Active Matter Workshop 2022

Active Matter Workshop 2022

VENUE:
CMMA, Meiji Universityand via Zoom webinar

DATE:
28 - 29 January, 2022

1

Active Matter Workshop 2022

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 (RIKEN, BDR)

Web pagehttps://sites.google.com/view/activematter2022

Contact
email: active2022@googlegroups.com

2

Active Matter Workshop 2022

2022/1/28 Fri.
12:30 - 13:00
13:00 - 13:10
13:10 - 14:00
14:00 - 14:25
14:25 - 14:50
14:50 - 15:30
15:30 - 15:55
15:55 - 16:20
16:20 - 16:45
16:45 - 17:00

ProgramSelf-Registration
opening[IL:oS] Yamamoto, Takashi“Behavioral measurement of animals by biologging”[En:oL] Kuroda, Yuta
“Anomalous Long-Range Correlations in Fluid Phase of Active
Brownian Particles with Inertia”[Jp:oL] Hamada, Keisei“Spatial Correlation and Relaxation Time in Active E. coli
Suspensions”
Break[En:oL] Sugino, Yujiro“Rheology of Condensed Active Colloidal Suspension”[Jp:oL] Matsumoto, Eiji
“Mechanical adaptation of intracellular structures”[En:oL] Yasuda, Kento“Statistical property of the stochastic system with odd elasticity”
discussion===========
Presentation time
IL: Invited lectures [50 min each, including discussions]
En/Jp: Contributed presentation in English/Japanese [25 min each including
discussions]
oL/oS: online/on-site presentations, on-site presentations are also broadcast
via the Zoom webinar.
3

Active Matter Workshop 2022

2022/1/29 Sat.
9:30 - 10:00
10:00 - 10:05
10:05 - 10:55
10:55 - 11:20
11:20 - 11:45
11:45 - 13:15
13:15 - 13:40
13:40 - 14:05
14:05 - 14:30
14:30 - 15:00
15:00 - 15:25
15:25 - 15:50
15:50 - 16:40
16:40 - 17:00

Self-Registration
opening of Day 2[IL:oS] Matsuo, Muneyuki“Self-oscillating propulsion of chemically active droplet”[En/oL] Ishikawa, Hiroaki“Pairing-induced motion driven by the surface tension gradientand attractive lateral capillary interaction.”[En/oS] Moreau, Clement“Self-organised swimming with odd elasticity”
Break[En/oS] Schnyder, Simon“Role of the Cell Cycle in Collective Cell Dynamics”[En/oS] Li, Jintao“Mechanical competition between different cell types”[Jp/oL] Takada, Sakura“Shaping dynamic and static patterns in artificial cells by
modulating reaction-diffusion coupling of Min system”
Break[En:oL] Goto, Hirotaka“The emergence of aggregation phenomena in a microscopic
model of labor force migration”[En:oL] Yamagishi, Manami“Defining a Quantum Active Particle Using Non-Hermitian
Quantum Walk”[IL:oL] Kawaguchi, Kyogo“Active matter physics in multicellular dynamics and quantum
models”
discussion and closing===========
Presentation time
IL: Invited lectures [50 min each, including discussions]
En/Jp: Contributed presentation in English/Japanese [25 min each including
discussions]
oL/oS: online/on-site presentations, on-site presentations are also broadcast
via the Zoom webinar.
4

Active Matter Workshop 2022

Abstracts5Active Matter Workshop 2022

Day 1
28 Jan., 2022
12:30 - 13:00

Self-Registration

13:00 - 13:10
13:10 - 14:00

opening[IL:oS] Yamamoto, Takashi“Behavioral measurement of animals by biologging”[En:oL] Kuroda, Yuta
“Anomalous Long-Range Correlations in Fluid Phase of Active
Brownian Particles with Inertia”[Jp:oL] Hamada, Keisei“Spatial Correlation and Relaxation Time in Active E. coli
Suspensions”
Break

14:00 - 14:25
14:25 - 14:50
14:50 - 15:30
15:30 - 15:55
15:55 - 16:20
16:20 - 16:45
16:45 - 17:00[En:oL] Sugino, Yujiro“Rheology of Condensed Active Colloidal Suspension”[Jp:oL] Matsumoto, Eiji
“Mechanical adaptation of intracellular structures”[En:oL] Yasuda, Kento“Statistical property of the stochastic system with odd elasticity”
discussion===========
Presentation time
IL: Invited lectures [50 min each, including discussions]
En/Jp: Contributed presentation in English/Japanese [25 min each including
discussions]
oL/oS: online/on-site presentations, on-site presentations are also broadcast
via the Zoom webinar.
6

