From: Subject: PLoS Biology: Using Biology to Create Complex Patterns Date: Fri, 20 Oct 2006 11:04:22 +0200 MIME-Version: 1.0 Content-Type: multipart/related; type="text/html"; boundary="----=_NextPart_000_0000_01C6F437.7FB2CA00" X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.2962 This is a multi-part message in MIME format. ------=_NextPart_000_0000_01C6F437.7FB2CA00 Content-Type: text/html; charset="utf-8" Content-Transfer-Encoding: quoted-printable Content-Location: http://biology.plosjournals.org/perlserv?request=get-document&doi=10.1371/journal.pbio.0020448 =EF=BB=BF PLoS Biology: Using = Biology to Create Complex Patterns

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Using Biology to Create Complex Patterns

DOI: = 10.1371/journal.pbio.0020448

Published: December 7, 2004

Copyright: =C2=A9 2004 Public = Library of=20 Science. This is an open-access article distributed under the = terms of the=20 Creative Commons Attribution License, which permits unrestricted = use,=20 distribution, and reproduction in any medium, provided the = original work=20 is properly cited.

Citation: (2004) Using Biology = to Create=20 Complex Patterns. PLoS Biol 2(12): e448

In his seminal exploration of the properties of living = organisms,=20 What Is Life?, Erwin Schroedinger concluded that life = depends in=20 large part on storing and processing information. For genetic = material to=20 carry the diverse instructions required for living processes, he = proposed,=20 it must be stored in an aperiodic crystal. Just nine years later, = it was=20 clear that DNA is indeed an aperiodic crystal and that genetic = information=20 is conveyed through this irregular pattern. Much like computers,=20 biological systems are programmed to follow a precise set of = rules, or=20 algorithms, to store information and solve problems. These = biological=20 algorithms direct all manner of biochemical processes to create = complex=20 patterns and structures by chemically modifying and assembling = individual=20 components.

Of course, cells use biochemical circuits not electronic = circuits.=20 Single tubulin proteins, for example, follow precise rules of = chemistry=20 and physics to spontaneously self-assemble, or polymerize, into = the=20 microtubules essential for cell transport and motility. The = proteins'=20 binding interactions effect rules that specify how the pieces fit = together=20 to form the resulting structure. They also specify when and how = tubulins=20 assemble from a nucleation complex=E2=80=94a molecular algorithm = governing the=20 logic of polymerization. These complex structures self-assemble = with=20 remarkably few mistakes. Though considered quite simple, little is = understood about the principles that govern programmable = structural order=20 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=20 indefinitely in all directions. If you know the position of one = unit in=20 the pattern, you can tell the exact position of every other unit. = In a new=20 study, Rothemund and colleagues use DNA to show that crystal = growth can be=20 programmed to create specific aperiodic patterns. Inspired by a = model of=20 crystal growth as a computational process, they have programmed = DNA=20 molecules to act as molecular building blocks, arranging = themselves=20 according to local rules that in turn create a complex global = pattern. The=20 resulting two-dimensional structures, which self-assemble from = knotted DNA=20 complexes (called tiles), grow to create a fractal pattern known = as a=20 Sierpinski triangle. These DNA structures=E2=80=94neither periodic = (as in quartz),=20 nor random (as in glass), nor pseudorandom (as in quasicrystals = with=20 =E2=80=9Cforbidden=E2=80=9D five-fold = symmetries)=E2=80=94demonstrate a form of self organization=20 in crystalline materials determined by programmable growth rules, = and are=20 hence dubbed =E2=80=9Calgorithmic crystals.=E2=80=9D

How can such growth algorithms be encoded in biological = molecules? The=20 rules of chemical base-pairing follow regular, predictable = patterns,=20 allowing the authors to use DNA to determine the tiles' binding=20 interactions.

