Complexity classes for self-assembling flexible tiles

Theoretical Computer Science

Volumn 410, Issue 4-5, 2009, Pages 332-346

  Jonoska, Nataša ^a   McColm, Gregory L ^a  

^a UNIVERSITY OF SOUTH FLORIDA   (United States)

Author keywords

Assembling complexes; Complexity classes of self assembly; DNA junction molecules; DNA based graph structures; Self assembly

Indexed keywords

BUILDING MATERIALS; DNA; GENES; ORGANIC ACIDS; SELF ASSEMBLY;

ASSEMBLING COMPLEXES; COMPLEXITY CLASSES OF SELF-ASSEMBLY; DNA TILES; THEORETICAL MODELS;

NUCLEIC ACIDS;

EID: 58249125011     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.tcs.2008.09.054     Document Type: Article

References (39)

1. Adleman L. Molecular computation of solutions of combinatorial problems. Science 266 (1994) 1021-1024
2. L.M. Adleman, Q. Cheng, A. Goel, M.-D. Huang, D. Kempe, P. Moisset de Espanés, P.W.K. Rothemund, Combinatorial optimization problems in self-assembly, in: STOC'02 Proceedings, Montreal Quebec, Canada, 2002
3. L.M. Adleman, J. Kari, L. Kari, D. Reishus, On the decidability of self-assembly of infinite ribbons, in: Proceedings of FOCS 2002, IEEE Symposium on Foundations of Computer Science, Washington, 2002, pp. 530-537
4. Angelov S., Khanna S., and Visontai M. On the complexity of graph self-assembly in accretive systems. Natural Computing October (2007)
5. Barish R.D., Rothemund P.W.K., and Winfree E. Two computational primitives for algorithmic self-assembly: Copying and counting. Nanoletters 5 12 (2005) 2586-2592
6. Chen J.H., and Seeman N.C. Synthesis from DNA of a molecule with the connectivity of a cube. Nature 350 (1991) 631-633
7. S. Cook, The complexity of theorem proving procedures, in: Proc. 3rd. ACM Ann. Symp. Theory of Comput., 1971, pp. 151-158
8. Fagin R. Generalized first-order spectra and polynomial-time recognizable sets. In: Karp R. (Ed). Complexity of Computation. SIAM-AMS Proceedings vol. 7 (1974) 43-73
9. Goodman R.P., Schaap I.A., Tardin C.F., Erben C.M., Berry R.M., Schmidt C.F., and Turberfield A.J. Rapid chiral assembly of rigid DNA building blocks for molecular nanofabrication. Science 310 5754 (2005) 1661-1665
10. Faulhammer D., Curkas A.R., Lipton R.J., and Landweber L.F. Molecular computation: RNA solution to chess problems. Proceedings of the National Academy of Sciences 97 (2000) 1385-1389
11. Fu T.J., and Seeman N.C. DNA double crossover structures. Biochemistry 32 (1993) 3211-3220
12. Garey M.R., and Johnson D.S. Computers and Intractability: A Guide to the Theory of NP-completeness (1979), W. H. Freeman
13. Head T., et al. Computing with DNA by operating on plasmids. BioSystems 57 (2000) 87-93
14. Jonoska N., Sa-Ardyen P., and Seeman N.C. Computation by self-assembly of DNA graphs. Genetic Programming and Evolvable Machines 4 (2003) 123-137
15. Jonoska N., Karl S., and Saito M. Three dimensional DNA structures in computing. BioSystems 52 (1999) 143-153
16. Jonoska N., Karl S., and Saito M. Creating 3-dimensional graph structures with DNA. In: Rubin H., and Wood D. (Eds). DNA Based Computers III. AMS DIMACS Series vol. 48 (1999) 123-136
17. Jonoska N., and McColm G. A computational model for self-assembling flexible tiles. In: Calude C.S., Dinneen M.J., Paun G., Pérez-Jiménez M.J., and Rozenberg G. (Eds). Proceedings of the 4th International Conference on Unconventional Computation (Sevilla, Spain, October 2005). LNCS vol. 3699 (2005), Springer 142-156
