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

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

doi:10.1007/s10910-018-0858-9

Cited by 5 publications

(2 citation statements)

References 56 publications

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“…This has led to molecular scaffoldings made of DNA and other proteins which have wideranging potential [44]. Such applications include construction of containers for the transport and release of nano-cargos, templates for the controlled growth of nano-objects, biomolecular computing, biosensors, fine screen filters (lattices) at the nano-size scale, nano-circuitry, robotics, and drug-delivery methods (see [1,10,14,17,20,27,28,33,35,41,48,53,54]). In particular, DNA nanotechnology is arguably the most powerful method for building nanoscale structures resembling macroscopic robots [18].…”

Section: Dna Self-assembly Backgroundmentioning

confidence: 99%

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Computational complexity and pragmatic solutions for flexible tile based DNA self-assembly

Almodóvar,

Ellis-Monaghan,

Harsy

et al. 2021

Preprint

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Branched junction molecule assembly of DNA nanostructures, pioneered by Seeman's laboratory in the 1980s, has become increasingly sophisticated, as have the assembly targets. A critical design step is finding minimal sets of branched junction molecules that will self-assemble into target structures without unwanted substructures forming. We use graph theory, which is a natural design tool for self-assembling DNA complexes, to address this problem. After determining that finding optimal design strategies for this method is generally NP-complete, we provide pragmatic solutions in the form of programs for special settings and provably optimal solutions for natural assembly targets such as platonic solids, regular lattices, and nanotubes. These examples also illustrate the range of design challenges.

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Section: Dna Self-assembly Backgroundmentioning

confidence: 99%

“…Thus, the mathematical model here assumes no geometric restrictions, for example on the inter-arm angles, edge lengths, or ability for any one arm to connect with any other. See [14] for a model that encompasses such geometric constraints. Definition 1.2.…”

Section: Graph Theoretical Definitions and Notationmentioning

confidence: 99%

Computational complexity and pragmatic solutions for flexible tile based DNA self-assembly

Almodóvar,

Ellis-Monaghan,

Harsy

et al. 2021

Preprint

View full text Add to dashboard Cite

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From Molecules to Mathematics

Ellis-Monaghan

Jonoska

2023

Natural Computing Series

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To celebrate the 40th anniversary of bottom-up DNA nanotechnology we highlight the interaction of the field with mathematics. DNA self-assembly as a method to construct nanostructures gave impetus to an emerging branch of mathematics, called here ‘DNA mathematics’. DNA mathematics models and analyzes structures obtained as bottom-up assembly, as well as the process of self-assembly. Here we survey some of the new tools from DNA mathematics that can help advance the science of DNA self-assembly. The theory needed to develop these tools is now driving the field of mathematics in new and exciting directions. We describe some of these rich questions, focusing particularly on those related to knot theory, graph theory, and algebra.

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Computational complexity and pragmatic solutions for flexible tile based DNA self-assembly

Almodóvar,

Ellis-Monaghan,

Harsy

et al. 2024

Nat Comput

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

Cited by 5 publications

References 56 publications

Computational complexity and pragmatic solutions for flexible tile based DNA self-assembly

Computational complexity and pragmatic solutions for flexible tile based DNA self-assembly

From Molecules to Mathematics

Computational complexity and pragmatic solutions for flexible tile based DNA self-assembly

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