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Volume
2 | Issue 12 | DECEMBER 2004
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All PLoS Biology research articles are accompanied by a synopsis
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Using Biology to Create Complex Patterns

DOI: 10.1371/journal.pbio.0020448

Published: December 7, 2004

Copyright: © 2004 Public Library of
Science. This is an open-access article distributed under the terms of the
Creative Commons Attribution License, which permits unrestricted use,
distribution, and reproduction in any medium, provided the original work
is properly cited.

Citation: (2004) Using Biology to Create
Complex Patterns. PLoS Biol 2(12): e448

In his seminal exploration of the properties of living organisms,
What Is Life?, Erwin Schroedinger concluded that life depends in
large part on storing and processing information. For genetic material to
carry the diverse instructions required for living processes, he proposed,
it must be stored in an aperiodic crystal. Just nine years later, it was
clear that DNA is indeed an aperiodic crystal and that genetic information
is conveyed through this irregular pattern. Much like computers,
biological systems are programmed to follow a precise set of rules, or
algorithms, to store information and solve problems. These biological
algorithms direct all manner of biochemical processes to create complex
patterns and structures by chemically modifying and assembling individual
components.

Of course, cells use biochemical circuits not electronic circuits.
Single tubulin proteins, for example, follow precise rules of chemistry
and physics to spontaneously self-assemble, or polymerize, into the
microtubules essential for cell transport and motility. The proteins'
binding interactions effect rules that specify how the pieces fit together
to form the resulting structure. They also specify when and how tubulins
assemble from a nucleation complex—a molecular algorithm governing the
logic of polymerization. These complex structures self-assemble with
remarkably few mistakes. Though considered quite simple, little is
understood about the principles that govern programmable structural order
underlying this type of spontaneous self-assembly.

In crystals, the simplest example of spontaneous self-assembly,
subunits of the whole are arranged in a repeating pattern that extends
indefinitely in all directions. If you know the position of one unit in
the pattern, you can tell the exact position of every other unit. In a new
study, Rothemund and colleagues use DNA to show that crystal growth can be
programmed to create specific aperiodic patterns. Inspired by a model of
crystal growth as a computational process, they have programmed DNA
molecules to act as molecular building blocks, arranging themselves
according to local rules that in turn create a complex global pattern. The
resulting two-dimensional structures, which self-assemble from knotted DNA
complexes (called tiles), grow to create a fractal pattern known as a
Sierpinski triangle. These DNA structures—neither periodic (as in quartz),
nor random (as in glass), nor pseudorandom (as in quasicrystals with
“forbidden” five-fold symmetries)—demonstrate a form of self organization
in crystalline materials determined by programmable growth rules, and are
hence dubbed “algorithmic crystals.”

How can such growth algorithms be encoded in biological molecules? The
rules of chemical base-pairing follow regular, predictable patterns,
allowing the authors to use DNA to determine the tiles' binding
interactions.

Fractal patterns from DNA

Desired binding interactions between tiles were programmed by endowing
each tile with single-stranded “sticky ends” whose sequence was
complementary to the sticky ends of tiles it should stick to. Each tile
was either white (0) or black (1): a black tile can fit at any site where
the two neighboring tiles are opposite colors, while a white tile can fit
at any site where the two neighboring tiles are the same color. Logically,
the new tile's color is the exclusive-or (XOR) of the tiles in the
previous layer.

That such logical layer-by-layer iteration of XOR computations will
produce the Sierpinski triangle is well known. What's remarkable is that
DNA molecules can be programmed to grow according to this logic. With this
programmable algorithmic crystal, Rothemund and colleagues demonstrate a
method for designing DNA molecules capable of implementing any pattern of
abstract logical tiles. What's more, the authors argue, any algorithmic
crystal growth process can, in principle, be experimentally investigated
using DNA self-assembly.

So how is algorithmic self-assembly related to biology? Like the
algorithmic crystals, many of the self-assembled structures in biology are
ordered but aperiodic. The hope is that the theoretical insights of
computer science—well-honed for describing, analyzing, and programming
computational systems—can direct investigations of biochemical
self-assembly and information processing. And with a method for
demonstrating how simple chemical and physical elements can create complex
organization, Rothemund and colleagues have added a concrete experimental
framework to bolster that work. (For more on DNA and complexity, see “The
Emergence of Complexity: Lessons from DNA” by Chengde Mao.)

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