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Documents authored by Thachuk, Chris

Document
DOI: 10.4230/LIPIcs.DNA.29.1
Minimum Free Energy, Partition Function and Kinetics Simulation Algorithms for a Multistranded Scaffolded DNA Computer

Authors: Ahmed Shalaby, Chris Thachuk, and Damien Woods

Published in: LIPIcs, Volume 276, 29th International Conference on DNA Computing and Molecular Programming (DNA 29) (2023)

Abstract
Polynomial time dynamic programming algorithms play a crucial role in the design, analysis and engineering of nucleic acid systems including DNA computers and DNA/RNA nanostructures. However, in complex multistranded or pseudoknotted systems, computing the minimum free energy (MFE), and partition function of nucleic acid systems is NP-hard. Despite this, multistranded and/or pseudoknotted systems represent some of the most utilised and successful systems in the field. This leaves open the tempting possibility that many of the kinds of multistranded and/or pseudoknotted systems we wish to engineer actually fall into restricted classes, that do in fact have polynomial time algorithms, but we've just not found them yet. Here, we give polynomial time algorithms for MFE and partition function calculation for a restricted kind of multistranded system called the 1D scaffolded DNA computer. This model of computation thermodynamically favours correct outputs over erroneous states, simulates finite state machines in 1D and Boolean circuits in 2D, and is amenable to DNA storage applications. In an effort to begin to ask the question of whether we can naturally compare the expressivity of nucleic acid systems based on the computational complexity of prediction of their preferred energetic states, we show our MFE problem is in logspace (the complexity class L), making it perhaps one of the simplest known, natural, nucleic acid MFE problems. Finally, we provide a stochastic kinetic simulator for the 1D scaffolded DNA computer and evaluate strategies for efficiently speeding up this thermodynamically favourable system in a constant-temperature kinetic regime.
Cite as

Ahmed Shalaby, Chris Thachuk, and Damien Woods. Minimum Free Energy, Partition Function and Kinetics Simulation Algorithms for a Multistranded Scaffolded DNA Computer. In 29th International Conference on DNA Computing and Molecular Programming (DNA 29). Leibniz International Proceedings in Informatics (LIPIcs), Volume 276, pp. 1:1-1:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{shalaby_et_al:LIPIcs.DNA.29.1,
  author =	{Shalaby, Ahmed and Thachuk, Chris and Woods, Damien},
  title =	{{Minimum Free Energy, Partition Function and Kinetics Simulation Algorithms for a Multistranded Scaffolded DNA Computer}},
  booktitle =	{29th International Conference on DNA Computing and Molecular Programming (DNA 29)},
  pages =	{1:1--1:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-297-6},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{276},
  editor =	{Chen, Ho-Lin and Evans, Constantine G.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DNA.29.1},
  URN =		{urn:nbn:de:0030-drops-187840},
  doi =		{10.4230/LIPIcs.DNA.29.1},
  annote =	{Keywords: thermodynamic computation, model of computation, molecular computing, minimum free energy, partition function, DNA computing, DNA self-assembly, DNA strand displacement, kinetics simulation}
}
Document
DOI: 10.4230/LIPIcs.DNA.28.1
Fast and Robust Strand Displacement Cascades via Systematic Design Strategies

Authors: Tiernan Kennedy, Cadence Pearce, and Chris Thachuk

Published in: LIPIcs, Volume 238, 28th International Conference on DNA Computing and Molecular Programming (DNA 28) (2022)

