北畑 裕之

Epithelia consist of proliferating and differentiating cells that often display patterned arrangements. However, the mechanism regulating these spatial arrangements remains unclear. Here, we show that cell-cell adhesion dictates multicellular patterning in stratified epithelia. When cultured keratinocytes, a type of epithelial cell in the skin, are subjected to starvation, they spontaneously develop a pattern characterized by areas of high and low cell density. Pharmacological and knockout experiments show that adherens junctions are essential for patterning, whereas the mathematical model that only considers local cell-cell adhesion as a source of attractive interactions can form regions with high/low cell density. This phenomenon, called cell-cell adhesion-induced patterning (CAIP), influences cell differentiation and proliferation through Yes-associated protein modulation. Starvation, which induces CAIP, enhances the stratification of the epithelia. These findings highlight the intrinsic self-organizing property of epithelial cells.

Abstract The mechanism of self-propelled particle motion has attracted much interest in mathematical and physical understanding of the locomotion of living organisms. In a top-down approach, simple time-evolution equations are suitable for qualitatively analyzing the transition between the different types of solutions and the influence of the intrinsic symmetry of systems despite failing to quantitatively reproduce the phenomena. We aim to rigorously show the existence of the rotational, oscillatory, and quasi-periodic solutions and determine their stabilities regarding a canonical equation proposed by Koyano et al. (J Chem Phys 143(1):014117, 2015) for a self-propelled particle confined by a parabolic potential. In the proof, the original equation is reduced to a lower dimensional dynamical system by applying Fenichel’s theorem on the persistence of normally hyperbolic invariant manifolds and the averaging method. Furthermore, the averaged system is identified with essentially a one-dimensional equation because the original equation is O(2)-symmetric.

Abstract In this study, we propose a mathematical model of self-propelled objects based on the Allen–Cahn type phase-field equation. We combine it with the equation for the concentration of surfactant used in previous studies to construct a model that can handle self-propelled object motion with shape change. A distinctive feature of our mathematical model is that it can represent both deformable self-propelled objects, such as droplets, and solid objects, such as camphor disks, by controlling a single parameter. Furthermore, we demonstrate that, by taking the singular limit, this phase-field based model can be reduced to a free boundary model, which is equivalent to the $$L^2$$-gradient flow model of self-propelled objects derived by the variational principle from the interfacial energy, which gives a physical interpretation to the phase-field model.

Experiments with rotating camphor boats revealed a new type of boat motion characterized by oscillating speed.

The dynamical behaviour of lateral domains on phase-separated lipid vesicles under external flow is reported. A microfluidic chamber was used for the immobilization of vesicles and the application of shear. Microscopic observation revealed that domains tended to be localized at the vortex center and to exhibit a stripe morphology as the flow speed increased. We clarified the dependency of domain behaviors on the flow speed and lipid mixing fraction. The cholesterol ratio in the membrane affected these domain behaviors. Next, we investigated the growth of domains under flow. We discuss the mechanism of these trends by considering the free energy of phase separation, and reproduce the experimental results by numerical simulations. These findings may lead to a better understanding of the dynamical properties of the membrane under nonequilibrium situations and the biophysical mechanism of cellular mechanotransduction.

I n our original manuscript, the parameter values were incorrectly described in the caption of Figure 5. The parameters should be “au/a = 1 and av/a = 0.1” instead of “αu/α = αv/α = 0.1”. In addition, “au = av = 3.7” was incorrect, and it should be “au = 37 and av = 3.7”. The errors are typographical, and thus, these corrections do not affect the conclusions of this work.

Vertebrates exhibit patterned epidermis, exemplified by scales/interscales in mice tails and grooves/ridges on the human skin surface (microtopography). Although the role of spatiotemporal regulation of stem cells (SCs) has been implicated in this process, the mechanism underlying the development of such epidermal patterns is poorly understood. Here, we show that collagen XVII (COL17), a niche for epidermal SCs, helps stabilize epidermal patterns. Gene knockout and rescue experiments revealed that COL17 maintains the width of the murine tail scale epidermis independently of epidermal cell polarity. Skin regeneration after wounding was associated with slender scale epidermis, which was alleviated by overexpression of human COL17. COL17-negative skin in human junctional epidermolysis bullosa showed a distinct epidermal pattern from COL17-positive skin that resulted from revertant mosaicism. These results demonstrate that COL17 contributes to defining mouse tail scale shapes and human skin microtopography. Our study sheds light on the role of the SC niche in tissue pattern formation.

