Volume
LIPIcs, Volume 276
29th International Conference on DNA Computing and Molecular Programming (DNA 29)
Publication Details
- published at: 2023-09-04
- Publisher: Schloss Dagstuhl – Leibniz-Zentrum für Informatik
- ISBN: 978-3-95977-297-6
- DBLP: db/conf/dna/dna2023
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Document
Complete Volume
LIPIcs, Volume 276, DNA 29, Complete Volume
Abstract
LIPIcs, Volume 276, DNA 29, Complete Volume
Cite as
29th International Conference on DNA Computing and Molecular Programming (DNA 29). Leibniz International Proceedings in Informatics (LIPIcs), Volume 276, pp. 1-230, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@Proceedings{chen_et_al:LIPIcs.DNA.29,
title = {{LIPIcs, Volume 276, DNA 29, Complete Volume}},
booktitle = {29th International Conference on DNA Computing and Molecular Programming (DNA 29)},
pages = {1--230},
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},
URN = {urn:nbn:de:0030-drops-187827},
doi = {10.4230/LIPIcs.DNA.29},
annote = {Keywords: LIPIcs, Volume 276, DNA 29, Complete Volume}
}
Document
Front Matter
Front Matter, Table of Contents, Preface, Conference Organization
Abstract
Front Matter, Table of Contents, Preface, Conference Organization
Cite as
29th International Conference on DNA Computing and Molecular Programming (DNA 29). Leibniz International Proceedings in Informatics (LIPIcs), Volume 276, pp. 0:i-0:xiv, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{chen_et_al:LIPIcs.DNA.29.0,
author = {Chen, Ho-Lin and Evans, Constantine G.},
title = {{Front Matter, Table of Contents, Preface, Conference Organization}},
booktitle = {29th International Conference on DNA Computing and Molecular Programming (DNA 29)},
pages = {0:i--0:xiv},
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.29.0},
URN = {urn:nbn:de:0030-drops-187839},
doi = {10.4230/LIPIcs.DNA.29.0},
annote = {Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
Minimum Free Energy, Partition Function and Kinetics Simulation Algorithms for a Multistranded Scaffolded DNA Computer
Abstract
Polynomial time dynamic programming algorithms play a crucial role in the design, analysis and engineering of nucleic acid systems including DNA computers and DNA/RNA nanostructures. However, in complex multistranded or pseudoknotted systems, computing the minimum free energy (MFE), and partition function of nucleic acid systems is NP-hard. Despite this, multistranded and/or pseudoknotted systems represent some of the most utilised and successful systems in the field. This leaves open the tempting possibility that many of the kinds of multistranded and/or pseudoknotted systems we wish to engineer actually fall into restricted classes, that do in fact have polynomial time algorithms, but we've just not found them yet.
Here, we give polynomial time algorithms for MFE and partition function calculation for a restricted kind of multistranded system called the 1D scaffolded DNA computer. This model of computation thermodynamically favours correct outputs over erroneous states, simulates finite state machines in 1D and Boolean circuits in 2D, and is amenable to DNA storage applications. In an effort to begin to ask the question of whether we can naturally compare the expressivity of nucleic acid systems based on the computational complexity of prediction of their preferred energetic states, we show our MFE problem is in logspace (the complexity class L), making it perhaps one of the simplest known, natural, nucleic acid MFE problems. Finally, we provide a stochastic kinetic simulator for the 1D scaffolded DNA computer and evaluate strategies for efficiently speeding up this thermodynamically favourable system in a constant-temperature kinetic regime.
