Yutaka Sumino

Large-scale vortex lattice emerging from collectively moving microtubules

Spontaneous collective motion, as in some flocks of bird and schools of fish, is an example of an emergent phenomenon. Such phenomena are at present of great interest and physicists have put forward a number of theoretical results that so far lack experimental verification. In animal behaviour studies, large-scale data collection is now technologically possible, but data are still scarce and arise from observations rather than controlled experiments. Multicellular biological systems, such as bacterial colonies or tissues, allow more control, but may have many hidden variables and interactions, hindering proper tests of theoretical ideas. However, in systems on the subcellular scale such tests may be possible, particularly in in vitro experiments with only few purified components. Motility assays, in which protein filaments are driven by molecular motors grafted to a substrate in the presence of ATP, can show collective motion for high densities of motors and attached filaments. This was demonstrated recently for the actomyosin system, but a complete understanding of the mechanisms at work is still lacking. Here we report experiments in which microtubules are propelled by surface-bound dyneins. In this system it is possible to study the local interaction: we find that colliding microtubules align with each other with high probability. At high densities, this alignment results in self-organization of the microtubules, which are on average 15 µm long, into vortices with diameters of around 400 µm. Inside the vortices, the microtubules circulate both clockwise and anticlockwise. On longer timescales, the vortices form a lattice structure. The emergence of these structures, as verified by a mathematical model, is the result of the smooth, reptation-like motion of single microtubules in combination with local interactions (the nematic alignment due to collisions)—there is no need for long-range interactions. Apart from its potential relevance to cortical arrays in plant cells and other biological situations, our study provides evidence for the existence of previously unsuspected universality classes of collective motion phenomena.

Spontaneous motion of a droplet coupled with a chemical wave.

We propose a framework for the spontaneous motion of a droplet coupled with internal dynamic patterns generated in a reaction-diffusion system. The spatiotemporal order of the chemical reaction gives rise to inhomogeneous surface tension and results in self-propulsion driven by the surrounding flow due to the Marangoni effect. Numerical calculations of internal patterns together with theoretical results of the flow fields at low Reynolds number reproduce well the experimental results obtained using a droplet of the Belousov-Zhabotinsky reaction medium.

Drift instability in the motion of a fluid droplet with a chemically reactive surface driven by Marangoni flow.

We theoretically derive the amplitude equations for a self-propelled droplet driven by Marangoni flow. As advective flow driven by surface tension gradient is enhanced, the stationary state becomes unstable and the droplet starts to move. The velocity of the droplet is determined from a cubic nonlinear term in the amplitude equations. The obtained critical point and the characteristic velocity are well supported by numerical simulations.

Spontaneous Deformation of an Oil Droplet Induced by the Cooperative Transport of Cationic and Anionic Surfactants through the Interface

Spontaneous deformation of a tetradecane droplet with palmitic acid on an aqueous phase with stearyltrimethylammonium chloride is reported. Palmitic acid is transported from the oil droplet to the aqueous phase by the concentration difference between the organic and the aqueous phases. The transport of palmitic acid causes the oil droplet interface to undergo various spontaneous deformations. When the oil droplet is placed on an aqueous surface, its diameter shrinks. Several tens of seconds later, the oil droplet suddenly expands and then shrinks in a second. After such a dramatic deformation, the oil droplet undergoes blebbing on its oil-water interface for over 1 h. We investigated the physicochemical mechanism of these phenomena. We discuss the cause of these deformations in terms of the spatiotemporal variation of the interfacial tension and elucidate that the blebbing deformation is due to the surfactant aggregate generated by cationic and anionic surfactants.

Collective Motion of Self-Propelled Particles with Memory

We show that memory, in the form of underdamped angular dynamics, is a crucial ingredient for the collective properties of self-propelled particles. Using Vicsek-style models with an Ornstein-Uhlenbeck process acting on angular velocity, we uncover a rich variety of collective phases not observed in usual overdamped systems, including vortex lattices and active foams. In a model with strictly nematic interactions the smectic arrangement of Vicsek waves giving rise to global polar order is observed. We also provide a calculation of the effective interaction between vortices in the case where a telegraphic noise process is at play, explaining thus the emergence and structure of the vortex lattices observed here and in motility assay experiments.

