On secondary structure avoidance of codes for DNA storage

A secondary structure in single-stranded DNA refers to its propensity to undergo self-folding, leading to functional inactivity and irreparable failures within DNA storage systems. Consequently, the property of secondary structure avoidance (SSA) becomes a crucial criterion in the design of single-stranded DNA sequences for DNA storage, as it prohibits the inclusion of reverse-complement subsequences that contribute to such structures. This work is specifically focused on addressing the avoidance of secondary structures in single-stranded DNA sequences. We propose a novel sequence replacement approach, which successfully resolves the SSA problem under conditions where the stem exceeds a length of 2 log 2 ⁡ n + 2 , and the loop is of length k ≥ 4 . These parameters have been carefully chosen to closely resemble the real-world scenarios encountered in biochemical processes, enhancing the practical relevance of our study.