TY - JOUR
T1 - Design formalism for DNA self-assembly of polyhedral skeletons using rigid tiles
AU - Ferrari, Margherita Maria
AU - Cook, Anna
AU - Houlihan, Alana
AU - Rouleau, Rebecca
AU - Seeman, Nadrian C.
AU - Pangborn, Greta
AU - Ellis-Monaghan, Joanna
N1 - Funding Information:
Acknowledgements The work of Joanna Ellis-Monaghan, Greta Pangborn, and Nadrian C. Seeman was supported by the National Science Foundation (NSF) under Grant DMS-1332411.
Publisher Copyright:
© 2018, Springer International Publishing AG, part of Springer Nature.
PY - 2018/5/1
Y1 - 2018/5/1
N2 - We describe the half-lap model, a mathematical framework that captures the geometric constraints of rigid tiles that are branched junction molecules used as building blocks for tile-based DNA self-assembly. The model captures not only the combinatorial structures of the sets of cohesive ends on the tiles, but also the specific geometry of the inter-arm angles of the tiles and most critically the relative orientations of adhering tiles. We illustrate the functionality of the model by providing provably optimal DNA self-assembly strategies to construct Platonic and Archimedean 3-regular polyhedral skeletons and computing the minimum number of tile types and bond-edge types for each target structure. We further demonstrate the utility of the model by using it to analyze the benefits and limitations of palindromic rigid tiles. Moreover, we give explicit combinatorial and geometric descriptions of the tiles needed for each construction.
AB - We describe the half-lap model, a mathematical framework that captures the geometric constraints of rigid tiles that are branched junction molecules used as building blocks for tile-based DNA self-assembly. The model captures not only the combinatorial structures of the sets of cohesive ends on the tiles, but also the specific geometry of the inter-arm angles of the tiles and most critically the relative orientations of adhering tiles. We illustrate the functionality of the model by providing provably optimal DNA self-assembly strategies to construct Platonic and Archimedean 3-regular polyhedral skeletons and computing the minimum number of tile types and bond-edge types for each target structure. We further demonstrate the utility of the model by using it to analyze the benefits and limitations of palindromic rigid tiles. Moreover, we give explicit combinatorial and geometric descriptions of the tiles needed for each construction.
KW - Bond-edge types
KW - DNA self-assembly strategies
KW - Platonic and Archimedean solids
KW - Rigid branched tiles
KW - Tile types
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U2 - 10.1007/s10910-018-0858-9
DO - 10.1007/s10910-018-0858-9
M3 - Article
AN - SCOPUS:85041214288
SN - 0259-9791
VL - 56
SP - 1365
EP - 1392
JO - Journal of Mathematical Chemistry
JF - Journal of Mathematical Chemistry
IS - 5
ER -