Exhaustive classification and systematic free-energy profile study of single-stranded DNA inter-overhang migration

Migration of a short single-stranded DNA (ssDNA) between DNA overhangs is a basic molecular process that is widely used in dynamic DNA nanotechnology. The migration rate is sensitive to migration gaits, and limits the speed of dynamic DNA systems like DNA nanowalkers and other functional devices. Here, we identify and exhaustively classify all possible inter-overhang migration gaits of a ssDNA into only four categories based on their intrinsic symmetry. Using the oxDNA package, we conduct a systematic computational study for a typical migrator-overhang system to identify the lowest-energy pathway for all four migration categories. The one-dimensional free-energy profile along this pathway allows a parameter-free estimation of migration rates for all the four categories by the first passage time theory plus benchmarking from experimental rates available for one migration category. The obtained rates indicate a big room to improve DNA nanowalkers' speed above 1 μm per minute. The free-energy profile for each migration category possesses distinct and robust symmetric patterns, which largely decide local barriers, trapping states, and thereby a migration's rate-limiting processes and capacity for directional bias. This study thus provides a unified symmetry-based framework to analyze and optimize ssDNA migrations in kinetics, bias capacity, and structural design for better dynamic DNA nanotechnology.