(a)

(b)

Silicone sheet
dispersed withmagnetic powder

(c)

(d)
2 mm
Silicone rubber

Fig. 2: Snapshots of actuated sample between
a gap under a rotating magnetic field.

Fig. 1: Flow of the fabrication process.

In the previous example, worm-like motion was realized with a simple arrangement of magnetic
elements. Next, we show one design method of this arrangement using genetic algorithm (GA). We prepareda mass-spring-damper model to express the elastic structure as shown in Fig. 3. We could set magnetic
elements inside, to which rotation moments were exerted by an applied magnetic field. This virtual structure
can deform periodically under a rotating magnetic field. We prepared 32 virtual crawlers in a computer for
GA. Figure 4 shows an example of a crawler. After evolution of 100 generation, the crawler obtained wavy
motion for locomotion.
Detailed explanation of the experiment and GA calculation will be given in the workshop.

Fig. 4: Crawler after evolution of 100
generation. The structure obtained wavy
motion for locomotion.

Fig. 3: Schematic of mass-spring-damper
model of a crawler.

18

Contributed talkActive Matter Workshop 2020

16:40 - 17:00

Emergence of large-scale propagative signals during epithelial cell
migration
Estelle Gauquelin1, Marc-Antoine Fardin2, Benoit Ladoux2
1

2

WPI-iCeMS, Kyoto University, Kyoto, Japan.
Institut Jacques Monod, Paris University, CNRS UMR 7592, Paris

Collective cell migration is a fundamental phenomenon in biology involved in processes such asmorphogenesis and tissue repair. Various mechanisms play a role in the regulation of tissue expansion
during collective cell migration, including cell proliferation, as it can indeed disturb the dynamic
organization of cell monolayer. This work was thus focusing on the study of collective cell behaviors
and their link with cell proliferation.
We developed an in vitro assay using micro-fabrication techniques (Figure 1.a), including microcontact printing, to compare the migrating behavior of cell monolayers with and without cellproliferation, and to measure the local effects of cell division on their environment in migrating tissues.
We first measured velocities within the monolayer on a global scale. In the case of migration
without proliferation, patterns of high velocities appear in the monolayer, propagating from the front of
migration toward the bulk (Figure 1.d) [1], [2]. Those velocity waves can propagate on distances aslong as few millimeters within the tissue. When there is proliferation, the waves are unable to propagate
on long distances and are rapidly damped within the monolayer (Figure 1.c) [1]. Our study of local
velocity fields surrounding division events during migration shows that there is a competition between
velocities induced by division events and the global velocity of migration, suggesting that divisions
create defects that prevent the propagation of the velocity waves towards the back of the migrating
monolayer.

Figure 1. (a) Schematic representation of the protocol. Cells are first cultured overnight on a segment of
micropatterned lines restricted by a block of PDMS (left), then the block is removed and the cells are free toinvaded the fibronectin substrate (right). (b) Snapshot of a monolayer 16 hours after the start of the experiment.
The white arrow indicates the location of the front at t = 0, that is when recording starts. (c) Spatiotemporal
diagrams of the velocity with divisions. (d) Spatiotemporal diagrams of the velocity without divisions.

Acknowledgements
We acknowledge Sham Tlili and Francois Graner for the discussions.
[1] E. Gauquelin et al., “Influence of proliferation on the motions of epithelial monolayers invading adherent
strips,” Soft Matter, vol. 15, no. 13, pp. 2798–2810, Mar. 2019.
[2] S. Tlili et al., “Collective cell migration without proliferation: density determines cell velocity and wave
velocity,” R. Soc. Open Sci., vol. 5, no. 5, p. 172421, May 2018.

