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Algorithmic SelfAssembly of DNA
, 1998
"... How can molecules compute? In his early studies of reversible computation, Bennett imagined an enzymatic Turing Machine which modified a heteropolymer (such as DNA) to perform computation with asymptotically low energy expenditures. Adleman's recent experimental demonstration of a DNA computat ..."
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Cited by 156 (6 self)
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How can molecules compute? In his early studies of reversible computation, Bennett imagined an enzymatic Turing Machine which modified a heteropolymer (such as DNA) to perform computation with asymptotically low energy expenditures. Adleman's recent experimental demonstration of a DNA computation, using an entirely different approach, has led to a wealth of ideas for how to build DNAbased computers in the laboratory, whose energy efficiency, information density, and parallelism may have potential to surpass conventional electronic computers for some purposes. In this thesis, I examine one mechanism used in all designs for DNAbased computer  the selfassembly of DNA by hybridization and formation of the double helix  and show that this mechanism alone in theory can perform universal computation. To do so, I borrow an important result in the mathematical theory of tiling: Wang showed how jigsawshaped tiles can be designed to simulate the operation of any Turing Machine. I propose...
Universal computation via selfassembly of DNA: Some theory and experiments
 In DNA Based Computers II, volume 44 of DIMACS
, 1996
"... In this paper we examine the computational capabilities inherent inthehybridization of DNA molecules. First we consider theoretical models, and show that the selfassembly of oligonucleotides into linear duplex DNA can only generate sets of sequences equivalent to regular languages. If branched DNA ..."
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Cited by 100 (12 self)
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In this paper we examine the computational capabilities inherent inthehybridization of DNA molecules. First we consider theoretical models, and show that the selfassembly of oligonucleotides into linear duplex DNA can only generate sets of sequences equivalent to regular languages. If branched DNA is used for selfassembly of dendrimer structures, only sets of sequences equivalent tocontextfree languages can be achieved. In contrast, the selfassembly of double crossover molecules into two dimensional sheets or three dimensional solids is theoretically capable of universal computation. The proof relies on a very direct simulation of a universal class of cellular automata. In the second part of this paper, we present results from preliminary experiments which investigate the critical computational step in atwodimensional selfassembly process. 1
Simulations of Computing by SelfAssembly
, 1998
"... Winfree (1996) proposed a Turinguniversal model of DNA selfassembly. In this abstract model, DNA doublecrossover molecules selfassemble to form an algorithmicallypatterned twodimensional lattice. Here, we develop a more realistic model based on the thermodynamics and kinetics of oligonucleo ..."
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Cited by 91 (15 self)
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Winfree (1996) proposed a Turinguniversal model of DNA selfassembly. In this abstract model, DNA doublecrossover molecules selfassemble to form an algorithmicallypatterned twodimensional lattice. Here, we develop a more realistic model based on the thermodynamics and kinetics of oligonucleotide hydridization. Using a computer simulation, we investigate what physical factors influence the error rates, i.e., when the more realistic model deviates from the ideal of the abstract model. We find, in agreement with rules of thumb for crystal growth, that the lowest error rates occur at the melting temperature when crystal growth is slowest, and that error rates can be made arbitrarily low by decreasing concentration and increasing binding strengths. 1 Introduction Early work in DNA computing (Adleman 1994; Lipton 1995; Boneh et al. 1996; Ouyang et al. 1997) showed how computations can be accomplished by first creating a combinatorial library of DNA and then, through successiv...
Two computational primitives for algorithmic selfassembly: Copying and counting
 Nano Letters
, 2005
"... Copying and counting are useful primitive operations for computation and construction. We have made DNA crystals that copy and crystals that count as they grow. For counting, 16 oligonucleotides assemble into four DNA Wang tiles that subsequently crystallize on a polymeric nucleating scaffold strand ..."