Invited Lecture

Active Matter Workshop 2022

13:10 - 14:00

Behavioral measurement of animals by biologging
Takashi Yamamoto

Meiji Institute for Advanced Study of Mathematical Sciences, Meiji University
Active matter includes living and non-living systems. Regarding animals, a classic example of active mattersystem is a flock of birds. Observation is the fundamental method used to study behavior of animals.
However, it is usually logistically difficult to keep chasing and observing free-ranging animals such as birds
and mammals in terrestrial/marine nature environments, and, therefore, taking observation/experiment isoften limited in time and space as well as situation. Recently, biologging technology, defined as ‘the use ofminiaturized animal-attached tags for logging and/or relying data about an animal’s movements, behavior,
physiology, and/or environment’ [1], enables us to take measurements from free-ranging animals as they
move undisturbed through their environment and interacting with other individuals [2]. For examples, GPS
device can record high-resolution spatiotemporal movement of animals (<1 second), and tracking a flock ofhoming pigeons (a consist of 10 individuals) revealed a synchronized role in pairwise interactions between
individuals [3]. Not only capturing movements, but also the use of tri-axial accelerometer tags has begun toresolve details of the 3-dimensional movement of animals [4], which can be indicative of energy
expenditures (i.e. the absolute sum of dynamic acceleration) [5]. Furthermore, the ability to instrument
animals and actively record physiological parameters such as body temperature, oxygen utilization [6], heart
rate [7] or EEG (electrical brain activity) [8] has provided important
new knowledge about how animals function. Gathering such novel
insights constructs a conceptual framework depicting the interplay
among four basic mechanistic components of organismal movement:
the internal state (why), motion (how), and navigation (when/where)capacities of the individual and external factors affecting movement,
named ‘movement ecology’ [9]. Biologging techniques could
constitute an aspect of active matter, and may enhance ourunderstanding of complex but interesting organisms’ system.

Fig.1: Data logger attached on the back of a seabird.

References
1. Rutz C., Hays G.C.: “New frontiers in biologging science”, Biology Letters 5, 289–292 (2009)
2. Boyd I.L., Kato A., Ropert-Coudert Y.: “Bio-logging science: sensing beyond the boundaries”, Memoirs of National
Institute of Polar Research 58, 1–14 (2004)
3. Nagy M., Ákos Z., Vicsek T.: “Hierarchical group dynamics in pigeon flocks”, Nature 464, 890–893 (2010)
4. Wilson R.P., Shepard E.L.C., Liebsch N.: “Prying into the intimate details of animal lives: use of a daily diary on animals”,
Endangered Species Research 4, 123–137 (2008)
5. Wilson R.P., White C.R., Quintana F., Halsey L.G., Liebsch N., Martin G.R., Butler P.J.: “Moving towards accelerationfor estimates of activity-specific metabolic rate in free-living animals: the case of the cormorant”, Journal of Animal
Ecology 75, 1081–1090 (2006)
6. Ponganis P.J., Stockard T.K., Meir J.U., Williams C.L., Ponganis K.V., Howard R.: “O2 store management in diving
emperor penguins”, Journal of Experimental Biology 212, 217–224 (2009)
7. Meir J.U., Stockard T.K., Williams C.L., Ponganis K.V., Ponganis P.J.: “Heart rate regulation and extreme bradycardia in
diving emperor penguins”, Journal of Experimental Biology 211, 1169–1179 (2008)
8. Vyssotski A., Dell’Omo G., Dell’Ariccia G., Abramchuk A.N., Serkov A.N., Latanov A.V., Loizzo A., Wolfer D.P., Lipp
H.-P.: “EEG responses to visual landmarks in flying pigeons”, Current Biology 19, 1159–1166 (2009)
9. Nathan R., Getz W.M., Revilla E., Holyoak M., Kadmon R., Saltz D., Smouse P.E.: “A movement ecology paradigm forunifying organismal movement research”, Proceedings of the National Academy of Sciences of the United States ofAmerica 105, 19052–19059 (2008)

7

Contributed Talk

Active Matter Workshop 2022

14:00 - 14:25

Anomalous Long-Range Correlations in Fluid Phase of
Active Brownian Particles with Inertia
Yuta Kuroda1, Hiromichi Matsuyama1, Takeshi Kawasaki1, Kunimasa Miyazaki1
1

Department of Physics, Nagoya University

Self-propelled particles have been widely studied as a model of active matter. The Vicsek model is oneof the most famous self-propelled particles. This model has the ordered phase reminiscent of bird flocks. In
the ordered phase, the system does not only exhibit the long-range order but is also accompanied by theanomalous increase of the number fluctuation, so-called giant number fluctuation (GNF) [1]. Anotherfamous example of self-propelled particles is the active Brownian particles (ABP). This model does not havethe alignment interaction like the Vicsek model. In the high activity regime, however, particles assemble
spontaneously and separate into dilute and dense phases. This phenomenon is called motility induced phaseseparation (MIPS).
The standard ABP model does not have the inertia term and is described by the overdamped Langevinequation. Recently, it was found that adding the inertia term to the ABP model suppresses the MIPS, and thesystem remains in the fluid phase even in high activity [3]. There are some studies of the effects of inertia on
the MIPS, but the fluid state with high activity, which arises by adding the inertia term, has not attracted
much attention so far.
We study properties of the fluid phase of the ABP with inertia term at the high activity regime andrelatively low-density. We have performed the Brownian dynamics simulation for this model and found thatthe velocity and density correlation become long-ranged and GNF is observed. While long-range velocity
correlation in the ABP model had been observed in only high-dense phases in previous studies [4], ourresults indicate that this long-range velocity correlation is not an intrinsic feature of dense systems but is a
general feature of the ABP system. Additionally, we have found that the longitudinal part of velocity
correlation is related to the density correlation and GNF. Theoretically, the part of these results can be
captured by the fluctuating hydrodynamics description qualitatively [4,5].
References
1. H. Chaté, F. Ginelli, G. Grégorie, and F. Raynaud: “Collective motion of self-propelled particles
interacting without cohesion”, Phys. Rev. E 77, 046113 (2008).
2. Y. Filly and M. C. Marchetti: “Athermal Phase Separation of Self-Propelled Particles with No
Alignment”, Phys. Rev. Lett. 108, 235702 (2012).
3. S. Mandal, B. Liebchen, and H. Leöwen: “Motility-Induced Temperature Difference in Coexisting
Phase”, Phys. Rev. Lett. 123, 228001 (2019).
4. G. Szamel and E. Flenner: “Long-ranged velocity correlations in dense systems of self-propelled
particles”, EPL. 133, 60002 (2021).
5. U. M. B. Marconi, L. Caprini, and A. Puglis: “Hydrodynamics of simple active liquid: the emergence ofvelocity correlation”, New J. Phys. 23 103024 (2021).

