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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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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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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.

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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

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.

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