Design formalism for DNA self-assembly of polyhedral skeletons using rigid tiles

Margherita Maria Ferrari, Anna Cook, Alana Houlihan, Rebecca Rouleau, Nadrian Seeman, Greta Pangborn, Joanna Ellis-Monaghan

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish (US)
Pages (from-to)1-28
Number of pages28
JournalJournal of Mathematical Chemistry
DOIs
StateAccepted/In press - Jan 31 2018

Fingerprint

Self-assembly
Tile
Skeleton
Self assembly
DNA
Geometric Constraints
Design
Model
Building Blocks
Molecules
Angle
Target
Geometry
Computing
Demonstrate

Keywords

  • Bond-edge types
  • DNA self-assembly strategies
  • Platonic and Archimedean solids
  • Rigid branched tiles
  • Tile types

ASJC Scopus subject areas

  • Chemistry(all)
  • Applied Mathematics

Cite this

Ferrari, M. M., Cook, A., Houlihan, A., Rouleau, R., Seeman, N., Pangborn, G., & Ellis-Monaghan, J. (Accepted/In press). Design formalism for DNA self-assembly of polyhedral skeletons using rigid tiles. Journal of Mathematical Chemistry, 1-28. https://doi.org/10.1007/s10910-018-0858-9

Design formalism for DNA self-assembly of polyhedral skeletons using rigid tiles. / Ferrari, Margherita Maria; Cook, Anna; Houlihan, Alana; Rouleau, Rebecca; Seeman, Nadrian; Pangborn, Greta; Ellis-Monaghan, Joanna.

In: Journal of Mathematical Chemistry, 31.01.2018, p. 1-28.

Research output: Contribution to journalArticle

Ferrari, Margherita Maria ; Cook, Anna ; Houlihan, Alana ; Rouleau, Rebecca ; Seeman, Nadrian ; Pangborn, Greta ; Ellis-Monaghan, Joanna. / Design formalism for DNA self-assembly of polyhedral skeletons using rigid tiles. In: Journal of Mathematical Chemistry. 2018 ; pp. 1-28.
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