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LIPIcs, Volume 387
32nd International Conference on DNA Computing and Molecular Programming (DNA 32)
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- published at: 2026-07-27
- Publisher: Schloss Dagstuhl – Leibniz-Zentrum für Informatik
- ISBN: 978-3-95977-444-4
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Document
Complete Volume
LIPIcs, Volume 387, DNA 32, Complete Volume
Abstract
LIPIcs, Volume 387, DNA 32, Complete Volume
Cite as
32nd International Conference on DNA Computing and Molecular Programming (DNA 32). Leibniz International Proceedings in Informatics (LIPIcs), Volume 387, pp. 1-328, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@Proceedings{scalise_et_al:LIPIcs.DNA.32,
title = {{LIPIcs, Volume 387, DNA 32, Complete Volume}},
booktitle = {32nd International Conference on DNA Computing and Molecular Programming (DNA 32)},
pages = {1--328},
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},
URN = {urn:nbn:de:0030-drops-274859},
doi = {10.4230/LIPIcs.DNA.32},
annote = {Keywords: LIPIcs, Volume 387, DNA 32, Complete Volume}
}
Document
Front Matter
Front Matter, Table of Contents, Preface, Conference Organization
Abstract
Front Matter, Table of Contents, Preface, Conference Organization
Cite as
32nd International Conference on DNA Computing and Molecular Programming (DNA 32). Leibniz International Proceedings in Informatics (LIPIcs), Volume 387, pp. 0:i-0:xvi, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{scalise_et_al:LIPIcs.DNA.32.0,
author = {Scalise, Dominic and Schweller, Robert},
title = {{Front Matter, Table of Contents, Preface, Conference Organization}},
booktitle = {32nd International Conference on DNA Computing and Molecular Programming (DNA 32)},
pages = {0:i--0:xvi},
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.32.0},
URN = {urn:nbn:de:0030-drops-274836},
doi = {10.4230/LIPIcs.DNA.32.0},
annote = {Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
Sequential Non-Determinism in Tile Self-Assembly: A General Framework and an Application to Efficient Temperature-1 Self-Assembly of Squares
Abstract
In this paper, we work in a 2D version of the probabilistic variant of Winfree’s abstract Tile Assembly Model defined by Chandran, Gopalkrishnan and Reif (SICOMP 2012) in which attaching tiles are sampled uniformly with replacement. First, we develop a framework called "sequential non-determinism" for analyzing the probabilistic correctness of a non-deterministic, temperature-1 tile assembly system (TAS) in which most (but not all) tile attachments are deterministic and the non-deterministic attachments always occur in a specific order. Our main sequential non-determinism result equates the probabilistic correctness of such a TAS to a finite product of probabilities, each of which (1) corresponds to the probability of the correct type of tile attaching at a point where it is possible for two different types to attach, and (2) ignores all other tile attachments that do not affect the non-deterministic attachment. We then show that sequential non-determinism allows for efficient and geometrically expressive self-assembly. To that end, we constructively prove that for any positive integer N and any real δ ∈ (0,1), there exists a TAS that self-assembles into an N × N square with probability at least 1 - δ using only O(log N + log 1/(δ)) types of tiles. Our bound improves upon the previous state-of-the-art bound for this problem by Cook, Fu and Schweller (SODA 2011).
Cite as
David Furcy and Scott M. Summers. Sequential Non-Determinism in Tile Self-Assembly: A General Framework and an Application to Efficient Temperature-1 Self-Assembly of Squares. In 32nd International Conference on DNA Computing and Molecular Programming (DNA 32). Leibniz International Proceedings in Informatics (LIPIcs), Volume 387, pp. 1:1-1:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{furcy_et_al:LIPIcs.DNA.32.1,
author = {Furcy, David and Summers, Scott M.},
title = {{Sequential Non-Determinism in Tile Self-Assembly: A General Framework and an Application to Efficient Temperature-1 Self-Assembly of Squares}},
booktitle = {32nd International Conference on DNA Computing and Molecular Programming (DNA 32)},
pages = {1:1--1:18},
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.32.1},
URN = {urn:nbn:de:0030-drops-267710},
doi = {10.4230/LIPIcs.DNA.32.1},
annote = {Keywords: Self-assembly, tile assembly model, temperature 1, high probability self-assembly}
}
Document
Powers and Limitations of Synchronous Self-Assembly: Non-cooperative Assemblies and Limited Synchronization
Abstract
In abstract models of algorithmic self-assembly, synchronization between attachments has emerged as a crucial distinction between the classical asynchronous model (aTAM) and a new synchronous model, the syncTAM. This paper presents recent advances in gauging the additional power afforded by the syncTAM. While it is known that the syncTAM and the aTAM are each unable to fully simulate the other, this paper offers evidence that the syncTAM is computationally significantly more powerful than the aTAM, especially in the non-cooperative setting.
