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.
Highlights
IntroductionOne may look to biology, where we find the most sophisticated organization of matter, often spanning more than 24 orders of magnitude from component molecules (0.1 attograms) to entire organism (100 kilograms)
How is complex organization produced and maintained by physical processes? One may look to biology, where we find the most sophisticated organization of matter, often spanning more than 24 orders of magnitude from component molecules (0.1 attograms) to entire organism (100 kilograms)
How crystal morphology and patterning can be programmed by tile design in an inherently asynchronous assembly process is addressed by the abstract Tile Assembly Model (Winfree 1996, 1998a)
Summary
One may look to biology, where we find the most sophisticated organization of matter, often spanning more than 24 orders of magnitude from component molecules (0.1 attograms) to entire organism (100 kilograms) This organization is information-based: DNA sequences refined by evolution encode both the components and the processes that guide their development into an organism— the developmental program. The study of molecular algorithms has been hampered by the lack of suitable physical systems on which to hone such a theory: nature provides us with elementary chemical reactions too simple to program, full-blown life too complex to use as a model system, and few systems in between. This gap may be explored by synthesizing programmable biochemical systems in vitro, where we can implement and study a variety of molecular algorithms ranging gradually from simple to complex
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