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Cited by 68 (5 self)
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Copying and counting are useful primitive operations for computation and construction. We have made DNA crystals that copy and crystals that count as they grow. For counting, 16 oligonucleotides assemble into four DNA Wang tiles that subsequently crystallize on a polymeric nucleating scaffold strand, arranging themselves in a binary counting pattern that could serve as a template for a molecular electronic demultiplexing circuit. Although the yield of counting crystals is low, and pertile error rates in such crystals is roughly 10%, this work demonstrates the potential of algorithmic selfassembly to create complex nanoscale patterns of technological interest. A subset of the tiles for counting form informationbearing DNA tubes that copy bit strings from layer to layer along their length. The challenge of engineering complex devices at the nanometer scale has been approached from two radically different directions. In topdown synthesis, information about the desired structure is imposed by an external apparatus, as in photolithography. In bottomup synthesis, structure arises spontaneously due to chemical and physical forces intrinsic to the molecular components themselves. A significant challenge for bottomup techniques is how to design
Simulating Boolean Circuits on a DNA Computer
, 1997
"... We demonstrate that DNA computers can simulate Boolean circuits with a small overhead. Boolean circuits embody the notion of massively parallel signal processing and are jrequen,tly encountered in many parallel algorithms. Many important problems such as sorting, integer arithmetic, and matrix mult ..."
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Cited by 61 (8 self)
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We demonstrate that DNA computers can simulate Boolean circuits with a small overhead. Boolean circuits embody the notion of massively parallel signal processing and are jrequen,tly encountered in many parallel algorithms. Many important problems such as sorting, integer arithmetic, and matrix multiplication are known to be computable by small size Boolean circuits much faster than by ordinary sequential digital computers. This paper shows that DNA chemistry allows one to simulate large semiunbounded janin Boolean circuits with a logarithmic slowdown in computation time. Also, for the class NC¹, the slowdown can be reduced to a constant. In this algorathm we have encoded the inputs, the Boolean AND gates, and the OR gates to DNA oligonucleotide sequences. We operate on the gates and the inputs by standard molecular techniques of sequencespecific annealing, ligation, separation by size, amplification, sequencespecific cleavage, and detection by size. Additional steps of amplification are not necessary for NC¹ circuits. Preliminary biochemical experiments on a small test circuit have produced encouraging results. Further confirmatory experiments are in progress.
Proofreading tile sets: Error correction for algorithmic selfassembly
 DNA Computers
"... Abstract. For robust molecular implementation of tilebased algorithmic selfassembly, methods for reducing errors must be developed. Previous studies suggested that by control of physical conditions, such as temperature and the concentration of tiles, errors (") can be reduced to an arbitrar ..."
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Cited by 60 (11 self)
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Abstract. For robust molecular implementation of tilebased algorithmic selfassembly, methods for reducing errors must be developed. Previous studies suggested that by control of physical conditions, such as temperature and the concentration of tiles, errors (") can be reduced to an arbitrarily low rate { but at the cost of reduced speed (r) for the selfassembly process. For tile sets directly implementing blocked cellular automata, it was shown that r "2 was optimal. Here, we show that an improved construction, which we refer to as proofreading tile sets, can in principle exploit the cooperativity of tile assembly reactions to dramatically improve the scaling behavior to r " and better. This suggests that existing DNAbased molecular tile approaches may be improved to produce macroscopic algorithmic crystals with few errors. Generalizations and limitations of the proofreading tile set construction are discussed. 1
Local parallel biomolecular computing
 DNA Based Computers III, volume 48 of DIMACS
, 1999
"... Biomolecular Computation(BMC) is computation at the molecular scale, using biotechnology engineering techniques. Most proposed methods for BMC used distributed (molecular) parallelism (DP); where operations are executed in parallel on large numbers of distinct molecules. BMC done exclusively by DP r ..."
