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Tile-based
modeling of DNA self-assembly for two graph families with
appended paths
Chloe Griffin and Jessica Sorrells |
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Vol. 16 (2023), No. 1, 69–106
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Abstract |
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Branched molecules of deoxyribonucleic acid (DNA) can self-assemble into nanostructures through complementary cohesive strand base pairing. The production of DNA nanostructures is valuable in targeted drug delivery and biomolecular computing. With theoretical efficiency of laboratory processes in mind, we use a flexible tile model for DNA assembly. We aim to minimize the number of different types of branched junction molecules necessary to assemble certain target structures. We represent target structures as discrete graphs and branched DNA molecules as vertices with half-edges. We present the minimum numbers of required branched molecule and cohesive-end types under three levels of restrictive conditions for the tadpole and lollipop graph families. These families represent cycle and complete graphs with a path appended via a single cut-vertex. We include three general lemmas regarding such vertex-induced path subgraphs. Through proofs and examples, we demonstrate the challenges that can arise in determining optimal construction strategies. |
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Keywords
graph theory, discrete graph, lollipop graphs, tadpole
graphs, DNA self-assembly, nanostructures, flexible tile
model
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Mathematical Subject Classification
Primary: 92E10, 05C90
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Milestones
Received: 10 September 2021
Revised: 14 January 2022
Accepted: 8 March 2022
Published: 14 April 2023
Communicated by Vadim Ponomarenko
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Authors |
| Chloe Griffin | |
| Brown University Providence, RI United States |
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| Jessica Sorrells | |
| Converse University Spartanburg, SC United States |
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| © 2023 MSP (Mathematical Sciences Publishers). |
