Tile-Based DNA Nanostructures

Ellis-Monaghan, Joanna A.; Jonoska, Nataša; Pangborn, Greta

doi:10.1016/b978-0-12-814066-6.00002-7

Cited by 3 publications

(1 citation statement)

References 40 publications

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“…In this research we will use the flexible-tile model as described in [3] and use the graph theoretical formalism of [4] and [8] to help build targeted structures from self-assembling DNA. We define a tile to be a vertex with n-half edges, where n is the degree of the vertex that the tile is representing.…”

Section: Methodsmentioning

confidence: 99%

Optimal Tilings of Bipartite Graphs Using Self-Assembling DNA

Redmon,

Mena,

Vesta

et al. 2023

PUMP J. Undergrad. Res.

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Motivated by the recent advancements in nanotechnology and the discovery of new laboratory techniques using the Watson-Crick complementary properties of DNA strands, formal graph theory has recently become useful in the study of self-assembling DNA complexes. Construction methods based on graph theory have resulted in significantly increased efficiency. We present the results of applying graph theoretical and linear algebra techniques for constructing crossed-prism graphs, crown graphs, book graphs, stacked book graphs, and helm graphs, along with kite, cricket, and moth graphs. In particular, we explore various design strategies for these graph families in two sets of laboratory constraints.

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Section: Methodsmentioning

confidence: 99%

Optimal Tilings of Bipartite Graphs Using Self-Assembling DNA

Redmon,

Mena,

Vesta

et al. 2023

PUMP J. Undergrad. Res.

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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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Tile-based modeling of DNA self-assembly for two graph families with appended paths

Griffin

Sorrells

2023

Involve

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Tile-Based DNA Nanostructures

Cited by 3 publications

References 40 publications

Optimal Tilings of Bipartite Graphs Using Self-Assembling DNA

Optimal Tilings of Bipartite Graphs Using Self-Assembling DNA

From Molecules to Mathematics

Tile-based modeling of DNA self-assembly for two graph families with appended paths

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