Simulating Self-replicating Patterns of DNA Tiles

This paper presents a simulation framework in which a pre-assembled rectangular pattern of DNA tiles can be put together with sets of other DNA tiles to autonomously assemble replicas of itself in a discrete two-dimensional grid. The simulator implements both abstract and chemical kinetics based modelling to simulate the tile pattern self-replication. While the abstract model uses only logical matching between the edges of tiles to guide the assembly process, the chemical kinetics model calculates stochastic preference for attachment and/or detachment of each tile during the self-replication. A comparison is made between pattern self-replication timing in the abstract model and cellular automata based models. Simulation of chemical kinetics behaviour shows that the physico-chemical parameters of tile self-assembly govern the tractability of self-replication process and reliability of replicating patterns. Observations are made about the limitations of the simulator, and a few suggestions for improvement and further studies are discussed.