Tiny Tubes Racing in a Donut-Shaped Track

Original paper: Transition from turbulent to coherent flows in confined three-dimensional active fluids


The shape of a container can affect the flow of the fluid inside it. Water in a narrow stream flows smoothly, but once the water molecules make their way into a pond, they spread out and no longer flow coherently. If you blow into a long, narrow straw, the air will go straight through. Once the air flows into the large room you are standing in, it slows down as it mixes with the air around it, so someone standing five feet away from you won’t feel a breeze at all.

The above examples show how the shape of a container affects the flow of passive fluids. In today’s study, Kun-Ta Wu and colleagues investigated how the motion of active fluids, fluids that flow using an internal source of energy, is also affected by the shape of their container. They used a system of microtubules, chains of proteins assembled into long, stiff rods. Clusters of a protein called kinesin exert a force on microtubules by “walking” along them. Microtubules interact with each other to form swarms or turbulent-like flows.

Wu and colleagues created 3D toroidal racetracks with rectangular cross-sections to confine the microtubule bundles. They saw coherent flows in racetracks with square cross-sections, but if the channels got either too thin and wide or too tall and narrow, the flow became turbulent (Figure 1). This result is described in this Softbites post from last year.

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Figure 1: Comparison of coherent and turbulent flows around a track. The left side of each track shows the motion in an instant, while the right side shows the average motion over a long time. The color represents the local direction of spinning and the black arrows indicate the direction of motion. Microtubules in a red spot are spinning clockwise, those in a yellow spot are not spinning, and those in a blue spot are spinning counterclockwise. Image adapted from original article.

After Wu and colleagues got microtubules to flow by themselves, they placed them in increasingly complicated tracks. Active flows happened in any closed loop with an approximately square cross-section. Microtubule flows solved a maze, as in Figure 2, by flowing through the connected straight and curved sections, but not sections leading to dead ends. The dead ends slowed down the flow in the connected sections to about half the speed of a toroidal racetrack with an equivalent length.

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Figure 2: Microtubules flow in straight and curved sections of the maze in closed loop, and no net flow loop in sections leading to dead ends. Black arrows show the direction of the flow and colorful arrows point to sections at which mean flows are measured. Figure adapted from original article.

Wu and colleagues then created tracks made out of overlapping tori, or donuts. In the tori, microtubules spontaneously flowed in the same or in different directions, as in Figure 3. When the active flow was clockwise in one torus and counterclockwise in the other, the direction of flow in the overlap was the same, and the flow kept going (A). When they were both counterclockwise, two flows came into the overlap in opposite directions, and there was no flow in between the tori (B). Watch a video of this here.

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Figure 3: Microtubules can flow in connected tori in (A) the same direction and (B) opposite directions. Figure adapted from original article.

Microtubules created an active flow when a third torus was added (Figure 4A). They also navigated a square racetrack, although the corners created small vortices and slowed them down (Figure 4B). Finally, microtubules still flowed in a very long torus made out of a 1.1 meter-long tube joined at the ends by a needle (Figure 3C).

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Figure 4: (A) Flows in 3 overlapping tori. (B) Microtubules flow around a square racetrack in the direction of the blue arrow. (C) Microtubules even flowed around a very long (1.1 meter) track. The closeup shows a time-averaged flow inside a small section of the tube. Figure adapted from original article.

 

Thus, these flows of microtubules aren’t just a one-time phenomenon that’s hard to replicate—no matter how much the researchers changed the system, as long as there was a closed loop with an appropriate cross-sectional aspect ratio, there was a flow.

These flows inside channels are interesting—but are they useful? The researchers suggest that a system like this could act as an internal power source for very small devices, but this application is still far in the future. It is also possible that a similar motion is used inside living cells to transport materials in a process called cytoplasmic streaming. More importantly, these flows are a beautiful example of collective motion induced by physical forces, helping scientists elucidate how swarms can form at all length scales.

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