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On Low Energy Barrier Folding Pathways for Nucleic Acid Sequences

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 9211)

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.

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Acknowledgments

We thank the reviewers of the paper for their detailed and thoughtful comments, for raising their significant concerns about the value of our results in light of the underlying simplistic energy model, and for pointing us to the work of Reader and Joyce [11]. Their comments on follow-on work are reflected in Sect. 5 and, while beyond the scope of what we could address in our revisions, will guide us in our future work.

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Correspondence to Anne Condon .

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Mathieson, LA., Condon, A. (2015). On Low Energy Barrier Folding Pathways for Nucleic Acid Sequences. In: Phillips, A., Yin, P. (eds) DNA Computing and Molecular Programming. DNA 2015. Lecture Notes in Computer Science(), vol 9211. Springer, Cham. https://doi.org/10.1007/978-3-319-21999-8_12

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  • DOI: https://doi.org/10.1007/978-3-319-21999-8_12

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