Computation by Self-assembly of DNA Graphs (original) (raw)
Related papers
Self-Assembly of Irregular Graphs Whose Edges Are DNA Helix Axes
Journal of The American Chemical Society, 2004
A variety of computational models have been introduced recently that are based on the properties of DNA. In particular, branched junction molecules and graphlike DNA structures have been proposed as computational devices, although such models have yet to be confirmed experimentally. DNA branched junction molecules have been used previously to form graph-like three-dimensional DNA structures, such as a cube and a truncated octahedron, but these DNA constructs represent regular graphs, where the connectivities of all of the vertexes are the same. Here, we demonstrate the construction of an irregular DNA graph structure by a single step of self-assembly. A graph made of five vertexes and eight edges was chosen for this experiment. DNA branched junction molecules represent the vertexes, and duplex molecules represent the edges; in contrast to previous work, specific edge molecules are included as components. We demonstrate that the product is a closed cyclic single-stranded molecule that corresponds to a double cover of the graph and that the DNA double helix axes represent the designed graph. The correct assembly of the target molecule has been demonstrated unambiguously by restriction analysis.
Nature, 2000
Recent work has demonstrated the self-assembly of designed periodic two-dimensional arrays composed of DNA tiles, in which the intermolecular contacts are directed by 'sticky' ends. In a mathematical context, aperiodic mosaics may be formed by the self-assembly of 'Wang' tiles , a process that emulates the operation of a Turing machine. Macroscopic self-assembly has been used to perform computations ; there is also a logical equivalence between DNA sticky ends and Wang tile edges . This suggests that the self-assembly of DNA-based tiles could be used to perform DNA-based computation . Algorithmic aperiodic self-assembly requires greater fidelity than periodic self-assembly, because correct tiles must compete with partially correct tiles. Here we report a one-dimensional algorithmic self-assembly of DNA triple-crossover molecules that can be used to execute four steps of a logical (cumulative XOR) operation on a string of binary bits.
2-D DNA self-assembly for satisfiability
DNA based computers V, 2000
DNA self-assembly has been proposed as a way to cope with huge combinatorial NP-HARD problems, such as satis ability. However, the algorithmic designs proposed so far either involve many biosteps or are highly dependent on the particular instance to be solved. This paper presents an algorithmic design for solving satis ability problems using two-dimensional DNA self-assembly (tiling). The main driving factor in this work was the design and encoding of the algorithm in a general way that separates the algorithm from the data and minimizes the dependency on particular instances. In e ect, a large amount of work and preparation can be done in advance as a batch process. In practice, it is likely that the total time for computation will be decreased signi cantly and laboratory procedures will be simpli ed.
Computational complexity and pragmatic solutions for flexible tile based DNA self-assembly
2021
Branched junction molecule assembly of DNA nanostructures, pioneered by Seeman’s laboratory in the 1980s, has become increasingly sophisticated, as have the assembly targets. A critical design step is finding minimal sets of branched junction molecules that will self-assemble into target structures without unwanted substructures forming. We use graph theory, which is a natural design tool for self-assembling DNA complexes, to address this problem. After determining that finding optimal design strategies for this method is generally NP-complete, we provide pragmatic solutions in the form of programs for special settings and provably optimal solutions for natural assembly targets such as platonic solids, regular lattices, and nanotubes. These examples also illustrate the range of design challenges.
A DNA computer model for solving vertex coloring problem
Chinese Science Bulletin, 2006
A special DNA computer was designed to solve the vertex coloring problem. The main body of this kind of DNA computer was polyacrylamide gel electrophoresis which could be classified into three parts: melting region, unsatisfied solution region and solution region. This polyacrylamide gel was connected with a controllable temperature device, and the relevant temperature was T m1, T m2 and T m3, respectively. Furthermore, with emphasis on the encoding way, we succeeded in performing the experiment of a graph with 5 vertices. In this paper we introduce the basic structure, the principle and the method of forming the library DNA sequences.
