(

A02-003 SAKURAI

Paper | Original Paper

2017

*Shuji Ishihara, Philippe Marcq, Kaoru Sugimura,
From cells to tissue: A continuum model of epithelial mechanics,
Physical Review E 96, 022418 (2017).

[Summary] A two-dimensional continuum model of epithelial tissue mechanics was formulated using cellular-level mechanical ingredients and cell morphogenetic processes, including cellular shape changes and cellular rearrangements. This model incorporates stress and deformation tensors, which can be compared with experimental data. Focusing on the interplay between cell shape changes and cell rearrangements, we elucidated dynamical behavior underlying passive relaxation, active contraction-elongation, and tissue shear flow, including a mechanism for contraction-elongation, whereby tissue flows perpendicularly to the axis of cell elongation. This study provides an integrated scheme for the understanding of the orchestration of morphogenetic processes in individual cells to achieve epithelial tissue morphogenesis.

Yasuyuki Kobayashi*, Hiroyuki Kitahata, and Masaharu Nagayama,
Sustained dynamics of a weakly excitable system with nonlocal interactions,
Physical Review E 96, 022213/1-8 (2017).

[Summary] We investigate a two-dimensional spatially extended system that has a weak sense of excitability, where an excitation wave has a uniform profile and propagates only within a finite range. Using a cellular automaton model of such a weakly excitable system, we show that three kinds of sustained dynamics emerge when nonlocal spatial interactions are provided, where a chain of local wave propagation and nonlocal activation forms an elementary oscillatory cycle. Transition between different oscillation regimes can be understood as different ways of interactions among these cycles. Analytical expressions are given for the oscillation probability near the onset of oscillations.

*Yuki Koyano, Marian Gryciuk, Paulina Skrobanska, Maciej Malecki, Yutaka Sumino, Hiroyuki Kitahata, and Jerzy Gorecki,
Relationship between the size of a camphor-driven rotor and its angular velocity,
Physical Review E 96, 021609/1-8 (2017).

[Summary] We consider a rotor made of two camphor disks glued below the ends of a plastic stripe. The disks are floating on a water surface and the plastic stripe does not touch the surface. The system can rotate around a vertical axis located at the center of the stripe. The disks dissipate camphor molecules. The driving momentum comes from the nonuniformity of surface tension resulting from inhomogeneous surface concentration of camphor molecules around the disks. We investigate the stationary angular velocity as a function of rotor radius ℓ. For large ℓ the angular velocity decreases for increasing ℓ. At a specific value of ℓ the angular velocity reaches its maximum and, for short ℓ it rapidly decreases. Such behavior is confirmed by a simple numerical model. The model also predicts that there is a critical rotor size below which it does not rotate. Within the introduced model we analyze the type of this bifurcation.

*Jerzy Gorecki, Hiroyuki Kitahata, Nobuhiko J. Suematsu, Yuki Koyano, Paulina Skrobanska, Marian Gryciuk, Maciej Malecki, Takahiro Tanabe, Hiroya Yamamoto, and Satoshi Nakata,
Unidirectional motion of a camphor disk on water forced by interactions between surface camphor concentration and dynamically changing boundaries,
Physical Chemistry Chemical Physics 19, 18767-18772 (2017).

[Summary] We study the motion of a camphor disk on the water surface in a system with flexible boundaries. The boundaries can be dynamically modified by non-uniform surface tension resulting from the nonhomogeneous surface concentration of the camphor molecules dissipated by the disk. We investigate the geometry of the boundaries that forces unidirectional motion of the disk. The studied system can be regarded as a signal diode if the presence or absence of a camphor disk at a specific point is interpreted as the binary TRUE and FALSE ariables. The diode can be incorporated into more complex devices, like a ring that imposes unidirectional rotation of camphor disks.

*Kei Nishi, Shogo Suzuki, Katsuhiko Kayahara, Masakazu Kuze, Hiroyuki Kitahata, *Satoshi Nakata, and *Yasumasa Nishiura,
Achilles’ heel of a traveling pulse subject to a local external stimulus,
Physical Review E 95, 062209/1-8 (2016).

[Summary] The response of a traveling pulse to a local external stimulus is considered numerically for a modified threecomponent Oregonator, which is a model system for the photosensitive Belousov-Zhabotinsky (BZ) reaction. The traveling pulse is traced and constantly stimulated, with the distance between the pulse and the stimulus being kept constant.We are interested in theminimal strength of the spatially localized stimulus in order to eliminate the pulse. The use of a stimulus of small width allows us to detect the point in the pulse most sensitive to the external stimulus, referred to as the “Achilles’ heel” of the traveling pulse, at which minimal strength of stimulus causes a collapse of the pulse. Our findings are demonstrated experimentally as well with the photosensitive BZ reaction.

