DROPS

Volume

LIPIcs, Volume 174

26th International Conference on DNA Computing and Molecular Programming (DNA 26)

DNA 26, September 14-17, 2020, Oxford, UK (Virtual Conference)

Editors: Cody Geary and Matthew J. Patitz

Document

Algorithmic Foundations of Programmable Matter (Dagstuhl Seminar 23091)

Authors: Aaron Becker, Sándor Fekete, Irina Kostitsyna, Matthew J. Patitz, Damien Woods, and Ioannis Chatzigiannakis

Published in: Dagstuhl Reports, Volume 13, Issue 2 (2023)

Abstract

This report documents the program and the outcomes of Dagstuhl Seminar 23091, "Algorithmic Foundations of Programmable Matter", a new and emerging field that combines theoretical work on algorithms with a wide spectrum of practical applications that reach all the way from small-scale embedded systems to cyber-physical structures at nano-scale. The aim of this seminar was to bring together researchers from computational geometry, distributed computing, DNA computing, and swarm robotics who have worked on programmable matter to inform one another about the newest developments in each area and to discuss future models, approaches, and directions for new research. Similar to the first two Dagstuhl Seminars on programmable matter (16271 and 18331), we did focus on some basic problems, but also considered new problems that were now within reach to be studied.

Cite as

Aaron Becker, Sándor Fekete, Irina Kostitsyna, Matthew J. Patitz, Damien Woods, and Ioannis Chatzigiannakis. Algorithmic Foundations of Programmable Matter (Dagstuhl Seminar 23091). In Dagstuhl Reports, Volume 13, Issue 2, pp. 183-198, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)

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@Article{becker_et_al:DagRep.13.2.183,
  author =	{Becker, Aaron and Fekete, S\'{a}ndor and Kostitsyna, Irina and Patitz, Matthew J. and Woods, Damien and Chatzigiannakis, Ioannis},
  title =	{{Algorithmic Foundations of Programmable Matter (Dagstuhl Seminar 23091)}},
  pages =	{183--198},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2023},
  volume =	{13},
  number =	{2},
  editor =	{Becker, Aaron and Fekete, S\'{a}ndor and Kostitsyna, Irina and Patitz, Matthew J. and Woods, Damien and Chatzigiannakis, Ioannis},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.13.2.183},
  URN =		{urn:nbn:de:0030-drops-191848},
  doi =		{10.4230/DagRep.13.2.183},
  annote =	{Keywords: computational geometry, distributed algorithms, DNA computing, programmable matter, swarm robotics}
}

Document

DOI: 10.4230/LIPIcs.DNA.29.7

Accelerating Self-Assembly of Crisscross Slat Systems

Authors: David Doty, Hunter Fleming, Daniel Hader, Matthew J. Patitz, and Lukas A. Vaughan

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

Abstract

We present an abstract model of self-assembly of systems composed of "crisscross slats", which have been experimentally implemented as a single-stranded piece of DNA [Minev et al., 2021] or as a complete DNA origami structure [Wintersinger et al., 2022]. We then introduce a more physically realistic "kinetic" model and show how important constants in the model were derived and tuned, and compare simulation-based results to experimental results [Minev et al., 2021; Wintersinger et al., 2022]. Using these models, we show how we can apply optimizations to designs of slat systems in order to lower the numbers of unique slat types required to build target structures. In general, we apply two types of techniques to achieve greatly reduced numbers of slat types. Similar to the experimental work implementing DNA origami-based slats, in our designs the slats oriented in horizontal and vertical directions are each restricted to their own plane and sets of them overlap each other in square regions which we refer to as macrotiles. Our first technique extends their previous work of reusing slat types within macrotiles and requires analyses of binding domain patterns to determine the potential for errors consisting of incorrect slat types attaching at undesired translations and reflections. The second technique leverages the power of algorithmic self-assembly to efficiently reuse entire macrotiles which self-assemble in patterns following designed algorithms that dictate the dimensions and patterns of growth. Using these designs, we demonstrate that in kinetic simulations the systems with reduced numbers of slat types self-assemble more quickly than those with greater numbers. This provides evidence that such optimizations will also result in greater assembly speeds in experimental systems. Furthermore, the reduced numbers of slat types required have the potential to vastly reduce the cost and number of lab steps for crisscross assembly experiments.