<jats:p>It is known that a camphor particle at a water surface exhibits self-propulsion since it releases camphor molecules at the surface and reduces the surface tension, and the gradient of surface tension drives the camphor particle itself. Such a motion is considered to be driven by the concentration field of the chemicals emitted by the particle itself. It is also known that the shape of the particle seriously affects the mode of motion. In order to understand the universal mechanism on the effect of the shape on such a self-propelled motion, we theoretically investigated the bifurcation structure of the motion of the camphor float with <jats:italic>n</jats:italic>-fold rotational symmetry, which comprises <jats:italic>n</jats:italic> camphor disks attached to a rigid light circular plate along a periphery with an equivalent spacing. Here, we mainly studied the cases with <jats:italic>n</jats:italic> = 2 and 3. We found that the camphor float with <jats:italic>n</jats:italic> = 2 moves in the direction perpendicular to the line connecting the two camphor disks, while that with <jats:italic>n</jats:italic> = 3 changes its direction of motion depending on the size of the camphor float.</jats:p>

We studied the self-propulsion of a camphor disk placed on a surfactant solution to clarify the relationship between the speed of motion and the depth of the aqueous phase. At lower concentrations of sodium dodecyl sulfate (SDS) in the aqueous phase, the speed of motion for the deeper aqueous phase was higher than that for the shallower aqueous phase. However, this relationship was reversed at higher SDS concentrations. The surface tension of the aqueous phase and diffusion rate around the camphor disk were measured to determine this reverse relationship at higher SDS concentrations. Numerical calculation considering the flow field coupled with the concentration field qualitatively reproduced the experimental results on the diffusion rate depending on the SDS concentration. These results suggest that the amount of camphor dissolved in the aqueous phase plays an important role in reversing the speed of motion depending on the depth of the aqueous phase.

The human hand can detect both form and texture information of a contact surface. The detection of skin displacement (sustained stimulus) and changes in skin displacement (transient stimulus) are thought to be mediated in different tactile channels; however, tactile form perception may use both types of information. Here, we studied whether both the temporal frequency and the temporal coherency information of tactile stimuli encoded in sensory neurons could be used to recognize the form of contact surfaces. We used the fishbone tactile illusion (FTI), a known tactile phenomenon, as a probe for tactile form perception in humans. This illusion typically occurs with a surface geometry that has a smooth bar and coarse textures in its adjacent areas. When stroking the central bar back and forth with a fingertip, a human observer perceives a hollow surface geometry even though the bar is physically flat. We used a passive high-density pin matrix to extract only the vertical information of the contact surface, suppressing tangential displacement from surface rubbing. Participants in the psychological experiment reported indented surface geometry by tracing over the FTI textures with pin matrices of the different spatial densities (1.0 and 2.0 mm pin intervals). Human participants reported that the relative magnitude of perceived surface indentation steeply decreased when pins in the adjacent areas vibrated in synchrony. To address possible mechanisms for tactile form perception in the FTI, we developed a computational model of sensory neurons to estimate temporal patterns of action potentials from tactile receptive fields. Our computational data suggest that (1) the temporal asynchrony of sensory neuron responses is correlated with the relative magnitude of perceived surface indentation and (2) the spatiotemporal change of displacements in tactile stimuli are correlated with the asynchrony of simulated sensory neuron responses for the fishbone surface patterns. Based on these results, we propose that both the frequency and the asynchrony of temporal activity in sensory neurons could produce tactile form perception.

