Ken Nagai

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 15u2009µm long, into vortices with diameters of around 400u2009µm. 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.

Synchrony of limit-cycle oscillators induced by random external impulses

The mechanism of phase synchronization between uncoupled limit-cycle oscillators induced by common external impulsive forcing is analyzed. By reducing the dynamics of the oscillator to a random phase map, it is shown that phase synchronization generally occurs when the oscillator is driven by weak external impulses in the limit of large inter-impulse intervals. The case where the inter-impulse intervals are finite is also analyzed perturbatively for small impulse intensity. For weak Poissonian impulses, it is shown that the phase synchronization persists up to the first order approximation.

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.

Change in the Mode of Spontaneous Motion of an Alcohol Droplet Caused by a Temperature Change

An alcohol (pentanol) droplet exhibits spontaneous motion on an aqueous solution, driven by a solutal Marangoni effect. We found that the mode of such droplet motion changes depending on the temperature of the aqueous phase. When the temperature of the aqueous phase is 20 °C, a droplet with a volume of 1 μl exhibits vectorial motion, whereas when the temperature is 25 °C, the droplet exhibits irregular motion. We discuss the mode change in relation to the solubility of pentanol in water.

Reproducibility of a Noisy Limit-Cycle Oscillator Induced by a Fluctuating Input

Reproducibility of a noisy limit-cycle oscillator driven by a random piecewise constant signal is analyzed. By reducing the model to random phase maps, it is shown that the reproducibility of the limit cycle generally improves when the phase maps are monotonically increasing.

Autonomous motion of droplet powered by chemical potential and by photon-flux

Living organisms maintain their lives through the dissipation of chemical energy under isothermal conditions. They transduce chemical energy into macroscopic motion with high efficiency, but the mechanism is not fully understood yet. By considering experimental model systems together with experimental results reported for the molecular machinery, it would be possible to attain an essential understanding of mechanism on the chemo-mechanical energy transduction in living organisms. In the present paper, we introduce several simple experimental systems where spontaneous motion of a droplet is induced by chemical energy gradient or by photon flux