Naoko Ueno, Taisuke Banno, Arisa Asami, Yuki Kazayama, Yuya Morimoto, Toshihisa Osaki, Shoji Takeuchi, Hiroyuki Kitahata, and *Taro Toyota,
Self-propelled motion of monodisperse underwater oil droplets formed by a microfluidic device,
Langmuir 33, 5593-5597 (2017).

[Summary] We evaluated the speed profile of self-propelled underwater oil droplets comprising a hydrophobic aldehyde derivative in terms of their diameter and the surrounding surfactant concentration using a microfluidic device. We found that the speed of the oil droplets is dependent on not only the surfactant concentration but also the droplet size in a certain range of the surfactant concentration. This tendency is interpreted in terms of combination of the oil and surfactant affording spontaneous emulsification in addition to the Marangoni effect.

Keita Kamino, Yohei Kondo, Akihiko Nakajima, Mai Honda-Kitahara, Kunihiko Kaneko, Satoshi Sawai,
Fold-change detection and scale-invariance of cell-cell signaling in social amoeba,
Proceedings of the National Academy of Sciences of the United States of America 114(21), E4149-E4157 (2017).

[Summary] Cell-cell signaling is subject to variability in the extracellular volume, cell number, and dilution that potentially increase uncertainty in the absolute concentrations of the extracellular signaling molecules. To direct cell aggregation, the social amoebae Dictyostelium discoideum collectively give rise to oscillations and waves of cyclic adenosine 3',5'-monophosphate (cAMP) under a wide range of cell density. To date, the systems-level mechanism underlying the robustness is unclear. By using quantitative live-cell imaging, here we show that the magnitude of the cAMP relay response of individual cells is determined by fold change in the extracellular cAMP concentrations. The range of cell density and exogenous cAMP concentrations that support oscillations at the population level agrees well with conditions that support a large fold-change-dependent response at the single-cell level. Mathematical analysis suggests that invariance of the oscillations to density transformation is a natural outcome of combining secrete-and-sense systems with a fold-change detection mechanism.

*Hiroyuki Kitahata, Hiroya Yamamoto, Misato Hata, Yumihiko S. Ikura, *Satoshi Nakata,
Relaxation dynamics of the Marangoni convection roll structure induced by camphor concentration gradient,
Colloids and Surfaces A 520, 436-441 (2017).

[Summary] When a camphor disk is placed close to a water surface, Marangoni convection occurs due to the surfacetension gradient originating from the spatial distribution of camphor molecules at the water surface. Weput plastic floats on the water surface to investigate the surface Marangoni flow, and observed that theplastic floats moved away from the camphor disk due to Marangoni convection. When the camphor diskwas pulled up away from the water surface, the Marangoni convection weakened and finally disappeared.At that time, we observed that the floats approached the position just below the camphor disk. We discussthe mechanism of such float motion as related to the change in the structure of Marangoni convectionand the change in the water level.

2016

Yuki Koyano, Tatsunari Sakurai, and *Hiroyuki Kitahata,
Oscillatory motion of a camphor grain in a one-dimensional finite region,
Physical Review E 94, 042215/1-8 (2016).

[Summary] The motion of a self-propelled particle is affected by its surroundings, such as boundaries or external fields. In this paper, we investigated the bifurcation of the motion of a camphor grain, as a simple actual self-propelled system, confined in a one-dimensional finite region. A camphor grain exhibits oscillatory motion or remains at rest around the center position in a one-dimensional finite water channel, depending on the length of the water channel and the resistance coefficient. A mathematical model including the boundary effect is analytically reduced to an ordinary differential equation. Linear stability analysis reveals that the Hopf bifurcation occurs, reflecting the symmetry of the system.

Akihiko Nakajima, Motohiko Ishida, Taihei Fujimori, Yuichi Wakamoto, *Satoshi Sawai,
The Microfluidic lighthouse: an omnidirectional gradient generator,
Lab on Chip 16(22), 4382-4394 (2016).

[Summary] Studies of chemotactic cell migration rely heavily on various assay systems designed to evaluate the ability of cells to move in response to attractant molecules. In particular, the development of microfluidics-based devices in recent years has made it possible to spatially distribute attractant molecules in graded profiles that are sufficiently stable and precise to test theoretical predictions regarding the accuracy and efficiency of chemotaxis and the underlying mechanism of stimulus perception. However, because the gradient is fixed in a direction orthogonal to the laminar flow and thus the chamber geometry, conventional devices are limited for the study of cell re-orientation to gradients that move or change directions. Here, we describe the development of a simple radially symmetric microfluidics device that can deliver laminar flow in 360°. A stimulant introduced either from the central inlet or by photo uncaging is focused into the laminar flow in a direction determined by the relative rate of regulated flow from multiple side channels. Schemes for flow regulation and an extended duplexed device were designed to generate and move gradients in desired orientations and speed, and then tested to steer cell migration of Dictyostelium and neutrophil-like HL60 cells. The device provided a high degree of freedom in the positioning and orientation of attractant gradients, and thus may serve as a versatile platform for studying cell migration, re-orientation, and steering.