19

Contributed talkActive Matter Workshop 2020

17:00 - 17:20

Spontaneous spatiotemporal ordering of shape oscillations
enhances cell migration
Matteo Campo1,2, Simon K. Schnyder3, John J. Molina4, Thomas Speck1, and Ryoichi Yamamoto4,5
1 Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudingerweg 7-9, 55128 Mainz, Germany.
2 Graduate School Materials Science in Mainz, Staudinger Weg 9, 55128 Mainz, Germany
3 Fukui Institute for Fundamental Chemistry, Kyoto University, Kyoto, 606-8103, Japan
4 Department of Chemical Engineering, Kyoto University, Kyoto, 615-8510, Japan
5 Institute of Industrial Science, The University of Tokyo, Tokyo 153-8505, JapanThe migration of cells is relevant for processes such as morphogenesis, wound healing, and invasion ofcancer cells. In order to move, single cells deform cyclically. However, it is not understood how these shapeoscillations influence collective properties. Here we demonstrate, using numerical simulations, that theinterplay of directed motion, shape oscillations, and excluded volume enables cells to locally ‘‘synchronize’’
their motion and thus enhance collective migration. Our model captures elongation and contraction of
crawling ameboid cells controlled by an internal clock with a fixed period, mimicking the internal cycle ofbiological cells. We show that shape oscillations are crucial for local rearrangements that induce ordering ofneighboring cells according to their internal clocks even in the absence of signaling and regularization. Ourfindings reveal a novel, purely physical mechanism through which the internal dynamics of cells influences
their collective behavior, which is distinct from well known mechanisms like chemotaxis, cell division, andcell–cell adhesion.

Figure: a) Sketch of cell shape and forces in the extension and contraction states. b) Illustration of the cyclic
crawling. c) The flux of cells is significantly enhanced when increasing the duration of the cell cycle, and thecritical packing fraction shifts from 0.65 to 0.8. (d,e) Local correlation function of the internal time C(r) andstage S(r) for long cycle duration, showing the emergence of the correlation/anti-correlation pattern in space,responsible for the enhancement of the flux.
References
1. Schnyder, S. K., Molina, J. J., Tanaka, Y. & Yamamoto, R. Collective motion of cells crawling on asubstrate: Roles of cell shape and contact inhibition. Sci. Rep. 7, 5163 (2017).
2. Campo, M., Schnyder, S. K., Molina, J. J., Speck, T. & Yamamoto, R. Spontaneous spatiotemporalordering of shape oscillations enhances cell migration. Soft Matter 15, 4939–4946 (2019).

20

Contributed talkActive Matter Workshop 2020

17:30 - 17:50

Polar pattern formation induced by contact 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 650-0047, Japan
2
Mechanobiology Institute, National University of Singapore, Singapore 117411, Singapore.
3
Universal Biology Institute, University of Tokyo, 7-3-1 Hongo Bunkyo-ku, Tokyo 113-0033, Japan
4
Faculty of Life and Environmental Sciences, University of Tsukuba, Tennodai, 1-1-1, Tsukuba, Ibaraki 305–
8572, Japan

Biophysical mechanisms underlying collective cell migration of eukaryotic cells have been studied
extensively in recent years. One paradigm 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 bandshowing 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 bandpropagation. These findings describe a novel mechanism of collective cell migration involving cell–
cell interactions capable of inducing traveling band with polar order.

21

Focus lecture

Active Matter Workshop 2020

17:50 - 18:30

Comparative Mapping of Migrating Cell Morphology and Phase-Field Modeling
Daisuke Imoto1, Nen Saito2, Satoshi Sawai1
1

3

Graduate School of Arts and Sciences, University of Tokyo
Research Center for Complex Systems Biology, Universal Biology Institute, University of Tokyo
2
Department of Physics, Graduate School of Science, University of Tokyo

Cell shape itself is one of the key factors in deciphering how the direction of cell migration isdetermined. Studies over the years have described the shape dynamics of migrating cells mathematically.
Due to the complexity and the dynamic nature, however, how well mathematical models describe the realcell morphologies has remained almost completely untested. This is challenging especially for highly
dynamic and varying morphologies in various cell-types of amoeboid and mesenchymal natures that arelargely context-dependent and plastic. In this talk, I will introduce a conceptual model that describes thecore regulatory logics of cytoskeletal regulation combined with interface dynamics using the phase-fieldapproach. We demonstrate that similarities between the simulated data and real cell data can be assessed byfeature extraction by deep learning and that by doing so allows one to understand some key parameter
important for shape determination both between species and within differentiating cells.

