On Low Energy Barrier Folding Pathways for Nucleic Acid Sequences

Abstract

Secondary structure folding pathways correspond to the execution of DNA programs such as DNA strand displacement systems. It is helpful to understand the full diversity of features that such pathways can have, when designing novel folding pathways. In this work, we show that properties of folding pathways over a 2-base strand (a strand with either A and T, or C and G, but not all four bases) may be quite different than those over a 4-base alphabet. Our main result is that, for a simple energy model in which each base pair contributes $-1$, 2-base sequences of length n always have a folding pathway of length $O(n^3)$ with energy barrier at most 2. We provide an efficient algorithm for constructing such a pathway. In contrast, it is unknown whether minimum energy barrier pathways for 4-base sequences can be found efficiently, and such pathways can have barrier $\varTheta (n)$. We also present several results that show how folding pathways with temporary and/or repeated base pairs can have lower energy barrier than pathways without such base pairs.