Elisa Herawati, Daisuke Taniguchi, Hatsuho Kanoh, Kazuhiro Tateishi, Shuji Ishihara, and Sachiko Tsukita,
Multiciliated cell basal bodies align in stereotypical patterns coordinated by the apical cytoskeleto,
The Journal of Cell Biology 214, 571–586 (2016).

[Summary] Multiciliated cells (MCCs) promote fluid flow through coordinated ciliary beating, which requires properly organized basal bodies (BBs). Airway MCCs have large numbers of BBs, which are uniformly oriented and, as we show here, align linearly. The mechanism for BB alignment is unexplored. To study this mechanism, we developed a long-term and high-resolution live-imaging system and used it to observe green fluorescent protein–centrin2–labeled BBs in cultured mouse tracheal MCCs. During MCC differentiation, the BB array adopted four stereotypical patterns, from a clustering “floret” pattern to the linear “alignment.” This alignment process was correlated with BB orientations, revealed by double immunostaining for BBs and their asymmetrically associated basal feet (BF). The BB alignment was disrupted by disturbing apical microtubules with nocodazole and by a BF-depleting Odf2 mutation. We constructed a theoretical model, which indicated that the apical cytoskeleton, acting like a viscoelastic fluid, provides a self-organizing mechanism in tracheal MCCs to align BBs linearly for mucociliary transport.

Yuki Koyano, Hiroyuki Kitahata, *Alexander S. Mikhailov,
Hydrodynamic collective effects of active proteins in biological membranes,
Physical Review E 94, 022416/1-11 (2016).

[Summary] Lipid bilayers forming biological membranes are known to behave as viscous two-dimensional fluids on submicrometer scales; usually they contain a large number of active protein inclusions. Recently, it was shown that such active proteins should induce nonthermal fluctuating lipid flows leading to diffusion enhancement and chemotaxislike drift for passive inclusions in biomembranes. Here, a detailed analytical and numerical investigation of such effects is performed. The attention is focused on the situations when proteins are concentrated within lipid rafts. We demonstrate that passive particles tend to become attracted by active rafts and are accumulated inside them.

Taisuke Banno, Arisa Asami, Naoko Ueno, Hiroyuki Kitahata, Yuki Koyano, Kouichi Asakura, *Taro Toyota,
Deformable self-propelled micro-object comprising underwater oil droplets,
Scientific Reports 6, 31292/1-9 (2016).

[Summary] The self-propelled motion with deformation of micrometer-sized soft matter in water has potential application not only for underwater carriers or probes in very narrow spaces but also for understanding cell locomotion in terms of non-equilibrium physics. As far as we know, there have been no reports about micrometer-sized self-propelled soft matter mimicking amoeboid motion underwater. Here, we report an artificial molecular system of underwater oil droplets exhibiting self-propelled motion with deformation as an initial experimental model. We describe the heterogeneity in a deformable self-propelled oil droplet system in aqueous and oil phases and at their interface based on the behavior and interaction of surfactant and oil molecules. The current results have great importance for scientific frontiers such as developing deformable micro-swimmers and exploring the emergence of self-locomotion of oil droplet-type protocells.

*Satoshi Nakata, Hiroya Yamamoto, Yuki Koyano, Osamu Yamanaka, Yutaka Sumino, Nobuhiko J. Suematsu, Hiroyuki Kitahata, Paulina Skrobanska, and Jerzy Gorecki,
Selection of the Rotation Direction for a Camphor Disk Resulting from Chiral Asymmetry of a Water Chamber,
Journal of Physical Chemistry B 120, 9166-9172 (2016).

[Summary] Self-motion of a camphor disk rotating inside a water chamber composed of two half-disks was investigated. The half-disks were joined along their diameter segments, and the distance between their midpoints (ds) was considered as the control parameter. Various types of camphor disk motions were observed depending on ds. When ds = 0, the chamber had a circular shape, so it was symmetric. A camphor disk showed either a clockwise (CW) or ounterclockwise (CCW) rotation with the direction determined by its initial state. The symmetry of the chamber was broken for ds > 0. For moderate distances between the midpoints, a unidirectional orbital motion of the disk was observed. The preferred rotation direction was determined by the shape of the chamber, and it did not depend on the initial rotation direction. For yet larger ds, the unidirectional circular motion was no longer observed and the trajectory became irregular. A mathematical model coupling the camphor disk motion with the dynamics of the developed camphor molecular layer on water was constructed, and the numerical results were compared with the experimental results. The selection of motion type can be explained by considering the influence of camphor concentration on the disk trajectory through the surface tension gradient.

