Algorithmic Self-Assembly of DNA Sierpinski Triangles

TLDR

Algorithms and information are fundamental to technological and biological organization and are essential to many elementary physical phenomena, such as molecular self‑assembly. The study reports a molecular realization of a DNA‑tile based cellular automaton that computes XOR to fabricate a growing Sierpinski triangle. The authors translated abstract tiles into DNA double‑crossover motifs and used long single‑stranded DNA to nucleate tile growth into algorithmic crystals. Atomic force microscopy showed recognizable Sierpinski triangles with 100–200 correct tiles, error rates of 1–10%, and demonstrated that DNA self‑assembly can implement arbitrary cellular automata, establishing it as a Turing‑universal biomolecular system.

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.