Shear-Induced Nonequilibrium Patterns in Lipid Bilayer Membranes Exhibiting Phase Separation.

The nonequilibrium dynamics of a fluid lipid membrane under external stimuli is an important issue that spans disciplines such as soft matter, biophysical chemistry, and interface science. This study investigated the dynamic response of lipid vesicles with order-disorder phase separation, which mimics a plasma membrane heterogeneity, to shear flow. Lipid vesicles were immobilized in a microfluidic chamber, and shear-induced nonequilibrium patterns on the membrane surface were observed by an optical microscope. We found that phase-separated membranes exhibit a dissipative structure of stripe patterns along the vortex flow on the membrane surface, and the number of stripes increased with the flow rate. At a high flow rate, the membrane exhibited a stripe-to-wave transition, where striped domains often migrated and the replacement of two different phases happened at vortex centers with time. We obtained a dynamic phase diagram of the shear-induced wave pattern by changing the flow rate, membrane components, and temperature. These findings could provide insight into the dissipative structures of lipid membranes out of equilibrium and flow-mediated mechanotransduction of biological membranes.

New types of complex motion of a simple camphor boat.

We discuss the motion of a rectangular camphor boat, considering the position of a camphor pill in relation to the boat's stern as the control parameter. The boat moves because the pill releases surface active molecules that decrease the surface tension and support the motion. We introduce a new experimental system in which the boat rotates on a long arm around the axis located at the centre of a Petri dish; thus, the motion is restricted to a circle and can be studied under stationary conditions for a long time. The experiments confirmed two previously reported modes of motion: continuous motion when the pill was located at the boat edge and pulsating (intermittent) motion if it was close to the boat centre (Suematsu et al., J. Phys. Chem. C, 2010, 114(21), 9876-9882). For intermediate pill locations, we observed a new, unreported type of motion characterised by oscillating speed (i.e. oscillating motion). Different modes of motion can be observed for the same pill location. The experimental results are qualitatively confirmed using a simple reaction-diffusion model of the boat evolution used in the above-mentioned paper.

Collagen XVII deficiency alters epidermal patterning.

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.

Domain dynamics of phase-separated lipid membranes under shear flow.

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.

Complexity and bifurcations in the motion of a self-propelled rectangle confined in a circular water chamber.

We consider the motion of a self-propelled object of rectangular shape inside a circular water chamber. The mathematical model of self-motion includes equations for the orientation and location of the rectangle and reaction-diffusion equation with an effective diffusion coefficient for the time evolution of the surface concentration of active molecules. Numerical simulations of motion were performed for different values of the ratio between the supply rate S and the evaporation rate a of active molecules. Treating S0 = S/a as a control parameter, we found the critical behavior in variables characterizing the trajectory and identified different types of motion. If the value of S0 is small, the rectangle rests at the chamber center. For larger S0, a reciprocal motion during which the rectangle passes through the center is observed. At yet higher supply rates, the star-polygonal motion appears, and the trajectory remains at a distance from the chamber center. In the experiments with a rectangle made of camphor-camphene-polypropylene plastic moving in a Petri dish, we observed the transition from the star-polygonal motion to the reciprocal motion in time. This transition can be understood on the basis of the developed model if we assume that the supply rate decreases in time.

Traveling waves propagating through coupled microbeads in the Belousov-Zhabotinsky reaction.

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.

Inversion probability of three-bladed self-propelled rotors after forced stops of different durations.

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.

Local bifurcation structure of a bouncing ball system with a piecewise polynomial function for table displacement.

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.

On a simple model that explains inversion of a self-propelled rotor under periodic stop-and-release-operations.

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.

Start of Micrometer-Sized Oil Droplet Motion through Generation of Surfactants.

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.

Bifurcation in the angular velocity of a circular disk propelled by symmetrically distributed camphor pills.

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.

Distinguishing the Dynamic Fingerprints of Two- and Three-Dimensional Chemical Waves in Microbeads.

Spatiotemporal oscillations confined to quasi-2D surface layers or 3D volumes play an important role for wave-based information relay and global oscillations in living systems. Here, we describe experiments with the Belousov-Zhabotinsky reaction confined to microbeads, in which the catalyst is selectively loaded either onto the surface or into the body of the spherical beads. We find that the dynamics of global oscillations, traveling reaction fronts, and rotating spiral waves under surface confinement are strikingly different from those in the bead volume. Our results establish a useful model system for the study of geometrical effects on nonlinear chemical processes and provide diagnostic features that allow the distinction of membrane-mediated 2D and cytosolic 3D processes in biological cells.

Effective diffusion coefficient including the Marangoni effect.

Surface-active molecules supplied from a particle fixed at the water surface create a spatial gradient of the molecule concentration, resulting in Marangoni convection. Convective flow transports the molecules far from the particle, enhancing diffusion. We analytically derive the effective diffusion coefficient associated with the Marangoni convection rolls. The resulting estimated effective diffusion coefficient is consistent with our numerical results and the apparent diffusion coefficient measured in experiments.

Self-Propelled Motion of Monodisperse Underwater Oil Droplets Formed by a Microfluidic Device.

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.

Unidirectional motion of a camphor disk on water forced by interactions between surface camphor concentration and dynamically changing boundaries.

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 variables. The diode can be incorporated into more complex devices, like a ring that imposes unidirectional rotation of camphor disks.

Mechanism of Spontaneous Blebbing Motion of an Oil-Water Interface: Elastic Stress Generated by a Lamellar-Lamellar Transition.

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.

Mathematical model for calcium-assisted epidermal homeostasis.

Using a mathematical model of the epidermis, we propose a mechanism of epidermal homeostasis mediated by calcium dynamics. We show that calcium dynamics beneath the stratum corneum can reduce spatio-temporal fluctuations of the layered structure of the epidermis. We also demonstrate that our model can reproduce experimental results that the recovery from a barrier disruption is faster when the disrupted site is exposed to air. In particular, simulation results indicate that the recovery speed depends on the size of barrier disruption.

Mathematical model for self-propelled droplets driven by interfacial tension.

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.

Effects of medium flow on axon growth with or without nerve growth factor.

Axon growth is a crucial process in regeneration of damaged nerves. On the other hand, elongation of nerve fibers in the epidermis has been observed in skin of atopic dermatitis patients. Thus, regulation of nerve fiber extension might be an effective strategy to accelerate nerve regeneration and/or to reduce itching in pruritus dermatosis. We previously demonstrated that neurons and epidermal keratinocytes similarly contain multiple receptors that are activated by various environmental factors, and in particular, keratinocytes are influenced by shear stress. Thus, in the present study, we evaluated the effects of micro-flow of the medium on axon growth in the presence or absence of nerve growth factor (NGF), using cultured dorsal-root-ganglion (DRG) cells. The apparatus, AXIS™, consists of two chambers connected by a set of microgrooves, through which signaling molecules and axons, but not living cells, can pass. When DRG cells were present in chamber 1, NGF was present in chamber 2, and micro-flow was directed from chamber 1 to chamber 2, axon growth was significantly increased compared with other conditions. Acceleration of axon growth in the direction of the micro-flow was also observed in the absence of NGF. These results suggest that local micro-flow might significantly influence axon growth.