Takayuki Torisawa, Daisuke Taniguchi, Shuji Ishihara, Kazuhiro Oiwa,
Spontaneous Formation of a Globally Connected Contractile Network in a Microtubule-Motor System,
Biophysical Journal 111, 373–385 (2016).

[Summary] Microtubule (MT) networks play key roles in cell division, intracellular transport, and cell motility. These functions of MT networks occur through interactions between MTs and various associated proteins, notably motor proteins that bundle and slide MTs. Our objective in this study was to address the question of how motors determine the nature of MT networks. We conducted in vitro assays using homotetrameric kinesin Eg5, a motor protein involved in the formation and maintenance of the mitotic spindle. The mixing of Eg5 and MTs produced a range of spatiotemporal dynamics depending on the motor/filament ratio. Low motor/filament ratios produced globally connected static MT networks with sparsely distributed contractile active nodes (motor-accumulating points with radially extending MTs). Increasing the motor/filament ratio facilitated the linking of contractile active nodes and led to a global contraction of the network. When the motor/filament ratio was further increased, densely distributed active nodes formed local clusters and segmented the network into pieces with their strong contractile forces. Altering the properties of the motor through the use of chimeric Eg5, which has kinesin-1 heads, resulted in the generation of many isolated asters. These results suggest that the spatial distribution of contractile active nodes determines the dynamics of MT-motor networks. We then developed a coarse-grained model of MT-motor networks and identified two essential features for reproducing the experimentally observed patterns: an accumulation of motors that form the active nodes necessary to generate contractile forces, and a nonlinear dependency of contractile force on motor densities. Our model also enabled us to characterize the mechanical properties of the contractile network. Our study provides insight into how local motor-MT interactions generate the spatiotemporal dynamics of macroscopic network structures.

Fumihito Fukujin, Akihiko Nakajima, Nao Shimada, *Satoshi Sawai,
Self-organization of chemoattractant waves in Dictyostelium depends on F-actin and cell–substrate adhesion,
Journal of The Royal Society Interface 13 (2016).

[Summary] In the social amoeba Dictyostelium discoideum, travelling waves of extracellular cyclic adenosine monophosphate (cAMP) self-organize in cell populations and direct aggregation of individual cells to form multicellular fruiting bodies. In contrast to the large body of studies that addressed how movement of cells is determined by spatial and temporal cues encoded in the dynamic cAMP gradients, how cell mechanics affect the formation of a self-generated chemoattractant field has received less attention. Here, we show, by live cell imaging analysis, that the periodicity of the synchronized cAMP waves increases in cells treated with the actin inhibitor latrunculin. Detail analysis of the extracellular cAMP-induced transients of cytosolic cAMP (cAMP relay response) in well-isolated cells demonstrated that their amplitude and duration were markedly reduced in latrunculin-treated cells. Similarly, in cells strongly adhered to a poly-l-lysine-coated surface, the response was suppressed, and the periodicity of the population-level oscillations was markedly lengthened. Our results suggest that cortical F-actin is dispensable for the basic low amplitude relay response but essential for its full amplification and that this enhanced response is necessary to establish high-frequency signalling centres. The observed F-actin dependence may prevent aggregation centres from establishing in microenvironments that are incompatible with cell migration.

Hironobu Nogucci and Shuji Ishihara,
Collective dynamics of active filament complexes,
Physical Review E 93, 052406/1-10 (2016).

[Summary] Networks of biofilaments are essential for the formation of cellular structures that support various biologicalfunctions. For the most part, previous studies have investigated the collective dynamics of rodlike biofilaments;however, the shapes of the actual subcellular components are often more elaborate. In this study, weconsidered an active object composed of two active filaments, which represents the progression from rodlikebiofilaments to complex-shaped biofilaments. Specifically, we numerically assessed the collective behaviorsof these active objects in two dimensions and observed several types of dynamics, depending on the densityand the angle of the two filaments as shape parameters of the object. Among the observed collectivedynamics, a moving density band that we named a “moving smectic” is introduced here for the first time.By analyzing the trajectories of individual objects and the interactions among them, this study demonstrated howinteractions among active biofilaments with complex shapes could produce collective dynamics in a nontrivialmanner.

Yui Matsuda, Nobuhiko J. Suematsu, Hiroyuki Kitahata, Yumihiko S.Ikura, and *Satoshi Nakata,
Acceleration or deeleration of self-motion by the Marangoni effect,
Chemical Physics Letters 654, 92-96 (2016).

