Error-resistant scaling of three-dimensional nanoscale shapes on the basis of DNA-tiles

One of the main problems in nano computing and nano networking is the physical construction of nano machines. DNA is a prime candidate for nanoscale constructions because it is a chemically and structurally stable molecule. Short DNA strands can be combined to form so called DNA tiles. These tiles form the basic building blocks for bigger structures which come into existence through self-assembly – given a sufficient supply of different tiletypes, the tiles automatically bind together. Self-assembly is a functional tool at the nanoscale, where top-down interaction tends to be difficult. However, DNA-based construction is prone to errors. Therefore, algorithmic strategies mitigating these errors, by a system called proofreading, have been developed. In this paper, we adapt a two-dimensional proofreading strategy for three dimensions in order to create functional 3D structures at the nanoscale. An algorithm is presented which creates a scaled 3D proofreading tileset, given any 3D tileset. The algorithm creates a k × k × k block of Snaked Proofreading tiletypes for each tile t in the original tileset using O(|t|k³) tiletypes. These proofreading tilesets can be used to reliably assemble nanoscale devices or to scale up shapes while simultaneously reducing errors.