Cite as
Ahmed Shalaby, Chris Thachuk, and Damien Woods. Minimum Free Energy, Partition Function and Kinetics Simulation Algorithms for a Multistranded Scaffolded DNA Computer. In 29th International Conference on DNA Computing and Molecular Programming (DNA 29). Leibniz International Proceedings in Informatics (LIPIcs), Volume 276, pp. 1:1-1:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{shalaby_et_al:LIPIcs.DNA.29.1,
author = {Shalaby, Ahmed and Thachuk, Chris and Woods, Damien},
title = {{Minimum Free Energy, Partition Function and Kinetics Simulation Algorithms for a Multistranded Scaffolded DNA Computer}},
booktitle = {29th International Conference on DNA Computing and Molecular Programming (DNA 29)},
pages = {1:1--1:22},
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.29.1},
URN = {urn:nbn:de:0030-drops-187840},
doi = {10.4230/LIPIcs.DNA.29.1},
annote = {Keywords: thermodynamic computation, model of computation, molecular computing, minimum free energy, partition function, DNA computing, DNA self-assembly, DNA strand displacement, kinetics simulation}
}
Document
DNA Tile Self-Assembly for 3D-Surfaces: Towards Genus Identification
Abstract
We introduce a new DNA tile self-assembly model: the Surface Flexible Tile Assembly Model (SFTAM), where 2D tiles are placed on host 3D surfaces made of axis-parallel unit cubes glued together by their faces, called polycubes. The bonds are flexible, so that the assembly can bind on the edges of the polycube. We are interested in the study of SFTAM self-assemblies on 3D surfaces which are not always embeddable in the Euclidean plane, in order to compare their different behaviors and to compute the topological properties of the host surfaces.
We focus on a family of polycubes called order-1 cuboids. Order-0 cuboids are polycubes that have six rectangular faces, and order-1 cuboids are made from two order-0 cuboids by substracting one from the other. Thus, order-1 cuboids can be of genus 0 or of genus 1 (then they contain a tunnel). We are interested in the genus of these structures, and we present a SFTAM tile assembly system that determines the genus of a given order-1 cuboid. The SFTAM tile assembly system which we design, contains a specific set Y of tile types with the following properties. If the assembly is made on a host order-1 cuboid C of genus 0, no tile of Y appears in any producible assembly, but if C has genus 1, every terminal assembly contains at least one tile of Y.
Thus, for order-1 cuboids our system is able to distinguish the host surfaces according to their genus, by the tiles used in the assembly. This system is specific to order-1 cuboids but we can expect the techniques we use to be generalizable to other families of shapes.
Cite as
Florent Becker and Shahrzad Heydarshahi. DNA Tile Self-Assembly for 3D-Surfaces: Towards Genus Identification. In 29th International Conference on DNA Computing and Molecular Programming (DNA 29). Leibniz International Proceedings in Informatics (LIPIcs), Volume 276, pp. 2:1-2:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{becker_et_al:LIPIcs.DNA.29.2,
author = {Becker, Florent and Heydarshahi, Shahrzad},
title = {{DNA Tile Self-Assembly for 3D-Surfaces: Towards Genus Identification}},
booktitle = {29th International Conference on DNA Computing and Molecular Programming (DNA 29)},
pages = {2:1--2:21},
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.29.2},
URN = {urn:nbn:de:0030-drops-187851},
doi = {10.4230/LIPIcs.DNA.29.2},
annote = {Keywords: Tile self-assembly, DNA computing, Geometric surfaces}
}
Document
On the Runtime of Chemical Reaction Networks Beyond Idealized Conditions
Abstract
This paper studies the (discrete) chemical reaction network (CRN) computational model that emerged in the last two decades as an abstraction for molecular programming. The correctness of CRN protocols is typically established under one of two possible schedulers that determine how the execution advances: (1) a stochastic scheduler that obeys the (continuous time) Markov process dictated by the standard model of stochastic chemical kinetics; or (2) an adversarial scheduler whose only commitment is to maintain a certain fairness condition. The latter scheduler is justified by the fact that the former one crucially assumes "idealized conditions" that more often than not, do not hold in real wet-lab experiments. However, when it comes to analyzing the runtime of CRN protocols, the existing literature focuses strictly on the stochastic scheduler, thus raising the research question that drives this work: Is there a meaningful way to quantify the runtime of CRNs without the idealized conditions assumption?
The main conceptual contribution of the current paper is to answer this question in the affirmative, formulating a new runtime measure for CRN protocols that does not rely on idealized conditions. This runtime measure is based on an adapted (weaker) fairness condition as well as a novel scheme that enables partitioning the execution into short rounds and charging the runtime for each round individually (inspired by definitions for the runtime of asynchronous distributed algorithms). Following that, we turn to investigate various fundamental computational tasks and establish (often tight) bounds on the runtime of the corresponding CRN protocols operating under the adversarial scheduler. This includes an almost complete chart of the runtime complexity landscape of predicate decidability tasks.
