Can self-propelled objects escape from compression stimulation?

We studied circular papers impregnated with camphor (CPs) and CPs with magnets (MCPs) as self-propelled objects floating on water under the compression of the water surface as an inanimate system for evacuation in an emergency. Two water chambers-Cin and Cout-were connected via a plastic gate, and eight CPs or eight MCPs were placed on Cin. We monitored the movement of the CPs or MCPs from Cin to Cout when the gate was opened and the area of Cin (Ain) was decreased using a barrier. When Ain was large, CPs moved stochastically from Cin to Cout while exhibiting random motion. The escape probability from Cin to Cout (P) at time t = 20 s increased with a decrease in Ain, and the rate of increase in P increased depending on the width of the gate (Wg). By contrast, clustering was observed for MCPs. Consequently, P of MCPs was lower than that of CPs. The difference in the surface tension between Cin and Cout (Δγ) increased with a decrease in Ain. P is discussed in relation to Δγ as the driving force for emergencies and the repulsive forces between CPs or attractive forces between MCPs. These results suggest that the repulsive force enhances the self-propulsion of objects towards the gate, that is, as a result, higher values of P are obtained.

Coexistence of oscillatory and reduced states on a spherical field controlled by electrical potential.

The Belousov-Zhabotinsky (BZ) reaction was investigated to elucidate features of oscillations depending on the applied electrical potential, E. A cation-exchange resin bead loaded with the catalyst of the BZ reaction was placed on a platinum plate as a working electrode and then E was applied. We found that global oscillations (GO) and a reduced state coexisted on the bead at a negative value of E and that the source point of GO changed depending on E. The thickness of the reduced state was determined by a yellow colored region which corresponded to the distribution of Br2. The present studies suggest that the distribution of the inhibitor, Br-, which is produced from Br2, plays an important role in the existence of the reduced state and GO, and the source point of GO.

Visual Sensing System to Investigate Self-Propelled Motion and Internal Color of Multiple Aqueous Droplets.

This study proposes a visual sensing system to investigate the self-propelled motions of droplets. In the visual sensing of self-propelled droplets, large field-of-view and high-resolution images are both required to investigate the behaviors of multiple droplets as well as chemical reactions in the droplets. Therefore, we developed a view-expansive microscope system using a color camera head to investigate these chemical reactions; in the system, we implemented an image processing algorithm to detect the behaviors of droplets over a large field of view. We conducted motion tracking and color identification experiments on the self-propelled droplets to verify the effectiveness of the proposed system. The experimental results demonstrate that the proposed system is able to detect the location and color of each self-propelled droplet in a large-area image.

Interfacial Dynamics in the Spontaneous Motion of an Aqueous Droplet.

Self-propelled droplets can spontaneously move using chemical energy. In several reports of self-propelled droplets, interfacial chemical reactions occur at the oil/aqueous interface to induce the Marangoni flow. While the dynamics of interfacial tension is essential to the droplet motion, there are few reports that quantitatively discuss the moving mechanism based on interfacial tension measurements. In this study, we focused on the self-propelled motion of an aqueous droplet in the oil phase, where the surfactant monoolein reacts with bromine at the interface, and estimated the physicochemical parameters related to the droplet motion based on the time series of interfacial tension. These results may reveal the general mechanism for the self-propelled motion of aqueous/oil droplets driven by the interfacial chemical reaction.

Chemical Wave Propagation in the Belousov-Zhabotinsky Reaction Controlled by Electrical Potential.

The Belousov-Zhabotinsky (BZ) reaction is an important experimental model for the study of chemical oscillations and waves far from the thermodynamic equilibrium. Earlier studies had observed that individual BZ microbeads can show both global oscillations and traveling waves, but failed to select these different dynamic states. Here, we report experiments, in which this control was achieved by an externally applied electrical potential. The spherical microbeads were first loaded with the catalyst, then immersed into a catalyst-free BZ solution, and finally placed onto a planar platinum electrode. For positive electrical potentials, we observed global oscillations, whereas negative potentials resulted in traveling waves. The spatio-temporal characteristics of these phenomena are discussed in relation to the activator, HBrO2, which is produced by an electrochemical reaction.

