Invadable self-assembly: combining robustness with efficiency

DNA self-assembly is emerging as a key paradigm for nano-technology, nano-computation, and several related disciplines. In nature, DNA self-assembly is often equipped with explicit mechanisms for both error prevention and error correction. For artificial self-assembly, these problems are even more important since we are interested in assembling large systems with great precision. So far, theoretical studies of DNA self-assembly have primarily focused on the efficiency of the assembly process in terms of the program size and the running time. In this paper, we perform a preliminary study of algorithms for DNA self-assembly that are both robust and efficient.Strand invasion is an important error-correction mechanism observed in several natural self-assembling systems. We first define invadable self-assemblies as self-assembling systems which can effectively use the strand invasion mechanism for error-correction. We then show that O(log² n/ log log n) tiles are sufficient to assemble an n × n square in this model. The running time of our system is Õ (n). We obtain our result by growing a counter which simulates Chinese remaindering. The running time and the program size of our invadable system are within polylogarithmic factors of known lower bounds for general systems, i.e. the efficiency penalty for obtaining robustness is small in our model. We also show how to simulate an arbitrary Turing machine using an invadable self-assembly system.