Cite as

David Doty, Hunter Fleming, Daniel Hader, Matthew J. Patitz, and Lukas A. Vaughan. Accelerating Self-Assembly of Crisscross Slat Systems. In 29th International Conference on DNA Computing and Molecular Programming (DNA 29). Leibniz International Proceedings in Informatics (LIPIcs), Volume 276, pp. 7:1-7:23, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)

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@InProceedings{doty_et_al:LIPIcs.DNA.29.7,
  author =	{Doty, David and Fleming, Hunter and Hader, Daniel and Patitz, Matthew J. and Vaughan, Lukas A.},
  title =	{{Accelerating Self-Assembly of Crisscross Slat Systems}},
  booktitle =	{29th International Conference on DNA Computing and Molecular Programming (DNA 29)},
  pages =	{7:1--7:23},
  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.29.7},
  URN =		{urn:nbn:de:0030-drops-187908},
  doi =		{10.4230/LIPIcs.DNA.29.7},
  annote =	{Keywords: DNA origami, self-assembly, kinetic modeling, computational modeling}
}

Document

Track A: Algorithms, Complexity and Games

DOI: 10.4230/LIPIcs.ICALP.2023.71

The Impacts of Dimensionality, Diffusion, and Directedness on Intrinsic Cross-Model Simulation in Tile-Based Self-Assembly

Authors: Daniel Hader and Matthew J. Patitz

Published in: LIPIcs, Volume 261, 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)

Abstract

Algorithmic self-assembly occurs when components in a disorganized collection autonomously combine to form structures and, by their design and the dynamics of the system, are forced to intrinsically follow the execution of algorithms. Motivated by applications in DNA-nanotechnology, theoretical investigations in algorithmic tile-based self-assembly have blossomed into a mature theory with research strongly leveraging tools from computability theory, complexity theory, information theory, and graph theory to develop a wide range of models and to show that many are computationally universal, while also exposing a wide variety of powers and limitations of each. In addition to computational universality, the abstract Tile-Assembly Model (aTAM) was shown to be intrinsically universal (FOCS 2012), a strong notion of completeness where a single tile set is capable of simulating the full dynamics of all systems within the model; however, this result fundamentally required non-deterministic tile attachments. This was later confirmed necessary when it was shown that the class of directed aTAM systems, those in which all possible sequences of tile attachments eventually result in the same terminal assembly, is not intrinsically universal (FOCS 2016). Furthermore, it was shown that the non-cooperative aTAM, where tiles only need to match on 1 side to bind rather than 2 or more, is not intrinsically universal (SODA 2014) nor computationally universal (STOC 2017). Building on these results to further investigate the impacts of other dynamics, Hader et al. examined several tile-assembly models which varied across (1) the numbers of dimensions used, (2) restrictions imposed on the diffusion of tiles through space, and (3) whether each system is directed, and determined which models exhibited intrinsic universality (SODA 2020). Such results have shed much light on the roles of various aspects of the dynamics of tile-assembly and their effects on the universality of each model. In this paper we extend that previous work to provide direct comparisons of the various models against each other by considering intrinsic simulations between models. Our results show that in some cases, one model is strictly more powerful than another, and in others, pairs of models have mutually exclusive capabilities. This direct comparison of models helps expose the impacts of these three important aspects of self-assembling systems, and further helps to define a hierarchy of tile-assembly models analogous to the hierarchies studied in traditional models of computation.

Cite as

Daniel Hader and Matthew J. Patitz. The Impacts of Dimensionality, Diffusion, and Directedness on Intrinsic Cross-Model Simulation in Tile-Based Self-Assembly. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 71:1-71:19, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)

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@InProceedings{hader_et_al:LIPIcs.ICALP.2023.71,
  author =	{Hader, Daniel and Patitz, Matthew J.},
  title =	{{The Impacts of Dimensionality, Diffusion, and Directedness on Intrinsic Cross-Model Simulation in Tile-Based Self-Assembly}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{71:1--71:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.71},
  URN =		{urn:nbn:de:0030-drops-181238},
  doi =		{10.4230/LIPIcs.ICALP.2023.71},
  annote =	{Keywords: Tile-Assembly, Tiles, aTAM, Intrinsic Simulation, Simulation}
}

Document

Extended Abstract

DOI: 10.4230/LIPIcs.DNA.28.2

Universal Shape Replication via Self-Assembly with Signal-Passing Tiles (Extended Abstract)