Evolution of Self-Propelled Objects: From the Viewpoint of Nonlinear Science.

A variety of moving objects driven by chemical energy have been reported. In this Minireview, we focus on self-propelled objects driven by interfacial tension and explain three types of basic mechanisms for such self-propelled motion, that is, driven by a) surface tension difference, b) contact angle difference, and c) axisymmetric swirling flow in a droplet. Simple behavior induced from the basic mechanisms is then extended by coupling to a chemical reaction or increasing the number of moving objects. Even though the chemicals used here are still simple, the extended systems could show characteristic nonlinear behavior, such as reciprocating motion, oscillatory motion, and spatiotemporal pattern formation. Combining the dynamical information about these characteristic motions with the knowledge of molecular structures will lead to the development of more advanced self-propelled objects. We believe this Minireview can help chemists in investigating self-propelled objects displaying various functional motions observed in a biological system.

Asymmetries in leaf branch are associated with differential speeds along growth axes: A theoretical prediction.

BACKGROUND: Morphogenesis, when accompanied by continuous growth, requires stable positional information to create a balanced shape in an organism. Evenly spaced branches are examples of such morphogenesis. Previously, we created a model that showed when a one-dimensional (1D) ring (a boundary of a 2D field) was periodically deformed based on a stable, doubled iterative pattern during expansion; a nested, regularly spaced, symmetrically branched structure was generated. The characteristic divaricating pattern is common in the leaves of many plant species; however, the divarication symmetry was often broken. To evaluate this type of asymmetry, we investigated several species with dissected or compound leaves. RESULTS: Sometimes these leaves showed asymmetries in the number of lobes or segments positioned on either side of the secondary axes. The direction of the asymmetry, i.e., which side of a secondary axis has more axes, appeared to be species-specific. CONCLUSIONS: When different growth speeds along axes of a divaricating leaf were introduced into our previous model, robust and directed asymmetries were reproduced. The differences in growth speed could be predicted from the distributions of leaf segments in actual leaves. Developmental Dynamics 246:981-991, 2017. © 2017 Wiley Periodicals, Inc.

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.

Periodic Oscillatory Motion of a Self-Propelled Motor Driven by Decomposition of H2 O2 by Catalase.

A self-propelled motor driven by the enzymatic reaction of catalase adsorbed onto a filter paper floating on an aqueous solution of H2 O2 was used to study nonlinear behavior in the motor's motion. An increase in the concentration of H2 O2 resulted in a change from no motion to irregular oscillatory motion, periodic oscillatory motion, and continuous motion. The mechanisms underlying oscillation and mode bifurcation are discussed based on experimental results on O2 bubble formation and growth on the underside of the motor.

Physicochemical design and analysis of self-propelled objects that are characteristically sensitive to environments.

The development of self-propelled motors that mimic biological motors is an important challenge for the transport of either themselves or some material in a small space, since biological systems exhibit high autonomy and various types of responses, such as taxis and swarming. In this perspective, we review non-living systems that behave like living matter. We especially focus on nonlinearity to enhance autonomy and the response of the system, since characteristic nonlinear phenomena, such as oscillation, synchronization, pattern formation, bifurcation, and hysteresis, are coupled to self-motion of which driving force is the difference in the interfacial tension. Mathematical modelling based on reaction-diffusion equations and equations of motion as well as physicochemical analysis from the point of view of the molecular structure are also important for the design of non-living motors that mimic living motors.

Quantitative estimation of the parameters for self-motion driven by difference in surface tension.

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.

Periodic Precipitation in a Confined Liquid Layer.

Pattern formation is a ubiquitous phenomenon in animate and inanimate systems generated by mass transport and reaction of chemical species. The Liesegang phenomenon is a self-organized periodic precipitation pattern always studied in porous media such as hydrogels and aerogels for over a century. The primary consideration of applying the porous media is to prevent the disintegration of the precipitation structures due to the sedimentation of the precipitate and induced fluid flow. Here, we show that the periodic precipitation patterns can be engineered using a Hele-Shaw cell in a confined liquid phase, restricting hydrodynamic instability. The patterns generated in several precipitation reaction systems exhibit spatiotemporal properties consistent with patterns obtained in solid hydrogels. Furthermore, analysis considering the Rayleigh-Darcy number emphasizes the crucial role of fluidity in generating periodic precipitation structures in a thin liquid film. This exploration promises breakthroughs at the intersection of fundamental understanding and practical applications.