The additional power of the non-cooperative syncTAM is witnessed by the following constructions, all impossible in the non-cooperative aTAM: a flagpole, a strict self-assembly of a variant of the discrete Sierpinski triangle, and the ability to build the same assemblies (modulo scale factor) as directed aTAM systems.
The second topic is that of limited synchronization, wherein, when the number of attachments is smaller than some threshold l, they happen synchronously, but attachments in excess of that number must wait. In that context, the precise value of l is crucial, and changes to that value prevent simulation and can change which shapes can be obtained.
Cite as
Florent Becker, Phillip Drake, Matthew J. Patitz, and Ryder Smith. Powers and Limitations of Synchronous Self-Assembly: Non-cooperative Assemblies and Limited Synchronization. In 32nd International Conference on DNA Computing and Molecular Programming (DNA 32). Leibniz International Proceedings in Informatics (LIPIcs), Volume 387, pp. 2:1-2:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{becker_et_al:LIPIcs.DNA.32.2,
author = {Becker, Florent and Drake, Phillip and Patitz, Matthew J. and Smith, Ryder},
title = {{Powers and Limitations of Synchronous Self-Assembly: Non-cooperative Assemblies and Limited Synchronization}},
booktitle = {32nd International Conference on DNA Computing and Molecular Programming (DNA 32)},
pages = {2:1--2:23},
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.32.2},
URN = {urn:nbn:de:0030-drops-267728},
doi = {10.4230/LIPIcs.DNA.32.2},
annote = {Keywords: self-assembly, noncooperative self-assembly, models of computation, tile assembly systems}
}
Document
Shape Reachability in Oritatami Is Complete for P
Abstract
RNA co-transcriptional folding is a process in which an RNA sequence, or transcript, folds upon itself while being synthesized nucleotide by nucleotide according to its DNA template. Geary, Rothemund, and Andersen have demonstrated how to program a rectangular tile-like shape into (the DNA template of) an RNA transcript that folds co-transcriptionally into the shape in vitro. Using the oritatami model of co-transcriptional folding, we launch the study on the verification of co-transcriptionally folding systems. Shapes are the primary verification target of practical signification; it is abstracted as a set S of points on the 2D triangular grid. Thus, the shape reachability problem asks if the transcript of a given oritatami system goes through all and only the points in S and halts. We demonstrate a logspace reduction from the circuit value problem (CVP), a well-known P-complete problem, into a subproblem of the shape reachability whose input oritatami system is promised to be deterministic and at delay 3 (abstraction of the relative speed of local optimization to that of transcription), thus concluding that this subproblem DSR(3) is also P-complete. What to be verified may specify not only which points to be visited, but also which route should be taken (path reachability), and, moreover, how abstract nucleotides (beads) along the transcript should bind with each other (conformation reachability). We show that as long as the delay is bounded from above by a constant, the conformation reachability can be solved in logspace, and to this problem, path reachability can be reduced in logspace under the promise that a given oritatami system lets beads form as many bonds as possible (maximum arity).