Fractal patterns from DNA

Desired binding interactions between tiles were programmed by = endowing=20 each tile with single-stranded =E2=80=9Csticky ends=E2=80=9D whose = sequence was=20 complementary to the sticky ends of tiles it should stick to. Each = tile=20 was either white (0) or black (1): a black tile can fit at any = site where=20 the two neighboring tiles are opposite colors, while a white tile = can fit=20 at any site where the two neighboring tiles are the same color. = Logically,=20 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=20 produce the Sierpinski triangle is well known. What's remarkable = is that=20 DNA molecules can be programmed to grow according to this logic. = With this=20 programmable algorithmic crystal, Rothemund and colleagues = demonstrate a=20 method for designing DNA molecules capable of implementing any = pattern of=20 abstract logical tiles. What's more, the authors argue, any = algorithmic=20 crystal growth process can, in principle, be experimentally = investigated=20 using DNA self-assembly.

So how is algorithmic self-assembly related to biology? Like = the=20 algorithmic crystals, many of the self-assembled structures in = biology are=20 ordered but aperiodic. The hope is that the theoretical insights = of=20 computer science=E2=80=94well-honed for describing, analyzing, and = programming=20 computational systems=E2=80=94can direct investigations of = biochemical=20 self-assembly and information processing. And with a method for=20 demonstrating how simple chemical and physical elements can create = complex=20 organization, Rothemund and colleagues have added a concrete = experimental=20 framework to bolster that work. (For more on DNA and complexity, = see =E2=80=9CThe=20 Emergence of Complexity: Lessons from DNA=E2=80=9D by Chengde = Mao.)