Periodical alternation between precipitation and dissolution of camphor solid film on an ethanol solution.

Rhythmic behaviors are generally observed in nonlinear chemical reactions such as the Belousov-Zhabotinsky reaction and enzymatic reactions. Similarly, a simple phase change can also lead to rhythmic behavior. It has been reported previously that camphor solid films alternate between generation and disappearance on ethanol (EtOH) solution, and a phenomenological mechanism has been suggested for this. The evaporation of EtOH decreases the temperature on the surface of the solution via vaporization heat and induces precipitation in the camphor solid film. At this time, the film prevents evaporation, and thus, the surface temperature increases due to thermal diffusion from the atmosphere, resulting in dissolution of the solid film. To verify the previously suggested phenomenological mechanism, we controlled the evaporation rate of EtOH using a porous plastic cover. As a result, the period of oscillation increased with decreasing pore diameter, and finally, the oscillation did not occur without pore in the cover, where the camphor solid film was not observed. Additionally, a new mathematical model was proposed, and the numerical calculations agreed well with experimental observations. Linear stability and bifurcation analyses revealed the detailed mechanism of this phenomenon, which agreed well with the phenomenological explanation mentioned above.

Reproduction of bacterial chemotaxis by a non-living self-propelled object.

Taxic behavior as a response to an external stimulus is a fundamental function of living organisms. Some bacteria successfully implement chemotaxis without directly controlling the direction of movement. They periodically alternate between run and tumble, i.e., straight movement and change in direction, respectively. They tune their running period depending on the concentration gradient of attractants around them. Consequently, they respond to a gentle concentration gradient stochastically, which is called "bacterial chemotaxis." In this study, such a stochastic response was reproduced by a non-living self-propelled object. We used a phenanthroline disk floating on an aqueous solution of Fe[Formula: see text]. The disk spontaneously alternated between rapid motion and rest, similar to the run-and-tumble motion of bacteria. The movement direction of the disk was isotropic independent of the concentration gradient. However, the existing probability of the self-propelled object was higher at the low-concentration region, where the run length was longer. To explain the mechanism underlying this phenomenon, we proposed a simple mathematical model that considers random walkers whose run length depends on the local concentration and direction of movement against the gradient. Our model adopts deterministic functions to reproduce the both effects, which is instead of stochastic tuning the period of operation used in the previous reports. This allows us to analyze the proposed model mathematically, which indicated that our model reproduces both positive and negative chemotaxis depending on the competition between the local concentration effect and it's gradient effect. Owing to the newly introduced directional bias, the experimental observations were reproduced numerically and analytically. The results indicate that the directional bias response to the concentration gradient is an essential parameter for determining bacterial chemotaxis. This rule might be universal for the stochastic response of self-propelled particles in living and non-living systems.

Bioconvection pattern of Euglena under periodical illumination.

Microorganisms respond to environmental conditions and often spontaneously form highly ordered convection patterns. This mechanism has been well-studied from the viewpoint of self-organization. However, environmental conditions in nature are usually dynamic. Naturally, biological systems respond to temporal changes in environmental condition. To elucidate the response mechanisms in such a dynamic environment, we observed the bioconvection pattern of Euglena under periodical changes in illumination. It is known that Euglena shows localized bioconvection patterns under constant homogeneous illumination from the bottom. Periodical changes in light intensity induced two different types of spatiotemporal patterns: alternation of formation and decomposition over a long period and complicated transition of pattern over a short period. Our observations suggest that pattern formation in a periodically changing environment is of fundamental importance to the behavior of biological systems.

Long-time behavior of swimming Euglena gracilis in a heterogenous light environment.