22Active Matter Workshop 2020

Day 2
11 Jan., 2020
10:00 - 10:20
10:20 - 10:40
10:40 - 11:00
11:00 - 11:20

Contributed talk (H. Ebata)
Contributed talk (R. Kurita)
Contributed talk (M. Okada)Contributed talk (K. Yasuda)

11:30 - 12:10 Focus lecture (Y. Iwadate)
13:40 - 14:20 Focus lecture (J. J. Molina)
14:20 - 15:00 Focus lecture (P. Sens)
15:00 - 15:10 Closing

23

Contributed talkActive Matter Workshop 2020

10:00 - 10:20

Self-replicating pattern driven by granular segregation
Hiroyuki Ebata1, Shio Inagaki2
1

Institute for materials Chemistry and Engineering, Kyushu University, Fukuoka 812-8581, Japan2
Department of Physics, Kyushu University, Fukuoka 812-8581, Japan

Self-replicating patterns reminiscent of biological cell replication have been discovered in chemical
reaction-diffusion systems [1] and vertically vibrated wet granular systems [2]. However, it is still unclear
whether universal laws underlay the dynamics of self-replicating patterns in the different systems. Does selfreplication in different systems merely resemble each other in appearance? To answer the question, weinvestigate the statistical features of different types of self-replication especially around the bifurcation point.
Here, we report a new experimental system of self-replicating pattern, which is horizontally shaken dry
granular bed. The granular bed that consists of two different particles is placed in quasi-2D container (Fig. 1(a)). We horizontally shake the container parallel to short axis of the container. As a result, granularsegregation occurs, and band pattern appears parallel to the short axis. Segregation bands are widely reported
for the granular mixture in the rotating drum. In the case of rotating drum, segregation is driven by theavalanche. Similar to the rotating drum, in our experiment, segregation is driven by surface flow. As we
increase the size ratio of two particles, the dynamics of bands bifurcate from coarsening through replication
to oscillation (Fig. 1 (b)). Above certain vibration frequency, the bands continuously replicate and annihilate
as they spread out upon the surface of the granular bed. Spatiotemporal plot of the replicating band
resembles the Sierpinski Gasket which was found in the replicating spot of a 1D reaction-diffusion system[3]. Statistical properties of birth and death rates of patterns are similar to those in the Gray-Scott model [4]and vibrated wet granular systems [2] (Figs. 1 (c) and (d)).

Fig. 1 (a) Experimental set up. Orange and blue colors indicate different types of granules. (b) Snap shot of aself-replicating band. Black and white color indicate small and large particles. (c) Birth (blue) and death (red)rates of bands as a function of total number of bands. (d) Probability distribution function of duration time ofreplication.

References
1. J. E. Pearson, Science 261, 189 (1993).
2. H. Ebata and M. Sano, Phys. Rev. Lett. 107, 088301 (2011).
3. Yumino Hayase and Takao Ohta, Phys. Rev. Lett. 81, 1726 (1998).
4. H. Wang and Q. Ouyang, Phys. Rev. Lett. 99, 214102 (2007).

24

Contributed talkActive Matter Workshop 2020

10:20 - 10:40

Active hole generation in an ionic liquid droplet into a binary
solvent
Noriko Oikawa1,2, Rei Kurita2
1

2

Osaka Prefecture University, 1-1 Gakuen-cho, Nakaku, Sakai, Osaka
Tokyo Metropolitan University, 1-1 Minamioosawa Hachioji-chi, Tokyo

Liquid–liquid dissolution, which is a dissolution of a liquid solute into a liquid solvent, is one of thebasic and typical processes in non-equilibrium systems. In the liquid–liquid dissolution, in which substances
are transported and exchanged in the solvent, the local free energy should be taken into account, as well as
the total free energy of the whole system. The dynamics of the dissolution is separated by a critical point of
the phase separation. Above the critical temperature, the dissolution follows the diffusion equation, on theother hand, the droplet shrinks with sharp interface below the critical temperature. In liquid–liquid
dissolution, the critical point of phase separation is determined by the temperature. When the solvent consistsof multi-components, in contrast, the mole fractions in the solvent also take on the role of control parameter.
In this study, an ionic liquid dissolves into a binary solvent composed of ethanol and water. It is found in
this system that, near the critical point, a hole is spontaneously created in the droplet of the ionic liquid [1].
The creation of the hole is initiated by a mutual interaction between the concentrations of the ionic liquid andthe binary solvent via their affinity. A spatial inhomogeneity of the interfacial tension is induced through anamplification of fluctuation in the concentration due to an instability mechanism, and causes the Marangoni
effect to create the hole. The hole moves inside the droplet and consequently leads to the motion of thedroplet. The present system provides not only a new type of dissolution process but also a peculiar exampleof active matter realized in a liquid droplet.