Authors: Andrew Alseth, Daniel Hader, and Matthew J. Patitz

Published in: LIPIcs, Volume 238, 28th International Conference on DNA Computing and Molecular Programming (DNA 28) (2022)

Abstract

In this paper, we investigate shape-assembling power of a tile-based model of self-assembly called the Signal-Passing Tile Assembly Model (STAM). In this model, the glues that bind tiles together can be turned on and off by the binding actions of other glues via "signals". In fact, we prove our positive results in a version of the model in which it is slightly more difficult to work (where tiles are allowed to rotate) but show that they also hold in the standard STAM. Specifically, the problem we investigate is "shape replication" wherein, given a set of input assemblies of arbitrary shape, a system must construct an arbitrary number of assemblies with the same shapes and, with the exception of size-bounded junk assemblies that result from the process, no others. We provide the first fully universal shape replication result, namely a single tile set capable of performing shape replication on arbitrary sets of any 3-dimensional shapes without requiring any scaling or pre-encoded information in the input assemblies. Our result requires the input assemblies to be composed of signal-passing tiles whose glues can be deactivated to allow deconstruction of those assemblies, which we also prove is necessary by showing that there are shapes whose geometry cannot be replicated without deconstruction. Additionally, we modularize our construction to create systems capable of creating binary encodings of arbitrary shapes, and building arbitrary shapes from their encodings. Because the STAM is capable of universal computation, this then allows for arbitrary programs to be run within an STAM system, using the shape encodings as input, so that any computable transformation can be performed on the shapes.

Cite as

Andrew Alseth, Daniel Hader, and Matthew J. Patitz. Universal Shape Replication via Self-Assembly with Signal-Passing Tiles (Extended Abstract). In 28th International Conference on DNA Computing and Molecular Programming (DNA 28). Leibniz International Proceedings in Informatics (LIPIcs), Volume 238, pp. 2:1-2:24, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)

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@InProceedings{alseth_et_al:LIPIcs.DNA.28.2,
  author =	{Alseth, Andrew and Hader, Daniel and Patitz, Matthew J.},
  title =	{{Universal Shape Replication via Self-Assembly with Signal-Passing Tiles}},
  booktitle =	{28th International Conference on DNA Computing and Molecular Programming (DNA 28)},
  pages =	{2:1--2:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-253-2},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{238},
  editor =	{Ouldridge, Thomas E. and Wickham, Shelley F. J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DNA.28.2},
  URN =		{urn:nbn:de:0030-drops-167876},
  doi =		{10.4230/LIPIcs.DNA.28.2},
  annote =	{Keywords: Algorithmic self-assembly, Tile Assembly Model, shape replication}
}

Document

DOI: 10.4230/LIPIcs.DNA.27.3

Self-Replication via Tile Self-Assembly (Extended Abstract)

Authors: Andrew Alseth, Daniel Hader, and Matthew J. Patitz

Published in: LIPIcs, Volume 205, 27th International Conference on DNA Computing and Molecular Programming (DNA 27) (2021)

Abstract

In this paper we present a model containing modifications to the Signal-passing Tile Assembly Model (STAM), a tile-based self-assembly model whose tiles are capable of activating and deactivating glues based on the binding of other glues. These modifications consist of an extension to 3D, the ability of tiles to form "flexible" bonds that allow bound tiles to rotate relative to each other, and allowing tiles of multiple shapes within the same system. We call this new model the STAM*, and we present a series of constructions within it that are capable of self-replicating behavior. Namely, the input seed assemblies to our STAM* systems can encode either "genomes" specifying the instructions for building a target shape, or can be copies of the target shape with instructions built in. A universal tile set exists for any target shape (at scale factor 2), and from a genome assembly creates infinite copies of the genome as well as the target shape. An input target structure, on the other hand, can be "deconstructed" by the universal tile set to form a genome encoding it, which will then replicate and also initiate the growth of copies of assemblies of the target shape. Since the lengths of the genomes for these constructions are proportional to the number of points in the target shape, we also present a replicator which utilizes hierarchical self-assembly to greatly reduce the size of the genomes required. The main goals of this work are to examine minimal requirements of self-assembling systems capable of self-replicating behavior, with the aim of better understanding self-replication in nature as well as understanding the complexity of mimicking it.

