Programmed DNA forms fractal

By Kimberly Patch, Technology Research News

A decade after the idea became the topic of his doctoral dissertation, a researcher at the California Institute of Technology has showed that it is possible to coax short strands of artificial DNA to spontaneously assemble into a Sierpinski triangle.

A Sierpinski triangle is a type of crystal, or structure that regularly repeats. The Sierpinski triangle is fractal -- a pattern of triangles that looks the same in zoomed-in or zoomed-out views.

The ability is a step toward embedding programming instructions in chemical processes. This is a corollary to the way computer instructions are embedded in everything from automobile engines to cell phones via microprocessors. "Programmable embedded control makes things possible that were virtually inconceivable," said Erik Winfree, an assistant professor of computer science at The California Institute of Technology.

The DNA Sierpinski triangles show that there is no theoretical barrier to using molecular self-assembly to carry out any kind of computing and nanoscale fabrication, according to Winfree. If someone comes up with the right rules, the right set of molecules should be able to carry out the instructions, he said.

This type of algorithmic self-assembly is a testing ground for learning how to embed logical rules within a molecular system so that information processed by the molecules themselves is responsible for directing the local processes, said Winfree. In the case of a Sierpinski pattern, the molecules are directing the process of self-assembly, he said.

Although today's technology does not have electronics-like control of chemical and molecular-scale processes, biology does, said Winfree. "The only place one finds sophisticated embedded control of chemical processes is in biology, where biochemical information processing controls, orchestrates [and] organizes all of life's functions."

Algorithmic self-assembly can be thought of as an extremely simplified version of organismal development, said Winfree. Coaxing artificial strands of DNA to form a Sierpinski pattern is "a far cry from an organism," he said. "But it is also far more complex than the four DNA rule tiles that directed its growth."

DNA is made up of four bases -- adenine, cytosine, guanine and thymine -- strung along a sugar-phosphate backbone. Adenine and thymine, and cytosine and guanine can combine with each other. Biological DNA forms the familiar double helix when a pair of single strands that contain matching bases combine and coil up. Researchers can make artificial strands form DNA tiles by engineering stretches of one strand that match another strand.

The researchers formed short strands of DNA capable of combining into tiles that represent logic rules, short strands capable of combining into tiles that represent input, and long nucleating strands. They mixed the strands, heated the solution, then let it cool slowly over several hours. "At about 60 to 70 degrees Celsius, the tiles spontaneously self-assemble from their components strands, but it remains too hot for the tiles to associate with each other," said Winfree.

At the same or a slightly lower temperature, the input tiles stick to the long nucleating strands. And somewhere between 30 and 40 degrees Celsius the rule tiles begin to assemble onto the nucleating structure to form, tile by tile, and layer by layer, the algorithmic crystal, said Winfree. "In some, few errors occur, and the Sierpinski pattern emerges intact."

The researchers have made Sierpinski patterns on surfaces and more complicated Sierpinski triangles in solution. Sierpinski triangles involve more types of tiles. Some of the researchers' triangles were as large as one micron, or thousandth of a millimeter.

The keys to the researchers' success was using the long nucleating DNA strands to get things started and a better microscope technique to see what was happening, said Winfree.

The errors were as interesting as the successful Sierpinski patterns, said Winfree. The experiments' error rates ranged from 1 to 10 percent. "We expected lots of errors, but we didn't expect the kinds of errors that we saw," he said. In general, several errors would normally increase the randomness of a pattern.

However, there were places within some samples where several errors conspired to create large patches of zero tiles or to perfectly terminate nascent Sierpinski triangles at the corners, said Winfree. "Such coincidences should be so rare that one would never see a single instance in one million crystals," he said.

The researchers have a hypothesis capable of explaining how these correlated errors arise, "but it remains to be proven," said Winfree.

The researchers were also surprised to see that one of the tile designs, instead of simply forming two-dimensional sheets, formed a long tube with the sheets rolled up. The DNA nanotubes are similar to but 10 times larger than carbon nanotubes, which are rolled-up sheets of carbon atoms that form naturally in soot; they are more similar to protein microtubules that self-assemble as part of the cellular cytoskeleton, said Winfree.

Carbon nanotubes can be narrower than a single nanometer, or 5,000 times narrower than a red blood cell. A nanometer is one millionth of a millimeter.

The researchers are working to decrease the method's error rate. "We have developed some ideas for how to embed error correction within the crystal growth process -- somewhat analogous to error-correcting codes in information theory -- and we are now trying to experimentally demonstrate this scheme," said Winfree.

If they are successful in reducing assembly errors to insignificant levels "as the theory optimistically predicts… creating complex structures by self-assembly becomes a form of programming," said Winfree. "If you can conceive of a logical method for growing your structure, then it will work in practice," he said.

Winfree's research colleagues were Paul W. K. Rothemund and Nick Papadakis. The work appeared in the December, 2004 issue of Plos Biology. The research was funded by the National Science Foundation (NSF), the Defense Advanced Research Projects Agency (DARPA), the National Aeronautics and Space Administration (NASA), and GenTel.

Timeline:   Unknown
Funding:   Corporate; Government
TRN Categories:   DNA; Nanotechnology
Story Type:   News
Related Elements:  Technical paper, "Algorithmic Self-Assembly of DNA, Sierpinski Triangles," Plos Biology, December, 2004; Movie of DNA self-assembling into a Sierpinski triangle posted at


April 6/13, 2005

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