Complexity of graph self-assembly in accretive systems and self-destructible systems

Theoretical Computer Science

Volumn 412, Issue 17, 2011, Pages 1592-1605

  Reif, John H ^a   Sahu, Sudheer ^a   Yin, Peng ^a  

^a Duke University   (United States)

Author keywords

Complexity; DNA; Graph; Nanostrcture; NP; NP complete; PSPACE complete; Self assembly

Indexed keywords

COMPLEXITY; GRAPH; NANOSTRCTURE; NP; NP COMPLETE; PSPACE-COMPLETE;

ASSEMBLY; COMPUTATIONAL COMPLEXITY; NUCLEIC ACIDS; POLYNOMIALS; SELF ASSEMBLY;

STOCHASTIC MODELS;

EID: 79952073349     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.tcs.2010.10.034     Document Type: Article

References (45)

1. http://mrsec.wisc.edu/edetc/selfassembly/
2. L. Adleman, Towards a mathematical theory of self-assembly, Technical Report 00-722, University of Southern California, 2000.
3. L. Adleman, Q. Cheng, A. Goel, and M.D. Huang Running time and program size for self-assembled squares Proceedings of the Thirty-Third Annual ACM Symposium on Theory of Computing 2001 ACM Press 740 748 (Pubitemid 32865792)
4. L. Adleman, Q. Cheng, A. Goel, M.D. Huang, D. Kempe, P.M. de Espans, and P.W.K. Rothemund Combinatorial optimization problems in self-assembly Proceedings of the Thirty-Fourth Annual ACM Symposium on Theory of Computing 2002 ACM Press 23 32 (Pubitemid 35009357)
5. L. Adleman, Q. Cheng, A. Goel, M.D. Huang, H. Wasserman, Linear self-assemblies: Equilibria, entropy, and convergence rate, in: Sixth International Conference on Difference Equations and Applications, 2001.
6. G. Aggarwal, M.H. Goldwasser, M.Y. Kao, and R.T. Schweller Complexities for generalized models of self-assembly Proceedings of 15th Annual ACM-SIAM Symposium on Discrete Algorithms SODA 2004 ACM Press 880 889
7. N. Bowden, A. Terfort, J. Carbeck, and G.M. Whitesides Self-assembly of mesoscale objects into ordered two-dimensional arrays Science 276 11 1997 233 235 (Pubitemid 27172675)
8. R.F. Bruinsma, W.M. Gelbart, D. Reguera, J. Rudnick, and R. Zandi Viral self-assembly as a thermodynamic process Phys. Rev. Lett. 90 24 2003 248101 June 20
9. N. Chelyapov, Y. Brun, M. Gopalkrishnan, D. Reishus, B. Shaw, and L. Adleman DNA triangles and self-assembled hexagonal tilings J. Am. Chem. Soc. 126 2004 13924 13925 (Pubitemid 39447058)
10. H.L. Chen, Q. Cheng, A. Goel, M.D. Huang, P.M. de Espanes, Invadable self-assembly: Combining robustness with efficiency, in: Proceedings of the 15th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA, 2004, pp. 890899.
11. H.L. Chen, and A. Goel Error free self-assembly using error prone tiles DNA Based Computers 10 2004 274 283
12. Q. Cheng, A. Goel, P. Moisset, Optimal self-assembly of counters at temperature two, in: Proceedings of the First Conference on Foundations of Nanoscience: Self-assembled Architectures and Devices, 2004.
13. M. Cook, P.W.K. Rothemund, and E. Winfree Self-assembled circuit patterns DNA Based Computers 9 LNCS vol. 2943 2004 91 107
14. K. Fujibayashi, and S. Murata A method for error suppression for self-assembling DNA tiles DNA Based Computing 10 2004 284 293
15. Y. He, Y. Chen, H. Liu, A.E. Ribbe, and C. Mao Self-assembly of hexagonal DNA two-dimensional (2D) arrays J. Am. Chem. Soc. 127 2005 12202 12203 (Pubitemid 41279226)
16. N. Jonoska, S.A. Karl, and M. Saito Three dimensional DNA structures in computing BioSystems 52 1999 143 153 (Pubitemid 29518358)
17. N. Jonoska, and G. McColm A computational model for self-assembling flexible tiles C.S. Calude, M.J. Dinnen, G. Paun, M.J. Perez-Jimenez, G. Rozenberg, Lecture Notes for Computer Science (LNCS) vol. 3699 2005 Springer-Verlag Berlin 142 156 (Pubitemid 41491499)
18. N. Jonoska, P. Sa-Ardyen, and N.C. Seeman Computation by self-assembly of DNA graphs Journal of Genetic Programming and Evolvable Machines 4 2003 123 137 (Pubitemid 36768092)
