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Documents authored by Winfree, Erik

Document
DOI: 10.4230/LIPIcs.DNA.32.11
Universal Spatial Distribution Approximation in Equilibrium Lattice Models with Local Pairwise Interactions

Authors: Cameron Chalk and Erik Winfree

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

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.
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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
DOI: 10.4230/LIPIcs.DNA.32.13
Contrastive Hebbian Learning for Multicomponent Liquids

Authors: Yancheng Du, Cameron Chalk, Salvador Buse, Lulu Qian, and Erik Winfree

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

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
DOI: 10.4230/LIPIcs.DNA.31.4
Differentiable Programming of Indexed Chemical Reaction Networks and Reaction-Diffusion Systems

Authors: Inhoo Lee, Salvador Buse, and Erik Winfree

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

Abstract
Many molecular systems are best understood in terms of prototypical species and reactions. The central dogma and related biochemistry are rife with examples: gene i is transcribed into RNA i, which is translated into protein i; kinase n phosphorylates substrate m; protein p dimerizes with protein q. Engineered nucleic acid systems also often have this form: oligonucleotide i hybridizes to complementary oligonucleotide j; signal strand n displaces the output of seesaw gate m; hairpin p triggers the opening of target q. When there are many variants of a small number of prototypes, it can be conceptually cleaner and computationally more efficient to represent the full system in terms of indexed species (e.g. for dimerization, M_p, D_pq) and indexed reactions (M_p + M_q → D_pq). Here, we formalize the Indexed Chemical Reaction Network (ICRN) model and describe a Python software package designed to simulate such systems in the well-mixed and reaction-diffusion settings, using a differentiable programming framework originally developed for large-scale neural network models, taking advantage of GPU acceleration when available. Notably, this framework makes it straightforward to train the models’ initial conditions and rate constants to optimize a target behavior, such as matching experimental data, performing a computation, or exhibiting spatial pattern formation. The natural map of indexed chemical reaction networks onto neural network formalisms provides a tangible yet general perspective for translating concepts and techniques from the theory and practice of neural computation into the design of biomolecular systems.
Cite as

Inhoo Lee, Salvador Buse, and Erik Winfree. Differentiable Programming of Indexed Chemical Reaction Networks and Reaction-Diffusion Systems. In 31st International Conference on DNA Computing and Molecular Programming (DNA 31). Leibniz International Proceedings in Informatics (LIPIcs), Volume 347, pp. 4:1-4:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{lee_et_al:LIPIcs.DNA.31.4,
  author =	{Lee, Inhoo and Buse, Salvador and Winfree, Erik},
  title =	{{Differentiable Programming of Indexed Chemical Reaction Networks and Reaction-Diffusion Systems}},
  booktitle =	{31st International Conference on DNA Computing and Molecular Programming (DNA 31)},
  pages =	{4:1--4:23},
  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.31.4},
  URN =		{urn:nbn:de:0030-drops-238534},
  doi =		{10.4230/LIPIcs.DNA.31.4},
  annote =	{Keywords: Differentiable Programming, Chemical Reaction Networks, Reaction-Diffusion Systems}
}
Document
DOI: 10.4230/LIPIcs.DNA.30.5
Learning and Inference in a Lattice Model of Multicomponent Condensates

Authors: Cameron Chalk, Salvador Buse, Krishna Shrinivas, Arvind Murugan, and Erik Winfree

Published in: LIPIcs, Volume 314, 30th International Conference on DNA Computing and Molecular Programming (DNA 30) (2024)

Abstract
Life is chemical intelligence. What is the source of intelligent behavior in molecular systems? Here we illustrate how, in contrast to the common belief that energy use in non-equilibrium reactions is essential, the detailed balance equilibrium properties of multicomponent liquid interactions are sufficient for sophisticated information processing. Our approach derives from the classical Boltzmann machine model for probabilistic neural networks, inheriting key principles such as representing probability distributions via quadratic energy functions, clamping input variables to infer conditional probability distributions, accommodating omnidirectional computation, and learning energy parameters via a wake phase / sleep phase algorithm that performs gradient descent on the relative entropy with respect to the target distribution. While the cubic lattice model of multicomponent liquids is standard, the behaviors exhibited by the trained molecules capture both previously-observed phenomena such as core-shell condensate architectures as well as novel phenomena such as an analog of Hopfield associative memories that perform recall by contact with a patterned surface. Our final example demonstrates equilibrium classification of MNIST digits. Experimental implementation using DNA nanostar liquids is conceptually straightforward.
Cite as