8

Contributed Talk

14:25 - 14:50

Active Matter Workshop 2022

6SDWLDO&RUUHODWLRQDQG5HOD[DWLRQ7LPH
LQ$FWLYH(FROL6XVSHQVLRQVKeisei Hamada<XMLUR6XJLQR, +LUR\XNL(EDWD'DLVXNH0L]XQR'HSDUWPHQWRI3K\VLFV)DFXOW\RI6FLHQFH.\XVKX8QLYWhen colloidal suspensions are concentrated, rearrangements of colloids become increasingly rare,leading to their dynamic arrest (glass transition). It has been believed that the cooperativity or
heterogeneity of thermal fluctuations underlies this anomalous phenomenon. Meanwhile, a thicksuspension of self-driven colloids, referred to as ³DFWLYH JODVV´ attracts recent interests. Numericalstudies have suggested that the active glass may avoid glass transition and remain fluidic [Nandi etal., PNAS (2018) 115, 7688] whereas cooperative dynamics during the active fluidization are largely
elusive.
The purpose of this study is to establish an experimental model system of active glass and investigate
the glassy dynamics associated with the active fluidization. By exchanging small-molecular
metabolites and metabolic byproducts via a semipermeable membrane, active glass composed of
migrating E. coli were prepared up to a volume fraction of about 40%. By varying the ratio of
migrating and non-migrating E. coli, we investigated the cooperativity of the fluctuations and therelaxation time for the rearrangement of bacteria. From the velocity fields measured by PIV (Particle
Image Velocimetry) (Fig. 1, 2), the spatial correlation of the fluctuation was calculated for both
longitudinal (‫ )צ‬and transversal (٣) directions (Fig. 3). The relaxation time of the density correlation
was also obtained by the image analysis of the E. coli suspensions (Fig. 4). It was observed that thestrength of the fluctuation and the relaxation time depended on migration activity whereas the spatial
correlation of the fluctuation did not.

Fig. 1: Velocity field (w/o migration)

Fig. 2: Velocity field (w/ migration)

w/ migration

w/ migration

w/o migration

w/o migration

mix

mix

‫צ‬
ԋ

Fig. 3: Spatial correlation of velocity field

Fig. 4: Intermediate scattering function
9

Contributed Talk



15:30 - 15:55

Active Matter Workshop 2022

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10

Contributed Talk

Active Matter Workshop 2022

15:55 - 16:20

Mechanical adaptation of intracellular structures
Eiji Matsumoto1, Daiki Matsunaga2, Shinji Deguchi2
12School of Engineering Science, Osaka University
Graduate School of Engineering Science, Osaka University

1. Introduction
In the cell, there are various protein polymers (e.g. actin filaments and microtubules), which are implicated in cell
motility and detection of the surrounding environment. These structures allow the cell to maintain homeostasis throughturnover, in which the basic condition of the cell is sustained. Currently, it remains unclear how these structures enablehomeostasis under changes in surrounding mechanical environment. In this study, we describe the adaptative behavior
of intracellular structures subjected to turnover to evaluate the cellular mechanical homeostasis.
2. Theory
In this study, intracellular structures ± such as actin filaments ± subjected to turnover are considered and assumed
to be a one-dimensional homogeneous and isotropic linear viscoelastic body (Voigt model). The structures are assumed,
as experimentally suggested1,2, to have a stable stress ߪ௦ in a mechanically adaptative state (tensional homeostasis). We
show with this model how the structure exhibits adaptive response in response to stress fluctuations caused by, e.g.,interaction with the surrounding environment and other proteins. The model is described byߪሺ‫ݐ‬ሻ ൌ ‫߳ܧ‬ሺ‫ݐ‬ሻ ൅ ߟ݀߳ሺ‫ݐ‬ሻߣ ൅ ݀ െ ߜሺ‫ݐ‬ሻ‫ ܮ‬൅ ߣ ൅ ݀ ݀ߜሺ‫ݐ‬ሻ
ൌ‫ܧ‬
െߟ
ଶ
݀‫ݐ‬
‫ ܮ‬൅ ߜሺ‫ݐ‬ሻ൫‫ ܮ‬൅ ߜሺ‫ݐ‬ሻ൯ ݀‫ݐ‬ሺͳሻ݀ߜሺ‫ݐ‬ሻሺʹሻൌ ݇ሺߪሺ‫ݐ‬ሻ െ ߪ௦ ሻ݀‫ݐ‬where stress, ߪ; strain, ߳; <RXQJ¶V modulus, ‫ ;ܧ‬viscosity, ߟ; initial length, ‫ ;ܮ‬stable elastic deformation, ߣ; disturbance,
݀; length change for turnover, ߜ; and, turnover rate, ݇.
3. Result and discussion
With a linear approximation in the adaptive model consisting of equations (1) and (2), we showed that the turnover௅ା௞ఎ
behaves as a first-order lag system with time constant of ܶ ൌ, and that the structures are described by a specific௞ா
feedback system containing an integral element that assures stabilization of the structures (Fig. 1).

