Algorithmic design of self-folding polyhedra

Proceedings of the National Academy of Sciences of the United States of America

Volumn 108, Issue 50, 2011, Pages 19885-19890

  Pandey, Shivendra ^a   Ewing, Margaret ^b   Kunas, Andrew ^c   Nguyen, Nghi ^d   Gracias, David H ^a,e   Menon, Govind ^f  

^a Johns Hopkins University   (United States)

^b UNIVERSITY OF MINNESOTA   (United States)

^c Brown Univerity   (United States)

^d UNIVERSITY OF MASSACHUSETTS   (United States)

^e JOHNS HOPKINS UNIVERSITY   (United States)

^f BROWN UNIVERSITY   (United States)

Author keywords

Microfabrication; Origami; Programmable matter; Viral capsid

Indexed keywords

ALGORITHM; ARTICLE; CHEMICAL STRUCTURE; GEOMETRY; MATHEMATICAL MODEL; MICROSCOPY; POLYHEDRA; PRIORITY JOURNAL; PROTEIN ASSEMBLY; PROTEIN FOLDING; SCANNING ELECTRON MICROSCOPY; VIRUS CAPSID;

ALGORITHMS; MICROSCOPY, ELECTRON, SCANNING; MODELS, MOLECULAR; MOLECULAR CONFORMATION;

EID: 84055207469     PISSN: 00278424     EISSN: 10916490     Source Type: Journal    
DOI: 10.1073/pnas.1110857108     Document Type: Article

References (33)

1. Whitesides G, Grzybowski B (2002) Self-assembly at all scales. Science 295:2418-2421. (Pubitemid 34270248)
2. Caspar D, Klug A (1962) Physical principles in the construction of regular viruses. Cold Spring Harb Symp Quant Biol 27:1-24.
3. Lau K, Dill K (1989) A lattice statistical mechanics model of the conformational and sequence spaces of proteins. Macromolecules 22:3986-3997. (Pubitemid 20598764)
4. Chan H, Dill K (1990) The effects of internal constraints on the configurations of chain molecules. J Chem Phys 92:3118-3135.
5. Chen J, Seeman N (1991) Synthesis from DNA of a molecule with the connectivity of a cube. Nature 350:631-633. (Pubitemid 21912289)
6. He Y, et al. (2008) Hierarchical self-assembly of DNA into symmetric supramolecular polyhedra. Nature 452:198-201. (Pubitemid 351380239)
7. Zimmermann J, Cebulla M, Mönninghoff S, von Kiedrowski G (2008) Self-assembly of a DNA dodecahedron from 20 trisoligonucleotides with c3h linkers. Angew Chem Int Ed Engl 47:3626-3630.
8. Douglas S, et al. (2009) Self-assembly of DNA into nanoscale three-dimensional shapes. Nature 459:414-418.
9. Leong T, Zarafshar A, Gracias D (2010) Three-dimensional fabrication at small size scales. Small 6:792-806.
10. Boncheva M, Gracias D, Jacobs H, Whitesides G (2002) Biomimetic self-assembly of a functional asymmetrical electronic device. Proc Natl Acad Sci USA 99:4937-4940. (Pubitemid 34411481)
11. Mahadevan L, Rica S (2005) Self-organized origami. Science 307:1740. (Pubitemid 40388609)
12. Rechtsman M, Stillinger F, Torquato S (2006) Designed interaction potentials via inverse methods for self-assembly. Phys Rev E Stat Nonlin Soft Matter Phys 73:011406.
13. Cohn H, Kumar A (2009) Algorithmic design of self-assembling structures. Proc Natl Acad Sci USA 106:9570-9575.
14. Bassik N, Stern G, Gracias D (2009) Microassembly based on hands free origami with bidirectional curvature. Appl Phys Lett 95:091901.
15. Barish R, Schulman R, Rothemund P, Winfree E (2009) An information-bearing seed for nucleating algorithmic self-assembly. Proc Natl Acad Sci USA 106:6054-6059.
16. Hormoz S, Brenner M (2011) Design principles for self-assembly with short-range interactions. Proc Natl Acad Sci USA 108:5193-5198.
17. Demaine E, O'Rourke J (2007) Geometric Folding Algorithms. Linkages, Origami, Polyhedra (Cambridge Univ Press, New York), pp 299-338.
18. Dürer A, Strauss W (1977) The Painter's Manual (Abaris, New York) p 433.
19. Cromwell P (1999) Polyhedra (Cambridge Univ Press, Cambridge, UK), pp 126-127.
20. Wenninger M (1974) Polyhedron Models (Cambridge Univ Press).
21. Shephard G (1975) Convex polytopes with convex nets. Math Proc Cambridge Philos Soc 78:389-403.
22. Buekenhout F, Parker M (1998) The number of nets of the regular convex polytopes in dimension 4. Discrete Math 186:69-94. (Pubitemid 128391873)
23. Horiyama T, ShojiW(2011) Edge unfoldings of Platonic solids never overlap. Proc 23rd Canadian Conf Computational Geom (CCCG2011), www.2011.cccg.ca.
24. Leong T, Lester P, Koh T, Emma K, Gracias D (2007) Surface tension-driven self-folding polyhedra. Langmuir 23:8747-8751. (Pubitemid 47294281)
25. Azam A, Laflin K, Jamal M, Fernandes R, Gracias D (2011) Self-folding micropatterned polymeric containers. Biomed Microdevices 1-8.
26. Wale M, Edge C, Randle F, Pedder D (1989) A new self-aligned technique for the assembly of integrated optical devices with optical fibre and electrical interfaces. Proceedings of the 15th European Conference on Optical Communications (ECOC) (Novum Grafiska AB, Stockholm), pp 368-371.
27. Syms R (1999) Surface tension powered self-assembly of 3-D micro-optomechanical structures. J Microelectromech Syst 8:448-455.
28. Gimi B, et al. (2005) Self-assembled three dimensional radio frequency (RF) shielded containers for cell encapsulation. Biomed Microdevices 7:341-345.
29. Azam A, Leong T, Zarafshar A, Gracias D (2009) Compactness determines the success of cube and octahedron self-assembly. PloS One 4:e4451.
30. Endres D, Miyahara M, Moisant P, Zlotnick A (2009) A reaction landscape identifies the intermediates critical for self-assembly of virus capsids and other polyhedral structures. Prot Sci 14:1518-1525. (Pubitemid 41007915)
31. Dill K, Chan H (1997) From Levinthal to pathways to funnels. Nat Struct Biol 4:10-19. (Pubitemid 27020916)
32. Verdier P, Stockmayer W (1962) Monte Carlo calculations on the dynamics of polymers in dilute solution. J Chem Phys 36:227-235.
33. Wales D (1987) Closed-shell structures and the building game. Chem Phys Lett 141:478-484.