Abstract
It has been shown theoretically that three dimensional graph structure and DNA self-assembly can be used to solve numerous computational problems such as 3-SAT and 3-colorability in a constant number of laboratory steps. In this assembly, junction molecules and duplex DNA molecules are the basic building blocks. This paper presents experimental results of DNA self-assembly of non regular graphs using junction molecules as vertices and duplex DNA molecules as edge connections.
Similar content being viewed by others
References
Bates AD and Maxwell A (1993) DNA Topology. IRL Press, Oxford
Chen JH and Seeman NC (1991) Synthesis from DNA of a molecule with the connectivity of a cube. Nature 350: 631–633
Chen JH and Kallenbach NR and Seeman NC (1989) A specific quadrilateral synthesized from DNA branched junctions. J. Am. Chem. Soc. 111: 6402–6407
Feldkamp U, Saghafi S and Rauhe H (2002) DNASequenceGenerator: A program for the construction of DNA sequences. In: Jonoska N and Seeman NC (eds) DNA Computing: Proceedings of the 7th International Meeting on DNA Based Computers, pp. 23–32. Springer LNCS 2340
Fischer SG and Lerman LS (1979) Length-Independent Separation of DNA Restriction Fragments in 2-Dimensional Gel-Electrophoresis. Cell 16(1): 191–200
Head T (1987) Formal language theory and DNA: An analysis of generative capacity of recombinant behaviours. Bul. of Mathematical Biology 49: 735–759
Jonoska N, Karl S and Saito M (1999) Three dimensional DNA structures in computing. BioSystems 52: 143–153
Jonoska N and Saito M (2002) Boundary components of thickened graphs. In: Jonoska N and Seeman NC (eds) DNA Computing: Proceedings of the 7th International Meeting on DNA Based Computers, pp. 70–81. Springer LNCS 2340
Mao C, LaBean TH, Reif JH and Seeman NC (2000) Logical computation using algorithmic self-assembly of DNA triple-crossover molecules. Nature 407: 493–496
Reif JH (1999) Local parallel biomolecular computation. In: Rubin H and Wood DH (eds) DNA Based Computers III, pp. 217–254. AMS DIMACS series 48
Sakakibara Y and Ferretti C (1999) Splicing on tree-like structures. In: Rubin H and Wood DH (eds) DNA Computers III, pp. 361–275. AMS DIMACS series 48
Seeman NC (1990) De novo design of sequences for nucleic acid structural engineering. J. of Biomolecular Structure & Dynamics 8(3): 573–581
Seeman NC and Kallenbach NR (1988) Nucleic acid junctions: A successful experiment in macromolecular design. In: Stezowski JJ, Huang JL and Shao MC (eds) Molecular Structure: Chemical Reactivity and Biological Activity, pp. 189-194. Oxford University Press, Oxford
Uejima H, Hagiya M and Kobayashi S (2002) Horn clause computation by self-assembly of DNA molecules. In: Jonoska N and Seeman NC (eds) DNA Computing: Proceedings of the 7th International Meeting on DNA Based Computers, pp. 308–320. Springer LNCS 2340
Wasserman SA and Cozzarelli NR (1986) Biochemical topology: Applications to DNA recombination and replication. Science 232: 951–960
Winfree E, Yang X and Seeman NC (1998) Universal computation via self-assembly of DNA: Some theory and experiments. In: Landweber L and Baum E (eds) DNA Computers II, pp. 191–214. AMS DIMACS series 44
Winfree E, Liu F, Wenzler LA and Seeman NC (1998) Design and self-assembly of two-dimensional DNA crystals. Nature 394: 539–544
Zhang Y and Seeman NC (1994) The construction of a DNA truncated octahedron. J. Am. Chem. Soc. 160: 1661–1669
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Sa-Ardyen, P., Jonoska, N. & Seeman, N.C. Self-assembling DNA graphs. Natural Computing 2, 427–438 (2003). https://doi.org/10.1023/B:NACO.0000006771.95566.34
Issue Date:
DOI: https://doi.org/10.1023/B:NACO.0000006771.95566.34