Fig. 1 Block diagram of the adaptation of intracellular structures
4. Conclusion
We focused on the adaptation of intracellular structures and described their behavior. Our results show that thetime constant of the adaptation that characterizes the response of the system contains the turnover rate and how it relates
to the intrinsic viscoelastic properties of the intracellular structures.
References
1. Huang et al., ³Mechanosensitive myosin II but not cofilin primarily contributes to cyclic cell stretch-induced
selective disassembly of actin stress fibers´, American Journal of Physiology Cell Physiology 320, C1153±C1163(2021).
2. Saito et al., ³What factors determine the number of nonmuscle myosin II in the sarcomeric unit of stress fibers?´
Biomechanics and Modeling in Mechanobiology 20, 155-166 (2021).

11

Contributed Talk

Active Matter Workshop 2022

16:20 - 16:45

Statistical property of the stochastic system with odd elasticity
K. Yasuda1, A. Kobayashi2, L.-S. Lin2, Y. Hosaka2, I. Sou2, S. Komura2,3,4
1

Research Institute for Mathematical Sciences, Kyoto University
Department of Chemistry, Graduate School of Science, Tokyo Metropolitan University
3
Wenzhou Institute, University of Chinese Academy of Sciences
4
Oujiang Laboratory

2

Recently, the concept of odd viscosity and elasticity has been introduced to describe interactions in theactive materials1). To describe the stochastic dynamics of a micromachine such as an enzyme (Fig.1(a)), we
have considered the over damped Langevin equations with odd elasticity which represents the activity
induced by catalytic chemical reaction. In this talk, we focus on two statistical quantities, the timecorrelation functions and the most probable path.
As the first topic, we focus on the time reversal symmetry of time-correlation functions and show that it
will be broken in the presence of odd elasticity2). The time reversal symmetry holds for the cross-correlation
function for systems in equilibrium, such symmetry does not exist for non-equilibrium systems. We foundthat the time reversal symmetry of time correlation functions is broken in proportion to the odd elasticity.
In the second work, we investigate how the presence of odd elasticity influences the most probable paththat is derived by the variation of the OM integral, i.e., the OM variational principle. We show that the mostprobable outward path is different from that of the return path in micromachines (Fig.1(b)), and hence thewhole process becomes non-reciprocal due to odd elasticity3).

Figure 1 (a) A coarse-grained model of an enzyme consisting of domains that are connected to springs. A
substrate (green circle) changes into a product (orange circle) via a catalytic chemical reaction. (b) The
most probable outward path (black line) and the return path (red line). The initial and final conditions aregreen circles and orange circles, respectively.

References
1. C. Scheibner et al., Nat. Phys. 16, 475 (2020).
2. K. Yasuda et al., in preparation.
3. K. Yasuda et al., J. Phys. Soc. Jpn. 91, 015001 (2022).

12

Active Matter Workshop 2022

Day 2
29 Jan., 2022
10:00 - 10:05
10:05 - 10:55
10:55 - 11:20
11:20 - 11:45
11:45 - 13:15
13:15 - 13:40
13:40 - 14:05
14:05 - 14:30
14:30 - 15:00
15:00 - 15:25
15:25 - 15:50
15:50 - 16:40
16:40 - 17:00

opening of Day 2[IL:oS] Matsuo, Muneyuki“Self-oscillating propulsion of chemically active droplet”[En/oL] Ishikawa, Hiroaki“Pairing-induced motion driven by the surface tension gradientand attractive lateral capillary interaction.”[En/oS] Moreau, Clement“Self-organised swimming with odd elasticity”
Break[En/oS] Schnyder, Simon“Role of the Cell Cycle in Collective Cell Dynamics”[En/oS] Li, Jintao“Mechanical competition between different cell types”[Jp/oL] Takada, Sakura“Shaping dynamic and static patterns in artificial cells by
modulating reaction-diffusion coupling of Min system”
Break[En:oL] Goto, Hirotaka“The emergence of aggregation phenomena in a microscopic
model of labor force migration”[En:oL] Yamagishi, Manami“Defining a Quantum Active Particle Using Non-Hermitian
Quantum Walk”[IL:oL] Kawaguchi, Kyogo“Active matter physics in multicellular dynamics and quantum
models”
discussion and closing===========
Presentation time
IL: Invited lectures [50 min each, including discussions]
En/Jp: Contributed presentation in English/Japanese [25 min each including
discussions]
oL/oS: online/on-site presentations, on-site presentations are also broadcast
via the Zoom webinar.
13

