Description
Knots are some of the most remarkable topological features in nature. Self-assembly of knotted polymers without breaking or forming covalent bonds is challenging, as the chain needs to be steered through the previously formed loops in a predefined order. Here we describe principles to guide the folding of highly knotted single-chain DNA nanostructures as demonstrated on a nano-sized square pyramid. Folding of knots is encoded by the arrangement of modules of different stability based on derived topological and kinetic rules. Among DNA designs composed of the same modules and encoding the same topology only the one with the folding pathway designed according to the “free-end” rule folded efficiently into the target structure. Besides high folding yields upon slow annealing, this design also folded rapidly upon temperature quenching and dilution from chemical denaturant. We anticipate that this strategy could be used to design the folding of other knotted programmable molecules.