Fig. 1 : Dynamics of the active holes [1]. The time interval between the images is 10 s. The images aretrimmed at the same position and the contrast was added. The bar in (a) indicates 1 cm.

References
1. Noriko Oikawa, Keita Fukagawa and Rei Kurita : “Active hole generation in a liquid droplet dissolving
into a binary solvent”, Soft Matter, 14, 4952-4957 (2018).

25

Contributed talkActive Matter Workshop 2020

10:40 - 11:00

Relationships between spontaneous deformation and fission of an oil
droplet on a surfactant aqueous solution.
Masahide Okada1, Hiroaki Ito2, Yutaka Sumino3, Hiroyuki Kitahata2
1

Graduate School of Science and Engineering, Chiba University,
2
Graduate School of Science, Chiba University
3
Department of Applied Physics, Faculty of Science, Tokyo University of Science
Oil droplets of tetradecane with palmitic acid (PA) on an aqueous solution of stearyltrimethylammonium
chloride (STAC) exhibit spontaneous deformation and fission[1-2]. The droplet behavior depending on theconcentration of STAC and PA was reported[1]. The droplet that exhibits deformation without fission has been
well studied. Boundaries of the droplets expand in a circular shape and then shrink (blebbing). The blebbingof the droplet is driven by the generation and rupture of a gel layer composed of STAC and PA and leads thedroplet deformation and fission[2]. The fission mechanism of the droplet is different from that of typical
droplet systems, in which droplet fission is driven by Marangoni effect[3].
Figure 1 shows typical droplet behaviors for the STAC concentration C =2 mM. The oil droplet
spontaneously splits into small fragments. To investigate the characteristics of the fission, we measured thetime series of the number of the droplets for various C. From the time series, we confirmed that the final
number of the droplets Nfin has a peak at a certain C as shown in Fig. 2. Since the droplet fission should be
induced by the deformation, we analyzed the droplet deformation for various C and obtained the time evolutionof the boundary velocities of the droplet deformation. From the analysis, we estimated the four parameters that
may have positive correlation with the droplet fission: typical angle of blebbing, typical timescale ofexpansion, growth rate of blebbing, and blebbing size. From our experimental results, we will discuss therelationship between the droplet fission and the four parameters.

Fig. 1: Typical snapshots of the droplet fission for the
STAC concentration C =2 mM. Scale bar: 10 mm.

Fig. 2: Finial number of the droplet Nfin for various C.
Error bars represent standard deviations.

References
1. Y. Sumino et al., “Spontaneous Deformation of an Oil Droplet Induced by the Cooperative Transport of
Cationic and Anionic Surfactants through the Interface”, J. Phys. Chem. B 113, 48 (2009).
2. Y. Sumino et al., “Mechanism of Spontaneous Blebbing Motion of an Oil−Water Interface: Elastic Stress
Generated by a Lamellar−Lamellar Transition”, Langmuir 32, 2891 (2016).
3. L. Keiser et al., “Marangoni Bursting: Evaporation-Induced Emulsification of Binary Mixtures on a
Liquid Layer”, Phys. Rev. Lett 118, 074504 (2017).

26

Contributed talkActive Matter Workshop 2020

11:00 - 11:20

State cycle of biological nanomachines
Kento Yasuda, Shigeyuki Komura
Department of Chemistry, Graduate School of Science, Tokyo Metropolitan University

Recently, biological nanomachines, such as enzymes and motor proteins, are studied froma physical point of view [1]. These machines are defined as micromachines performing
mechanical works through catalyzed reactions of chemical spices such as ATP. It is importantto understand the physical chemistry of chemical reactions and dynamics of these micro
objects. In the over dumped systems, it was pointed out that a cycle in the state space isimportant for the net functions [2]. In this research, we focus on the state cycle and propose a
simple model of nanomachines. Especially, we investigate the relationships between the state
cycle and the parameters of chemical reactions.
To describe the system including the nanomachines and the chemical spices, we introduce
the reaction coordinate 𝜃 describing the level of chemical reactions, and the state variables 𝑠𝑖
which characterizing the state of a nanomachine. The free energy is given by𝑘𝑖
𝐺 = −𝐴𝑐𝑜𝑠𝜃 − 𝐹𝜃 + ∑ (𝑠𝑖 − 𝑑𝑖 sin(𝜃 − 𝜙𝑖 ))2 ,2𝑖where 𝐴 is the activation energy of the chemical spices, 𝐹 is the tilting force of this system.
The third term describes the coupling between chemical reaction and state of a nanomachine.
In the above, the reaction coordinate and the state variables interact periodically, and 𝑘𝑖 is theconnectivity, 𝑑𝑖 is the amplitude, 𝜙𝑖 is the phase shift. We assume that the dynamics of thevariables obey Onsager’s phenomenological equations with thermal fluctuations determinedby the fluctuation dissipation theorem. Furthermore, we focus on the state cycle quantified by“state cyclone” ,which is defined by
2 𝑡
C = lim ∫ 𝑑𝑡 ′ 𝑠1̇ 𝑠2 .
𝑡→∞ 𝑡 0First, we perform the Langevin simulation of the model and calculate the state cyclone.
The state cyclone shows nontrivial dependences on 𝐴 and 𝐹 (see Fig 1). To understand thisnontrivial results, we solve the Fokker-Planck equation analytically.