[Summary] We investigated the water-depth dependence of the self-motion of a camphor disk and camphor boat. With increasing water depth, the speed of motion of the camphor disk increased, but that of the camphor boat decreased in an annular one-dimensional system. We discussed the difference in the water-depth dependence of the speed of the camphor objects in relation to Marangoni flow. We concluded that Marangoni flow, which became stronger with increasing the water depth, positively and negatively affected the speed of the disk and boat, respectively.

Ken H. Nagai, Kunihito Tachibana, Yuta Tobe, Masaki Kazama, Hiroyuki Kitahata, Seiro Omata, *Masaharu Nagayama,
Mathematical model for self-propelled droplets driven by interfacial tension,
Journal of Chemical Physics 144, 114707/1-8 (2016).

[Summary] We propose a model for the spontaneous motion of a droplet induced by inhomogeneity in interfacial tension. The model is derived from a variation of the Lagrangian of the system and we use a time-discretized Morse flow scheme to perform its numerical simulations. Our model can naturally simulate the dynamics of a single droplet, as well as that of multiple droplets, where the volume of each droplet is conserved. We reproduced the ballistic motion and fission of a droplet, and the collision of two droplets was also examined numerically.

*Yutaka Sumino, Norifumi L. Yamada, Michihiro Nagao, Takuya Honda, Hiroyuki Kitahata, Yuri B. Melnichenko, and Hideki Seto,
Mechanism of Spontaneous Blebbing Motion of an Oil−Water Interface: Elastic Stress Generated by a Lamellar−Lamellar Transition,
Langmuir 32, 2891-2899 (2016).

[Summary] A quaternary system composed of surfactant, cosurfactant, oil, and water showing spontaneous motion of the oil–water interface under far-from-equilibrium condition is studied in order to understand nanometer-scale structures and their roles in spontaneous motion. The interfacial motion is characterized by the repetitive extension and retraction of spherical protrusions at the interface, i.e, blebbing motion. During the blebbing motion, elastic aggregates are accumulated, which were characterized as surfactant lamellar structures with mean repeat distances d of 25 to 40 nm. Still unclear is the relationship between the structure formation and the dynamics of the interfacial motion. In the present study, we find that a new lamellar structure with d larger than 80 nm is formed at the blebbing oil–water interface, while the resultant elastic aggregates, which are the one reported before, have a lamellar structure with smaller d (25 to 40 nm). Such transition of lamellar structures from the larger d to smaller d is induced by a penetration of surfactants from an aqueous phase into the aggregates. We propose a model in which elastic stress generated by the transition drives the blebbing motion at the interface. The present results explain the link between nanometer-scale transition of lamellar structure and millimeter-scale dynamics at an oil–water interface.

Masanobu Horie, Tatsunari Sakurai, and *Hiroyuki Kitahata,
Experimental and theoretical approach for the clustering of globally coupled density oscillators based on phase response,
Physical Review E 93, 012212/1-9 (2016).

[Summary] We investigated the phase-response curve of a coupled system of density oscillatorswith an analytical approach. The behaviors of two-, three-, and four-coupled systems seen in the experiments were reproduced by the model considering the phase-response curve. Especially in a four-coupled system, the clustering state and its incidence rate as functions of the coupling strength are well reproduced with this approach.Moreover, we confirmed that the shape of the phase-response curve we obtained analytically was close to that observed in the experiment where a perturbation is added to a single-density oscillator. We expect that this approach to obtaining the phase-response curve is general in the sense that it could be applied to coupled systems of other oscillators such as electrical-circuit oscillators, metronomes, and so on.

Haruka Sugiura, Manami Ito, Tomoya Okuaki, Yoshihito Mori, Hiroyuki Kitahata, and *Masahiro Takinoue,
Pulse-density modulation control of chemical oscillation far from equilibrium in a droplet open-reactor system,
Nature Communications 7, 10212/1-9 (2016).

[Summary] The design, construction and control of artificial self-organized systems modelled on dynamical behaviours of living systems are important issues in biologically inspired engineering. Such systems are usually based on complex reaction dynamics far from equilibrium; therefore, the control of non-equilibrium conditions is required. Here we report a droplet open-reactor system, based on droplet fusion and fission, that achieves dynamical control over chemical fluxes into/out of the reactor for chemical reactions far from equilibrium. We mathematically reveal that the control mechanism is formulated as pulse-density modulation control of the fusion–fission timing. We produce the droplet open-reactor system using microfluidic technologies and then perform external control and autonomous feedback control over autocatalytic chemical oscillation reactions far from equilibrium. We believe that this system will be valuable for the dynamical control over self-organized phenomena far from equilibrium in chemical and biomedical studies.

2015

Boris Guirao, Stéphane Rigaud, Floris Bosveld, Anaïs Bailles, Jesus Lopez-Gay, Shuji Ishihara, Kaoru Sugimura, *François Graner, *Yohanns Bellaïche,
Unified quantitative characterization of epithelial tissue development,
eLIFE , 08519 (2015).