Cite as
Anne Condon, Yuval Emek, and Noga Harlev. On the Runtime of Chemical Reaction Networks Beyond Idealized Conditions. In 29th International Conference on DNA Computing and Molecular Programming (DNA 29). Leibniz International Proceedings in Informatics (LIPIcs), Volume 276, pp. 3:1-3:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{condon_et_al:LIPIcs.DNA.29.3,
author = {Condon, Anne and Emek, Yuval and Harlev, Noga},
title = {{On the Runtime of Chemical Reaction Networks Beyond Idealized Conditions}},
booktitle = {29th International Conference on DNA Computing and Molecular Programming (DNA 29)},
pages = {3:1--3:22},
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.29.3},
URN = {urn:nbn:de:0030-drops-187861},
doi = {10.4230/LIPIcs.DNA.29.3},
annote = {Keywords: chemical reaction networks, adversarial runtime, weak fairness, predicate decidability}
}
Document
Rational Design of DNA Sequences with Non-Orthogonal Binding Interactions
Abstract
Molecular computation involving promiscuous, or non-orthogonal, binding interactions between system components is found commonly in natural biological systems, as well as some proposed human-made molecular computers. Such systems are characterized by the fact that each computational unit, such as a domain within a DNA strand, may bind to several different partners with distinct, prescribed binding strengths. Unfortunately, implementing systems of molecular computation that incorporate non-orthogonal binding is difficult, because researchers lack a robust, general-purpose method for designing molecules with this type of behavior. In this work, we describe and demonstrate a process for the rational design of DNA sequences with prescribed non-orthogonal binding behavior. This process makes use of a model that represents large sets of non-orthogonal DNA sequences using fixed-length binary strings, and estimates the differential binding affinity between pairs of sequences through the Hamming distance between their corresponding binary strings. The real-world applicability of this model is supported by simulations and some experimental data. We then select two previously described systems of molecular computation involving non-orthogonal interactions, and apply our sequence design process to implement them using DNA strand displacement. Our simulated results on these two systems demonstrate both digital and analog computation. We hope that this work motivates the development and implementation of new computational paradigms based on non-orthogonal binding.
Cite as
Joseph Don Berleant. Rational Design of DNA Sequences with Non-Orthogonal Binding Interactions. In 29th International Conference on DNA Computing and Molecular Programming (DNA 29). Leibniz International Proceedings in Informatics (LIPIcs), Volume 276, pp. 4:1-4:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{berleant:LIPIcs.DNA.29.4,
author = {Berleant, Joseph Don},
title = {{Rational Design of DNA Sequences with Non-Orthogonal Binding Interactions}},
booktitle = {29th International Conference on DNA Computing and Molecular Programming (DNA 29)},
pages = {4:1--4:22},
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.29.4},
URN = {urn:nbn:de:0030-drops-187877},
doi = {10.4230/LIPIcs.DNA.29.4},
annote = {Keywords: DNA sequence design, binding networks, promiscuous binding, non-orthogonal binding, isometric graph embeddings}
}
Document
Revisiting Hybridization Kinetics with Improved Elementary Step Simulation
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}
}
Document
Reversible Bond Logic
Abstract
The field of molecular programming allows for the programming of the structure and behavior of matter at the molecular level, even to the point of encoding arbitrary computation. However, current approaches tend to be wasteful in terms of monomers, gate complexes, and free energy. In response, we present a novel abstract model of molecular programming, Reversible Bond Logic (RBL), which exploits the concepts of reversibility and reversible computing to help address these issues. RBL systems permit very general manipulations of arbitrarily complex "molecular" structures, and possess properties such as component reuse, modularity, compositionality. We will demonstrate the implementation of a common free-energy currency that can be shared across systems, initially using it to power a biased walker. Then we will introduce some basic motifs for the manipulation of structures, which will be used to implement such computational primitives as conditional branching, looping, and subroutines. Example programs will include logical negation, and addition and squaring of arbitrarily large numbers. As a consequence of reversibility, we will also obtain the inverse programs (subtraction and square-rooting) for free. Due to modularity, multiple instances of these computations can occur in parallel without cross-talk. Future work aims to further characterize RBL, and develop variants that may be amenable to experimental implementation.
