Coding and geometrical shapes in nanostructures: A fractal DNA-assembly

Fractal patterns represent an important class of aperiodic arrangements. Generating fractal structures by self-assembly is a major challenge for nanotechnology. The specificity of DNA sticky-ended interactions and the well-behaved structural nature of DNA parallelogram motifs has previously led to a protocol that appears likely to be capable of producing fractal constructions [A. Carbone and N.C. Seeman, A route to fractal DNA assembly, Natural Computing 1, 469-480, 2002]. That protocol depends on gluing the set of tiles with special 'glue tiles' to produce the fractal structure. It is possible to develop a fractal-assembly protocol that does not require the participation of gluing components. When designed with similar DNA parallelogram motifs, the protocol involves sixteen specific tiles, sixteen closely related tiles, and a series of protecting groups that are designed to be removed by the introduction of specific strands into the solution. One novel aspect of the construction on the theoretical level is the interplay of both geometry and coding in tile design. A second feature, related to the implementation, is the notion of generalized protecting groups.