Cite as
Sota Kano and Shinnosuke Seki. Shape Reachability in Oritatami Is Complete for P. In 32nd International Conference on DNA Computing and Molecular Programming (DNA 32). Leibniz International Proceedings in Informatics (LIPIcs), Volume 387, pp. 3:1-3:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{kano_et_al:LIPIcs.DNA.32.3,
author = {Kano, Sota and Seki, Shinnosuke},
title = {{Shape Reachability in Oritatami Is Complete for P}},
booktitle = {32nd International Conference on DNA Computing and Molecular Programming (DNA 32)},
pages = {3:1--3:18},
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.32.3},
URN = {urn:nbn:de:0030-drops-267737},
doi = {10.4230/LIPIcs.DNA.32.3},
annote = {Keywords: RNA co-transcriptional folding, Oritatami model, Reachability problems, P-completeness}
}
Document
PENSim: A Toolkit for PEN-DNA Systems
Abstract
The PEN-DNA toolbox has emerged as a versatile framework for implementing chemical reaction networks with DNA and enzymes, enabling applications ranging from molecular sensing to neural computation. A simulation tool, DACCAD, has provided a standardized approach for translating network schematics into dynamical models, facilitating in silico design and validation. However, the evolution of the PEN-DNA toolbox - particularly the transition from inhibitor-based regulation to drain-template-based inactivation - introduces mechanisms that are only partially captured by existing simulation frameworks, limiting the ability to reliably simulate and design recent PEN-DNA systems.
In this context, we introduce PENSim, a simulation package that aims to realign computational modeling with current experimental practices. By extending the repertoire of simulated reactions and incorporating thermodynamic dependencies into kinetic rate calculations via NUPACK, PENSim enables a more faithful representation of modern PEN-DNA systems. In particular, accounting for thermodynamic effects is essential for accurately modeling inactivation via drain templates.
PENSim is validated through qualitative reproduction of existing experimental results, including inactivation-driven bistability, microRNA detection circuits, and linear classifiers based on neural networks. By bridging legacy modeling approaches with recent experimental advances, PENSim provides a step toward more realistic and flexible in silico design of systems based on the PEN-DNA toolbox.
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Gwendal Ducloz and Nicolas Schabanel. PENSim: A Toolkit for PEN-DNA Systems. In 32nd International Conference on DNA Computing and Molecular Programming (DNA 32). Leibniz International Proceedings in Informatics (LIPIcs), Volume 387, pp. 4:1-4:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{ducloz_et_al:LIPIcs.DNA.32.4,
author = {Ducloz, Gwendal and Schabanel, Nicolas},
title = {{PENSim: A Toolkit for PEN-DNA Systems}},
booktitle = {32nd International Conference on DNA Computing and Molecular Programming (DNA 32)},
pages = {4:1--4:24},
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.32.4},
URN = {urn:nbn:de:0030-drops-267743},
doi = {10.4230/LIPIcs.DNA.32.4},
annote = {Keywords: PEN-DNA toolbox, DNA circuit simulation, DNA reaction kinetics, Enzymatic DNA reaction kinetics}
}
Document
Geometric Constraint Optimization for Localized Strand Displacement Reactions
Abstract
Localized molecular circuits offer practical advantages over those implemented using components freely diffusing in bulk solution, such as computation speed and component reuse. A common framework for implementing such circuits uses DNA strand displacement reactions with components localized via tethering to a DNA origami tile. While a number of papers have demonstrated the capability of such circuits, design tools for enumerating localized reactions and analyzing their behavior are relatively scarce. The key difficulty in modeling such circuits is that the geometric constraints imposed by the tethering of specific components at specific points on the tile surface are critical in determining whether or not a particular reaction may occur. In previous work, we deployed simple techniques based on random sampling of the structure space in an attempt to find geometric structures for candidate reaction products that satisfy all of the geometric constraints. In this paper, we show that this approach can be enhanced by using an optimization algorithm that takes initial guessed structures that fail to satisfy certain constraints and attempts to refine them into structures that do satisfy all of the constraints. We illustrate this approach on simple example reactions as well as a strand displacement-based signal transmission example from the literature. This work thus advances the state of the art in modeling tools for localized molecular circuits.
