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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