Invited Lecture

Active Matter Workshop 2022

10:05 - 10:55

Self-oscillating propulsion of chemically active droplet
1

0XQH\XNL0DVWXR1
Graduate School of Integrated Life Sciences, Hiroshima University

The significant factor enabling the self-organization of organisms is the recursiveness of the living thingitself or a part of its state. In order to develop highly sustainable artificial systems, introducing such oscillatory
phenomenon into the system is an essential approach. Recently, recursively growing and dividing that isproliferating droplets have been reported via an autocatalytic reaction with periodic addition of a precursor
and a stimulus1. Generally, droplets could easily transport materials in and out of the liquid phase because
droplets are in a liquid phase. The construction of self-propelled droplets that self-oscillate is expected todevelop highly sustainable intelligent materials. Here we report a novel chemically active droplet that exhibits
self-oscillating propulsion independently of any oscillating reactions or perturbations in an isotropic
environment.
A hydrolysis reaction of menthylacetate (MA) intomethanol (MOH) and acetic acid was introduced to theexperimental system. When MA (2-8 PL) was dropped onto
3 mL of NaOH aqueous solution (0.1-10 mM) or ultrapure
water which filled a glass Petri dish, MA spread wet on thesurface of an aqueous solution. However, MA gradually reaggregated, and MA droplets were formed. The formed
droplets exhibited self-propulsion. Surface tension
measurements revealed that the hydrolysis product MOH
reduced the interfacial tension by up to 13 mN/m. Dropletscomposed of decyl acetate, in which MOH was replaced bydecanol, did not exhibit self-propulsion. These results
strongly suggest that self-propulsion is induced by the MOH-derived inhomogeneity of the surface tension(Figure 1). The droplet could be regarded as a chemically active swimmer.
Furthermore, at a NaOH concentration of 10 mM, MA droplets with an initial volume of more than 6 PL
exhibited oscillatory self-propulsion, i.e., repeatedly stopped and moved (Figure 2a). The oscillation was led
by the deformation of the droplet (Figure 2b). When a droplet position was fixed, a droplet beat, i.e., repeatedlyswelled and shrank. When a Petri dish was covered with a cap, no oscillating and beating were observed. These
results indicate that the oscillatory motion of the droplets is due to the synergy of MOH production andsublimation. Synchronization of chemically active droplets in self-oscillating propulsion was also observed
and should be induced by long-range interactions generated by the synergy of MOH.

Acknowledgments
This work was financially supported by the Astrobiology Center, National Institutes of Sciences, Project
Research (AB031012).
References
1. M. Matsuo, K. Kurihara: ³Proliferating Coacervate Droplets as the Missing Link between Chemistry
and Biology in the Origins of Life´ Nat. Commun., 12, 1-13 (2021).

14

Contributed Talk

Active Matter Workshop 2022

10:55 - 11:20

Pairing-induced motion driven by the surface tension gradient andattractive lateral capillary interaction.
۶Ǥ ۷‫܉ܟ܉ܓܑܐܛ‬૚, ۶Ǥ ۹ܑ‫ ܉ܜ܉ܐ܉ܜ‬૚, ‫܇‬Ǥ۹‫ܗܖ܉ܡܗ‬૛, ‫܇‬Ǥ ‫ܗܖܑܕܝ܁‬૜ଵ࡯ࢎ࢏࢈ࢇࢁ࢔࢏࢜Ǥǡଶଷࢀ࢕ࢎ࢕࢑࢛ࢁ࢔࢏࢜Ǥ ǡ ࢀ࢕࢑࢟࢕ࢁ࢔࢏࢜Ǥ ࡿࢉ࢏ǤA self-propelled particle refers a particle that creates its momentum by a free energy consumption. In
this study [1], we focus on self-propelled particles driven by the gradient in the chemical concentration
fields. In particular, we consider a system in which two species with different effects on conc entration are
mixed. In such a binary mixed particle system, as a pioneering theoretical work, a certain type of particle
chases other particles [2]. However, the previous studies have not considered the distortion of theconcentration field due to the velocity of the particles. Therefore, we considered a situation where therelaxation of the concentration field is not sufficiently fast with respect to the velocity of the particles.
Here, we construct an experimental system in which a pair of source and inert particles is driven by
surface tension gradient and attractive force. The source particle spreads the surface-active moleculesaround itself, though the inert particle does not affect the concentration field. The source and inert particles
are driven by the surface tension gradient due to the inhomogeneous concentration field. In the present
system, we used a camphor disk as the source particle. As for the inert particle we used a metal washer. In
the actual experimental systems, an attractive lateral capillary forc e is exerted between them through thedistortion of the aqueous surface. As a result, they got close to each other and then started pairing-induced
motion. They exhibited circular (Fig.1(a)) and straight (Fig.1(b)) motions for the lower and higher PEG
concentrations, respectively. Numerical calculations using a model that considers forces caused by thesurface tension gradient and lateral capillary interaction reproduced the observed circular (Fig. 1(c)) andstraight motions. In both the cases, the inert particle was in the front side, while the source particle was in
the rear side. Our results show that the effect of particle velocity cannot be overlooked in order to describe
the interaction through the concentration field.