Abstract
A barrier to wider adoption of molecular computation is the difficulty of implementing arbitrary chemical reaction networks (CRNs) that are robust and replicate the kinetics of designed behavior. DNA Strand Displacement (DSD) cascades have been a favored technology for this purpose due to their potential to emulate arbitrary CRNs and known principles to tune their reaction rates. Progress on leakless cascades has demonstrated that DSDs can be arbitrarily robust to spurious "leak" reactions when incorporating systematic domain level redundancy. These improvements in robustness result in slower kinetics of designed reactions. Existing work has demonstrated the kinetic and thermodynamic effects of sequence mismatch introduction and elimination during displacement. We present a systematic, sequence modification strategy for optimizing the kinetics of leakless cascades without practical cost to their robustness. An in-depth case study explores the effects of this optimization when applied to a typical leakless translator cascade. Thermodynamic analysis of energy barriers and kinetic experimental data support that DSD cascades can be fast and robust.
Cite as

Tiernan Kennedy, Cadence Pearce, and Chris Thachuk. Fast and Robust Strand Displacement Cascades via Systematic Design Strategies. In 28th International Conference on DNA Computing and Molecular Programming (DNA 28). Leibniz International Proceedings in Informatics (LIPIcs), Volume 238, pp. 1:1-1:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{kennedy_et_al:LIPIcs.DNA.28.1,
  author =	{Kennedy, Tiernan and Pearce, Cadence and Thachuk, Chris},
  title =	{{Fast and Robust Strand Displacement Cascades via Systematic Design Strategies}},
  booktitle =	{28th International Conference on DNA Computing and Molecular Programming (DNA 28)},
  pages =	{1:1--1:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-253-2},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{238},
  editor =	{Ouldridge, Thomas E. and Wickham, Shelley F. J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DNA.28.1},
  URN =		{urn:nbn:de:0030-drops-167869},
  doi =		{10.4230/LIPIcs.DNA.28.1},
  annote =	{Keywords: DNA strand displacement, Energy barriers, Kinetics}
}
Document
DOI: 10.4230/LIPIcs.DNA.27.9
Predicting Minimum Free Energy Structures of Multi-Stranded Nucleic Acid Complexes Is APX-Hard

Authors: Anne Condon, Monir Hajiaghayi, and Chris Thachuk

Published in: LIPIcs, Volume 205, 27th International Conference on DNA Computing and Molecular Programming (DNA 27) (2021)

Abstract
Given multiple nucleic acid strands, what is the minimum free energy (MFE) secondary structure that they can form? As interacting nucleic acid strands are the basis for DNA computing and molecular programming, e.g., in DNA self-assembly and DNA strand displacement systems, determining the MFE structure is an important step in the design and verification of these systems. Efficient dynamic programming algorithms are well known for predicting the MFE pseudoknot-free secondary structure of a single nucleic acid strand. In contrast, we prove that for a simple energy model, the problem of predicting the MFE pseudoknot-free secondary structure formed from multiple interacting nucleic acid strands is NP-hard and also APX-hard. The latter result implies that there does not exist a polynomial time approximation scheme for this problem, unless 𝖯 = NP, and it suggests that heuristic methods should be investigated.
Cite as

Anne Condon, Monir Hajiaghayi, and Chris Thachuk. Predicting Minimum Free Energy Structures of Multi-Stranded Nucleic Acid Complexes Is APX-Hard. In 27th International Conference on DNA Computing and Molecular Programming (DNA 27). Leibniz International Proceedings in Informatics (LIPIcs), Volume 205, pp. 9:1-9:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{condon_et_al:LIPIcs.DNA.27.9,
  author =	{Condon, Anne and Hajiaghayi, Monir and Thachuk, Chris},
  title =	{{Predicting Minimum Free Energy Structures of Multi-Stranded Nucleic Acid Complexes Is APX-Hard}},
  booktitle =	{27th International Conference on DNA Computing and Molecular Programming (DNA 27)},
  pages =	{9:1--9:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-205-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{205},
  editor =	{Lakin, Matthew R. and \v{S}ulc, Petr},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DNA.27.9},
  URN =		{urn:nbn:de:0030-drops-146765},
  doi =		{10.4230/LIPIcs.DNA.27.9},
  annote =	{Keywords: Nucleic Acid Secondary Structure Prediction, APX-Hardness, NP-Hardness}
}
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