Logical computation using algorithmic self-assembly of DNA triple-crossover molecules

Abstract

Recent work^1,2,3 has demonstrated the self-assembly of designed periodic two-dimensional arrays composed of DNA tiles, in which the intermolecular contacts are directed by ‘sticky’ ends. In a mathematical context, aperiodic mosaics may be formed by the self-assembly of ‘Wang’ tiles⁴, a process that emulates the operation of a Turing machine. Macroscopic self-assembly has been used to perform computations⁵; there is also a logical equivalence between DNA sticky ends and Wang tile edges^6,7. This suggests that the self-assembly of DNA-based tiles could be used to perform DNA-based computation⁸. Algorithmic aperiodic self-assembly requires greater fidelity than periodic self-assembly, because correct tiles must compete with partially correct tiles. Here we report a one-dimensional algorithmic self-assembly of DNA triple-crossover molecules⁹ that can be used to execute four steps of a logical (cumulative XOR) operation on a string of binary bits.