Figure 1: (a, b) Experimental results representing by superimposed images of the camphor disk and themetal washer. (a) Circular and (b) straight motions observed on the PEG aqueous solutions at C =(a)0.001 and (b) 10 g/L. (c) Obtained by numerical results representing by superimposed images obtainedusing numerical calculations, in which the color map shows the profile of the concentration field u. The
green and pink disks represent the source and inert particles, respectively.
[1] H.Ishikawa, Y. Koyano, H. Kitahata and Y. Sumino, arXiv, 2110.11753 (2021).
[2] J. Agudo-Canalejo and R. Golestanian, Phys. Rev. Lett. 123, 018101 (2019).

15

Contributed Talk

Active Matter Workshop 2022

11:20 - 11:45

Self-organised swimming with odd elasticity
Kenta Ishimoto1, Clément Moreau1, Kento Yasuda1
1Research Institute for Mathematical Sciences, Kyoto University

Swimming in a fluid is generated by interactions between elasticity and activity of a material. In particular,
time-periodic wave-like beating is ubiquitous in nature, as seen from active elastic filaments of cilia andflagella at the microscopic scale. For an elastic material, this activity has recently been described by antisymmetric components of material elastic moduli, termed as odd elasticity [1].
In this talk, using the fundamental Purcell's three-link microswimmer model, we will show how odd
elasticity can generate a self-organised, stable swimming gait resembling those of a "pusher'' swimmer.
Moreover, motivated by the shape fluctuations originating from internal molecular motors, we demonstratethat this type of swimmer can produce net motion in one direction from random noise [2].

Fig.!" Odd-elastic three-link swimmer and its cyclic behaviour.

We focus on the elastic three-link swimmer (Fig. 1a), to which we add an antisymmetric elasticity
component. We will numerically investigate the existence of a stable limit cycle producing net locomotion,
depending on the geometry and elasticity parameters. With shape fluctuations added as a Gaussian noise, wewill then analytically study the net displacement of the swimmer using gauge field formalism [3].
The stability analysis and numerical simulations show a bifurcation occurring from a critical value of the odd
elasticity strength, with the appearance of a stable swimming pattern (Fig. 1b) materialised by a closed loop
in the phase plane of the shape angles α1, α2 (Fig. 1a,c). Furthermore, we explicitly calculate thedisplacement produced by random shape fluctuations and observe that the noisy swimmer can reach the limit
cycle from its equilibrium position (Fig. 1c,d). Beyond Purcell's swimmer, we additionally show how ourtheoretical formalism for odd elastic fluctuations can be applied to a general swimmer such as an elastic
flagellum.
This study provides a simple yet powerful model of odd elastic material to produce beating-like swimming
patterns and contributes to the understanding of the role of shape fluctuations in the displacement of microorganisms. General features of the microscopic noisy elastohydrodynamics will be useful in modelling,understanding and designing biological and artificial active materials.

References
1. C. Scheibner, A. Souslov, D. Banerjee, P. Surówka, W. T. Irvine, and V. Vitelli: “Odd elasticity”, Nature
Physics 16(475) (2020).
2. K. Ishimoto, C. Moreau, and K. Yasuda: “Self-organized swimming with odd elasticity”,
arXiv:2109.14301 (2021).
3. A. Shapere and F. Wilczek: “Geometry of self-propulsion at low Reynolds number”, Journal of Fluid
Mechanics 198(557) (1989).

16

Contributed Talk

Active Matter Workshop 2022

13:15 - 13:40

Role of the Cell Cycle in Collective Cell Dynamics
Jintao Li1, Simon K. Schnyder2, Matthew S. Turner2,1, Ryoichi Yamamoto1
1

2

Department of Chemical Engineering, Kyoto University, Kyoto 615-8510, Japan
Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom

Living cells coexist in colonies or tissues. We develop a simplified model of the cell cycle, thefundamental regulatory network controlling growth and division, and couple this to physical stress [1]. In its
simplest form, this model involves three characteristic times (for adaptation of the cell cycle, τr, and volume,τv as well as a division time, τdiv), two cell volumes (unstressed and quiescent) and a pressure at which thecell cycle stalls. We employed both particle-based computer simulations and a continuum theory to study
quasi-2D colonies growing in a channel, see Fig. 1, and on a substrate. These colonies exhibit moving
growth fronts with a profile and speed that are non-trivially related to the substrate friction and the mechanochemical cell cycle parameters, providing a possible approach to measure such parameters in experiments. In
this talk we focus on the continuum theory.

Fig. 1: The mechanochemical variables exhibit different profiles behind the moving growing front with thesimulations and continuum theory in semiquantitative agreement. Shown are steady-state average values of (a)lab-frame cell velocity u, (b) local cell pressure p, (c) cell-cycle activity r, and (d) 2D cell volume (area) v,
measured a distance z behind the leading edge of the growing colony. The solid lines are from particle-based
simulations with τ! = τ" = 5 τ#$" (darker) and τ! = τ" = τ#$" (lighter) (one standard deviation shown in gray).
The dashed lines show the continuum solution.