Spatio-temporal patterns, namely global oscillations (GO) and traveling waves (TW), were investigated in spherical microbeads loaded with a catalyst for the Belousov-Zhabotinsky (BZ) reaction onto the surface (2D-loaded) or the entire volume of the bead (3D-loaded). GO and TW selectively appeared in the 2D- and 3D-loaded beads, respectively, placed on a polyethylene terephthalate (PET) sheet in the catalyst-free BZ solution. We examined two types of coupling of the two beads: 2D-3D and 3D-3D couplings. In both cases, synchronization occurred when the minimum distance between the two beads, l, was shorter than the threshold. Herein, we reported not only temporal information, that is, phase difference, but also spatial information, that is, the directions of the TW propagating through the coupled BZ beads. In the synchronization for the 2D-3D coupling, TW in the 3D-loaded bead were initiated from the point near the 2D-loaded bead as a pacemaker and propagated in the opposite direction. By contrast, the directions of the TW in the 3D-loaded bead changed depending on l in the synchronization for the 3D-3D coupling. These experimental results can be quantitatively reproduced by numerical calculations based on the diffusion dynamics of an activator of the BZ reaction. Our results suggest that the features of spatio-temporal wave propagation are indicative of the configuration of the oscillators.

Droplet-based microfluidics is a powerful tool for producing monodispersed micrometer-sized droplets with controlled sizes and shapes; thus, it has been widely applied in diverse fields from fundamental science to industries. Toward a simpler method for fabricating microparticles with front–back asymmetry in their shapes, we studied anisotropic gelation of alginate droplets, which occurs inside a flow-focusing microfluidic device. In the proposed method, sodium alginate (NaAlg) aqueous phase fused with a calcium chloride (CaCl2) emulsion dispersed in the organic phase just before the aqueous phase breaks up into the droplets. The fused droplet with a front–back asymmetric shape was generated, and the asymmetric shape was kept after geometrical confinement by a narrow microchannel was removed. The shape of the fused droplet depended on the size of prefused NaAlg aqueous phase and a CaCl2 emulsion, and the front–back asymmetry appeared in the case of the smaller emulsion size. The analysis of the velocity field inside and around the droplet revealed that the stagnation point at the tip of the aqueous phase also played an important role. The proposed mechanism will be potentially applicable as a novel fabrication technique of microparticles with asymmetric shapes.

The authors regret that the experimental condition was wrongly described in Section 4 in page 20 and the caption of Fig. 5 in page 21. The concentration of camphor methanol solution was 3 mol/L, not 0.3 mol/L. The authors would like to apologise for any inconvenience caused.

We investigated the bifurcation structure on the self-propelled motion of a camphor rotor at a water surface. The center of the camphor rotor was fixed by the axis, and it showed rotational motion around it. Due to the chiral asymmetry of its shape, the absolute values of the angular velocities in clockwise and counterclockwise directions were different. This asymmetry in the angular velocities implies an imperfect bifurcation. From the numerical simulation results, we discuss the condition for the occurrence of the imperfect bifurcation.

A model of an autonomous three-sphere microswimmer is proposed by implementing a coupling effect between the two natural lengths of an elastic microswimmer. Such a coupling mechanism is motivated by the previous models for synchronization phenomena in coupled oscillator systems. We numerically show that a microswimmer can acquire a nonzero steady state velocity and a finite phase difference between the oscillations in the natural lengths. These velocity and phase differences are almost independent of the initial phase difference. There is a finite range of the coupling parameter for which a microswimmer can have an autonomous directed motion. The stability of the phase difference is investigated both numerically and analytically in order to determine its bifurcation structure.

Monovalent and divalent cations were added to a phospholipid (1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC)) solution in order to evaluate the effect of metal cations on the phospholipid monolayer. While the surface pressure-area (Π-A) isotherm of the phospholipid monolayer at the air-water interface did not change when monovalent cations (Na , K ) were added, Π increased with the addition of divalent cations (Mg , Ca , Sr ) according to their atomic numbers. Fourier-transform infrared spectroscopy and differential scanning calorimetry were used to evaluate the interactions between DOPC and cations. Experimental results suggest that cation valence and atomic number play an important role in the characteristic interactions with DOPC. + + 2+ 2+ 2+