[Summary] Understanding the mechanisms regulating development requires a quantitative characterization of cell divisions, rearrangements, cell size and shape changes, and apoptoses. We developed a multiscale formalism that relates the characterizations of each cell process to tissue growth and morphogenesis. Having validated the formalism on computer simulations, we quantifed separately all morphogenetic events in the Drosophila wing and dorsal thorax pupal epithelia to obtain comprehensive statistical maps linking cell and tissue scale dynamics. While globally cell shape changes, rearrangements and divisions all signifcantly participate in tissue morphogenesis, locally, their relative participations display major variations in space and time. By blocking division we analyzed the impact of division on rearrangements, cell shape changes and tissue morphogenesis. Finally, by combining the formalism with mechanical stress measurement, we evidenced unexpected interplays between patterns of tissue elongation, cell division and stress. Our formalism provides a novel and rigorous approach to uncover mechanisms governing tissue development.

*Hiroyuki Kitahata, Rui Tanaka, Yuki Koyano, Satoshi Matsumoto, Katsuhiro Nishinari, Tadashi Watanabe,Koji Hasegawa, Tetsuya Kanagawa, Akiko Kaneko, and Yutaka Abe,
Oscillation of a rotating levitated droplet: Analysis with a mechanical model,
Physical Review E 92, 062904/1-8 (2015).

[Summary] A droplet of millimeter-to-centimeter scale can exhibit electrostatic levitation, and such levitated droplets can be used for the measurement of the surface tension of the liquids by observing the characteristic frequency of oscillatory deformation. In the present study, a simple mechanical model is proposed by considering a single mode of oscillation in the ellipsoidal deformation of a levitated rotating droplet. By measuring the oscillation frequency with respect to the rotational speed and oscillation amplitude, it is expected that the accuracy of the surface tensionmeasurement could be improved. Using the proposed model, the dependences of the characteristic frequency of oscillatory deformation and the averaged aspect ratio are calculated with respect to the rotational angular velocity of a rotating droplet. These dependences are found to be consistent with the experimental observations.

Masanobu Tanaka, Marcel Hörning, *Hiroyuki Kitahata, and Kenichi Yoshikawa,
Elimination of a spiral wave pinned at an obstacle by a train of plane waves: Effect of diffusion between obstacles and surrounding media,
Chaos 25, 103127/1-9 (2015).

[Summary] In excitable media such as cardiac tissue and Belousov-Zhabotinsky reaction medium, spiral waves tend to anchor (pin) to local heterogeneities. In general, such pinned waves are difficult to eliminate and may progress to spatio-temporal chaos. Heterogeneities can be classified as either the absence or presence of diffusive interaction with the surrounding medium. In this study, we investigated the difference in the unpinning of spiral waves from obstacles with and without diffusive interaction, and found a profound difference. The pacing period required for unpinning at fixed obstacle size is larger in case of diffusive obstacles. Further, we deduced a generic theoretical framework that can predict the minimal unpinning period. Our results explain the difference in pacing periods betweenfor the obstacles with and without diffusive interaction, and the difference is interpreted in terms of the local decrease of spiral wave velocity close to the obstacle boundary caused in the case of diffusive interaction.

Shingo Miyazaki, Tatsunari Sakurai, and *Hiroyuki Kitahata,
Coupling between a chemical wave and motion in a Belousov-Zhabotinsky droplet,
Current Physical Chemistry 5, 82-90 (2015).

[Summary] As a simple physico-chemical system that exhibits droplet motion induced by the pattern formation inside it, we investigate the motion of a droplet of Belousov-Zhabotinsky (BZ) reaction medium depending on the size and initial point of the chemical wave. We also observe the profile of Marangoni flow induced in the BZ droplet. In ourprevious paper, we reported the BZ-droplet motion and proposed a mechanism based on low-Reynolds-number hydrodynamics. Here, we discuss the validity of the uggested mechanism based on experimental results.

*Yasuaki Kobayashi, Hiroyuki Kitahata, and Masaharu Nagayama,
Model for calcium-mediated reduction of structural fluctuations in epidermis,
Physical Review E 92, 022709/1-7 (2015).

[Summary] We propose a reaction-advection-diffusion model of epidermis consisting of two variables, the degree of differentiation and the calcium ion concentration, where calcium ions enhance differentiation. By analytically and numerically investigating this system, we show that a calcium localization layer formed beneath the stratum corneum helps reduce spatiotemporal fluctuations of the structure of the stratum corneum. In particular, spatially or temporally small-scale fluctuations in the lower structure are suppressed and do not affect the upper structure, due to acceleration of differentiation by calcium ions. Analytical expressions for the reduction rate of fluctuation amplitudes are shown.