Cite as

Andrew Alseth, Daniel Hader, and Matthew J. Patitz. Self-Replication via Tile Self-Assembly (Extended Abstract). In 27th International Conference on DNA Computing and Molecular Programming (DNA 27). Leibniz International Proceedings in Informatics (LIPIcs), Volume 205, pp. 3:1-3:22, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)

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@InProceedings{alseth_et_al:LIPIcs.DNA.27.3,
  author =	{Alseth, Andrew and Hader, Daniel and Patitz, Matthew J.},
  title =	{{Self-Replication via Tile Self-Assembly (Extended Abstract)}},
  booktitle =	{27th International Conference on DNA Computing and Molecular Programming (DNA 27)},
  pages =	{3:1--3:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-205-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{205},
  editor =	{Lakin, Matthew R. and \v{S}ulc, Petr},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DNA.27.3},
  URN =		{urn:nbn:de:0030-drops-146707},
  doi =		{10.4230/LIPIcs.DNA.27.3},
  annote =	{Keywords: Algorithmic self-assembly, tile assembly model, self-replication}
}

Document

Complete Volume

DOI: 10.4230/LIPIcs.DNA.2020

LIPIcs, Volume 174, DNA 26, Complete Volume

Authors: Cody Geary and Matthew J. Patitz

Published in: LIPIcs, Volume 174, 26th International Conference on DNA Computing and Molecular Programming (DNA 26) (2020)

Abstract

LIPIcs, Volume 174, DNA 26, Complete Volume

Cite as

Cody Geary and Matthew J. Patitz. LIPIcs, Volume 174, DNA 26, Complete Volume. In 26th International Conference on DNA Computing and Molecular Programming (DNA 26). Leibniz International Proceedings in Informatics (LIPIcs), Volume 174, pp. 1-230, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)

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@Proceedings{geary_et_al:LIPIcs.DNA.2020,
  title =	{{LIPIcs, Volume 174, DNA 26, Complete Volume}},
  booktitle =	{26th International Conference on DNA Computing and Molecular Programming (DNA 26)},
  pages =	{1--230},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-163-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{174},
  editor =	{Geary, Cody and Patitz, Matthew J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DNA.2020},
  URN =		{urn:nbn:de:0030-drops-129529},
  doi =		{10.4230/LIPIcs.DNA.2020},
  annote =	{Keywords: LIPIcs, Volume 174, DNA 26, Complete Volume}
}

Document

Front Matter

DOI: 10.4230/LIPIcs.DNA.2020.0

Front Matter, Table of Contents, Preface, Conference Organization

Authors: Cody Geary and Matthew J. Patitz

Published in: LIPIcs, Volume 174, 26th International Conference on DNA Computing and Molecular Programming (DNA 26) (2020)

Abstract

Front Matter, Table of Contents, Preface, Conference Organization

Cite as

Cody Geary and Matthew J. Patitz. Front Matter, Table of Contents, Preface, Conference Organization. In 26th International Conference on DNA Computing and Molecular Programming (DNA 26). Leibniz International Proceedings in Informatics (LIPIcs), Volume 174, pp. 0:i-0:xiv, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)

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@InProceedings{geary_et_al:LIPIcs.DNA.2020.0,
  author =	{Geary, Cody and Patitz, Matthew J.},
  title =	{{Front Matter, Table of Contents, Preface, Conference Organization}},
  booktitle =	{26th International Conference on DNA Computing and Molecular Programming (DNA 26)},
  pages =	{0:i--0:xiv},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-163-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{174},
  editor =	{Geary, Cody and Patitz, Matthew J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DNA.2020.0},
  URN =		{urn:nbn:de:0030-drops-129533},
  doi =		{10.4230/LIPIcs.DNA.2020.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}

Document

DOI: 10.4230/LIPIcs.DNA.2020.1

The Topology of Scaffold Routings on Non-Spherical Mesh Wireframes

Authors: Abdulmelik Mohammed, Nataša Jonoska, and Masahico Saito

Published in: LIPIcs, Volume 174, 26th International Conference on DNA Computing and Molecular Programming (DNA 26) (2020)

Abstract

The routing of a DNA-origami scaffold strand is often modelled as an Eulerian circuit of an Eulerian graph in combinatorial models of DNA origami design. The knot type of the scaffold strand dictates the feasibility of an Eulerian circuit to be used as the scaffold route in the design. Motivated by the topology of scaffold routings in 3D DNA origami, we investigate the knottedness of Eulerian circuits on surface-embedded graphs. We show that certain graph embeddings, checkerboard colorable, always admit unknotted Eulerian circuits. On the other hand, we prove that if a graph admits an embedding in a torus that is not checkerboard colorable, then it can be re-embedded so that all its non-intersecting Eulerian circuits are knotted. For surfaces of genus greater than one, we present an infinite family of checkerboard-colorable graph embeddings where there exist knotted Eulerian circuits.