In this study, we discovered that, when an acidic solution with a low surface tension spreads on the surface of a glycerol solution mixed with milk, a star-shaped pattern is spontaneously formed on the surface in the horizontal plane during the spreading process. We experimentally investigated the emergence of the star-shaped pattern caused by an interfacial instability by using glycerol and aqueous 2-methoxyethanol solutions, which are acidic solutions; we chose the viscosity of the glycerol solution and concentration of both solutions as free parameters. The result demonstrated that the star-shaped pattern emerged when the concentration of 2-methoxyethanol was high. We proposed a phenomenological model based on our experimental results, which explains the following three points: the spreading of the aqueous 2-methoxyethanol solution on the surface of the glycerol solution; colloidal aggregation of the milk protein colloids caused by the denaturation that occurs when mixed with 2-methoxyethanol; accumulation of the aggregates toward the dent regions of the moving interface by a sweeping effect. The model reproduced the star-shaped pattern, which was similar to the experimental one. Furthermore, the concentration of the 2-methoxyethanol solution and the viscosity of the glycerol solution were taken as control parameters in our experiments and were varied, and a phase diagram was obtained. The phase diagram was similar to that obtained from our experiments. The results suggest that the above three points are important for the formation of the star-shaped pattern.

We investigated the spontaneous deformation and fission of a tetradecane droplet containing palmitic acid (PA) on a stearyltrimethylammonium chloride (STAC) aqueous solution. In this system, the generation and rupture of the gel layer composed of PA and STAC induce the droplet deformation and fission. To investigate the characteristics of the droplet-fission dynamics, we obtained the time series of the number of the droplets produced by fission and confirmed that the number has a peak at a certain STAC concentration. Since the fission of the droplet should be led by the deformation, we analyzed four parameters which may relate to the fission dynamics from the spatiotemporal correlation of the droplet-boundary velocity. We found that the parameter which corresponds to the expansion speed had the strongest positive correlation among them, and thus we concluded that the faster deformation would be the key factor for the fission dynamics.

Self-propelled droplets made of organic materials can be an influential candidate for understanding cell migration from the viewpoint of nonequilibrium physics and have attracted significant attention with regard to soft-matter-type rovers. Because self-propelled droplets are soft enough to be easily deformed, they should be useful as chemically artificial rovers that can move in small areas with many obstacles in water and can be applied as ‘motile’ carriers for exploring and curing of biological bodies or remediation of the natural environment. Here, we review recent research progress on designing self-propelled droplets of micrometer size.

The spontaneous motion of a camphor particle with a slight modification from a circle is investigated. The effect of the shape on the motion is examined by the perturbation method. We introduce a slight n-mode modification from a circle, where the profile is described by r ¼ Rð1 þ ε cos nθÞ in polar coordinates. The results predict that a camphor particle with an n = 3 mode modification from a circle, i.e., a triangular modification, moves in the direction of a corner for a small particle, while it moves in the direction of a side for a large particle. The numerical simulation results well reproduce the theoretical prediction. The present study will help understand the effect of the particle shape on spontaneous motion.

Recent experimental results indicate that mixing is enhanced by a reciprocal flow induced inside a levitated droplet with an oscillatory deformation [T. Watanabe et al., Sci. Rep. 8, 10221 (2018)2045-232210.1038/s41598-018-28451-5]. Generally, reciprocal flow cannot convect the solutes in time average, and agitation cannot take place. In the present paper, we focus on the diffusion process coupled with the reciprocal flow. We theoretically derive that the diffusion process can be enhanced by the reciprocal flow, and the results are confirmed via numerical calculation of the over-damped Langevin equation with a reciprocal flow.

The system in which a small rigid ball is bouncing repeatedly on a heavy flat table vibrating vertically, so-called the bouncing ball system, has been widely studied. Under the assumption that the table is vibrating with a piecewise polynomial function of time, the bifurcation diagram changes qualitatively depending on the order of the polynomial function. We elucidate the mechanism of the difference in the bifurcation diagrams by focusing on the two-period solution. In addition, we derive the approximate curve of the branch close to the period-doubling bifurcation point in the case of the piecewise cubic function of time for the table vibration. We also performed numerical calculation, and we demonstrate that the approximations well reproduce the numerical results.

We consider a mathematical model for a two-particle system driven by the spatial gradient of a concentration field of chemicals with conservative attractive interactions in one dimension. This setup corresponds to an experimental system with floating camphor particles at a water surface. A repulsive interaction is introduced, as well as a self-propelling force, through the concentration field of camphor molecules at the water surface. Here, we newly adopt the attractive lateral capillary force due to the deformation of the water surface. The particles experience competing dissipative repulsion and conservative attraction. We numerically investigated the mathematical model and found six different modes of motion. The theoretical approach revealed that some of such mode transitions can be understood in terms of bifurcation.

