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      Algorithmic Self-Assembly of DNA Sierpinski Triangles

      1 , 2 , 2 , , 1 , 2

      PLoS Biology

      Public Library of Science

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          Abstract

          Algorithms and information, fundamental to technological and biological organization, are also an essential aspect of many elementary physical phenomena, such as molecular self-assembly. Here we report the molecular realization, using two-dimensional self-assembly of DNA tiles, of a cellular automaton whose update rule computes the binary function XOR and thus fabricates a fractal pattern—a Sierpinski triangle—as it grows. To achieve this, abstract tiles were translated into DNA tiles based on double-crossover motifs. Serving as input for the computation, long single-stranded DNA molecules were used to nucleate growth of tiles into algorithmic crystals. For both of two independent molecular realizations, atomic force microscopy revealed recognizable Sierpinski triangles containing 100–200 correct tiles. Error rates during assembly appear to range from 1% to 10%. Although imperfect, the growth of Sierpinski triangles demonstrates all the necessary mechanisms for the molecular implementation of arbitrary cellular automata. This shows that engineered DNA self-assembly can be treated as a Turing-universal biomolecular system, capable of implementing any desired algorithm for computation or construction tasks.

          Abstract

          Engineered DNA self-assembly to produce a fractal pattern demonstrates all the necessary mechanisms for the molecular implementation of arbitrary cellular automata

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          Most cited references 73

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          On Computable Numbers, with an Application to the Entscheidungsproblem

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            Nucleic acid junctions and lattices.

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              DNA-templated assembly and electrode attachment of a conducting silver wire.

              Recent research in the field of nanometre-scale electronics has focused on two fundamental issues: the operating principles of small-scale devices, and schemes that lead to their realization and eventual integration into useful circuits. Experimental studies on molecular to submicrometre quantum dots and on the electrical transport in carbon nanotubes have confirmed theoretical predictions of an increasing role for charging effects as the device size diminishes. Nevertheless, the construction of nanometre-scale circuits from such devices remains problematic, largely owing to the difficulties of achieving inter-element wiring and electrical interfacing to macroscopic electrodes. The use of molecular recognition processes and the self-assembly of molecules into supramolecular structures might help overcome these difficulties. In this context, DNA has the appropriate molecular-recognition and mechanical properties, but poor electrical characteristics prevent its direct use in electrical circuits. Here we describe a two-step procedure that may allow the application of DNA to the construction of functional circuits. In our scheme, hybridization of the DNA molecule with surface-bound oligonucleotides is first used to stretch it between two gold electrodes; the DNA molecule is then used as a template for the vectorial growth of a 12 microm long, 100 nm wide conductive silver wire. The experiment confirms that the recognition capabilities of DNA can be exploited for the targeted attachment of functional wires.
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                Author and article information

                Journal
                PLoS Biol
                pbio
                PLoS Biology
                Public Library of Science (San Francisco, USA )
                1544-9173
                1545-7885
                December 2004
                7 December 2004
                : 2
                : 12
                Affiliations
                1simpleComputation and Neural Systems, California Institute of Technology Pasadena, CaliforniaUnited States of America
                2simpleComputer Science, California Institute of Technology Pasadena, CaliforniaUnited States of America
                Article
                10.1371/journal.pbio.0020424
                534809
                15583715
                Copyright: © 2004 Rothemund et al. 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
                Categories
                Research Article
                Bioengineering
                Bioinformatics/Computational Biology
                In Vitro

                Life sciences

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