Cite as
Matthew R. Lakin. Geometric Constraint Optimization for Localized Strand Displacement Reactions. In 32nd International Conference on DNA Computing and Molecular Programming (DNA 32). Leibniz International Proceedings in Informatics (LIPIcs), Volume 387, pp. 5:1-5:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{lakin:LIPIcs.DNA.32.5,
author = {Lakin, Matthew R.},
title = {{Geometric Constraint Optimization for Localized Strand Displacement Reactions}},
booktitle = {32nd International Conference on DNA Computing and Molecular Programming (DNA 32)},
pages = {5:1--5:23},
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.32.5},
URN = {urn:nbn:de:0030-drops-267756},
doi = {10.4230/LIPIcs.DNA.32.5},
annote = {Keywords: Localized circuits, reaction enumeration, DNA strand displacement, constraint solving, geometry, molecular computing}
}
Document
Reverse-Robust Computation with Chemical Reaction Networks
Abstract
Chemical reaction networks, or CRNs, are known to stably compute semilinear Boolean-valued predicates and functions, provided that all reactions are irreversible. However, this property does not hold for wet-lab implementations, as all chemical reactions are reversible, even at very slow rates. We study the computational power of CRNs under the reverse-robust computation model, where reactions are permitted to occur either in forward or in reverse up to a cutoff point, after which they may only occur in forward. Our main results show that all semilinear predicates and all semilinear functions can be computed reverse-robustly, and in fact, that existing constructions continue to hold under the reverse-robust computational model. A key tool used to prove correctness under the reverse-robust computation model is invariants: linear (or linear modulo some m) combinations of the counts of the species that are preserved by all reactions.
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Ravi Kini and David Doty. Reverse-Robust Computation with Chemical Reaction Networks. In 32nd International Conference on DNA Computing and Molecular Programming (DNA 32). Leibniz International Proceedings in Informatics (LIPIcs), Volume 387, pp. 6:1-6:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{kini_et_al:LIPIcs.DNA.32.6,
author = {Kini, Ravi and Doty, David},
title = {{Reverse-Robust Computation with Chemical Reaction Networks}},
booktitle = {32nd International Conference on DNA Computing and Molecular Programming (DNA 32)},
pages = {6:1--6:16},
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.32.6},
URN = {urn:nbn:de:0030-drops-267769},
doi = {10.4230/LIPIcs.DNA.32.6},
annote = {Keywords: chemical reaction networks, reverse-robust computation, semilinear}
}
Document
Scaling up Thermodynamically Favoured Scaffolded DNA Computing by Sculpting the Energy Landscape
Abstract
Thermodynamically favoured molecular computation offers advantages over more typical out-of-equilibrium computing, including simpler experimental protocols and automatic error correction. But as systems scale to large sizes the number of states increases dramatically, increasing the need for efficiently navigable energy landscapes. We give results in two theoretical models of Scaffolded DNA Computing (SDC), a recently implemented form of thermodynamically favoured DNA computing [Stérin, Eshra et al, bioRχiv 2025]. We show their computational power is characterised by logarithmic space complexity classes, meaning they are expressive at scale. Our first energy landscape result is an exact relation between the probability of target configurations (outputs), temperature and DNA sequence domain length, showing that domain length merely logarithmic in scaffold length is sufficient for the probability of the target configuration to outcompete all off-target structures. We show that even in the presence of imperfect/unequal binding strength scaffold domains we still achieve good kinetics: O(N²) or O(N³) expected completion time, depending on model assumptions, and there are even narrow conditions that yield fast O(N)-time kinetics. Finally, we address a thorny scaling problem: SDC outputs often have repeated compute domains and any binding energy variances get exaggerated under repetition making errors favourable, but we give a construction that reprograms the energy landscape to convert such a non-isoenergetic system into one with almost perfectly isoenergetic energy plateaus. We also show that systems maintain good (polynomial-time) kinetics, even in the face of a poor (uphill) scaffold energy landscape. These results give a roadmap for scaling up the SDC while highlighting the role kinetics and energy landscape programming could play in thermodynamically-favoured computing more generally.
