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Computing Properties of Thermodynamic Binding Networks: An Integer Programming Approach

Authors David Haley, David Doty

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David Haley
  • University of California, Davis, CA, USA
David Doty
  • University of California, Davis, CA, USA

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David Haley and David Doty. Computing Properties of Thermodynamic Binding Networks: An Integer Programming Approach. In 27th International Conference on DNA Computing and Molecular Programming (DNA 27). Leibniz International Proceedings in Informatics (LIPIcs), Volume 205, pp. 2:1-2:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)


The thermodynamic binding networks (TBN) model [Breik et al., 2021] is a tool for studying engineered molecular systems. The TBN model allows one to reason about their behavior through a simplified abstraction that ignores details about molecular composition, focusing on two key determinants of a system’s energetics common to any chemical substrate: how many molecular bonds are formed, and how many separate complexes exist in the system. We formulate as an integer program the NP-hard problem of computing stable (a.k.a., minimum energy) configurations of a TBN: those configurations that maximize the number of bonds and complexes. We provide open-source software solving this integer program. We give empirical evidence that this approach enables dramatically faster computation of TBN stable configurations than previous approaches based on SAT solvers [Breik et al., 2019]. Furthermore, unlike SAT-based approaches, our integer programming formulation can reason about TBNs in which some molecules have unbounded counts. These improvements in turn allow us to efficiently automate verification of desired properties of practical TBNs. Finally, we show that the TBN has a natural representation with a unique Hilbert basis describing the "fundamental components" out of which locally minimal energy configurations are composed. This characterization helps verify correctness of not only stable configurations, but entire "kinetic pathways" in a TBN.

Subject Classification

ACM Subject Classification
  • Theory of computation → Theory and algorithms for application domains
  • thermodynamic binding networks
  • integer programming
  • constraint programming


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  1. 4ti2 team. 4ti2 - A software package for algebraic, geometric and combinatorial problems on linear spaces.
  2. Keenan Breik, Cameron Chalk, David Haley, David Doty, and David Soloveichik. Programming substrate-independent kinetic barriers with thermodynamic binding networks. IEEE/ACM Transactions on Computational Biology and Bioinformatics, 18(1):283-295, 2021. Special issue of invited papers from CMSB 2018. Google Scholar
  3. Keenan Breik, Chris Thachuk, Marijn Heule, and David Soloveichik. Computing properties of stable configurations of thermodynamic binding networks. Theoretical Computer Science, 785:17-29, 2019. Google Scholar
  4. Yuan-Jyue Chen, Neil Dalchau, Niranjan Srinivas, Andrew Phillips, Luca Cardelli, David Soloveichik, and Georg Seelig. Programmable chemical controllers made from DNA. Nature Nanotechnology, 8(10):755-762, 2013. Google Scholar
  5. Yuan-Jyue Chen, Benjamin Groves, Richard A. Muscat, and Georg Seelig. DNA nanotechnology from the test tube to the cell. Nature Nanotechnology, 10:748-760, 2015. Google Scholar
  6. Michele Conforti, Gérard Cornuéjols, Giacomo Zambelli, et al. Integer programming, volume 271. Springer, 2014. Google Scholar
  7. Jesús A De Loera, Raymond Hemmecke, and Matthias Köppe. Algebraic and geometric ideas in the theory of discrete optimization. SIAM, 2012. Google Scholar
  8. Leonardo De Moura and Nikolaj Bjørner. Z3: An efficient smt solver. In International conference on Tools and Algorithms for the Construction and Analysis of Systems, pages 337-340. Springer, 2008. Google Scholar
  9. David Doty, Trent A Rogers, David Soloveichik, Chris Thachuk, and Damien Woods. Thermodynamic binding networks. In DNA 2017: Proceedings of the 23rd International Meeting on DNA Computing and Molecular Programming, pages 249-266. Springer, 2017. Google Scholar
  10. Friedrich Eisenbrand, Christoph Hunkenschröder, Kim-Manuel Klein, Martin Koutecky, Asaf Levin, and Shmuel Onn. An algorithmic theory of integer programming. arXiv preprint, 2019. URL:
  11. Gerald Gamrath, Daniel Anderson, Ksenia Bestuzheva, Wei-Kun Chen, Leon Eifler, Maxime Gasse, Patrick Gemander, Ambros Gleixner, Leona Gottwald, Katrin Halbig, Gregor Hendel, Christopher Hojny, Thorsten Koch, Pierre Le Bodic, Stephen J. Maher, Frederic Matter, Matthias Miltenberger, Erik Mühmer, Benjamin Müller, Marc E. Pfetsch, Franziska Schlösser, Felipe Serrano, Yuji Shinano, Christine Tawfik, Stefan Vigerske, Fabian Wegscheider, Dieter Weninger, and Jakob Witzig. The SCIP Optimization Suite 7.0. Technical report, Optimization Online, March 2020. URL:
  12. LLC Gurobi Optimization. Gurobi optimizer reference manual, 2020. URL:
  13. David Haley. Stable-TBN - a software package for computing the stable configurations of thermodynamic binding networks. URL:
  14. Dionis Minev, Christopher M Wintersinger, Anastasia Ershova, and William M Shih. Robust nucleation control via crisscross polymerization of highly coordinated DNA slats. Nature Communications, 12(1):1-9, 2021. Google Scholar
  15. Laurent Perron and Vincent Furnon. OR-tools. URL:
  16. Lulu Qian and Erik Winfree. Scaling up digital circuit computation with DNA strand displacement cascades. Science, 332(6034):1196-1201, 2011. Google Scholar
  17. Paul W. K. Rothemund. Folding DNA to create nanoscale shapes and patterns. Nature, 440(7082):297-302, 2006. Google Scholar
  18. Paul Shaw, Vincent Furnon, and Bruno De Backer. A constraint programming toolkit for local search. In Optimization Software Class Libraries, pages 219-261. Springer, 2003. Google Scholar
  19. Niranjan Srinivas, James Parkin, Georg Seelig, Erik Winfree, and David Soloveichik. Enzyme-free nucleic acid dynamical systems. Science, 358(6369):eaal2052, 2017. Google Scholar
  20. Chris Thachuk, Erik Winfree, and David Soloveichik. Leakless DNA strand displacement systems. In DNA 2015: Proceedings of the 21st International Meeting on DNA Computing and Molecular Programming, pages 133-153. Springer, 2015. Google Scholar
  21. Andrew C Trapp and Oleg A Prokopyev. Solving the order-preserving submatrix problem via integer programming. INFORMS Journal on Computing, 22(3):387-400, 2010. Google Scholar
  22. Boya Wang, Chris Thachuk, Andrew D Ellington, Erik Winfree, and David Soloveichik. Effective design principles for leakless strand displacement systems. Proceedings of the National Academy of Sciences, 115(52):E12182-E12191, 2018. Google Scholar
  23. Damien Woods^†, David Doty^†, Cameron Myhrvold, Joy Hui, Felix Zhou, Peng Yin, and Erik Winfree. Diverse and robust molecular algorithms using reprogrammable DNA self-assembly. Nature, 567(7748):366-372, 2019. ^†joint first authors. URL:
  24. David Yu Zhang and Georg Seelig. Dynamic DNA nanotechnology using strand-displacement reactions. Nature chemistry, 3(2):103-113, 2011. Google Scholar
  25. David Yu Zhang and Erik Winfree. Control of DNA strand displacement kinetics using toehold exchange. Journal of the American Chemical Society, 131(47):17303-17314, 2009. Google Scholar
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