Yuki Koyano, Natsuhiko Yoshinaga, and *Hiroyuki Kitahata,
General criteria for determining rotation or oscillation in a two-dimensional axisymmetric system,
Journal of Chemical Physics 143, 014117/1-6 (2015).

[Summary] A self-propelled particle in a two-dimensional axisymmetric system, such as a particle in a central force field or confined in a circular region, may show rotational or oscillatory motion. These motions do not require asymmetry of the particle or the boundary, but arise through spontaneous symmetry breaking. We propose a generic model for a self-propelled particle in a two-dimensional axisymmetric system. A weakly nonlinear analysis establishes criteria for determining rotational or oscillatory motion.

Tomohiro Sasaki, Nobuhiko J. Suematsu, Tatsunari Sakurai, and *Hiroyuki Kitahata,
Spontaneous recurrence of deposition and dissolution of a solid layer on a solution surface,
Journal of Physical Chemistry B 119, 9970-9974 (2015).

[Summary] We investigated the spontaneous recurrence of deposition and dissolution of camphor layer on the surface of camphor methanol solution. This recurrence is a novelrhythmic process concerned with solid−liquid phase transition. To elucidate the underlying mechanism, we measured the solution temperature at different times, and found that the temperature increased and decreased repetitively, correlating with the camphor layer’s deposition and dissolution. These experimental results show that the solution temperature plays an important role in recurrence of deposition and dissolution.

*Kenji Kashima, Toshiyuki Ogawa, Tatsunari Sakurai,
Selective pattern formation control: Spatial spectrum consensus and Turing instability approach,
Automatica 56, 25-35 (2015).

[Summary] Autonomous pattern formation phenomena are ubiquitous throughout nature. The goal of this paper is to show the possibility to effectively generate various desired spatial patterns by guiding such phenomena suitably. To this end, we employ a reaction–diffusion system as a mathematical model, and formulate and solve a novel pattern formation control problem. First, we describe the control objective in terms of spatial spectrum consensus, which enables utilize recent advances on networked control system theory. Next, the effectiveness of the proposed control law is evaluated theoretically by exploiting the center manifold theorem, and also numerically by simulation. The Turing instabilities play a crucial role throughout the paper.

*Satoshi Nakata, Shogo Suzuki, Takato Ezaki, Hiroyuki Kitahata, Kei Nishi, and Yasumasa Nishiura,
Response of a chemical wave to local pulse irradiation in the ruthenium-catalyzed Belousov–Zhabotinsky reaction,
Physical Chemistry Chemistry Physics 17, 9148-9152 (2015).

[Summary] The photo-sensitive Belousov–Zhabotinsky (BZ) reaction system was investigated to understand the response of wave propagation to local pulse stimulation in an excitable field. When the chemical wave was irradiated with a bright pulse or a dark pulse, the speed of wave propagation decreased or increased. The timing of pulse irradiation that significantly affected the speed of chemical wave propagation was different with the bright and dark pulses. That is, there is a sensitive point in the chemical wave. The experimental results were qualitatively reproduced by a numerical calculation based on a three-variable Oregonator model that was modified for the photosensitive BZ reaction. These results suggest that the chemical wave is sensitive to the timing of pulse irradiation due to the rates of production of an activator and an inhibitor in the photochemical reaction.

2014

Akihiko Nakajima, Shuji Ishihara, Daisuke Imoto, and *Satoshi Sawai,
Rectified directional sensing in long-range cell migration,
Nature Communications 5, 5367/1-14 (2014).

[Summary] How spatial and temporal information are integrated to determine the direction of cell migration remains poorly understood. Here, by precise microfluidics emulation of dynamic chemoattractant waves, we demonstrate that, in Dictyostelium, directional movement as well as activation of small guanosine triphosphatase Ras at the leading edge is suppressed when the chemoattractant concentration is decreasing over time. This ‘rectification’ of directional sensing occurs only at an intermediate range of wave speed and does not require phosphoinositide-3-kinase or F-actin. From modelling analysis, we show that rectification arises naturally in a single-layered incoherent feedforward circuit with zero-order ultrasensitivity. The required stimulus time-window predicts ~5 s transient for directional sensing response close to Ras activation and inhibitor diffusion typical for protein in the cytosol. We suggest that the ability of Dictyostelium cells to move only in the wavefront is closely associated with rectification of adaptive response combined with local activation and global inhibition.

*Satoshi Nakata, Tomoaki Ueda, Tatsuya Miyaji, Yui Matsuda, Yukiteru Katsumoto, Hiroyuki Kitahata, Takafumi Shimoaka, and Takeshi Hasegawa,
Transient reciprocating motion of a self-propelled object controlled by a molecular layer of a N‑stearoyl‑p‑nitroaniline: dependence on the temperature of an aqueous phase,
Journal of Physical Chemistry C 118, 14888-14893 (2014).