Cite as

Abdulmelik Mohammed, Nataša Jonoska, and Masahico Saito. The Topology of Scaffold Routings on Non-Spherical Mesh Wireframes. In 26th International Conference on DNA Computing and Molecular Programming (DNA 26). Leibniz International Proceedings in Informatics (LIPIcs), Volume 174, pp. 1:1-1:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)

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@InProceedings{mohammed_et_al:LIPIcs.DNA.2020.1,
  author =	{Mohammed, Abdulmelik and Jonoska, Nata\v{s}a and Saito, Masahico},
  title =	{{The Topology of Scaffold Routings on Non-Spherical Mesh Wireframes}},
  booktitle =	{26th International Conference on DNA Computing and Molecular Programming (DNA 26)},
  pages =	{1:1--1:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-163-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{174},
  editor =	{Geary, Cody and Patitz, Matthew J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DNA.2020.1},
  URN =		{urn:nbn:de:0030-drops-129540},
  doi =		{10.4230/LIPIcs.DNA.2020.1},
  annote =	{Keywords: DNA origami, Scaffold routing, Graphs, Surfaces, Knots, Eulerian circuits}
}

Document

DOI: 10.4230/LIPIcs.DNA.2020.2

Simplifying Chemical Reaction Network Implementations with Two-Stranded DNA Building Blocks

Authors: Robert F. Johnson and Lulu Qian

Published in: LIPIcs, Volume 174, 26th International Conference on DNA Computing and Molecular Programming (DNA 26) (2020)

Abstract

In molecular programming, the Chemical Reaction Network model is often used to describe real or hypothetical systems. Often, an interesting computational task can be done with a known hypothetical Chemical Reaction Network, but often such networks have no known physical implementation. One of the important breakthroughs in the field was that any Chemical Reaction Network can be physically implemented, approximately, using DNA strand displacement mechanisms. This allows us to treat the Chemical Reaction Network model as a programming language and the implementation schemes as its compiler. This also suggests that it would be useful to optimize the result of such a compilation, and in general to find effective ways to design better DNA strand displacement systems. We discuss DNA strand displacement systems in terms of "motifs", short sequences of elementary DNA strand displacement reactions. We argue that describing such motifs in terms of their inputs and outputs, then building larger systems out of the abstracted motifs, can be an efficient way of designing DNA strand displacement systems. We discuss four previously studied motifs in this abstracted way, and present a new motif based on cooperative 4-way strand exchange. We then show how Chemical Reaction Network implementations can be built out of abstracted motifs, discussing existing implementations as well as presenting two new implementations based on 4-way strand exchange, one of which uses the new cooperative motif. The new implementations both have two desirable properties not found in existing implementations, namely both use only at most 2-stranded DNA complexes for signal and fuel complexes and both are physically reversible. There are reasons to believe that those properties may make them more robust and energy-efficient, but at the expense of using more fuel complexes than existing implementation schemes.

Cite as

Robert F. Johnson and Lulu Qian. Simplifying Chemical Reaction Network Implementations with Two-Stranded DNA Building Blocks. In 26th International Conference on DNA Computing and Molecular Programming (DNA 26). Leibniz International Proceedings in Informatics (LIPIcs), Volume 174, pp. 2:1-2:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)

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@InProceedings{johnson_et_al:LIPIcs.DNA.2020.2,
  author =	{Johnson, Robert F. and Qian, Lulu},
  title =	{{Simplifying Chemical Reaction Network Implementations with Two-Stranded DNA Building Blocks}},
  booktitle =	{26th International Conference on DNA Computing and Molecular Programming (DNA 26)},
  pages =	{2:1--2:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-163-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{174},
  editor =	{Geary, Cody and Patitz, Matthew J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DNA.2020.2},
  URN =		{urn:nbn:de:0030-drops-129557},
  doi =		{10.4230/LIPIcs.DNA.2020.2},
  annote =	{Keywords: Molecular programming, DNA computing, Chemical Reaction Networks, DNA strand displacement}
}

