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Thermodynamic Binding Networks Capture Equilibrium Monomer-Polymer Thermodynamics

Authors: And Kaan Ata Yilmaz, David Soloveichik, and Austin Luchsinger

Published in: LIPIcs, Volume 387, 32nd International Conference on DNA Computing and Molecular Programming (DNA 32) (2026)

Abstract

Thermodynamic Binding Networks (TBNs) are a minimal model for molecular thermodynamics. Despite their simplicity, the stable behavior of these systems can be unexpectedly nontrivial. To better understand the expressive power of the model, we compare TBNs with Thermodynamic Affinity Networks (TANs), a partition-scoring formalism in which polymer-level favorability is specified directly, rather than derived from domain-level interactions. We show that these two models are thermodynamically equivalent at the level of stable configurations: every TBN can be represented directly by a TAN, and every TAN can be indirectly realized by a TBN whose stable configurations map exactly to the stable configurations of the TAN. The key idea in the latter direction is to use auxiliary monomers that allow the system to convert polymer-level free-energy rewards specified by the TAN into entropic gains from separate complexes in the TBN. This correspondence shows that the local rules of TBNs do not limit their equilibrium expressive power nearly as much as one might expect. In this minimum-free-energy sense of equilibrium, TBNs capture the coarse-grained monomer-polymer thermodynamics formalized by TANs.

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And Kaan Ata Yilmaz, David Soloveichik, and Austin Luchsinger. Thermodynamic Binding Networks Capture Equilibrium Monomer-Polymer Thermodynamics. In 32nd International Conference on DNA Computing and Molecular Programming (DNA 32). Leibniz International Proceedings in Informatics (LIPIcs), Volume 387, pp. 9:1-9:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{yilmaz_et_al:LIPIcs.DNA.32.9,
  author =	{Yilmaz, And Kaan Ata and Soloveichik, David and Luchsinger, Austin},
  title =	{{Thermodynamic Binding Networks Capture Equilibrium Monomer-Polymer Thermodynamics}},
  booktitle =	{32nd International Conference on DNA Computing and Molecular Programming (DNA 32)},
  pages =	{9:1--9:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-444-4},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{387},
  editor =	{Scalise, Dominic and Schweller, Robert},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DNA.32.9},
  URN =		{urn:nbn:de:0030-drops-267796},
  doi =		{10.4230/LIPIcs.DNA.32.9},
  annote =	{Keywords: Thermodynamic Binding Networks, Thermodynamic Affinity Networks, Equilibrium Thermodynamics}
}

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DOI: 10.4230/LIPIcs.DNA.32.10

Modularity of Signal Propagation Networks in the Thermodynamic Binding Network Model

Authors: And Kaan Ata Yilmaz and David Soloveichik

Published in: LIPIcs, Volume 387, 32nd International Conference on DNA Computing and Molecular Programming (DNA 32) (2026)

Abstract

The Thermodynamic Binding Network (TBN) model provides an equilibrium-based abstraction for molecular systems, but proving correctness of large networks built from individually verified modules remains difficult because modules can interact through shared binding-site types. We develop a method for proving correctness of modular TBNs by reducing a composition of arbitrarily many modules to a fixed coarse-grained TBN, computing the Hilbert basis of the reduced system, and lifting the resulting entropy bounds and polymer characterizations back to the original network. We apply this method to reversible signal-propagation modules: For the previously studied module implementing A+B ⟷ C, we show that stable configurations of an arbitrary network of such modules have the intended local structure, implying that firing an individual module preserves global stability. Under certain restrictions on the reaction set, these networks faithfully simulate a class of reversible chemical reaction networks: every bounded-length CRN execution can be realized by a height-2 path between stable TBN configurations, and any two stable TBN configurations map to CRN states in the same stoichiometric compatibility class. We further show that the same proof strategy extends to a novel module implementing reactions with two reactants and products like A+B ⟷ C+D.

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And Kaan Ata Yilmaz and David Soloveichik. Modularity of Signal Propagation Networks in the Thermodynamic Binding Network Model. In 32nd International Conference on DNA Computing and Molecular Programming (DNA 32). Leibniz International Proceedings in Informatics (LIPIcs), Volume 387, pp. 10:1-10:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{yilmaz_et_al:LIPIcs.DNA.32.10,
  author =	{Yilmaz, And Kaan Ata and Soloveichik, David},
  title =	{{Modularity of Signal Propagation Networks in the Thermodynamic Binding Network Model}},
  booktitle =	{32nd International Conference on DNA Computing and Molecular Programming (DNA 32)},
  pages =	{10:1--10:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-444-4},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{387},
  editor =	{Scalise, Dominic and Schweller, Robert},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DNA.32.10},
  URN =		{urn:nbn:de:0030-drops-267809},
  doi =		{10.4230/LIPIcs.DNA.32.10},
  annote =	{Keywords: Thermodynamic Binding Networks, Chemical Reaction Networks, Modular Composition, Verification, Simulation}
}

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Documents authored by Yilmaz, And Kaan Ata

Thermodynamic Binding Networks Capture Equilibrium Monomer-Polymer Thermodynamics

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Modularity of Signal Propagation Networks in the Thermodynamic Binding Network Model

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