Biological physics

Swarming microtubules

An artificial system of microtubules propelled by dynein motor proteins self-organizes into a pattern of whirling rings. This observation may provide insight into collective motion in biological systems. See Letter p.448

The spectacle of animals moving en masse is arguably one of the most fascinating phenomena in biology. For example, schools of fish can move in an orderly manner, and then change direction abruptly or, if under pressure from a nearby predator, swirl like a vigorously stirred fluid. The non-living world also has examples of collective motion, in systems that consist of units ranging from macromolecules to metallic rods, or even robots. On page 448 of this issue, Sumino et al.1 describe another, until now unobserved, example of such behaviour: the coordinated motion of hundreds of thousands of subcellular structures known as microtubules, which spontaneously self-organize into a lattice-like structure of vortices. When considered in the context of about half a dozen known universal classes of collective-motion pattern2, this new structure poses challenges in terms of explaining how it can arise and its relevance to applications.

If two or more moving units such as self-propelled rods interact, their direction of motion is likely to change. When pairwise interactions dominate over multiparty ones, the process of two units approaching each other, then adopting a new direction and leaving the area of interaction, can be interpreted as a collision. In closed systems at equilibrium, such collisions conserve energy and momentum, whereas, for example, when two birds interact and decide which way to fly in the open expanses of the sky, the concept of conservation of momentum is not applicable.

Typically, local interactions between organisms result in a consensus: fish or mammals tend to adopt a common direction of motion. Such 'polar' interactions are widespread and have been observed even for bacteria3 and locusts4. Nonetheless, it was a great achievement when, in 2010, two groups5,6 observed motional patterns associated with polar interactions on a molecular scale — that is, for a huge number of actin filaments on a layer of immobilized myosin protein heads.

In addition to polar interactions, 'nematic' interactions also occur. In this case, if the directions of motion of two units approaching one another form an angle smaller than 90°, both parts will take the same direction after the approach. But if the units come towards one another from directions that differ by more than 90°, they will leave in opposite directions.

Sumino et al.1 have constructed a biological system in which nematic collisions take place (Fig. 1). The authors achieved this by choosing an assay of moving microtubules propelled by modified motor proteins (one-headed dynein molecules) in which the microtubules cannot, for the most part, cross each other's trajectories and maintain their own trajectory's direction and curvature. The authors find that, in this setting, and for relatively high densities (typically 5 microtubules in 100 square micrometres), the moving microtubules self-organize into a semiregular pattern of whirling rings, or vortices, within which they move either clockwise or anticlockwise. Furthermore, as time goes on, the microtubules jump from one vortex to another and change their rotational direction. The size of the observed pattern is large compared with the 15-micrometre length of each microtubule: the system shows regularities on a millimetre scale.

Figure 1: Nematic collisions.

Sumino et al.1 have studied a system of microtubules in which nematic collisions occur. The microtubules are propelled by one-headed dynein molecules attached to the surface of a substrate. Three microtubules are shown here: a, approaching one another; b, colliding; and c, after the collision has taken place. Their final direction of motion depends on the angles at which they approach one another. In this case, the two leftmost microtubules adopt the same direction, whereas the rightmost microtubule leaves in the opposite direction.

One of the strengths of the present study is the authors' ability to explain the main features of the microtubules' intricate motion with a simple model. The model draws on studies aimed at understanding the rich, large-scale behaviour that results from simple bilateral interactions between point-like, self-propelled particles.

But Sumino and colleagues' results also prompt several questions. For example, is the observation that individual microtubules have a slight preference to rotate anticlockwise a necessary condition for the observed semi-regular pattern of vortices? How is the persistence of the curvature of the microtubules' trajectories relevant? Furthermore, it would be interesting to investigate why actin filaments undergo polar interactions, whereas microtubules undergo nematic ones.

Whether the authors' observations are system specific or belong to a new class of collective-motion pattern remains to be seen. But one possibility is that the observed lattice-like structure falls within the group of patterns of vortex formation seen in many systems made up of self-propelled units. Typically, vortex formation can be closely related to the geometry of the confined area within which the collective motion occurs. In the current case, it seems that, owing to the persistence of curvature in the individual microtubules' motion, curved 'walls' of microtubules are spontaneously formed and enforce the formation of the vortices. Indeed, it has been shown7 that, without such curvature persistence, nematic interactions in a system of self-propelled rods do not result in a similar arrangement of vortices.

Potential applications of Sumino and colleagues' study remain, for the time being, in the realm of speculation. But it is conceivable that the complex fluid currents generated in the stems of various plants relate to the collective motion of microtubules observed by the authors1. The streams of energy-supplying and waste materials in a stem have to fulfil a number of criteria, which could be best met through a coordinated action of motor molecules. The authors' demonstration that such action can be attained in a relatively simple assay is a step towards a better understanding of the role of collective motion in plants and other biological systems.


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Correspondence to Tamás Vicsek.

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Vicsek, T. Swarming microtubules. Nature 483, 411–412 (2012).

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