19. M. Kao, R. Schweller, Reduce complexity for tile self-assembly through temperature programming, in: Proceedings of 17th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA, ACM Press, 2006 (in press).
20. E. Klavins Toward the control of self-assembling systems Control Problems in Robotics vol. 4 2002 Springer Verlag 153 168
21. E. Klavins, Directed self-assembly using graph grammars, in: Foundations of Nanoscience: Self Assembled Architectures and Devices, Snowbird, UT, 2004.
22. E. Klavins, R. Ghrist, D. Lipsky, Graph grammars for self-assembling robotic systems, in: Proceedings of the International Conference on Robotics and Automation, 2004.
23. T.H. LaBean, H. Yan, J. Kopatsch, F. Liu, E. Winfree, J.H. Reif, and N.C. Seeman The construction, analysis, ligation and self-assembly of DNA triple crossover complexes J. Am. Chem. Soc. 122 2000 1848 1860 (Pubitemid 30143885)
24. D. Lichtenstein Planar formulae and their uses SIAM J. Comput. 11 2 1982 329 343
25. A. Middleton Computational complexity of determining the barriers to interface motion in random systems Phys. Rev. E 59 3 1999 2571 2577 (Pubitemid 129306020)
26. J. Malo, J.C. Mitchell, C. Venien-Bryan, J.R. Harris, H. Wille, D.J. Sherratt, and A.J. Turberfield Engineering a 2D protein-DNA crystal Angew. Chem. Intl. Ed. 44 2005 3057 3061 (Pubitemid 40689844)
27. C.M. Papadimitriou Computational Complexity 1st edition 1994 Addison-Wesley Publishing Company, Inc.
28. J.H. Reif, S. Sahu, P. Yin, Compact error-resilient computational DNA tiling assemblies, in: Proc. 10th International Meeting on DNA Computing, 2004, pp. 248260.
29. R.M. Robinson Undecidability and non periodicity of tilings of the plane Invent. Math. 12 1971 177 209
30. P.W.K. Rothemund Using lateral capillary forces to compute by self-assembly Proc. Natl. Acad. Sci. USA 97 3 2000 984 989 (Pubitemid 30080799)
31. P.W.K. Rothemund, N. Papadakis, and E. Winfree Algorithmic self-assembly of DNA Sierpinski triangles PLoS Bio. 12 2004 2:e424
32. P.W.K. Rothemund, and E. Winfree The program-size complexity of self-assembled squares (extended abstract) Proceedings of the Thirty-Second Annual ACM Symposium on Theory of Computing 2000 ACM Press 459 468
33. P. Sa-Ardyen, N. Jonoska, and N.C. Seeman Self-assembling DNA graphs Lect. Notes Comput. Sci. 2568 2003 1 9
34. S. Sahu, P. Yin, J.H. Reif, A self assembly model of time-dependent glue strength, in: Proc. 11th International Meeting on DNA Computing, 2005, pp. 113124.
35. R. Schulman, S. Lee, N. Papadakis, and E. Winfree One dimensional boundaries for DNA tile self-assembly DNA Based Computers 9 LNCS vol. 2943 2004 108 125
36. R. Schulman, and E. Winfree Programmable control of nucleation for algorithmic self-assembly DNA Based Computers 10 LNCS 2005
37. R. Schulman, E. Winfree, Self-replication and evolution of DNA crystals, in: The 13th European Conference on Artificial Life, ECAL, 2005.
38. D. Soloveichik, E. Winfree, Complexity of compact proofreading for self-assembled patterns, in: Proc. 11th International Meeting on DNA Computing, 2005, pp. 125135.
39. D. Soloveichik, and E. Winfree Complexity of self-assembled shapes DNA Based Computers 10 LNCS 2005
40. A. Strasser, L. O'Connor, and V.M. Dixit Apoptosis signaling Annu. Rev. Biochem. 69 2000 217 245
41. H. Wang Proving theorems by pattern recognition ii Bell Syst. Tech. J. 40 1961 1 41
42. E. Winfree, Self-healing tile sets, Draft, 2005.
43. E. Winfree, and R. Bekbolatov Proofreading tile sets: Error correction for algorithmic self-assembly DNA Based Computers 9 LNCS vol. 2943 2004 126 144
44. E. Winfree, F. Liu, L.A. Wenzler, and N.C. Seeman Design and self-assembly of two-dimensional DNA crystals Nature 394 6693 1998 539 544 (Pubitemid 28366820)
45. H. Yan, T.H. LaBean, L. Feng, and J.H. Reif Directed nucleation assembly of DNA tile complexes for barcode patterned DNA lattices Proc. Natl. Acad. Sci. USA 100 14 2003 8103 8108 (Pubitemid 36842505)