[Summary] The mode-bifurcation of a self-propelled system inducedby the property of a N-stearoyl-p-nitroaniline (C18ANA) monolayer developed on an aqueous phase was studied. A camphor disk was placed on a C18ANA monolayer, which indicated a characteristic surface pressure−area (π−A) isotherm. A camphor disk transiently exhibited reciprocating motion at a higher surface density of C18ANA. The amplitude of the reciprocating motion increased with an increase in the temperature of the aqueous phase below 290 K, but reciprocating motionvaried to irregular motion over 290 K. The temperature-dependent reciprocating motion is discussed in terms of the π−A curve for C18ANA depending on the temperature. The interaction between C18ANA molecules was measured by Fourier transform IR spectrometry and Brewster-angle microscopy. As an extension of the study, the trajectory ofreciprocating motion could be determined by writing with a camphor pen on the C18ANA monolayer.

*Nobuhiko J. Suematsu, Tomohiro Sasaki, Satoshi Nakata, and Hiroyuki Kitahata,
Quantitative estimation of the parameters for self-motion driven by difference in surface tension,
Langmuir 30, 8101-8108 (2014).

[Summary] Quantitative information on the parameters associated with self-propelled objects would enhance the potential of this research field; for example, finding a realistic way to develop a functional self-propelled object and quantitative understanding of the mechanism of self-motion. We therefore estimated five main parameters, including the driving force, of a camphor boat as a simple self-propelled object that spontaneously moves on water due to difference in surface tension. The experimental results and mathematical model indicated that the camphor boat generated a driving force of 4.2 μN, which corresponds to a difference in surface tension of 1.1 mN m−1. The methods used in this study are not restricted to evaluate the parameters of self-motion of a camphor boat, but can be applied to other self-propelled objects driven by difference in surface tension. Thus, our investigation provides a novel method to quantitatively estimate the parameters for self-propelled objects driven by the interfacial tension difference.

*Nen Saito, Shuji Ishihara, and Kunihiko Kaneko,
Evolution of Genetic Redundancy : The Relevance of Complexity in Genotype-Phenotype Mapping,
New Journal of Physics 16, 063013/1-14 (2014).

[Summary] Despite its ubiquity among organisms, genetic redundancy is presumed to reduce total population fitness and is therefore unlikely to evolve. This study evaluates an evolutionary model with high-dimensional genotype–phenotype mapping (GPM) by applying a replica method to deal with quenched randomness. From the method, the dependence of fitness on genetic redundancy is analytically calculated. The results demonstrate that genetic redundancy can have higher population fitness under complex GPM, which tends to favor gene duplication in selection processes, further enhancing the potential for evolutionary innovations.

Keita Iida, Hiroyuki Kitahata, and *Masaharu Nagayama,
Theoretical study on the translation and rotation of an elliptic camphor particle,
Physica D 272, 39-50 (2014).

[Summary] The spontaneous motion of an elliptic camphor particle floating on water is studied theoretically and experimentally. Considering a mathematical model for the motion of an elliptic camphor particle in a two-dimensional space, we first investigate the asymptotic solutions with umerical computation. We then introduce a small parameter ε into the definition of the particle shape, which represents an elliptic deformation from a circular shape and, by means of perturbation theory, we analytically alculate the travelling solution to within O(ε). The results show that short-axis-directed travelling solutions primarily bifurcate from stationary solutions and that long-axis-directed ones are secondary which means that elliptic camphor particles are easier to move in the short-axis direction. Furthermore, we show that rotating solutions bifurcate from stationary solutions and that the bifurcation point changes with O(ε2), which suggests that elliptic camphor disks easily exhibit translational motion, rather than rotational, within the small deformation. Finally, our theoretical suggestions are confirmed by an experiment.

2013

Ryo Tanaka, Tomonori Nomoto, Taro Toyota, Hiroyuki Kitahata, and *Masanori Fujinami,
Delayed response of interfacial tension in propagating chemical waves of the Belousov-Zhabotinsky reaction without stirring,
The Journal of Physical Chemistry B 117, 13893–13898 (2013).

[Summary] Time-resolved measurements of the interfacial tension of propagating chemical waves of the Belousov–Zhabotinsky reaction based on the iron complex catalysts were carried out without stirring by monitoring the frequency of capillary waves with the quasi-elastic laser scattering method. A delayed response of the interfacial tension with respect to absorption was found with the delay being ligand-dependent when the reaction was conducted at a liquid/liquid interface. This behavior is attributed to differences in adsorption activity of the hydrophobic metal catalyst. The delay time and the increase in interfacial tension were also reproduced by a model considering the rate constants of equilibrium adsorption.