Fig. 1 State cyclone as the function of the reaction rate,
extracted from the Langevin simulations.

【References】[1] H. S. Muddana, S. Sengupta, T. E. Mallouk, A. Sen, and P. J. Butler, J. Am. Chem. Soc.
132(7), 2110–2111 (2010).
[2] I. Sou, Y. Hosaka, K. Yasuda, and S. Komura, Phys. Rev. E 100, 022607 (2019).

27

Focus lecture

Active Matter Workshop 2020

11:30 - 12:10

Rigidity sensing for directional migration in fast crawling cells
Yoshiaki Iwadate11Depertment of Biology and Chemistry, Yamaguchi Univ.

Living cells sense the mechanical properties of their surrounding environment and respond accordingly.
Crawling cells detect the rigidity of their substratum and migrate in certain directions. They can be classified
into two categories: slow-moving and fast-moving cell types. Slow-moving cell types, such as fibroblasts,smooth muscle cells, mesenchymal stem cells, etc., move toward rigid areas on the substratum in response toa rigidity gradient. This directional migration is called "durotaxis". However, there is not much information
on rigidity sensing in fast-moving cell types, such as neutrophils and Dictyostelium cells, whose size is ∼10
μm and migration velocity is ∼10 μm/min (Fig. 1A).
We recently demonstrated that both Dictyostelium cells and neutrophil-like differentiated HL-60 cells
show directional migration in response to repeated stretching of the substratum in myosin II-dependent
manner1. Cells that moved parallel to the direction of stretch changed their direction perpendicular to it2 (Fig.
1B). This observation suggests that not only slow-moving cell types but also fast types may sense the rigidityof the substratum and use this rigidity information to generate migration polarity.
To test this hypothesis, we used an anisotropic substratum that is rigid on the x axis but soft on the y axis
to demonstrate rigidity sensing by fast-moving Dictyostelium cells and HL-60 cells3. They migrated in the“soft” direction on the anisotropic substratum (Fig. 1C), although myosin II–null Dictyostelium cells
migrated in random directions, indicating that rigidity sensing of fast-moving cell types differs from that ofslow types and is induced by a myosin II–related process. This directional migration appears to be a strategy
adopted by fast-moving cells in which they do not migrate faster in the direction they want to go, but migrate
to avoid a direction they do not want to go.

Fig. 1: Rigidity sensing in fast-moving cells. A typical fast-moving cell type,neutrophil-like differentiated HL-60 cells (A). Migration of cells in response torepeated stretching of the substratum (B) and on an anisotropic substratum (C).
Acknowledgements
I acknowledge Okimura, C., Minami, K., Ueda, K. (Yamaguchi Univ.), Sato, K. (Tokushima Univ.),
Nakashima, Y. (Kumamoto Univ.), Tsujioka, M. (Tokyo Med. Dent. Univ.), Sakumura, Y. (NAIST) andShimabukuro, K. (Ube College) for their collaboration and discussion.
References
1. Iwadate, Y., Okimura, C., Sato, K., Nakashima, Y., Tsujioka, M. and Minami, K.: “Myosin-II-mediateddirectional migration of Dictyostelium cells in response to cyclic stretching of substratum”, BiophysicalJournal 104, 748-758 (2013).
2. Okimura, C., Ueda, K., Sakumura, Y., Iwadate, Y.: “Fast-crawling cell types migrate to avoid the
direction of periodic substratum stretching”, Cell adhesion & Migration 10, 331-341 (2016).
3. Okimura, C., Sakumura, Y., Shimabukuro, K., Iwadate, Y.: “Sensing of substratum rigidity anddirectional migration by fast-crawling cells”, Physical Review E 97, 052401 (2018).