The cell motion of Euglena gracilis in homogeneous and heterogeneous light environments was analyzed. Homogeneous and heterogeneous environments were prepared, with only a red color or with a red circle surrounded by brighter white regions, respectively. In a heterogeneous environment, the cells move into the red circle. Swimming orbits at 1/25 s intervals for 120 s were analyzed. The speed distribution of the 1 s-averaged cell orbits in a homogeneous environment was different from that in a heterogeneous environment, where the faster swimming fraction was enhanced. The relationship between speed and curvature radius was analyzed using a joint histogram. Histograms for short timescale motion, constructed by 1 s-averaged orbits, suggest that the cell swimming curves are not biased, while those for long timescale motion, constructed by 10 s-averaged orbits, suggest that the cell swimming curves are biased in the clockwise direction. Furthermore, the curvature radius determines the speed, which does not seem to depend on the light environment. The mean squared displacement in a heterogeneous environment is larger than that in a homogeneous environment on a 1 s timescale. These results will be the basis for constructing a model for the long-time behavior of photomovement for light differences.

Appearance and suppression of Turing patterns under a periodically forced feed.

Turing instability is a general and straightforward mechanism of pattern formation in reaction-diffusion systems, and its relevance has been demonstrated in different biological phenomena. Still, there are many open questions, especially on the robustness of the Turing mechanism. Robust patterns must survive some variation in the environmental conditions. Experiments on pattern formation using chemical systems have shown many reaction-diffusion patterns and serve as relatively simple test tools to study general aspects of these phenomena. Here, we present a study of sinusoidal variation of the input feed concentrations on chemical Turing patterns. Our experimental, numerical and theoretical analysis demonstrates that patterns may appear even at significant amplitude variation of the input feed concentrations. Furthermore, using time-dependent feeding opens a way to control pattern formation. The patterns settled at constant feed may disappear, or new patterns may appear from a homogeneous steady state due to the periodic forcing.

Photo-sensitive self-motion of a BQ disk.

The photo-sensitive self-motion of a benzoquinone (BQ) disk was investigated on a hydroquinone (HQ) aqueous solution. The mode-switching of self-motion, i.e., continuous → intermittent → no motion, was observed with an increase in the concentration of HQ. Upon irradiation with UV light (∼254 nm), the critical concentrations of HQ that were associated with the three modes of motion shifted to lower values, and the average speed of motion decreased. We discuss the mechanism of the photo-sensitive self-motion in relation to the photochemical reaction from BQ to HQ and the driving force of the disk.

Photoexcited chemical wave in the ruthenium-catalyzed Belousov-Zhabotinsky reaction.

The excitation of the photosensitive Belousov-Zhabotinsky (BZ) reaction induced by light stimulation was systematically investigated. A stepwise increase in the light intensity induced the excitation, whereas a stepwise decrease did not induce the excitation. The threshold values for the excitation were found to be a function of the initial and final light intensities, time variation in light intensity, and the concentration of NaBrO(3). The experimental results were qualitatively reproduced by a theoretical calculation based on a three-variable Oregonator model modified for the photosensitive BZ reaction. These results suggest that although the steady light irradiation is known to inhibit oscillation and chemical waves in the BZ system under almost all conditions, the stepwise increase in the light irradiation leads to the rapid production of an activator, resulting in the photoexcitation.

Instability of the Homogeneous Distribution of Chemical Waves in the Belousov-Zhabotinsky Reaction.

Chemical traveling waves play an important role in biological functions, such as the propagation of action potential and signal transduction in the nervous system. Such chemical waves are also observed in inanimate systems and are used to clarify their fundamental properties. In this study, chemical waves were generated with equivalent spacing on an excitable medium of the Belousov-Zhabotinsky reaction. The homogeneous distribution of the waves was unstable and low- and high-density regions were observed. In order to understand the fundamental mechanism of the observations, numerical calculations were performed using a mathematical model, the modified Oregonator model, including photosensitive terms. However, the homogeneous distribution of the traveling waves was stable over time in the numerical results. These results indicate that further modification of the model is required to reproduce our experimental observations and to discover the fundamental mechanism for the destabilization of the homogeneous-distributed chemical traveling waves.