Cite as
Joshua Petrack, Constantine G. Evans, Angel Cervera Roldan, Mahboobeh Enayati, and Damien Woods. Scaling up Thermodynamically Favoured Scaffolded DNA Computing by Sculpting the Energy Landscape. In 32nd International Conference on DNA Computing and Molecular Programming (DNA 32). Leibniz International Proceedings in Informatics (LIPIcs), Volume 387, pp. 7:1-7:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{petrack_et_al:LIPIcs.DNA.32.7,
author = {Petrack, Joshua and Evans, Constantine G. and Cervera Roldan, Angel and Enayati, Mahboobeh and Woods, Damien},
title = {{Scaling up Thermodynamically Favoured Scaffolded DNA Computing by Sculpting the Energy Landscape}},
booktitle = {32nd International Conference on DNA Computing and Molecular Programming (DNA 32)},
pages = {7:1--7:22},
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.32.7},
URN = {urn:nbn:de:0030-drops-267776},
doi = {10.4230/LIPIcs.DNA.32.7},
annote = {Keywords: Thermodynamically favoured computing, molecular programming, DNA computing, kinetics, computational power, Scaffolded DNA Computer}
}
Document
Amplification at Equilibrium: Structural and Thermodynamic Limitations, and Implementation
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.
Cite as
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}
}
Document
Thermodynamic Binding Networks Capture Equilibrium Monomer-Polymer Thermodynamics
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.
Cite as
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}
}
Document
Modularity of Signal Propagation Networks in the Thermodynamic Binding Network Model
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.
Cite as
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}
}
Document
Universal Spatial Distribution Approximation in Equilibrium Lattice Models with Local Pairwise Interactions
Abstract
Universality is one of the defining hallmarks of a useful neural network model: it means that the model is expressive enough, in principle, to learn arbitrary target behavior rather than being limited to a narrow class. Inspired by rigorous formal analogies between stochastic neural networks and lattice models in which molecules occupy discrete sites, contribute species-dependent interaction energies with neighbors, and rearrange according to the Boltzmann distribution, we ask whether interactions can be programmed to yield arbitrary spatial distributions. At the level of fine-grained spatial arrangements of species, universality fails: arbitrary spatial microstate distributions cannot be represented, as shown by a counting argument and explicit construction of unrepresentable distributions. Yet, for a natural observable - spatial patterns of molecular labels - universality can be achieved. We show that a grand-canonical lattice model of anisotropic molecules is universal for arbitrary label distributions, and a similar model with isotropic molecules is also universal given a simple symmetry-breaking boundary condition. Our results suggest that equilibrium systems of multivalent molecules undergoing stochastic rearrangement governed by local pairwise interactions can act similarly to probabilistic neural networks: with sufficient microstate detail in hidden dimensions, they can be universal in a meaningful macrostate observable.
Cite as
Cameron Chalk and Erik Winfree. Universal Spatial Distribution Approximation in Equilibrium Lattice Models with Local Pairwise Interactions. In 32nd International Conference on DNA Computing and Molecular Programming (DNA 32). Leibniz International Proceedings in Informatics (LIPIcs), Volume 387, pp. 11:1-11:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{chalk_et_al:LIPIcs.DNA.32.11,
author = {Chalk, Cameron and Winfree, Erik},
title = {{Universal Spatial Distribution Approximation in Equilibrium Lattice Models with Local Pairwise Interactions}},
booktitle = {32nd International Conference on DNA Computing and Molecular Programming (DNA 32)},
pages = {11:1--11:24},
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.32.11},
URN = {urn:nbn:de:0030-drops-267812},
doi = {10.4230/LIPIcs.DNA.32.11},
annote = {Keywords: universality, molecular programming, neural networks, self-assembly}
}
Document
Scalable Enumeration of Pareto-Optimal Polymers for Computing Equilibrium Concentrations
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.