Document

DOI: 10.4230/LIPIcs.DNA.2020.3

Composable Computation in Leaderless, Discrete Chemical Reaction Networks

Authors: Hooman Hashemi, Ben Chugg, and Anne Condon

Published in: LIPIcs, Volume 174, 26th International Conference on DNA Computing and Molecular Programming (DNA 26) (2020)

Abstract

We classify the functions f:ℕ^d → ℕ that are stably computable by leaderless, output-oblivious discrete (stochastic) Chemical Reaction Networks (CRNs). CRNs that compute such functions are systems of reactions over species that include d designated input species, whose initial counts represent an input x ∈ ℕ^d, and one output species whose eventual count represents f(x). Chen et al. showed that the class of functions computable by CRNs is precisely the semilinear functions. In output-oblivious CRNs, the output species is never a reactant. Output-oblivious CRNs are easily composable since a downstream CRN can consume the output of an upstream CRN without affecting its correctness. Severson et al. showed that output-oblivious CRNs compute exactly the subclass of semilinear functions that are eventually the minimum of quilt-affine functions, i.e., affine functions with different intercepts in each of finitely many congruence classes. They call such functions the output-oblivious functions. A leaderless CRN can compute only superadditive functions, and so a leaderless output-oblivious CRN can compute only superadditive, output-oblivious functions. In this work we show that a function f:ℕ^d → ℕ is stably computable by a leaderless, output-oblivious CRN if and only if it is superadditive and output-oblivious.

Cite as

Hooman Hashemi, Ben Chugg, and Anne Condon. Composable Computation in Leaderless, Discrete Chemical Reaction Networks. In 26th International Conference on DNA Computing and Molecular Programming (DNA 26). Leibniz International Proceedings in Informatics (LIPIcs), Volume 174, pp. 3:1-3:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)

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@InProceedings{hashemi_et_al:LIPIcs.DNA.2020.3,
  author =	{Hashemi, Hooman and Chugg, Ben and Condon, Anne},
  title =	{{Composable Computation in Leaderless, Discrete Chemical Reaction Networks}},
  booktitle =	{26th International Conference on DNA Computing and Molecular Programming (DNA 26)},
  pages =	{3:1--3:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-163-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{174},
  editor =	{Geary, Cody and Patitz, Matthew J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DNA.2020.3},
  URN =		{urn:nbn:de:0030-drops-129560},
  doi =		{10.4230/LIPIcs.DNA.2020.3},
  annote =	{Keywords: Chemical Reaction Networks, Stable Function Computation, Output-Oblivious, Output-Monotonic}
}

Document

DOI: 10.4230/LIPIcs.DNA.2020.4

CRNs Exposed: A Method for the Systematic Exploration of Chemical Reaction Networks

Authors: Marko Vasic, David Soloveichik, and Sarfraz Khurshid

Published in: LIPIcs, Volume 174, 26th International Conference on DNA Computing and Molecular Programming (DNA 26) (2020)

Abstract

Formal methods have enabled breakthroughs in many fields, such as in hardware verification, machine learning and biological systems. The key object of interest in systems biology, synthetic biology, and molecular programming is chemical reaction networks (CRNs) which formalizes coupled chemical reactions in a well-mixed solution. CRNs are pivotal for our understanding of biological regulatory and metabolic networks, as well as for programming engineered molecular behavior. Although it is clear that small CRNs are capable of complex dynamics and computational behavior, it remains difficult to explore the space of CRNs in search for desired functionality. We use Alloy, a tool for expressing structural constraints and behavior in software systems, to enumerate CRNs with declaratively specified properties. We show how this framework can enumerate CRNs with a variety of structural constraints including biologically motivated catalytic networks and metabolic networks, and seesaw networks motivated by DNA nanotechnology. We also use the framework to explore analog function computation in rate-independent CRNs. By computing the desired output value with stoichiometry rather than with reaction rates (in the sense that X → Y+Y computes multiplication by 2), such CRNs are completely robust to the choice of reaction rates or rate law. We find the smallest CRNs computing the max, minmax, abs and ReLU (rectified linear unit) functions in a natural subclass of rate-independent CRNs where rate-independence follows from structural network properties.

