Universal Computation and Optimal Construction in the Chemical Reaction Network-Controlled Tile Assembly Model

Schiefer, Nicholas; Winfree, Erik

doi:10.1007/978-3-319-21999-8_3

Cited by 17 publications

(18 citation statements)

References 33 publications

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“…The same authors extend these results in Ref. 50 to show that, in addition to the previously reported space and program size complexity efficiency, 49 the efficiency of computational and construction time complexity of the minimal model is at least as good if not better than either system alone.…”

Section: Resultssupporting

confidence: 61%

“…For example, the proposed minimal model in Ref. 49 incorporates the non-local nature of CRNs to influence the local assembly logic of tile assembly, and vice versa. This model is shown to be efficiently Turinguniversal even in (unbounded) 1D.…”

Section: Resultsmentioning

confidence: 99%

“…A new theoretical model or framework may be needed to answer this question since both of the theoretical works mentioned above enforce sequential computation/construction. 49,50 Even finding physical DNA tile implementations of the minimal model proposed in Ref. 49 may prove difficult since the abstract tile assembly model is grounded on different presumptions 58 .…”

Section: Resultsmentioning

confidence: 99%

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Kinetic Trans-Assembly of DNA Nanostructures

et al. 2018

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The central dogma of molecular biology is the principal framework for understanding how nucleic acid information is propagated and used by living systems to create complex biomolecules. Here, by integrating the structural and dynamic paradigms of DNA nanotechnology, we present a rationally designed synthetic platform that functions in an analogous manner to create complex DNA nanostructures. Starting from one type of DNA nanostructure, DNA strand displacement circuits were designed to interact and pass along the information encoded in the initial structure to mediate the self-assembly of a different type of structure, the final output structure depending on the type of circuit triggered. Using this concept of a DNA structure "trans-assembling" a different DNA structure through nonlocal strand displacement circuitry, four different schemes were implemented. Specifically, 1D ladder and 2D double-crossover (DX) lattices were designed to kinetically trigger DNA circuits to activate polymerization of either ring structures or another type of DX lattice under enzyme-free, isothermal conditions. In each scheme, the desired multilayer reaction pathway was activated, among multiple possible pathways, ultimately leading to the downstream self-assembly of the correct output structure.

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Section: Resultssupporting

confidence: 61%

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

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Kinetic Trans-Assembly of DNA Nanostructures

et al. 2018

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“…As recent advances in microfabrication and cellular engineering render the production of such particles increasingly possible, there has been a convergence of theoretical research interests on programmable matter from some areas of computer science, especially robotics, sensor networks, molecular self-assembly, and distributed computing. Several theoretical models of programmable matter have been proposed, ranging from DNA self-assembly systems (e.g., [8,17,18,20,21,24]) to shape-changing synthetic molecules and cells (e.g., [28]), from metamorphic robots (e.g., [4,27]) to natureinspired synthetic insects and micro-organisms (e.g., [12,13,16]), each model assigning special capabilities and constraints to the entities and focusing on specific applications.…”

Section: Introductionmentioning

confidence: 99%

Shape formation by programmable particles

et al. 2019

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Shape formation (or pattern formation) is a basic distributed problem for systems of computational mobile entities. Intensively studied for systems of autonomous mobile robots, it has recently been investigated in the realm of programmable matter, where entities are assumed to be small and with severely limited capabilities. Namely, it has been studied in the geometric Amoebot model, where the anonymous entities, called particles, operate on a hexagonal tessellation of the plane and have limited computational power (they have constant memory), strictly local interaction and communication capabilities (only with particles in neighboring nodes of the grid), and limited motorial capabilities (from a grid node to an empty neighboring node); their activation is controlled by an adversarial scheduler. Recent investigations have shown how, starting from a well-structured configuration in which the particles form a (not necessarily complete) triangle, the particles can form a large class of shapes. This result has been established under several assumptions: agreement on the clockwise direction (i.e., chirality), a sequential activation schedule, and randomization (i.e., particles can flip coins to elect a leader).In this paper we obtain several results that, among other things, provide a characterization of which shapes can be formed deterministically starting from any simply connected initial configuration of n particles. The characterization is constructive: we provide a universal shape formation algorithm that, for each feasible pair of shapes (S 0 , S F ), allows the particles to form the final shape S F (given in input) starting from the initial shape S 0 , unknown to the particles. The final configuration will be an appropriate scaled-up copy of S F depending on n.If randomization is allowed, then any input shape can be formed from any initial (simply connected) shape by our algorithm, provided that there are enough particles.Our algorithm works without chirality, proving that chirality is computationally irrelevant for shape formation. Furthermore, it works under a strong adversarial scheduler, not necessarily sequential.We also consider the complexity of shape formation both in terms of the number of rounds and the total number of moves performed by the particles executing a universal shape formation algorithm. We prove that our solution has a complexity of O(n 2 ) rounds and moves: this number of moves is also asymptotically optimal.

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“…Since then, the advancements of molecular programming have proceeded at a rate comparable to Moore's law and have led to methods for precise delivery of nanoscale cargo [25,66,19,59], self-assembling arbitrary two-and three-dimensional nano-structures [56,38,11], and implementing DNA-based circuits and neural nets [52,53,54]. Many useful models for chemical systems have also been proven to be Turing universal [6,20,51,57], including certain types of chemical reaction networks [63].…”

Section: Chapter 1 Introductionmentioning

confidence: 99%

Modular and Robust Computation with Deterministic Chemical Reaction Networks

Klinge

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Universal Computation and Optimal Construction in the Chemical Reaction Network-Controlled Tile Assembly Model

Cited by 17 publications

References 33 publications

Kinetic Trans-Assembly of DNA Nanostructures

Kinetic Trans-Assembly of DNA Nanostructures

Shape formation by programmable particles

Modular and Robust Computation with Deterministic Chemical Reaction Networks

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