Starfish embryos swim in a "living crystal" formation.

 Their swirling, clustering behavior could one day be used to design self-assembling robotic swarms.

A starfish embryo, long before it sprouts its signature appendages, looks like a tiny bead, spinning through the water like a miniature ball bearing.

When multiple starfish embryos spin up to the water's surface, they gravitate to each other and spontaneously assemble into a surprisingly organized, crystal-like structure, according to MIT researchers.

Even more intriguing, this collective "living crystal" can exhibit strange elasticity, an unusual property in which the spinning of individual units — in this case, embryos — causes much larger ripples to spread across the entire structure.

The researchers discovered that this rippling crystal configuration can last for long periods of time before dissolving as individual embryos mature.

"It's absolutely remarkable — these embryos look like beautiful glass beads, and they come to the surface to form this perfect crystal structure," says Thomas D. and Virginia W. Cabot Career Development Associate Professor of Physics Nikta Fakhri. "Perhaps this crystal structure, like a flock of birds that can avoid predators or fly more smoothly because they can organize in these large structures, could have some advantages we're not aware of yet."

She believes that, in addition to starfish, this self-assembling, rippling crystal assemblage could be used as a design principle, such as in the construction of robots that move and function collaboratively.

"Imagine creating a swarm of soft, spinning robots that can interact with one another like these embryos," says Fakhri. "They could be programmed to ripple and crawl through the sea to do useful work." These interactions open up a new realm of intriguing physics to investigate."

Fakhri and her colleagues published their findings in the journal Nature today. Tzer Han Tan, Alexander Mietke, Junang Li, Yuchao Chen, Hugh Higinbotham, Peter Foster, Shreyas Gokhale, and Jörn Dunkel are among the co-authors.

Spinning together

According to Fakhri, the team's observations of starfish crystals were a "fortuitous discovery." Her research group has been looking into how starfish embryos develop, specifically how embryonic cells divide in the early stages.

"Because of their large cells and optical transparency, starfish are one of the oldest model systems for studying developmental biology," Fakhri says.

The scientists were watching how embryos swim as they matured. When an embryo is fertilized, it grows and divides, forming a shell that sprouts tiny hairs, or cilia, that propel the embryo through the water. At some point, the cilia coordinate to spin an embryo in a specific rotational direction, known as "chirality." One of the group members, Tzer Han Tan, noticed that as embryos swam to the surface, they continued to spin toward each other.

"Every now and then, a small group would gather and sort of dance around," Fakhri says. "It turns out that other marine organisms, such as algae, do the same thing." So we thought this was interesting. "What happens if you combine a lot of them?"

She and her colleagues fertilized thousands of starfish embryos in their new study, then watched as they swam to the surface of shallow dishes.

Starfish embryos spontaneously swim together at the surface to form large crystal-like structures that collectively ripple and rotate for relatively long periods of time before dissolving as embryos mature, according to MIT scientists.
Starfish embryos spontaneously swim together at the surface to form large crystal-like structures that collectively ripple and rotate for relatively long periods of time before dissolving as embryos mature, according to MIT scientists.

"Thousands of embryos are in a dish, and they begin to form this crystal structure that can grow very large," Fakhri explains. "We call it a crystal because each embryo is surrounded by six neighboring embryos in a hexagon that repeats across the entire structure, which is very similar to graphene's crystal structure."

Jiggling crystals

To figure out what was causing embryos to assemble like crystals, the researchers first looked at a single embryo's flow field, or the way water flows around the embryo. They did this by immersing a single starfish embryo in water, then adding much smaller beads and photographing the beads as they flowed around the embryo at the water's surface.

The flow field around the embryo was mapped by the researchers based on the direction and flow of the beads. They discovered that the cilia on the embryo's surface beat in such a way that they spun the embryo in a specific direction, creating whirlpools on either side of the embryo, which drew in the smaller beads.

Mike, a postdoctoral researcher in Dunkel's applied mathematics group at MIT, transformed this flow field from a single embryo into a simulation of many embryos, then ran the simulation forward to see how they behaved. The model generated the same crystal structures as the team's experiments, confirming that the embryos' crystallizing behavior was most likely caused by their hydrodynamic interactions and chirality.

The team also discovered that once a crystal structure formed, it lasted for days, and that spontaneous ripples began to propagate across the crystal during this time.

"We were able to see this crystal rotating and jiggling for a very long time, which was completely unexpected," she says. "Because water is viscous and dampens these oscillations, you'd expect these ripples to fade quickly." This indicated that the system exhibited unusual elastic behavior."

The long-lasting ripples could be caused by interactions between individual embryos, which spin against each other like interlocking gears. The many individual spins of thousands of gears spinning in crystal formation could set off a larger, collective motion across the entire structure.

The scientists are now looking into whether other organisms, such as sea urchins, exhibit crystalline behavior. They are also investigating how to replicate this self-assembling structure in robotic systems.

"You can experiment with this interaction design principle and create something like a robotic swarm that can actually do work on the environment," she says.

The Sloan Foundation and the National Science Foundation both contributed to this study.


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