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

Authors

Erik D. Demaine, Massachusetts Institute of Technology
Elize Grizzell, The University of Texas Rio Grande Valley
Jayson Lynch, Massachusetts Institute of Technology
Ahmed Shalaby, National University of Ireland, Maynooth
Timothy Gomez, Massachusetts Institute of Technology
Markus Hecher, Massachusetts Institute of Technology
Robert Schweller, The University of Texas Rio Grande ValleyFollow
Damien Woods, National University of Ireland, Maynooth

Document Type

Conference Proceeding

Publication Date

9-9-2024

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.

Comments

© Erik D. Demaine, Timothy Gomez, Elise Grizzell, Markus Hecher, Jayson Lynch, Robert Schweller, Ahmed Shalaby, and Damien Woods; licensed under Creative Commons License CC-BY 4.0

Recommended Citation

Demaine, Erik D., 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)(2024). Schloss Dagstuhl–Leibniz-Zentrum für Informatik, 2024. https://doi.org/10.4230/LIPIcs.DNA.30.2

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

DOI

https://doi.org/10.4230/LIPIcs.DNA.30.2