Reporting in the December issue of the journal Public Library of Science (PLoS) Biology, Caltech assistant professor Erik Winfree and his colleagues show that DNA ''tiles'' can be programmed to assemble themselves into a crystal bearing a pattern of progressively smaller ''triangles within triangles,'' known as a Sierpinski triangle. This fractal pattern is more complex than patterns found in natural crystals because it never repeats. Natural crystals, by contrast, all bear repeating patterns like those commonly found in the tiling of a bathroom floor. And, because each DNA tile is a tiny knot of DNA with just 150 base pairs (an entire human genome has some 3 billion), the resulting Sierpinski triangles are microscopic. The Winfree team reports growing micron-size DNA crystals (about a hundredth the width of a human hair) that contain numerous Sierpinski trianglesSo where's the computation ?
The novel aspect of the research is the translation of an algorithm--the basic method underlying a computer program--into the process of crystal growth. A well-known algorithm for drawing a Sierpinski triangle starts with a sequence of 0s and 1s. It redraws the sequence over and over again, filling up successive rows on a piece of paper, each time performing binary addition on adjacent digits.Algorithmic self-assembly will be familiar to STOC/FOCS goers. My friend Ashish Goel has often tried to convince me that this is the Next Big Thing, and has a couple of papers (with Len Adleman and others) on this topic...
The result is a Sierpinski triangle built out of 0s and 1s. To embed this algorithm in crystal growth, the scientists represented written rows of binary ''0s'' and ''1s'' as rows of DNA tiles in the crystal--some tiles stood for 0, and others for 1. To emulate addition, the sticky ends were designed to ensure that whenever a free tile stuck to tiles already in the crystal, it represented the sum of the tiles it was sticking to.
....This concept, according to Winfree's coauthor and Caltech research fellow Paul W. K. Rothemund, has inspired an entirely new research field, ''algorithmic self-assembly,'' in which scientists study the implications of embedding computation into crystal growth.