Cite as

Marko Vasic, David Soloveichik, and Sarfraz Khurshid. CRNs Exposed: A Method for the Systematic Exploration of Chemical Reaction Networks. In 26th International Conference on DNA Computing and Molecular Programming (DNA 26). Leibniz International Proceedings in Informatics (LIPIcs), Volume 174, pp. 4:1-4:25, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)

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@InProceedings{vasic_et_al:LIPIcs.DNA.2020.4,
  author =	{Vasic, Marko and Soloveichik, David and Khurshid, Sarfraz},
  title =	{{CRNs Exposed: A Method for the Systematic Exploration of Chemical Reaction Networks}},
  booktitle =	{26th International Conference on DNA Computing and Molecular Programming (DNA 26)},
  pages =	{4:1--4:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-163-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{174},
  editor =	{Geary, Cody and Patitz, Matthew J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DNA.2020.4},
  URN =		{urn:nbn:de:0030-drops-129574},
  doi =		{10.4230/LIPIcs.DNA.2020.4},
  annote =	{Keywords: molecular programming, formal methods}
}

Document

DOI: 10.4230/LIPIcs.DNA.2020.5

Population-Induced Phase Transitions and the Verification of Chemical Reaction Networks

Authors: James I. Lathrop, Jack H. Lutz, Robyn R. Lutz, Hugh D. Potter, and Matthew R. Riley

Published in: LIPIcs, Volume 174, 26th International Conference on DNA Computing and Molecular Programming (DNA 26) (2020)

Abstract

We show that very simple molecular systems, modeled as chemical reaction networks, can have behaviors that exhibit dramatic phase transitions at certain population thresholds. Moreover, the magnitudes of these thresholds can thwart attempts to use simulation, model checking, or approximation by differential equations to formally verify the behaviors of such systems at realistic populations. We show how formal theorem provers can successfully verify some such systems at populations where other verification methods fail.

Cite as

James I. Lathrop, Jack H. Lutz, Robyn R. Lutz, Hugh D. Potter, and Matthew R. Riley. Population-Induced Phase Transitions and the Verification of Chemical Reaction Networks. In 26th International Conference on DNA Computing and Molecular Programming (DNA 26). Leibniz International Proceedings in Informatics (LIPIcs), Volume 174, pp. 5:1-5:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)

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@InProceedings{lathrop_et_al:LIPIcs.DNA.2020.5,
  author =	{Lathrop, James I. and Lutz, Jack H. and Lutz, Robyn R. and Potter, Hugh D. and Riley, Matthew R.},
  title =	{{Population-Induced Phase Transitions and the Verification of Chemical Reaction Networks}},
  booktitle =	{26th International Conference on DNA Computing and Molecular Programming (DNA 26)},
  pages =	{5:1--5:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-163-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{174},
  editor =	{Geary, Cody and Patitz, Matthew J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DNA.2020.5},
  URN =		{urn:nbn:de:0030-drops-129583},
  doi =		{10.4230/LIPIcs.DNA.2020.5},
  annote =	{Keywords: chemical reaction networks, molecular programming, phase transitions, population protocols, verification}
}

Document

DOI: 10.4230/LIPIcs.DNA.2020.6

ALCH: An Imperative Language for Chemical Reaction Network-Controlled Tile Assembly

Authors: Titus H. Klinge, James I. Lathrop, Sonia Moreno, Hugh D. Potter, Narun K. Raman, and Matthew R. Riley

Published in: LIPIcs, Volume 174, 26th International Conference on DNA Computing and Molecular Programming (DNA 26) (2020)

Abstract

In 2015 Schiefer and Winfree introduced the chemical reaction network-controlled tile assembly model (CRN-TAM), a variant of the abstract tile assembly model (aTAM), where tile reactions are mediated via non-local chemical signals. In this paper, we introduce ALCH, an imperative programming language for specifying CRN-TAM programs. ALCH contains common features like Boolean variables, conditionals, and loops. It also supports CRN-TAM-specific features such as adding and removing tiles. A unique feature of the language is the branch statement, a nondeterministic control structure that allows us to query the current state of tile assemblies. We also developed a compiler that translates ALCH to the CRN-TAM, and a simulator that simulates and visualizes the self-assembly of a CRN-TAM program. Using this language, we show that the discrete Sierpinski triangle can be strictly self-assembled in the CRN-TAM. This solves an open problem that the CRN-TAM is capable of self-assembling infinite shapes at scale one that the aTAM cannot. ALCH allows us to present this construction at a high level, abstracting species and reactions into C-like code that is simpler to understand. Our construction utilizes two new CRN-TAM techniques that allow us to tackle this open problem. First, it employs the branching feature of ALCH to probe the previously placed tiles of the assembly and detect the presence and absence of tiles. Second, it uses scaffolding tiles to precisely control tile placement by occluding any undesired binding sites.