Self-motion of an oil droplet: A simple physicochemical model of active Brownian motion

The self-motion of an oil droplet in an aqueous phase on a glass surface is reported. The aqueous phase contains a cationic surfactant, which tends to be adsorbed onto the glass surface. The oil droplet contains potassium iodide and iodine, which prefers to make an ion pair with the cationic surfactant. Since the ion pair is soluble in the oil droplet, dissolution of the surfactant into the oil droplet is promoted, i.e., the system is far from equilibrium with regard to surfactant concentration. The oil droplet is self-driven in a reactive manner by the spatial gradient of the glass surface tension. We discuss the intrinsic nature of this self-motion by developing a simple mathematical model that incorporates adsorption and desorption of the surfactant on the glass surface. Using this mathematical model we were able to construct an equation of motion that reproduces the observed self-motion of an oil droplet. This equation describes active Brownian motion. Theoretical considerations were used to predict the generation of the regular mode of oil-droplet motion, which was subsequently confirmed by experiments.

Oscillation and Synchronization in the Combustion of Candles

We investigate a simple experimental system using candles; stable combustion is seen when a single candle burns, while oscillatory combustion is seen when three candles burn together. If we consider a set of three candles as a component oscillator, two oscillators, that is, two sets of three candles, can couple with each other, resulting in both in-phase and antiphase synchronization depending on the distance between the two sets. The mathematical model indicates that the oscillatory combustion in a set of three candles is induced by a lack of oxygen around the burning point. Furthermore, we suggest that thermal radiation may be an essential factor of the synchronization.

Dynamical blebbing at a droplet interface driven by instability in elastic stress: a novel self-motile system

Dynamical blebbing in an oil–water system is reported together with a quantitative analysis of interfacial deformation. An oil droplet containing a fatty acid that floats on an aqueous phase containing a cationic surfactant shows blebbing-type deformation at the oil–water interface. Such deformation is caused by an out-of-equilibrium concentration distribution across the interface. The generation and breakage of aggregates at the interface is associated with the time-dependent instability of the interface that accompanies the blebbing. In a quantitative analysis, the size of the bleb depended on the size of the oil droplet: the size of the bleb was inversely proportional to the square root of the radius of the oil droplet approximately. Furthermore, the experimental results showed that an oil droplet undergoes translational motion, i.e., active Brownian motion, under a suitable size of the oil droplet. A simple mathematical model based on the elasticity of the aggregates is proposed, and this agrees well with the experimental results.

Rotational motion of a droplet induced by interfacial tension.

Spontaneous rotation of a droplet induced by the Marangoni flow is analyzed in a two-dimensional system. The droplet with the small particle which supplies a surfactant at the interface is considered. We calculated flow field around the droplet using the Stokes equation and found that advective nonlinearity breaks symmetry for rotation. Theoretical calculation indicates that the droplet spontaneously rotates when the radius of the droplet is an appropriate size. The theoretical results were validated through comparison with the experiments.

Formation of a Multiscale Aggregate Structure through Spontaneous Blebbing of an Interface

The motion of an oil-water interface that mimics biological motility was investigated in a Hele-Shaw-like cell where elastic surfactant aggregates were formed at the oil-water interface. With the interfacial motion, millimeter-scale pillar structures composed of the aggregates were formed. The pillars grew downward in the aqueous phase, and the separations between pillars were roughly equal. Small-angle X-ray scattering using a microbeam X-ray revealed that these aggregates had nanometer-scale lamellar structures whose orientation correlated well with their location in the pillar structure. It is suggested that these hierarchical spatial structures are tailored by the spontaneous interfacial motion.