Cite as
Hannah Amelie Earley. Reversible Bond Logic. In 29th International Conference on DNA Computing and Molecular Programming (DNA 29). Leibniz International Proceedings in Informatics (LIPIcs), Volume 276, pp. 6:1-6:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{earley:LIPIcs.DNA.29.6,
author = {Earley, Hannah Amelie},
title = {{Reversible Bond Logic}},
booktitle = {29th International Conference on DNA Computing and Molecular Programming (DNA 29)},
pages = {6:1--6:23},
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.29.6},
URN = {urn:nbn:de:0030-drops-187893},
doi = {10.4230/LIPIcs.DNA.29.6},
annote = {Keywords: Molecular Programming, Reversible Computing, Structural Manipulation}
}
Document
Accelerating Self-Assembly of Crisscross Slat Systems
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
Thermodynamically Driven Signal Amplification
Abstract
The field of chemical computation attempts to model computational behavior that arises when molecules, typically nucleic acids, are mixed together. By modeling this physical phenomenon at different levels of specificity, different operative computational behavior is observed. Thermodynamic binding networks (TBNs) is a highly abstracted model that focuses on which molecules are bound to each other in a "thermodynamically stable" sense. Stability is measured based only on how many bonds are formed and how many total complexes are in a configuration, without focusing on how molecules are binding or how they became bound. By defocusing on kinetic processes, TBNs attempt to naturally model the long-term behavior of a mixture (i.e., its thermodynamic equilibrium).
We study the problem of signal amplification: detecting a small quantity of some molecule and amplifying its signal to something more easily detectable. This problem has natural applications such as disease diagnosis. By focusing on thermodynamically favored outcomes, we seek to design chemical systems that perform the task of signal amplification robustly without relying on kinetic pathways that can be error prone and require highly controlled conditions (e.g., PCR amplification).
It might appear that a small change in concentrations can result in only small changes to the thermodynamic equilibrium of a molecular system. However, we show that it is possible to design a TBN that can "exponentially amplify" a signal represented by a single copy of a monomer called the analyte: this TBN has exactly one stable state before adding the analyte and exactly one stable state afterward, and those two states "look very different" from each other. In particular, their difference is exponential in the number of types of molecules and their sizes. The system can be programmed to any desired level of resilience to false positives and false negatives. To prove these results, we introduce new concepts to the TBN model, particularly the notions of a TBN’s entropy gap to describe how unlikely it is to be observed in an undesirable state, and feed-forward TBNs that have a strong upper bound on the number of polymers in a stable configuration.
We also show a corresponding negative result: a doubly exponential upper bound, meaning that there is no TBN that can amplify a signal by an amount more than doubly exponential in the number and sizes of different molecules that comprise it. We leave as an open question to close this gap by either proving an exponential upper bound, or giving a construction with a doubly-exponential difference between the stable configurations before and after the analyte is added.
Our work informs the fundamental question of how a thermodynamic equilibrium can change as a result of a small change to the system (adding a single molecule copy). While exponential amplification is traditionally viewed as inherently a non-equilibrium phenomenon, we find that in a strong sense exponential amplification can occur at thermodynamic equilibrium as well - where the "effect" (e.g., fluorescence) is exponential in types and complexity of the chemical components.