Cite as

Titus H. Klinge, James I. Lathrop, Sonia Moreno, Hugh D. Potter, Narun K. Raman, and Matthew R. Riley. ALCH: An Imperative Language for Chemical Reaction Network-Controlled Tile Assembly. In 26th International Conference on DNA Computing and Molecular Programming (DNA 26). Leibniz International Proceedings in Informatics (LIPIcs), Volume 174, pp. 6:1-6:22, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)

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@InProceedings{klinge_et_al:LIPIcs.DNA.2020.6,
  author =	{Klinge, Titus H. and Lathrop, James I. and Moreno, Sonia and Potter, Hugh D. and Raman, Narun K. and Riley, Matthew R.},
  title =	{{ALCH: An Imperative Language for Chemical Reaction Network-Controlled Tile Assembly}},
  booktitle =	{26th International Conference on DNA Computing and Molecular Programming (DNA 26)},
  pages =	{6:1--6:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-163-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{174},
  editor =	{Geary, Cody and Patitz, Matthew J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DNA.2020.6},
  URN =		{urn:nbn:de:0030-drops-129592},
  doi =		{10.4230/LIPIcs.DNA.2020.6},
  annote =	{Keywords: Tile assembly, Chemical reaction network, Sierpinski triangle}
}

Document

DOI: 10.4230/LIPIcs.DNA.2020.7

Implementing Non-Equilibrium Networks with Active Circuits of Duplex Catalysts

Authors: Antti Lankinen, Ismael Mullor Ruiz, and Thomas E. Ouldridge

Published in: LIPIcs, Volume 174, 26th International Conference on DNA Computing and Molecular Programming (DNA 26) (2020)

Abstract

DNA strand displacement (DSD) reactions have been used to construct chemical reaction networks in which species act catalytically at the level of the overall stoichiometry of reactions. These effective catalytic reactions are typically realised through one or more of the following: many-stranded gate complexes to coordinate the catalysis, indirect interaction between the catalyst and its substrate, and the recovery of a distinct "catalyst" strand from the one that triggered the reaction. These facts make emulation of the out-of-equilibrium catalytic circuitry of living cells more difficult. Here, we propose a new framework for constructing catalytic DSD networks: Active Circuits of Duplex Catalysts (ACDC). ACDC components are all double-stranded complexes, with reactions occurring through 4-way strand exchange. Catalysts directly bind to their substrates, and the "identity" strand of the catalyst recovered at the end of a reaction is the same molecule as the one that initiated it. We analyse the capability of the framework to implement catalytic circuits analogous to phosphorylation networks in living cells. We also propose two methods of systematically introducing mismatches within DNA strands to avoid leak reactions and introduce driving through net base pair formation. We then combine these results into a compiler to automate the process of designing DNA strands that realise any catalytic network allowed by our framework.

Cite as

Antti Lankinen, Ismael Mullor Ruiz, and Thomas E. Ouldridge. Implementing Non-Equilibrium Networks with Active Circuits of Duplex Catalysts. In 26th International Conference on DNA Computing and Molecular Programming (DNA 26). Leibniz International Proceedings in Informatics (LIPIcs), Volume 174, pp. 7:1-7:25, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)

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@InProceedings{lankinen_et_al:LIPIcs.DNA.2020.7,
  author =	{Lankinen, Antti and Mullor Ruiz, Ismael and Ouldridge, Thomas E.},
  title =	{{Implementing Non-Equilibrium Networks with Active Circuits of Duplex Catalysts}},
  booktitle =	{26th International Conference on DNA Computing and Molecular Programming (DNA 26)},
  pages =	{7:1--7:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-163-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{174},
  editor =	{Geary, Cody and Patitz, Matthew J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DNA.2020.7},
  URN =		{urn:nbn:de:0030-drops-129602},
  doi =		{10.4230/LIPIcs.DNA.2020.7},
  annote =	{Keywords: DNA strand displacement, Catalysis, Information-processing networks}
}

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