A density oscillator exhibits limit-cycle oscillations driven by the density difference of the two fluids. We performed two-dimensional hydrodynamic simulations with a simple model and reproduced the oscillatory flow observed in experiments. As the density difference is increased as a bifurcation parameter, a damped oscillation changes to a limit-cycle oscillation through a supercritical Hopf bifurcation. We estimated the critical density difference at the bifurcation point and confirmed that the period of the oscillation remains finite even around the bifurcation point.

Resonance, beats, and synchronization are general and fundamental phenomena in physics. Their existence and their in-depth understanding in physical systems have led to several applications and technological developments shaping our world today. Here we show the existence of chemical resonance, chemical beats, and frequency locking phenomena in periodically forced pH oscillatory systems (sulfite-hydrogen peroxide and sulfite-formaldehyde-gluconolactone pH oscillatory systems). Periodic forcing was realized by a superimposed sinusoidal modulation on the inflow rates of the reagents in the continuous-flow stirred tank reactor. The dependence of the time period of beats follows the relation known from classical physics for forced physical oscillators. Our developed numerical model describes qualitatively the resonance and beat phenomena experimentally revealed. Application of periodic forcing in autonomously oscillating systems can provide new types of oscillators with a controllable frequency and new insight into controlling irregular chemical oscillation regimes.

We propose a simple mathematical model that describes the time evolution of a self-propelled object on a liquid surface using variables such as object location, surface concentration of active molecules, and hydrodynamic surface flow. The model is applied to simulate the time evolution of a rotor composed of a polygonal plate with camphor pills at its corners. We have qualitatively reproduced results of experiments, in which the inversion of rotational direction under periodic stop-and-release-operations was investigated. The model correctly describes the probability of the inversion as a function of the duration of the phase when the rotor is stopped. Moreover, the model allows to introduce the rotor asymmetry unavoidable in real experiments and study its influence on the studied phenomenon. Our numerical simulations have revealed that the probability of the inversion of rotational direction is determined by the competition among the transport of the camphor molecules by the flow, the intrinsic asymmetry of the rotor, and the noise amplitude. Published under license by AIP Publishing.

We investigated self-propelled rotation of a symmetric three-bladed rotor on water under periodic halt and release operations. The rotation was driven by the difference in the surface tension around the blades of the rotor because camphor molecules developed from three camphor disks glued at the blade ends. Spontaneous inversion of rotation direction was observed after a forced stop of the rotor and the subsequent release. The probability of such inversion decreased with an increase in the halting time. The asymmetric distribution of camphor molecules around the blades was also inverted after the forced stop and the degree of asymmetry increased with an increase in the angular velocity characterizing the stationary rotation of the rotor. Our experimental results for rotors with different shapes indicate that there is a strong correlation between the stationary angular velocity of the rotor and the maximum time duration of the forced stop for which a high probability of inversion is observed.

<title>Abstract</title> Hydrodynamic instabilities often cause spatio-temporal pattern formations and transitions between them. We investigate a model experimental system, a density oscillator, where the bifurcation from a resting state to an oscillatory state is triggered by the increase in the density difference of the two fluids. Our results show that the oscillation amplitude increases from zero and the period decreases above a critical density difference. The detailed data close to the bifurcation point provide a critical exponent consistent with the supercritical Hopf bifurcation.

<title>Abstract</title> A simple model of an active colloid consisting of dumbbell-shaped particles that cyclically change their length without propelling themselves is proposed and analyzed. At nanoscales, it represents an idealization for bacterial cytoplasm or for a biomembrane with active protein inclusions. Our numerical simulations demonstrate that non-equilibrium conformational activity of particles can strongly affect diffusion and structural relaxation: while a passive colloid behaves as a glass, it gets progressively fluidized when the activity is turned on. Qualitatively, this agrees with experimental results on optical tracking of probe particles in bacterial and yeast cells where metabolism-induced fluidization of cytoplasm was observed.

