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Using DNA Self-assembly Design Strategies to Motivate Graph Theory Concepts

Published online by Cambridge University Press:  05 October 2011

J. Ellis-Monaghan  and
G. Pangborn
J. Ellis-Monaghan*
Affiliation:
Department of Mathematics, Saint Michael’s College, Colchester, VT 05404
G. Pangborn
Affiliation:
Department of Computer Science, Saint Michael’s College, Colchester, VT 05404
*
⋆Corresponding author. E-mail: [email protected]
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Abstract

A number of exciting new laboratory techniques have been developed using the Watson-Crick complementarity properties of DNA strands to achieve the self-assembly of graphical complexes. For all of these methods, an essential step in building the self-assembling nanostructure is designing the component molecular building blocks. These design strategy problems fall naturally into the realm of graph theory. We describe graph theoretical formalism for various construction methods, and then suggest several graph theory exercises to introduce this application into a standard undergraduate graph theory class. This application provides a natural framework for motivating central concepts such as degree sequence, Eulerian graphs, Fleury’s algorithm, trees, graph genus, paths, cycles, etc. There are many open questions associated with these applications which are accessible to students and offer the possibility of exciting undergraduate research experiences in applied graph theory.

Keywords

branched junction moleculesself-assemblyDNA complexesgraphs
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 6 , Issue 6: Biomathematics Education , 2011 , pp. 96 - 107
Copyright
© EDP Sciences, 2011

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