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BORDER-BOTTOM-WIDTH: 0px; PADDING-BOTTOM: 0px; = MARGIN: 0px; COLOR: #fff; PADDING-TOP: 0px; BORDER-RIGHT-WIDTH: 0px; = TEXT-DECORATION: none } .mainMenuGlobal { BORDER-RIGHT: #fff 1px solid; PADDING-RIGHT: 5px; BORDER-TOP: #fff 1px = solid; PADDING-LEFT: 5px; PADDING-BOTTOM: 0px; MARGIN: 0px; BORDER-LEFT: = #fff 1px solid; PADDING-TOP: 0px; BORDER-BOTTOM: #fff 1px solid } #mainMenuGlobal A:link { PADDING-RIGHT: 5px; DISPLAY: block; PADDING-LEFT: 5px; PADDING-BOTTOM: = 0px; MARGIN: 0px; FONT: bold 0.85em/1.3em = Verdana,Tahoma,Geneva,Arial,Helvetica,sans-serif; COLOR: #fff; = PADDING-TOP: 0px; TEXT-ALIGN: center; TEXT-DECORATION: none } #mainMenu A:visited { PADDING-RIGHT: 5px; DISPLAY: block; PADDING-LEFT: 5px; PADDING-BOTTOM: = 0px; MARGIN: 0px; FONT: bold 0.85em/1.3em = Verdana,Tahoma,Geneva,Arial,Helvetica,sans-serif; COLOR: #fff; = PADDING-TOP: 0px; TEXT-ALIGN: center; TEXT-DECORATION: none } #mainMenuGlobal A:hover { PADDING-RIGHT: 5px; PADDING-LEFT: 5px; PADDING-BOTTOM: 0px; 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TEXT-DECORATION: none } #secondMenu A:hover { BORDER-TOP-WIDTH: 0px; PADDING-RIGHT: 0px; PADDING-LEFT: 0px; = BORDER-LEFT-WIDTH: 0px; BACKGROUND: #9cf; BORDER-BOTTOM-WIDTH: 0px; = PADDING-BOTTOM: 0px; MARGIN: 0px; COLOR: #f63; PADDING-TOP: 0px; = BORDER-RIGHT-WIDTH: 0px; TEXT-DECORATION: none } #journalNav { FONT: bold 0.85em/1.3em = Verdana,Tahoma,Geneva,Arial,Helvetica,sans-serif; COLOR: #000 } #journalNav A:link { PADDING-RIGHT: 0.15em; PADDING-LEFT: 0.15em; FONT-WEIGHT: bold; = BACKGROUND: #fff; PADDING-BOTTOM: 0.15em; MARGIN: 0.5em 0px; COLOR: = #039; PADDING-TOP: 0.15em; FONT-FAMILY: = Verdana,Tahoma,Geneva,Arial,Helvetica,sans-serif; TEXT-DECORATION: none } #journalNav A:visited { PADDING-RIGHT: 0.15em; PADDING-LEFT: 0.15em; FONT-WEIGHT: bold; = BACKGROUND: #fff; PADDING-BOTTOM: 0.15em; MARGIN: 0.5em 0px; COLOR: = #039; PADDING-TOP: 0.15em; FONT-FAMILY: = Verdana,Tahoma,Geneva,Arial,Helvetica,sans-serif; TEXT-DECORATION: none } #journalNav SPAN { PADDING-RIGHT: 0.15em; 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BORDER-RIGHT: #666 1px solid; PADDING-RIGHT: 5px; BORDER-TOP: #666 1px = solid; PADDING-LEFT: 5px; PADDING-BOTTOM: 5px; MARGIN: 30px 0px 0px; = BORDER-LEFT: #666 1px solid; PADDING-TOP: 5px; BORDER-BOTTOM: #666 1px = solid; LIST-STYLE-TYPE: none } #sideNav LI { FONT: bold 0.85em/1.3em = Verdana,Tahoma,Geneva,Arial,Helvetica,sans-serif; COLOR: #000 } #sideNav P { PADDING-RIGHT: 5px; PADDING-LEFT: 5px; PADDING-BOTTOM: 5px; MARGIN: = 30px 0px 0px; COLOR: #000; PADDING-TOP: 5px } #sideNav A:link { FONT-WEIGHT: normal; BACKGROUND: #fff; COLOR: #039; TEXT-DECORATION: = none } #sideNav A:visited { FONT-WEIGHT: normal; BACKGROUND: #fff; COLOR: #039; TEXT-DECORATION: = none } #sideNav A:hover { BACKGROUND: #fff; COLOR: #f63; TEXT-DECORATION: underline } .figureFM { PADDING-RIGHT: 0px; PADDING-LEFT: 0px; PADDING-BOTTOM: 0px; MARGIN: 5px = 5px 5px 0px; PADDING-TOP: 0px } .figureFM H5 { MARGIN: 0px; FONT: 1em/1.5em = Verdana,Tahoma,Geneva,Arial,Helvetica,sans-serif } .figureFM P { FONT: 0.85em 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} .topNav A:hover { COLOR: #f63; TEXT-DECORATION: underline } .checkbox UL { LIST-STYLE-IMAGE: url(../images/checkbox.gif) } .checkbox LI { MARGIN-TOP: 1.25em } #responseList { BORDER-TOP-WIDTH: 0px; PADDING-RIGHT: 0px; PADDING-LEFT: 0px; = BORDER-LEFT-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; PADDING-BOTTOM: 0px; = MARGIN: 0px; PADDING-TOP: 0px; BORDER-RIGHT-WIDTH: 0px } #responseList UL { BORDER-TOP-WIDTH: 0px; PADDING-RIGHT: 5px; PADDING-LEFT: 5px; = BORDER-LEFT-WIDTH: 0px; BORDER-BOTTOM-WIDTH: 0px; PADDING-BOTTOM: 5px; = MARGIN: 0.5em 0px; PADDING-TOP: 5px; LIST-STYLE-TYPE: none; = BORDER-RIGHT-WIDTH: 0px } #responseList LI { PADDING-RIGHT: 5px; BORDER-TOP: #09c 1px solid; PADDING-LEFT: 5px; = PADDING-BOTTOM: 5px; MARGIN: 0px; FONT: 1em/1.5em = Verdana,Tahoma,Geneva,Arial,Helvetica,sans-serif; COLOR: #000; = PADDING-TOP: 5px } #responseList A:link { FONT-WEIGHT: bold; COLOR: #039; TEXT-DECORATION: none } #responseList A:visited { FONT-WEIGHT: bold; COLOR: #039; TEXT-DECORATION: none } 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