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Amplification at Equilibrium: Structural and Thermodynamic Limitations, and Implementation

Authors: Hamidreza Akef, Chia-Yu Sung, Aneesh Vanguri, and David Soloveichik

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

Abstract

Amplifying weak molecular signals is essential in both natural and engineered biochemical systems. While most amplification schemes operate out of equilibrium, relying on kinetic barriers and fuel-driven cascades, it is also possible to amplify at thermodynamic equilibrium by shifting the energy landscape upon addition of an analyte. Equilibrium amplification is appealing because, in principle, the system can remain indefinitely in the untriggered state. In this work, we establish fundamental structural and thermodynamic limits on equilibrium-based amplification. We first prove that dimerization networks - systems restricted to complexes of at most two monomers - are inherently incapable of equilibrium amplification. This no-go theorem explains the absence of amplification in prior undercomplementary "strand commutation" designs. We then show that allowing trimeric complexes breaks this barrier. We propose an isometric trimer-based equilibrium amplifier whose output preserves the size of the input, enabling modular composition, and validate it experimentally, achieving an amplification factor close to the expected 2×. Finally, we derive universal thermodynamic bounds applicable regardless of complex size: the maximum amplification factor scales linearly with the free energy of interaction between the analyte and the amplifier components. For nucleic acid systems, this implies that the analyte length must grow linearly with the desired amplification factor, and that composing modular amplifiers yields diminishing returns for a fixed analyte. Together, these results delineate the structural and energetic boundaries of equilibrium amplification and rigorously justify the necessity of out-of-equilibrium approaches for achieving high gain.

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Hamidreza Akef, Chia-Yu Sung, Aneesh Vanguri, and David Soloveichik. Amplification at Equilibrium: Structural and Thermodynamic Limitations, and Implementation. In 32nd International Conference on DNA Computing and Molecular Programming (DNA 32). Leibniz International Proceedings in Informatics (LIPIcs), Volume 387, pp. 8:1-8:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{akef_et_al:LIPIcs.DNA.32.8,
  author =	{Akef, Hamidreza and Sung, Chia-Yu and Vanguri, Aneesh and Soloveichik, David},
  title =	{{Amplification at Equilibrium: Structural and Thermodynamic Limitations, and Implementation}},
  booktitle =	{32nd International Conference on DNA Computing and Molecular Programming (DNA 32)},
  pages =	{8:1--8:24},
  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.32.8},
  URN =		{urn:nbn:de:0030-drops-267789},
  doi =		{10.4230/LIPIcs.DNA.32.8},
  annote =	{Keywords: Equilibrium amplification, Dimerization networks, Strand commutation, Thermodynamics of amplification}
}

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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.

Cite as

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 Akef, Hamidreza

Amplification at Equilibrium: Structural and Thermodynamic Limitations, and Implementation

Abstract

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Computing and Bounding Equilibrium Concentrations in Athermic Chemical Systems

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