Cite as
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}
}
Document
Contrastive Hebbian Learning for Multicomponent Liquids
Abstract
Molecules with designed interactions can serve as substrates for information processing; demonstrated examples include algorithmic self-assembly of DNA tiles and DNA strand displacement reactions. These two well-established paradigms correspond to solid-phase-like behavior, where spatially structured molecular assemblies grow by crystalline attachment, and gas-phase-like behavior, where a dilute mixture of freely diffusing molecules is governed by mass-action kinetics of reactions. A third paradigm, liquid-liquid phase separation, is a fundamental phenomenon in physical and biological systems, giving rise to membraneless compartments that facilitate complex information processing. Recent studies have shown that multicomponent liquid mixtures described by lattice models are analogous to Boltzmann machines and can implement neural computation. Mean-field models have also suggested a connection to Hopfield networks and illustrated complex decision-making during condensation from a reservoir. As an alternative to previous approaches to train liquid interaction energies using backpropagation through a loss function, here we derive "local" learning rules based on contrastive Hebbian learning that may be more biologically and physically plausible. The trained systems demonstrate a range of computational tasks, including associative recall, linear and nonlinear input-output relations, pattern classification, and spatial phase separation. Our work suggests that the computational potential of liquid-phase molecular systems could be unlocked in real physical systems with local learning rules.
Cite as
Yancheng Du, Cameron Chalk, Salvador Buse, Lulu Qian, and Erik Winfree. Contrastive Hebbian Learning for Multicomponent Liquids. In 32nd International Conference on DNA Computing and Molecular Programming (DNA 32). Leibniz International Proceedings in Informatics (LIPIcs), Volume 387, pp. 13:1-13:27, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{du_et_al:LIPIcs.DNA.32.13,
author = {Du, Yancheng and Chalk, Cameron and Buse, Salvador and Qian, Lulu and Winfree, Erik},
title = {{Contrastive Hebbian Learning for Multicomponent Liquids}},
booktitle = {32nd International Conference on DNA Computing and Molecular Programming (DNA 32)},
pages = {13:1--13:27},
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.32.13},
URN = {urn:nbn:de:0030-drops-267838},
doi = {10.4230/LIPIcs.DNA.32.13},
annote = {Keywords: multicomponent liquid, liquid-liquid phase separation, continuous Hopfield network, contrastive Hebbian learning}
}
Document
Bounded Analog Complexity
Abstract
Current analog complexity theory, built on the General-Purpose Analog Computer (GPAC) model and polynomial ODEs, allows unbounded state variables - an assumption that is physically unrealistic for chemical reaction networks and other laboratory-scale analog computers. We develop a bounded analog complexity theory in which all state variables remain in compact intervals and physical time is the only diverging resource.
Our main technical contribution is bounded surrogate compilation, a compilation framework that transforms unbounded polynomial ODE systems into bounded ones while preserving computational limits and time-to-precision guarantees. We prove that on compact domains, physical time and trajectory length differ by at most constant factors; combined with the Bournez-Graça-Pouly characterization, this yields: bounded-GPAC polynomial time equals 𝐏 over the reals.
We exhibit concrete constructions demonstrating fine-grained bounded time complexity - a tunable polynomial-degree family, a Lambert-W-based system achieving Θ(rlog r) time-to-precision (where r is the desired precision parameter, in nats: |x(t)-α| < e^{-r}), and an iterated-logarithm tower realizing arbitrarily high complexity classes - all for the task of computing the constant 1. We show that bounded GPACs are closed under exponentiation (α^β) with time complexity equal to the harder input, and that the full GPAC-to-CRN compilation pipeline preserves time complexity class via a low-pass filter analysis of readout modules.
Cite as
Ho-Lin Chen and Xiang Huang. Bounded Analog Complexity. In 32nd International Conference on DNA Computing and Molecular Programming (DNA 32). Leibniz International Proceedings in Informatics (LIPIcs), Volume 387, pp. 14:1-14:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)
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@InProceedings{chen_et_al:LIPIcs.DNA.32.14,
author = {Chen, Ho-Lin and Huang, Xiang},
title = {{Bounded Analog Complexity}},
booktitle = {32nd International Conference on DNA Computing and Molecular Programming (DNA 32)},
pages = {14:1--14:22},
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.32.14},
URN = {urn:nbn:de:0030-drops-267841},
doi = {10.4230/LIPIcs.DNA.32.14},
annote = {Keywords: Analog computation, GPAC, bounded complexity, chemical reaction networks, polynomial ODE}
}