Shape Replication through Self-Assembly and RNase Enzymes

Abel, Zachary; Benbernou, Nadia M.; Damian, Mirela; Demaine, Erik D.; Demaine, Martin L.; Flatland, Robin; Kominers, Scott Duke; Schweller, Robert T.

doi:10.1137/1.9781611973075.85

Cited by 49 publications

(102 citation statements)

References 3 publications

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“…4 We should mention that part of the ideas related to the pixel-encoding and the TM operating on pixels have been inspired by similar constructions of Woods et al [43]. 5 G is the shape of a labeled square S ∈ L in case L is defined in terms of such squares.…”

Section: Some Basic Constructionsmentioning

confidence: 99%

Terminating distributed construction of shapes and patterns in a fair solution of automata

Michail

2017

Distrib. Comput.

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In this work, we consider a solution of automata (or nodes) that move passively in a well-mixed solution without being capable of controlling their movement. Nodes can cooperate by interacting in pairs and every such interaction may result in an update of their local states. Additionally, the nodes may also choose to connect to each other in order to start forming some required structure. Such nodes can be thought of as small programmable pieces of matter, like tiny nanorobots or programmable molecules. The model that we introduce here is a more applied version of network constructors, imposing physical (or geometric) constraints on the connections that the nodes are allowed to form. Each node can connect to other nodes only via a very limited number of local ports. Connections are always made at unit distance and are perpendicular to connections of neighboring ports, which makes the model capable of forming 2D or 3D shapes. We provide direct constructors for some basic shape construction problems, like spanning line, spanning square, and self-replication. We then develop new techniques for determining the computational and constructive capabilities of our model. One of the main novelties of our approach is that of exploiting the assumptions that the system is well-mixed and has a unique leader, in order to give terminating protocols that are correct with high probability. This allows us to develop terminating subroutines that can be sequentially composed to form larger modular protocols. One of our main results is a terminating protocol counting the size n of the system with high probability. We then use this protocol as a subroutine in order to develop our universal constructors, establishing that it is possible for the nodes to become self-organized with high probability into arbitrarily complex shapes while still detecting termination of the construction.

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Section: Some Basic Constructionsmentioning

confidence: 99%

Terminating distributed construction of shapes and patterns in a fair solution of automata

Michail

2017

Distrib. Comput.

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“…All of the definitions used are equivalent to those found in prior work on the two-handed tile assembly model, e.g. [1,2,3,14].…”

Section: Definitionsmentioning

confidence: 99%

“…An alternative model, called the two-handed assembly model (2HAM) [1,2,4,6], hierarchical tile assembly model [3,14], or polyomino tile assembly model [9,10], allows "seedless" assembly, where tiles can attach spontaneously to form large assemblies that may attach to each other. This seedless assembly was proved by Cannon et al [2] to be capable of simulating any seeded assembly process, while also achieving more efficient assembly of some classes of shapes.…”

Section: Introductionmentioning

confidence: 99%

Size-separable tile self-assembly: a tight bound for temperature-1 mismatch-free systems

Winslow

2015

Nat Comput

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Abstract. We introduce a new property of tile self-assembly systems that we call size-separability. A system is size-separable if every terminal assembly is a constant factor larger than any intermediate assembly. Sizeseparability is motivated by the practical problem of filtering completed assemblies from a variety of incomplete "garbage" assemblies using gel electrophoresis or other mass-based filtering techniques. Here we prove that any system without cooperative bonding assembling a unique mismatch-free terminal assembly can be used to construct a size-separable system uniquely assembling the same shape. The proof achieves optimal scale factor and temperature for the size-separable system. As part of the proof, we obtain two results of independent interest on mismatch-free temperature-1 two-handed systems.

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“…However, recent advances in structural DNA self-assembly have opened up perspectives for the non-enzymatic self-replication of two-dimensional (2-D) and three-dimensional (3-D) patterns of DNA [14,18,9,2].…”

Section: Introductionmentioning

confidence: 99%

Simulating Self-replicating Patterns of DNA Tiles

Gautam¹,

Prasath²

2017

Proceedings of the 10th EAI International Conference on Bio-Inspired Information and Communications Technologies (Formerly BION

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This paper presents a simulation framework in which a pre-assembled rectangular pattern of DNA tiles can be put together with sets of other DNA tiles to autonomously assemble replicas of itself in a discrete two-dimensional grid.The simulator implements both abstract and chemical kinetics based modelling to simulate the tile pattern self-replication. While the abstract model uses only logical matching between the edges of tiles to guide the assembly process, the chemical kinetics model calculates stochastic preference for attachment and/or detachment of each tile during the self-replication. A comparison is made between pattern self-replication timing in the abstract model and cellular automata based models. Simulation of chemical kinetics behaviour shows that the physico-chemical parameters of tile self-assembly govern the tractability of self-replication process and reliability of replicating patterns. Observations are made about the limitations of the simulator, and a few suggestions for improvement and further studies are discussed.

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Shape Replication through Self-Assembly and RNase Enzymes

Cited by 49 publications

References 3 publications

Terminating distributed construction of shapes and patterns in a fair solution of automata

Terminating distributed construction of shapes and patterns in a fair solution of automata

Size-separable tile self-assembly: a tight bound for temperature-1 mismatch-free systems

Simulating Self-replicating Patterns of DNA Tiles

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