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Minimum Free Energy, Partition Function and Kinetics Simulation Algorithms for a Multistranded Scaffolded DNA Computer

Authors Ahmed Shalaby , Chris Thachuk , Damien Woods

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Author Details

Ahmed Shalaby
  • Hamilton Institute, Department of Computer Science, Maynooth University, Ireland
Chris Thachuk
  • Paul G. Allen School of Computer Science & Engineering, University of Washington, Seattle, WA, USA
Damien Woods
  • Hamilton Institute, Department of Computer Science, Maynooth University, Ireland

Funding

Damien Woods and Ahmed Shalaby were supported by European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 772766, Active-DNA project), and Science Foundation Ireland (SFI) under grant numbers 20/FFP-P/8843 and 18/ERCS/5746. Chris Thachuk was supported by a US NSF grant (CCF 2211792) and a Faculty Early Career Development Award from NSF (CCF 2143227).

Acknowledgements

We thank Abeer Eshra for extensive discussions on the thermodynamics and kinetics of SDC-based strand displacement and for experimental advice, Tristan Stérin for thoughts on the SDC model, Dave Doty for helpful comments, and Constantine Evans, David Soloveichik and Erik Winfree for insightful algorithmic discussions.

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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) https://doi.org/10.4230/LIPIcs.DNA.29.1

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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Models of computation
  • Applied computing → Physical sciences and engineering
Keywords
  • thermodynamic computation
  • model of computation
  • molecular computing
  • minimum free energy
  • partition function
  • DNA computing
  • DNA self-assembly
  • DNA strand displacement
  • kinetics simulation

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