Parallel Molecular Computations of pair-wise XOR using DNA “String Tile” Self- Assembly

DNA computing 1 potentially provides a degree of parallelism far beyond that of conventional silicon-based computers. A number of researchers 2 have experimentally demonstrated DNA computing in solving instances of the satisfiability problems. Self-assembly of DNA nanostructures is theoretically an efficient method of executing parallel computation where information is encoded in DNA tiles and a large number of tiles can be self-assembled via sticky-end associations. Winfree et al. 3 have shown that representations of formal languages can be generated by self-assembly of branched DNA nanostructures and that 2-dimensional DNA selfassembly is Turing-universal (i.e. capable of universal computation). Mao et al. 4 experimentally implemented the first algorithmic DNA self-assembly which performed a logical computation (cumulative XOR), however that study only executed two computations on fixed inputs. To further explore the power of computing using DNA self-assembly, experimental demonstrations of parallel computations are required. Here we describe the first parallel molecular computation using DNA tiling self-assembly in which a large number of distinct inputs are simultaneously processed. The experiments described here are based on the “string tile” model proposed by Winfree et al. , where they investigated computation by linear assemblies of complex DNA tiles. The concept of ‘string tile’ assemblies derives from Eng's observation 6 that by allowing neighboring tiles in an assembly to associate by sticky ends on each side, one could increase the computational complexity of languages generated by linear self-assemblies. Surprisingly sophisticated calculations can be performed with single-layer linear assemblies when contiguous strings of DNA trace through individual tiles and the entire assembly multiple times. In essence, a “string tile’ is the collapse of a multi-layer assembly into a simpler superstructure by allowing individual tiles to carry multiple segments of the reporter strands, thereby allowing an entire row of a truth table to be encode within each individual tile. ‘String tile’ arithmetic implementations have a number of advantageous properties. (i) Input and output strings assemble simultaneously. (ii) Each row in the truth table for the function being calculated is represented as a single tile type, where all input and output bits are encoded on that tile. Each pair-wise operation is directly encoded in the structure of a tile. (iii) Adjacent tiles associate via multiple sticky ends, all of which either agree or disagree, and therefore there is no need to differentiate between single and double pad matches (as required in two-dimensional (2D) assemblies). We have experimentally implemented “string tile” arithmetic using linear self-assembly of DNA double crossover tiles 7 (DX) to perform pair-wise XOR calculations. The molecular structure of the DX tiles used here is illustrated in Fig. 1a. It contains five strands that self-assemble through Watson-Crick base pairing to produce two double helices which are connected to each other at two points where their strands cross over between them. There are