Large-scale vortex lattice emerging from collectively moving microtubules

Abstract

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.

Light-activated self-propelled colloids

“…We do not observe experimentally or numerically the swarming behaviour predicted theoretically by many authors [62][63][64][65] for nematic self-propelled particles similar in spirit to the Vicsek model [66]: transition to a flocking behaviour with coherent groups of particles moving in the same direction, swarming or formation of travelling bands otherwise recently observed experimentally by the group of Bausch [67] or more recently the large-scale vortices observed by Sumino et al [68] or by the group of Bartolo with self-propelled rollers colloids [69], or active nematics [70]. In all those works, the self-propelled particles are polar with nematic interactions, i.e.…”

“…they align their velocity vectors in direction, as prescribed by 'Vicsek's rule'. The role of the nematic alignment owing to the collisions of rod-like microtubules have recently been pointed by [68] to explain the emergence of long-range interactions and vortices at high density (or in an granular context by Deseigne et al [71]). In our experiment, owing to the isotropic shape of the particles we do not observe any nematic interaction of the self-propelled particles, thus defining a different class of systems and non-equilibrium phases than the Vicsek model.…”

Hysteretic dynamics of active particles in a periodic orienting field

“…The level of consciousness of the individuals apparently plays a minor role in the large-scale dynamics as the same principles of self-organization that govern the dynamics of groups of animals or cells apply to human social phenomena, traffic, robotics and decisionmaking [11][12][13][14][15][16][17]. One of the best-studied collective dynamics phenomena is the onset of globally aligned motion in active swarms [18][19][20][21][22][23][24][25][26][27][28]. It demonstrates many of the features of the paramagnetic-ferromagnetic phase transition, where the onset of the orientationally ordered ferromagnetic phase is caused by aligning interactions between individual magnetic dipoles of the atoms [19,21,23,29].…”

The Aquatic Dance of Bacteria

“…The best-fit model allows for quantitative agreement with experimental data. [3][4][5][6][7][8] and microscale selforganization in motility assays [9,10]. Although very different in size and composition, these systems are often jointly termed ''active'' fluids, for which there is now a range of continuum theories [12,[14][15][16][17][18][19][20][21][22][23][24].…”

“…A series of experiments over the last decade [1][2][3][4][5][6][7][8][9][10] has shed light on generic ordering principles that appear to govern collective dynamics of living matter [11][12][13][14][15], from large-scale animal swarming [1,2] to mesoscale turbulence in microbial suspensions [3][4][5][6][7][8] and microscale selforganization in motility assays [9,10]. Although very different in size and composition, these systems are often jointly termed ''active'' fluids, for which there is now a range of continuum theories [12,[14][15][16][17][18][19][20][21][22][23][24].…”