Cameron Chalk, Salvador Buse, Krishna Shrinivas, Arvind Murugan, and Erik Winfree. Learning and Inference in a Lattice Model of Multicomponent Condensates. In 30th International Conference on DNA Computing and Molecular Programming (DNA 30). Leibniz International Proceedings in Informatics (LIPIcs), Volume 314, pp. 5:1-5:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{chalk_et_al:LIPIcs.DNA.30.5,
  author =	{Chalk, Cameron and Buse, Salvador and Shrinivas, Krishna and Murugan, Arvind and Winfree, Erik},
  title =	{{Learning and Inference in a Lattice Model of Multicomponent Condensates}},
  booktitle =	{30th International Conference on DNA Computing and Molecular Programming (DNA 30)},
  pages =	{5:1--5:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-344-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{314},
  editor =	{Seki, Shinnosuke and Stewart, Jaimie Marie},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DNA.30.5},
  URN =		{urn:nbn:de:0030-drops-209330},
  doi =		{10.4230/LIPIcs.DNA.30.5},
  annote =	{Keywords: multicomponent liquid, Boltzmann machine, phase separation}
}
Document
DOI: 10.4230/LIPIcs.DNA.29.5
Revisiting Hybridization Kinetics with Improved Elementary Step Simulation

Authors: Jordan Lovrod, Boyan Beronov, Chenwei Zhang, Erik Winfree, and Anne Condon

Published in: LIPIcs, Volume 276, 29th International Conference on DNA Computing and Molecular Programming (DNA 29) (2023)

Abstract
Nucleic acid strands, which react by forming and breaking Watson-Crick base pairs, can be designed to form complex nanoscale structures or devices. Controlling such systems requires accurate predictions of the reaction rate and of the folding pathways of interacting strands. Simulators such as Multistrand model these kinetic properties using continuous-time Markov chains (CTMCs), whose states and transitions correspond to secondary structures and elementary base pair changes, respectively. The transient dynamics of a CTMC are determined by a kinetic model, which assigns transition rates to pairs of states, and the rate of a reaction can be estimated using the mean first passage time (MFPT) of its CTMC. However, use of Multistrand is limited by its slow runtime, particularly on rare events, and the quality of its rate predictions is compromised by a poorly-calibrated and simplistic kinetic model. The former limitation can be addressed by constructing truncated CTMCs, which only include a small subset of states and transitions, selected either manually or through simulation. As a first step to address the latter limitation, Bayesian posterior inference in an Arrhenius-type kinetic model was performed in earlier work, using a small experimental dataset of DNA reaction rates and a fixed set of manually truncated CTMCs, which we refer to as Assumed Pathway (AP) state spaces. In this work we extend this approach, by introducing a new prior model that is directly motivated by the physical meaning of the parameters and that is compatible with experimental measurements of elementary rates, and by using a larger dataset of 1105 reactions as well as larger truncated state spaces obtained from the recently introduced stochastic Pathway Elaboration (PE) method. We assess the quality of the resulting posterior distribution over kinetic parameters, as well as the quality of the posterior reaction rates predicted using AP and PE state spaces. Finally, we use the newly parameterised PE state spaces and Multistrand simulations to investigate the strong variation of helix hybridization reaction rates in a dataset of Hata et al. While we find strong evidence for the nucleation-zippering model of hybridization, in the classical sense that the rate-limiting phase is composed of elementary steps reaching a small "nucleus" of critical stability, the strongly sequence-dependent structure of the trajectory ensemble up to nucleation appears to be much richer than assumed in the model by Hata et al. In particular, rather than being dominated by the collision probability of nucleation sites, the trajectory segment between first binding and nucleation tends to visit numerous secondary structures involving misnucleation and hairpins, and has a sizeable effect on the probability of overcoming the nucleation barrier.
Cite as

Jordan Lovrod, Boyan Beronov, Chenwei Zhang, Erik Winfree, and Anne Condon. Revisiting Hybridization Kinetics with Improved Elementary Step Simulation. In 29th International Conference on DNA Computing and Molecular Programming (DNA 29). Leibniz International Proceedings in Informatics (LIPIcs), Volume 276, pp. 5:1-5:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{lovrod_et_al:LIPIcs.DNA.29.5,
  author =	{Lovrod, Jordan and Beronov, Boyan and Zhang, Chenwei and Winfree, Erik and Condon, Anne},
  title =	{{Revisiting Hybridization Kinetics with Improved Elementary Step Simulation}},
  booktitle =	{29th International Conference on DNA Computing and Molecular Programming (DNA 29)},
  pages =	{5:1--5:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-297-6},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{276},
  editor =	{Chen, Ho-Lin and Evans, Constantine G.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DNA.29.5},
  URN =		{urn:nbn:de:0030-drops-187889},
  doi =		{10.4230/LIPIcs.DNA.29.5},
  annote =	{Keywords: DNA reaction kinetics, kinetic model calibration, simulation-based Bayesian inference, continuous-time Markov chains}
}
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