References
1. Li, J., Schnyder, S. K., Turner, M. S. & Yamamoto, R.: “Role of the Cell Cycle in Collective Cell
Dynamics”, Phys. Rev. X 11, 031025 (2021).

17

Contributed Talk

13:40 - 14:05

Active Matter Workshop 2022

Mechanical competition between different cell types
Jintao Li1, Simon K. Schnyder1, Matthew S. Turner2, 1, Ryoichi Yamamoto1,

1

Department of Chemical Engineering, Kyoto University, Kyoto 615-8510, Japan2
Department of Physics, University of Warwick, Coventry CV4 7AL, UK

Abstract
Competition between different cell or tissue types is a key process in fields as diverse as bacterial ecology,
developmental biology, and tumor growth. Recent studies have revealed that the homeostasis pressure issufficient to account for the output result in MDCK experiments. However, in vivo, different cell types canalso have different rates of programmed cell death (apoptosis). We study how the combination of homeostaticpressure and apoptosis rate can impact the competition process. Using an analytical model and discrete
simulation, we explore how cells coexist/outcompete with each other under two initial conditions: a nearlyplanar interface between two cell types and one in which a small nucleus of one cell type is surrounded by theother.
We explore the "boundary region" where two colonies can coexist. We found that not always the colony
with high homeostasis pressure invades the other, which apoptosis rate is also decisive for the competition
output. Also, the different dynamics from the two initial conditions indicate the tumor development needs
overcome statistical noise and Laplace pressure difference. Our findings shed light on how cancer develops
and draw attention to the cell cycle's role.

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Phase diagram for cell competition. Colorbars indicate the change in A cell as ∆ = [NA(t=100τdiv)-NA(0)]/NA(0) andprediction for the coexistence line, obtained from the continuum theory, is shown as a dashed line in each case. The
left panels (a-c) show the outcome from equal initial volumes of A and B in a channel setting. Three diﬀerent valuesof kB(0) are shown. The right panels (d-f) show three diﬀerent initial conditions containing small initial colonies ofA cells (NA(0) = 19, 7, 1 as shown in the insets) in host B tissue (0) at kB(0) = 0.1. These are results of simulations
in periodic systems of size 30 × 30.
References
1. J. Li, S. K. Schnyder, M. S. Turner, R. Yamamoto: "Role of the Cell Cycle in Collective Cell Dynamics."
Physical Review X 11.3 (2021): 031025.

18

Contributed Talk

Active Matter Workshop 2022

14:05 - 14:30

Shaping dynamic and static patterns in artificial cells by modulating
reaction-diffusion coupling of Min system
Sakura Takada1, Natsuhiko Yoshinaga2,3, Nobuhide Doi1, Kei Fujiwara1
1
2

Department of Biosciences and Informatics, Keio University.

WPI Advanced Institute for Materials Research, Tohoku University.
3

MathAM-OIL, AIST.

Reaction-diffusion coupling (RDc) is a mechanism to determine the spatiotemporal pattern of
biomolecules in cells. It induces two types of self-assembly: dynamic and static patterns. Here,
we investigated the selection mechanism of these spatiotemporal patterns by using Min waves
reconstituted in artificial cells. Min wave is a regulator of bacterial cell division plane, which
emerged by the RDc of MinD and MinE. We revealed that the balance of membrane binding anddissociation from the membrane of MinD determines the mode selection between traveling wave
and standing wave of the Min wave. We showed that the transition of the wave modes can be
regulated by controlling this balance (Fig. 1). Furthermore, by modulating the reaction networkof Min wave, we created Turing patterns (static patterns) within artificial cells. The number ofspots of Turing patterns increased depending on the spatial size, and single spots were observedin smaller space. The Turing patterns created here may explain the mechanism of moleculararrangement in living cells.

Fig. 1 Two modes of Min waves and summary of mode selection mechanism

19

Contributed Talk

Active Matter Workshop 2022

15:00 - 15:25

The emergence of aggregation phenomena in a microscopic
model of labor force migration
Hirotaka Goto1
1

School of Interdisciplinary Mathematical Sciences, Meiji University

Aggregation phenomena, which have been investigated thoroughly in biology and chemistry, arealso common to society. In this talk, we propose a mathematical model to describe the migration of
economic agents using Active Brownian particles and show by agent-based simulations that theworkforce clusters out of a random initial state. We also find that the model exhibits two well-known
empirical laws in social sciences called Zipf's and Okun's laws. Given that one can derive an extended
Keller-Segel system from the microscopic model, our results are a significant indication that theaggregation of labor force is accounted for by the same process as chemotaxis and is associated withblow-up phenomena in the PDE system.

Acknowledgements
The author thanks Dr. Kota Ikeda for thorough discussions and helpful advice.

