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Scalable Enumeration of Pareto-Optimal Polymers for Computing Equilibrium Concentrations

Authors: Archit Patil, Minki Hhan, and David Soloveichik

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

Abstract

Predicting equilibrium concentrations of molecular complexes is essential for verifying the behavior of engineered DNA systems. However, a finite set of monomer types can in principle generate infinitely many complexes. We study this candidate-enumeration problem in a geometry-free, domain-level abstraction called a domain-monomer system, generalizing Thermodynamic Binding Networks (TBNs) to the unsaturated setting where not every possible bond need be formed. We define Pareto-suboptimal polymers as those that can be split into non-interacting parts, and show that restricting attention to Pareto-optimal polymers is thermodynamically justified: no Pareto-suboptimal polymer appears in any minimum free-energy configuration, and the total equilibrium concentration of such polymers is small. We prove that there are finitely many Pareto-optimal polymers and exactly characterize them via a Hilbert basis computation, extending prior work from the saturated TBN model. To scale this approach to large systems, we develop a framework that restricts the number of different monomer types that a single polymer contains, and uses combinatorial covering designs to reduce the number of Hilbert basis computations required. We benchmark the method on several families of DNA molecular programming systems, demonstrating order-of-magnitude speedups over direct computation while recovering nearly all equilibrium-relevant polymers.

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Archit Patil, Minki Hhan, and David Soloveichik. Scalable Enumeration of Pareto-Optimal Polymers for Computing Equilibrium Concentrations. In 32nd International Conference on DNA Computing and Molecular Programming (DNA 32). Leibniz International Proceedings in Informatics (LIPIcs), Volume 387, pp. 12:1-12:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{patil_et_al:LIPIcs.DNA.32.12,
  author =	{Patil, Archit and Hhan, Minki and Soloveichik, David},
  title =	{{Scalable Enumeration of Pareto-Optimal Polymers for Computing Equilibrium Concentrations}},
  booktitle =	{32nd International Conference on DNA Computing and Molecular Programming (DNA 32)},
  pages =	{12:1--12:24},
  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.32.12},
  URN =		{urn:nbn:de:0030-drops-267823},
  doi =		{10.4230/LIPIcs.DNA.32.12},
  annote =	{Keywords: Molecular computation, Hilbert Basis, Thermodynamic Binding Network, covering design, equilibrium concentration}
}

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DOI: 10.4230/LIPIcs.DNA.31.10

Computing and Bounding Equilibrium Concentrations in Athermic Chemical Systems

Authors: Hamidreza Akef, Minki Hhan, and David Soloveichik

Published in: LIPIcs, Volume 347, 31st International Conference on DNA Computing and Molecular Programming (DNA 31) (2025)

Abstract

Computing equilibrium concentrations of molecular complexes is generally analytically intractable and requires numerical approaches. In this work we focus on the polymer-monomer level, where indivisible molecules (monomers) combine to form complexes (polymers). Rather than employing free-energy parameters for each polymer, we focus on the athermic setting where all interactions preserve enthalpy. This setting aligns with the strongly bonded (domain-based) regime in DNA nanotechnology when strands can bind in different ways, but always with maximum overall bonding - and is consistent with the saturated configurations in the Thermodynamic Binding Networks (TBNs) model. Within this context, we develop an iterative algorithm for assigning polymer concentrations to satisfy detailed-balance, where on-target (desired) polymers are in high concentrations and off-target (undesired) polymers are in low. Even if not directly executed, our algorithm provides effective insights into upper bounds on concentration of off-target polymers, connecting combinatorial arguments about discrete configurations such as those in the TBN model to real-valued concentrations. We conclude with an application of our method to decreasing leak in DNA logic and signal propagation. Our results offer a new framework for design and verification of equilibrium concentrations when configurations are distinguished by entropic forces.

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Hamidreza Akef, Minki Hhan, and David Soloveichik. Computing and Bounding Equilibrium Concentrations in Athermic Chemical Systems. In 31st International Conference on DNA Computing and Molecular Programming (DNA 31). Leibniz International Proceedings in Informatics (LIPIcs), Volume 347, pp. 10:1-10:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{akef_et_al:LIPIcs.DNA.31.10,
  author =	{Akef, Hamidreza and Hhan, Minki and Soloveichik, David},
  title =	{{Computing and Bounding Equilibrium Concentrations in Athermic Chemical Systems}},
  booktitle =	{31st International Conference on DNA Computing and Molecular Programming (DNA 31)},
  pages =	{10:1--10:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-399-7},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{347},
  editor =	{Schaeffer, Josie and Zhang, Fei},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DNA.31.10},
  URN =		{urn:nbn:de:0030-drops-238595},
  doi =		{10.4230/LIPIcs.DNA.31.10},
  annote =	{Keywords: Equilibrium concentrations, Thermodynamic Binding Networks, Monomer-polymer model, Detailed balance}
}

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Documents authored by Hhan, Minki

Scalable Enumeration of Pareto-Optimal Polymers for Computing Equilibrium Concentrations

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Computing and Bounding Equilibrium Concentrations in Athermic Chemical Systems

Abstract

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