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Cited by 55 (17 self)
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Biomolecular Computation(BMC) is computation at the molecular scale, using biotechnology engineering techniques. Most proposed methods for BMC used distributed (molecular) parallelism (DP); where operations are executed in parallel on large numbers of distinct molecules. BMC done exclusively by DP requires that the computation execute sequentially within any given molecule (though done in parallel for multiple molecules). In contrast, local parallelism (LP) allows operations to be executed in parallel on each given molecule. Winfree, et al [W96, WYS96]) proposed an innovative method for LPBMC, that of computation by unmediated selfassembly of � arrays of DNA molecules, applying known domino tiling techniques (see Buchi [B62], Berger [B66], Robinson [R71], and Lewis and Papadimitriou [LP81]) in combination with the DNA selfassembly techniques of Seeman et al [SZC94]. The likelihood for successful unmediated selfassembly of computations has not been determined (we discuss a simple model of assembly where there may be blockages in selfassembly, but more sophisticated models may have a higher likelihood of success). We develop improved techniques to more fully exploit the potential power of LPBMC. To increase
Compact ErrorResilient Computational DNA Tiling Assemblies
"... The selfassembly process for bottomup construction of nanostructures is of key importance to the emerging of the new scientific discipline of Nanoscience. For example, the selfassembly of DNA tile nanostructures into 2D and 3D lattices can be used to perform parallel universal computation and to ..."
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Cited by 53 (10 self)
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The selfassembly process for bottomup construction of nanostructures is of key importance to the emerging of the new scientific discipline of Nanoscience. For example, the selfassembly of DNA tile nanostructures into 2D and 3D lattices can be used to perform parallel universal computation and to manufacture patterned nanostructures from smaller unit components known as DNA tiles. However, selfassemblies at the molecular scale are prone to a quite high rate of error, and the key barrier to largescale experimental implementation of DNA tiling is the high error rate in the selfassembly process. One major challenge to nanostructure selfassembly is to eliminate/limit these errors. The goals of this paper are to develop theoretical methods for compact errorresilient selfassembly, to analyze these by stochastic analysis and computer simulation (at a future date we also intend to demonstrate these errorresilient selfassembly methods by a series of laboratory experiments). Prior work by Winfree provided a innovative approach to decrease tiling selfassembly errors without decreasing the intrinsic error rate # of assembling a single tile, however, his technique resulted in a final structure that is four times the size of the original one. This paper describes various compact errorresilient tiling methods that do not increase the size of the tiling assembly. These methods apply to assembly of boolean arrays which perform input sensitive computations (among other computations). We first describe an errorresilient tiling using 2way overlay redundancy such that a single pad mismatch between a tile and its immediate neighbor forces at least one further pad mismatch between a pair of adjacent tiles in the neighborhood of this tile. This drops the error rate from # to appr...
From genes to machines: DNA nanomechanical devices. Trends Biochem Sci,
, 2005
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Selfassembled circuit patterns
 In DNA Computing 9
, 2004
"... Abstract. Selfassembly is a process in which basic units aggregate under attractive forces to form larger compound structures. Recent theoretical work has shown that pseudocrystalline selfassembly can be algorithmic, in the sense that complex logic can be programmed into the growth process [26]. ..."
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Cited by 44 (14 self)
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Abstract. Selfassembly is a process in which basic units aggregate under attractive forces to form larger compound structures. Recent theoretical work has shown that pseudocrystalline selfassembly can be algorithmic, in the sense that complex logic can be programmed into the growth process [26]. This theoretical work builds on the theory of twodimensional tilings [8], using rigid square tiles called Wang tiles [24] for the basic units of selfassembly, and leads to Turinguniversal models such as the Tile Assembly Model [28]. Using the Tile Assembly Model, we show how algorithmic selfassembly can be exploited for fabrication tasks such as constructing the patterns that define certain digital circuits, including demultiplexers, RAM arrays, pseudowavelet transforms, and Hadamard transforms. Since DNA selfassembly appears to be promising for implementing the arbitrary Wang tiles [30, 13] needed for programming in the Tile Assembly Model, algorithmic selfassembly methods such as those presented in this paper may eventually become a viable method of arranging molecular electronic components [18], such as carbon nanotubes [10, 1], into molecularscale circuits. 1