Algorithmic Self-Assembly of DNA Sierpinski Triangles
PLOS Biology, 2004
Algorithms and information, fundamental to technological and biological organization, are also an essential aspect of many elementary physical phenomena, such as molecular self-assembly. Here we report the molecular realization, using two-dimensional self-assembly of DNA tiles, of a cellular automaton whose update rule computes the binary function XOR and thus fabricates a fractal pattern-a Sierpinski triangle-as it grows. To achieve this, abstract tiles were translated into DNA tiles based on double-crossover motifs. Serving as input for the computation, long singlestranded DNA molecules were used to nucleate growth of tiles into algorithmic crystals. For both of two independent molecular realizations, atomic force microscopy revealed recognizable Sierpinski triangles containing 100-200 correct tiles. Error rates during assembly appear to range from 1% to 10%. Although imperfect, the growth of Sierpinski triangles demonstrates all the necessary mechanisms for the molecular implementation of arbitrary cellular automata. This shows that engineered DNA self-assembly can be treated as a Turing-universal biomolecular system, capable of implementing any desired algorithm for computation or construction tasks.
DNA Solution of a Graph Coloring Problem
Journal of Chemical Information and Modeling, 2002
The graph-theoretic parameter that has probably received the most attention over the years is the chromatic number. As is well-known, the coloring problem is an NP-Complete problem. In this paper, it has been solved by means of molecular biology techniques. The algorithm is highly parallel and has satisfactory fidelity. This work shows further evidence for the ability of DNA computing to solve NP-Complete problems.
International Journal in Foundations of Computer Science & Technology (IJFCST), 2013
Although it has been evidenced that DNA computing is able to solve the graph coloring problem in a polynomial time complexity, but the exponential solution space is still a restrictive factor in applying this technique for solving really large problems. In this paper a modified DNA computing approach based on Adleman-Lipton model is proposed which tackles the mentioned restriction by coloring the vertices one by one. In each step, it expands the DNA strands encoding promising solutions and discards those which encode infeasible ones. A sample graph is colored by simulating the proposed approach and shows a notable reduction in the number of DNA strands used.
Molecular Computations Using Self-Assembled DNA Nanostructures and Autonomous Motors
Self-assembly is the spontaneous self-ordering of substructures into superstructures driven by the selective affinity of the substructures. DNA provides a molecular scale material for programmable self-assembly, using the selective affinity of pairs of DNA strands to form DNA nanostructures. DNA self-assembly is the most advanced and versatile system that has been experimentally demonstrated for programmable construction of patterned systems on the molecular scale. The methodology of DNA self-assembly begins with the synthesis of single-strand DNA molecules that self-assemble into macromolecular building blocks called DNA tiles. These tiles have sticky ends that match the sticky ends of other DNA tiles, facilitating further assembly into larger structures known as DNA tiling lattices. In principle, DNA tiling assemblies can form any computable two or three-dimensional pattern, however complex, with the appropriate choice of the tiles' component DNA. Two-dimensional DNA tiling lattices composed of hundreds of thousands of tiles have been demonstrated experimentally. These assemblies can be used as scaffolding on which to position molecular electronics and robotics components with precision and specificity. This programmability renders the scaffolding have the patterning required for fabricating complex devices made of these components. We overview the evolution of DNA self-assembly techniques from pure theory, through simulation and design, and then to experimental practice. We will begin with an overview of theoretical models and algorithms for DNA lattice self-assembly. Then we describe our software for the simulation and design of DNA tiling assemblies and DNA nanomechanical devices. As an example, we discuss models and algorithms for the key problem of error control in DNA lattice self-assembly, as well as the computer simulation of these methods for error control. We will then briefly discuss our experimental laboratory demonstrations, including those using the designs derived by our software. These experimental demonstrations of DNA self-assemblies include the assembly of patterned objects at the molecular scale, the execution of molecular computations, and freely running autonomous DNA motors.
Building Blocks for DNA Self-Assembly
DNA complexes, like the double crossover, are used as building blocks for the assembly of higher-order structures. Currently, the number of complexes that have been experimentally proven to be reliable is small. We have begun work on expanding the collection of such complexes with the intent that this will build new classes of structures (e.g. three-dimensional). Here we report on our design concepts and initial experiments.