Hierarchical self assembly of patterns from the Robinson tilings: DNA tile design in an enhanced Tile Assembly Model

Padilla, Jennifer E.; Liu, Wenyan; Seeman, Nadrian C.

doi:10.1007/s11047-011-9268-7

Cited by 34 publications

(27 citation statements)

References 52 publications

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“…There are many examples of incorporating signaltransmission strands on a DNA origami, and most of these models are based on the Yurke et al [29] design for a strand-displacement mechanism using toeholds. These signals are used for either static control of tile assemblies [50][51][52], or for designs of pathways simulating logic gates (e.g. [33,34]).…”

Section: Discussionmentioning

confidence: 99%

Molecular ping-pong Game of Life on a two-dimensional DNA origami array

Jonoska

Seeman

2015

Phil. Trans. R. Soc. A.

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We propose a design for programmed molecular interactions that continuously change molecular arrangements in a predesigned manner. We introduce a model where environmental control through laser illumination allows platform attachment/detachment oscillations between two floating molecular species. The platform is a two-dimensional DNA origami array of tiles decorated with strands that provide both, the floating molecular tiles to attach and to pass communicating signals to neighbouring array tiles. In particular, we show how algorithmic molecular interactions can control cyclic molecular arrangements by exhibiting a system that can simulate the dynamics similar to two-dimensional cellular automata on a DNA origami array platform.

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Section: Discussionmentioning

confidence: 99%

Molecular ping-pong Game of Life on a two-dimensional DNA origami array

Jonoska

Seeman

2015

Phil. Trans. R. Soc. A.

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“…For a number of such models simulation has been used as a method to compare their power. These include the experimentally motivated [56] Signal-Passing [57], and Active [58], Tile Assembly Models with tiles that have molecular (DNA) wires on their surface. Essentially there is a use-once circuit sitting on the assembly itself!…”

Section: (C) Signal Tiles Negative Glues Polyominosmentioning

confidence: 99%

Intrinsic universality and the computational power of self-assembly

Woods

2015

Phil. Trans. R. Soc. A.

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Molecular self-assembly, the formation of large structures by small pieces of matter sticking together according to simple local interactions, is a ubiquitous phenomenon. A challenging engineering goal is to design a few molecules so that large numbers of them can self-assemble into desired complicated target objects. Indeed, we would like to understand the ultimate capabilities and limitations of this bottom-up fabrication process. We look to theoretical models of algorithmic self-assembly, where small square tiles stick together according to simple local rules in order to carry out a crystal growth process. In this survey, we focus on the use of simulation between such models to classify and separate their computational and expressive powers. Roughly speaking, one model simulates another if they grow the same structures, via the same dynamical growth processes. Our journey begins with the result that there is a single intrinsically universal tile set that, with appropriate initialization and spatial scaling, simulates any instance of Winfree's abstract Tile Assembly Model. This universal tile set exhibits something stronger than Turing universality: it captures the geometry and dynamics of any simulated system in a very direct way. From there we find that there is no such tile set in the more restrictive non-cooperative model, proving it weaker than the full Tile Assembly Model. In the two-handed model, where large structures can bind together in one step, we encounter an infinite set of infinite hierarchies of strictly increasing simulation power. Towards the end of our trip, we find one tile to rule them all: a single rotatable flipable polygonal tile that simulates any tile assembly system. We find another tile that aperiodically tiles the plane (but with small gaps). These and other recent results show that simulation is giving rise to a kind of computational complexity theory for self-assembly. It seems this could be the beginning of a much longer journey, so directions for future work are suggested.

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“…For example, the abstract Tile Assembly Model, where individual square DNA tiles attach to a growing assembly lattice one at a time (Winfree 1998; Rothemund and Winfree 2000;Doty et al 2012), the two-handed (hierarchical) model where large multi-tile assemblies come together (Aggarwal et al 2005;Cannon et al 2013;Demaine et al 2008Demaine et al , 2013, and the signal tile model where DNA origami tiles that form an ''active'' lattice with DNA strand displacement signals running along them (Jonoska and Karpenko 2012;Padilla et al 2011Padilla et al , 2013. Other models enable one to program tile geometry (Demaine et al 2014;Fu et al 2012), temperature (Aggarwal et al 2005;Kao and Schweller 2006;Summers 2012), concentration (Becker et al 2006;Chandran et al 2012;Doty 2010;Kao and Schweller 2008), mixing stages and connectivity/flexibility (Jonoska and McColm 2009).…”

Section: Introductionmentioning

confidence: 99%

Parallel computation using active self-assembly

2014

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We study the computational complexity of the recently proposed nubots model of molecular-scale selfassembly. The model generalises asynchronous cellular automata to have non-local movement where large assemblies of molecules can be moved around, analogous to millions of molecular motors in animal muscle effecting the rapid movement of macroscale arms and legs. We show that nubots is capable of simulating Boolean circuits of polylogarithmic depth and polynomial size, in only polylogarithmic expected time. In computational complexity terms, we show that any problem from the complexity class NC is solved in polylogarithmic expected time on nubots that use a polynomial amount of workspace. Along the way, we give fast parallel algorithms for a number of problems including line growth, sorting, Boolean matrix multiplication and space-bounded Turing machine simulation, all using a constant number of nubot states (monomer types). Circuit depth is a well-studied notion of parallel time, and our result implies that nubots is a highly parallel model of computation in a formal sense. Asynchronous cellular automata are not capable of such parallelism, and our result shows that adding a movement primitive to such a model, to get the nubots model, drastically increases parallel processing abilities.

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Hierarchical self assembly of patterns from the Robinson tilings: DNA tile design in an enhanced Tile Assembly Model

Cited by 34 publications

References 52 publications

Molecular ping-pong Game of Life on a two-dimensional DNA origami array

Molecular ping-pong Game of Life on a two-dimensional DNA origami array

Intrinsic universality and the computational power of self-assembly

Parallel computation using active self-assembly

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