Cite as
Joshua Petrack, David Soloveichik, and David Doty. Thermodynamically Driven Signal Amplification. In 29th International Conference on DNA Computing and Molecular Programming (DNA 29). Leibniz International Proceedings in Informatics (LIPIcs), Volume 276, pp. 8:1-8:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{petrack_et_al:LIPIcs.DNA.29.8,
author = {Petrack, Joshua and Soloveichik, David and Doty, David},
title = {{Thermodynamically Driven Signal Amplification}},
booktitle = {29th International Conference on DNA Computing and Molecular Programming (DNA 29)},
pages = {8:1--8:22},
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.29.8},
URN = {urn:nbn:de:0030-drops-187917},
doi = {10.4230/LIPIcs.DNA.29.8},
annote = {Keywords: Thermodynamic binding networks, signal amplification, integer programming}
}
Document
Optimal Information Encoding in Chemical Reaction Networks
Abstract
Discrete chemical reaction networks formalize the interactions of molecular species in a well-mixed solution as stochastic events. Given their basic mathematical and physical role, the computational power of chemical reaction networks has been widely studied in the molecular programming and distributed computing communities. While for Turing-universal systems there is a universal measure of optimal information encoding based on Kolmogorov complexity, chemical reaction networks are not Turing universal unless error and unbounded molecular counts are permitted. Nonetheless, here we show that the optimal number of reactions to generate a specific count x ∈ ℕ with probability 1 is asymptotically equal to a "space-aware" version of the Kolmogorov complexity of x, defined as K̃s(x) = min_p {|p|/log|p| + log(space(𝒰(p))) : 𝒰(p) = x}, where p is a program for universal Turing machine 𝒰. This version of Kolmogorov complexity incorporates not just the length of the shortest program for generating x, but also the space usage of that program. Probability 1 computation is captured by the standard notion of stable computation from distributed computing, but we limit our consideration to chemical reaction networks obeying a stronger constraint: they "know when they are done" in the sense that they produce a special species to indicate completion. As part of our results, we develop a module for encoding and unpacking any b bits of information via O(b/log{b}) reactions, which is information-theoretically optimal for incompressible information. Our work provides one answer to the question of how succinctly chemical self-organization can be encoded - in the sense of generating precise molecular counts of species as the desired state.
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Austin Luchsinger, David Doty, and David Soloveichik. Optimal Information Encoding in Chemical Reaction Networks. In 29th International Conference on DNA Computing and Molecular Programming (DNA 29). Leibniz International Proceedings in Informatics (LIPIcs), Volume 276, pp. 9:1-9:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{luchsinger_et_al:LIPIcs.DNA.29.9,
author = {Luchsinger, Austin and Doty, David and Soloveichik, David},
title = {{Optimal Information Encoding in Chemical Reaction Networks}},
booktitle = {29th International Conference on DNA Computing and Molecular Programming (DNA 29)},
pages = {9:1--9:16},
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.29.9},
URN = {urn:nbn:de:0030-drops-187920},
doi = {10.4230/LIPIcs.DNA.29.9},
annote = {Keywords: chemical reaction networks, Kolmogorov complexity, stable computation}
}
Document
Complexity of Reconfiguration in Surface Chemical Reaction Networks
Abstract
We analyze the computational complexity of basic reconfiguration problems for the recently introduced surface Chemical Reaction Networks (sCRNs), where ordered pairs of adjacent species nondeterministically transform into a different ordered pair of species according to a predefined set of allowed transition rules (chemical reactions). In particular, two questions that are fundamental to the simulation of sCRNs are whether a given configuration of molecules can ever transform into another given configuration, and whether a given cell can ever contain a given species, given a set of transition rules. We show that these problems can be solved in polynomial time, are NP-complete, or are PSPACE-complete in a variety of different settings, including when adjacent species just swap instead of arbitrary transformation (swap sCRNs), and when cells can change species a limited number of times (k-burnout). Most problems turn out to be at least NP-hard except with very few distinct species (2 or 3).
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Robert M. Alaniz, Josh Brunner, Michael Coulombe, Erik D. Demaine, Jenny Diomidova, Timothy Gomez, Elise Grizzell, Ryan Knobel, Jayson Lynch, Andrew Rodriguez, Robert Schweller, and Tim Wylie. Complexity of Reconfiguration in Surface Chemical Reaction Networks. In 29th International Conference on DNA Computing and Molecular Programming (DNA 29). Leibniz International Proceedings in Informatics (LIPIcs), Volume 276, pp. 10:1-10:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
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@InProceedings{alaniz_et_al:LIPIcs.DNA.29.10,
author = {Alaniz, Robert M. and Brunner, Josh and Coulombe, Michael and Demaine, Erik D. and Diomidova, Jenny and Gomez, Timothy and Grizzell, Elise and Knobel, Ryan and Lynch, Jayson and Rodriguez, Andrew and Schweller, Robert and Wylie, Tim},
title = {{Complexity of Reconfiguration in Surface Chemical Reaction Networks}},
booktitle = {29th International Conference on DNA Computing and Molecular Programming (DNA 29)},
pages = {10:1--10:18},
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.29.10},
URN = {urn:nbn:de:0030-drops-187936},
doi = {10.4230/LIPIcs.DNA.29.10},
annote = {Keywords: Chemical Reaction Networks, reconfiguration, hardness}
}