28

Focus lecture

Active Matter Workshop 2020

13:40 - 14:20

Modeling the Mechanosensitive Response of Crawling Cells
John J. Molina1, Ryoichi Yamamoto1
1Department of Chemical Engineering, Kyoto University

In this work, we study the ability of cells to probe and dynamically adapt to the mechanical properties of
their surroundings, i.e., their mechanosensitivity. Experimentally, this can be studied by observing thereorientation of crawling cells over cyclically stretched substrates[1] or their motion across inhomogeneousor patterned substrates. To understand the observed cell-specific response, a model that couples the substrate
to the sub-cellular elements responsible for the cell shape and motility is needed: cell membrane, actin
cytoskeleton, and focal adhesions, among others. For such situations, continuum phase-field models havequickly become one of the most powerful and popular computational techniques. We will present a brief
overview of these modeling efforts, before showing how we have extended them in order to describe thereorientation of crawling cells over cyclically stretched substrates, among others.
Our results show that, depending on which of the sub-cellular processes is being probed, and the type of
coupling with the stretching substrate, the cells can exhibit no reorientation, a bi-stability in the parallel orperpendicular orientations, or a systematic reorientation in either direction[2]. In particular, we show that an
asymmetry in the adhesions dynamics during the loading and unloading phases of the stretching can be used
to selectively align the cells. The phase-field model we have proposed can be generalized to study themechanosensitive response of distinct cell types moving in complex environments, as well as incorporate
detailed bio-chemical/mechanical couplings, and will hopefully lead to a deeper understanding ofexperimental observations.
Acknowledgements
We acknowledge support from the Japan Society for the Promotion of Science (JSPS) Wakate B (17K17825)
and KAKENHI (17H1083) grants, as well as the JSPS bilateral joint research projects. We thank Natsuhiko
Yoshinaga, Takashi Taniguchi, Simon Schnyder, and Matthew Turner for helpful discussions.
References
1. C. Okimura, K. Ueda, Y. Sakumura, and Y. Iwadate: “Fast-crawling cell types migrate to avoid the
direction of periodic substratum stretching”, Cell Adhesion & Migration 10, 331 (2016).
2. J. J. Molina and R. Yamamoto: “Modeling the mechanosensitive response of fast-crawling cells on
cyclically stretched substrates”, Soft Matter 15, 683 (2019).

29

Focus lecture

Active Matter Workshop 2020

14:20 - 15:00

A scallop theorem for crawling cells
Pierre Sens

Institut Curie / CNRS
5 rue Pierre et Marie Curie, 75005 Paris, France
pierre.ens@curie,fr
Living cells have the ability to generate forces by converting biochemical energy into mechanicalenergy, mostly through the hydrolysis of ATP. This allows cells to actively change their shape and toundergo autonomous movement both on 2D substrates and in 3D networks. As cells typically operate at
small length scales, for which inertia can be neglected, the requirements for autonomous cell motion are very
different than those applying to macroscopic bodies. In the case of swimming cells, the “scallop theorem”
due to Ed. Purcell (1977) states that motion requires that cells undergo a series of shape changes that are
non-reciprocal in time.
In the first part of this talk, I will discuss an extension of the scallop theorem for crawling cells, whose
motion relies on the exchange of momentum with a rigid substrate. I will show in particular that, in addition
to non-reciprocal shape change, crawling also requires a mechanical feedback between the traction force
exerted by the cell on the substrate and the dynamics of cell-substrate adhesion. In the second part of thetalk, I will illustrate the relevance of temporal correlations of cellular activity for the motion of fibroblast in
3D extracellular matrix.

Fig.１： Sketch of the crawling cell model

References
1. M. Leoni and P. Sens: “Model of Cell Crawling Controlled by Mechanosensitive Adhesion”, {hys. Rev.
Lett. 118, 228101 (2017).
2. A. Godeau, M. Leoni, J. Comelles, H. Delanoe-Ayari, A. Ott, S. Harlepp, P. Sens, D. Riveline: “A scallop
theorem for crawling cells”, In preparation.

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