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Domain-Based Nucleic-Acid Minimum Free Energy: Algorithmic Hardness and Parameterized Bounds

Authors Erik D. Demaine, Timothy Gomez, Elise Grizzell, Markus Hecher, Jayson Lynch, Robert Schweller, Ahmed Shalaby, Damien Woods

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Author Details

Erik D. Demaine
  • Massachusetts Institute of Technology, USA
Timothy Gomez
  • Massachusetts Institute of Technology, USA
Elise Grizzell
  • University of Texas Rio Grande Valley, USA
Markus Hecher
  • Massachusetts Institute of Technology, USA
Jayson Lynch
  • Massachusetts Institute of Technology, USA
Robert Schweller
  • University of Texas Rio Grande Valley, USA
Ahmed Shalaby
  • Hamilton Institute, Department of Computer , Science, Maynooth University, Ireland
Damien Woods
  • Hamilton Institute, Department of Computer , Science, Maynooth University, Ireland

Funding

Damien Woods & Ahmed Shalaby: Supported by the European Research Council (ERC, Active-DNA, No. 772766); European Innovation Council (EIC, DISCO, No. 101115422); and Science Foundation Ireland (SFI) Nos. 18/ERCS/5746 & 20/FFP-P/8843.
  • Grizzell, Elise: Supported in part by the U.S. Department of Education grant P200A120256.
  • Hecher, Markus: Supported by the Austrian Science Fund grant J4656 and the Society for Research Funding NOE grant ExzF-0004.
  • Schweller, Robert: Supported in part by National Science Foundation Grant CCF2329918.

Acknowledgements

We thank Jenny Diomidova, Marco Rodriguez, Tim Wylie for helpful discussions.

Cite AsGet BibTex

Erik D. Demaine, Timothy Gomez, Elise Grizzell, Markus Hecher, Jayson Lynch, Robert Schweller, Ahmed Shalaby, and Damien Woods. Domain-Based Nucleic-Acid Minimum Free Energy: Algorithmic Hardness and Parameterized Bounds. In 30th International Conference on DNA Computing and Molecular Programming (DNA 30). Leibniz International Proceedings in Informatics (LIPIcs), Volume 314, pp. 2:1-2:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.DNA.30.2

Abstract

Molecular programmers and nanostructure engineers use domain-level design to abstract away messy DNA/RNA sequence, chemical and geometric details. Such domain-level abstractions are enforced by sequence design principles and provide a key principle that allows scaling up of complex multistranded DNA/RNA programs and structures. Determining the most favoured secondary structure, or Minimum Free Energy (MFE), of a set of strands, is typically studied at the sequence level but has seen limited domain-level work. We analyse the computational complexity of MFE for multistranded systems in a simple setting were we allow only 1 or 2 domains per strand. On the one hand, with 2-domain strands, we find that the MFE decision problem is NP-complete, even without pseudoknots, and requires exponential time algorithms assuming SAT does. On the other hand, in the simplest case of 1-domain strands there are efficient MFE algorithms for various binding modes. However, even in this single-domain case, MFE is P-hard for promiscuous binding, where one domain may bind to multiple as experimentally used by Nikitin [Nat Chem., 2023], which in turn implies that strands consisting of a single domain efficiently implement arbitrary Boolean circuits.

Subject Classification

ACM Subject Classification
  • Theory of computation → Problems, reductions and completeness
  • Computer systems organization → Molecular computing
Keywords
  • Domain-based DNA designs
  • minimum free energy
  • efficient algorithms
  • NP-hard
  • P-hard
  • NC
  • fixed-parameter tractable

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