Self-propelled motion of micrometer-sized oil droplets in surfactant solution has drawn much attention as an example of nonlinear life-like dynamics under far-from-equilibrium conditions. The driving force of this motion is thought to be induced by Marangoni convection based on heterogeneity in the interfacial tension at the droplet surface. Here, to clarify the required conditions for the self-propelled motion of oil droplets, we have constructed a chemical system, where oil droplet motion is induced by the production of 1,2,3-triazole-containing surfactants through the Cu-catalyzed azide-alkyne cycloaddition reaction. From the results of the visualization and analysis of flow fields around the droplet, the motion of the droplets could be attributed to the formation of flow fields, which achieved sufficient strength caused by the in situ production of surfactants at the droplet surface.

In a two-dimensional axisymmetric system, the system symmetry allows rotational or oscillatory motion as stable stationary motion for a symmetric self-propelled particle. In the present paper, we studied the motion of a camphor disk confined in a two-dimensional circular region. By reducing the mathematical model describing the dynamics of the motion of a camphor disk and the concentration field of camphor molecules on a water surface, we analyzed the reduced equations around a bifurcation point where the rest state at the center of the system becomes unstable. As a result, we found that rotational motion is stably realized through the double-Hopf bifurcation from the rest state. The theoretical results were confirmed by numerical calculation and corresponded well to the experimental results.

To elucidate the effect of polyols on a phospholipid molecular layer, different polyols with the formula H-(CH (OH))(m)-H (m = 2-6) were added to a phospholipid (1,2-dipalmitoleoyl-sn-glycero-3-phosphoethanolamine (DPoPE)) solution above and below the phase transition temperature between the lamellar and inverted hexagonal phases. As for the surface pressure (pi) - surface area (A) isotherm of the phospholipid monolayer at the air-water interface, at a constant value of A increased with increasing m, especially for xylitol (m = 5) and sorbitol (m = 6). Small angle X-ray scattering (SAXS) and Fourier transform IR spectrometry (FT-IR) were used to evaluate the interaction between DPoPE and the polyol molecules. The experimental results suggest that the number of CH(OH) groups in the polyol plays an important role in the characteristic interaction between DPoPE and the polyol in both the lamellar and inverted hexagonal phases.

We studied rotation of a disk propelled by a number of camphor pills symmetrically distributed at its edge. The disk was put on a water surface so that it could rotate around a vertical axis located at the disk center. In such a system, the driving torque originates from surface tension difference resulting from inhomogeneous surface concentration of camphor molecules released from the pills. Here, we investigated the dependence of the stationary angular velocity on the disk radius and on the number of pills. The work extends our previous study on a linear rotor propelled by two camphor pills [Y. Koyano et al., Phys. Rev. E 96, 012609 (2017)]. It was observed that the angular velocity dropped to zero after a critical number of pills was exceeded. Such behavior was confirmed by a numerical model of time evolution of the rotor. The model predicts that, for a fixed friction coefficient, the speed of pills can be accurately represented by a function of the linear number density of pills. We also present bifurcation analysis of the conditions at which the transition between a standing and a rotating disk appears. Published under license by AIP Publishing.

We consider spontaneous oscillation phenomena in three-phase liquid membrane systems in a horizontally-placed glass tube with different solutes in the aqueous phase and different oil phase solvents. The relationship between the induction period of electrical potential oscillation and the initial concentration of solute in the source aqueous phase highlights the importance of the density difference owing to differential concentrations of solute. Numerical calculations confirmed the effects of the density difference and revealed the occurrence of buoyant convection in the oil liquid membrane phase. The convection flow (buoyant convection roll) transported solute, which induced Marangoni convection at the interface between the oil phase and the receiving aqueous phase. Our new experimental and numerical approaches taking into account the density difference provide an explanation for the spontaneous non-linear oscillation phenomena at the oil/water interface in horizontal three-phase liquid membrane systems.

We investigated the velocity of an asymmetric camphor boat moving on aqueous solutions with glycerol. The viscosity was controlled by using several concentrations of glycerol into the solution. The velocity decreased with an increase in the glycerol concentration. We proposed a phenomenological model, and we showed that the velocity decreased with an increase in the viscosity according to power law. Our experimental result agreed with the one obtained from our model. These results suggest that a decay length of the camphor concentration at the front side of the boat is sufficiently shorter than that of the rear side.