Construction of one-dimensional random walk lattices using DNA algorithmic self-assembly

Algorithmic DNA lattices are constructed using pre-defined rules such as COPY, NOT, and XOR, where patterns are predicted based on initial values. However, the experimental implementation of an unpredictable random walk pattern (which is the implementation of a random rule, i.e., equally probable to move toward either the left or right in 1D systems) in DNA has not been reported yet. Here, we construct DNA lattices with DNA rule tiles implemented using the random rule. Patterns are visualized by atomic force microscopy. Finally, we discussed the average displacement, mean-square displacement, and number of displacement occurrences of experimental as well as simulated 1D random walk. The encoded information in sticky ends of DNA rule tiles demonstrates the feasibility of universal computation through DNA algorithmic self-assembly, which could be extremely beneficial in future computations.