18. Jonoska N., and McColm G. Flexible versus rigid tile assembly. In: Paun Gh., et al. (Ed). Unconventional Computers. LNCS vol. 4135 (2006), Springer 139-151
19. N. Jonoska, G. McColm, A. Staninska, Expectation and variance of self-assembled graph structures, in: Proceedings of 11th International Meeting on DNA Computing, London, Ontario, Canada, June 6-9, 2005, pp. 49-58
20. Jonoska N., McColm G., and Staninska A. Spectrum of a pot for DNA complexes in DNA Computing 12. In: Mao C., and Yokomori T. (Eds). LNCS vol. 4287 (2006), Springer 83-94
21. Kao M.-Y., and Ramachandran V. DNA self-assembly for constructing 3D boxes. Algorithms and Computation: ISAAC 2001 Proceedings. LNCS vol. 2223 (2001), Springer 429-440
22. LaBean T.H., Yan H., Kopatsch J., Liu F., Winfree E., Reif J.H., and Seeman N.C. The construction, analysis, ligation and self-assembly of DNA triple crossover complexes. Journal of American Chemical Society 122 (2000) 1848-1860
23. Mao C., LaBean T.H., Reif J.H., and Seeman N.C. Logical computation using algorithmic self-assembly of DNA triple-crossover molecules. Nature 407 (2000) 493-496
24. J.H. Reif, S. Sahu, P. Yin, Complexity of graph self-assembly in accretive systems and self-destructive systems, in: Proceedings of 11th International Meeting on DNA Computing, London, Ontario, Canada, June 6-9, 2005, pp. 101-112
25. Rothemund P.W. Folding DNA to create nanoscale shapes and patterns. Nature 440 7082 (2006) 297-302
26. P.W.K. Rothemund, E. Winfree, The program-size complexity of self-assembled squares, in: Proceedings of 33rd ACM meeting STOC 2001, Portland, Oregon, May 21-23, 2001, pp. 459-468
27. Rothemund P., Papadakis N., and Winfree E. Algorithmic self-assembly of DNA Sierpinski triangles. PLoS Biology 2 12 (2004) e424
28. Sa-Ardyen P., Jonoska N., and Seeman N. Self-assembly of graphs represented by DNA helix axis topology. Journal of American Chemical Society 126 21 (2004) 6648-6657
29. Seeman N.C. DNA junctions and lattices. Journal of Theoretical Biology 99 (1982) 237-247
30. Seeman N.C. DNA nicks and nodes and nanotechnology. NanoLetters 1 (2001) 22-26
31. Shihm W.M., Quispe J.D., and Joyce G.F. A 1.7-kilobase single-stranded DNA folds into a nano-scale octahedron. Nature 427 Feb. (2004) 618-621
32. D. Soloveichik, E. Winfree, Complexity of self-assembled shapes, preprint at http://arxiv.org/abs/cs.CC/0412096
33. Stockmeyer L. The polynomial-time hierarchy. Theoretical Computer Science 3 (1974) 1-22
34. Wang Y., Mueller J.E., Kemper B., and Seeman N.C. The assembly and characterization of 5-arm and 6-arm DNA junctions. Biochemistry 30 (1991) 5667-5674
35. Wang X., and Seeman N.C. Assembly and characterization of 8-arm and 12-arm DNA branched junctions. Journal of American Chemical Society Jun (2007)
36. Winfree E., Yang X., and Seeman N.C. Universal computation via self-assembly of DNA: Some theory and experiments. In: Landweber L., and Baum E. (Eds). DNA Based Computers II. AMS DIMACS series vol. 44 (1998) 191-214
37. Winfree E., Liu F., Wenzler L.A., and Seeman N.C. Design and self-assembly of two-dimensional DNA crystals. Nature 394 (1998) 539-544
38. G. Wu, N. Jonoska, N.C. Seeman, Self-assembly of a DNA nano-object demonstrates natural computation (submitted for publication)
39. Zhang Y., and Seeman N.C. The construction of a DNA truncated octahedron. Journal of American Chemical Society 160 (1994) 1661-1669