20

Contributed Talk

Active Matter Workshop 2022

15:25 - 15:50

Defining a Quantum Active Particle Using Non-Hermitian Quantum Walk
Manami Yamagishi1, Naomichi Hatano2, Hideaki Obuse2, 3
1

Department of Physics and 2Institute of Industrial Science, the University of Tokyo
3
Department of Applied Physics, Hokkaido University

We present a model of quantum active particles using non-Hermitian quantum walks. Although there are anumber of works on active matter, most of them are conducted in classical systems. Since neither the energy
nor the momentum is conserved, it is challenging to express active-matter dynamics in terms of a quantum
Hamiltonian. In the present work, we propose a quantum walk as a suitable tool to define an active particle
in a quantum system.
Schweitzer et al. [1] studied the motion of a Brownian particle with the ability to take up energy fromthe environment, to store it inside the particle, and to convert the internal energy into the kinetic energy. In
order to describe these processes, they added a new term expressing the internal energy of the particle !(#)
on the right-hand side of the Langevin equation as follows:(1)%&̇ + )! & + +,(-) = /" !(#)& + ℱ(#).
Here, %, &, and +, denote the mass, velocity, and the potential of the particle, respectively, while )!
denotes the friction coefficient. The stochastic force ℱ(#) satisfies the following equations:〈ℱ(#)〉 = 0; 〈ℱ(#)ℱ(# # )〉 = 289(# − # # ),(2)
and !(#) denotes the internal energy of the particle which evolves according to the following equation:d(3 )!(#) = =(-) − >!(#) − /" ? " !(# ), ? " = & ∙ &.
d#Here, =(-), >, and /" ? " indicate the space-dependent take-up of energy, the rate of internal dissipation of theinternal energy, and the rate of conversion of the internal energy into kinetic energy, respectively. The
authors revealed that the dynamics of the Brownian particle changes depending on =(-).
In order to reproduce the same energy-take-up
and energy-conversion processes in a quantum
system, we use a non-Hermitian quantum walk.
Quantum walk is a quantum analog of the classicalrandom walk. In the simplest case, the quantum
walker has two internal states, leftward andrightward, and there are two operators, namely thecoin operator which shuffles the two internal states
and the shift operator which moves the walker
according to the internal states. It is known that theequation of motion of discrete-time quantum walker
gives the Dirac equation in the continuum limit. If we
set the coin operator as B = ! $%&'! , C corresponds tothe mass term in the Dirac equation and hence the Fig. 1. Probability distribution of the quantum walker
walker runs faster with a small value of C [2].
after 70 time steps. The vertical and horizontal axes
In our research, we added the ground and excited indicate the probability at each site and the position ofstates as another internal degree of freedom to the walker, respectively. Red and blue curves
describe the same processes as the previous research correspond to the excited and ground states,on a classical system. We thereby introduce an respectively. Green curve indicates the sum of theprobabilities for both states.
additional operator D for the new space as follows:$/
D = ! $%("# ∆*⁄ℏ , E-. = F −G / −H! I .
(4)
−H!
G
Here, G, K, and H are real. The off-diagonal elements introduce non-Hermiticity which describes the “takeup” of energy from the environment. Combining the operator D with the coin and shift operators, we
introduce a non-Hermitian quantum walk which describes the active particle in a quantum system. Figure 1
shows an example of the dynamics.
References
1. F. Schweitzer et al.: “Complex Motion of Brownian Particles with Energy Depots”, Phys. Rev. Lett. 80, 23 (1998).
2. F. W. Strauch: “Relativistic quantum walks”, Phys. Rev. A 73, 054302 (2006).

21

Invited Lecture

Active Matter Workshop 2022

15:50 - 16:40

Active matter physics in multicellular dynamics and quantum models
Kyogo Kawaguchi
1

Nonequilibrium Physics of Living Matter RIKEN Hakubi Research Team,RIKEN Cluster for Pioneering Research
2
RIKEN Center for Biosystems Dynamics Research
2
Universal Biology Institute, The University of Tokyo

Experiments in active matter physics naturally involve biological materials, ranging from molecularmotors to mammalian cells. Here we use mouse neural progenitor cells, self-propelling bipolar-shaped cellswith nematic interactions, to demonstrate how topological concepts can govern the collective dynamics in an
active nematic system. We will first show how topological defects generated by the cells themselves makeanomalous flow, which eventually leads to cell accumulation and dispersion. Next, we will describe how
significant edge flow arises in the stamp culture experiment and discuss how the mechanism is related totopological insulators.
In light of these recent developments in the interface between nonequilibrium physics and condensed
matter, we have also been interested in exploring the possible realization of active matter-type phase transitionsin quantum many-body systems. We will describe one of our attempts to make a model of “quantum active
matter”, where hard-core Bosons undergo phase separation due to non-Hermiticity in the Hamiltonian. We
will also show how the quantum phase transitions in this model are mapped to the dynamical phase transitions
in a classical system, and explain how dynamical symmetry can help understand the phase diagram.

Acknowledgements
The talk will be based on collaboration works with Lisa Yamauchi (RIKEN BDR), Masahito Uwamichi (The
University of Tokyo), Tomoya Hayata (Keio University), Tomoki Ozawa (Tohoku University), Kazuaki
Takasan (UC Berkeley), and Kyosuke Adachi (RIKEN BDR)

22