Cellular Automata Analysis on Self-assembly Properties in DNA Tile Computing

An Analysis on the self-assembly process in DNA tile computing is presented using the cellular automata approach. It is known that a cellular automata model can simulate various complex systems by updating the states of calculation cells based on the local interaction rules. Generally DNA computing is operated through the local interaction between complimentary strands. Therefore the cellular automata approach is suitable to investigate qualitative features of such systems. Focusing on the cryptosystem using a DNA motif called a triple crossover (TX) tile, we construct a new cellular automata model. Our objective is to find a solution to improve the fragmentation problem in the self-assembly process of a calculation sheet of TX tiles, because the fragmentation prevents the system from realizing the sufficient performance. Our results suggest that such fragmentation occurs when the error correction function is lost due to the strong stability of local interaction. It is expected that these findings using cellular automata simulations provide effective information to solve the problems to develop practical applications of DNA-based computation.