+ Design Strategies for DNA Nanostructures Presented By: Jacob Girard & Keith Randall With collaboration from: Andrew Gilbert, Daniel Lewis, & Brian Goodhue

+ Outline Introduction & Problem Statement Differentiating the Molecular Building Blocks CategorizationGraphing Octet TrussOrientation Cohesive EndsApproach Constructions TetrahedronTruncated Octahedron Truncated TetrahedronCuboctahedron Octahedron Conclusions Extensions Future Problem Statement Questions or Answers Acknowledgements References 3 Source: MS Office Clip Art

+ Introduction DNA and Math? Chemical composition determines structure 4 Source: MS Office Clip Art

+ What is a tile? 5 A tile Branched-Junction Molecule

+ What are self-assembled DNA nanostructues? A self-assembled DNA cube and Octahedron 6

+ The molecular building blocks D. Luo, “The road from biology to materials,” Materials Today, 6 (2003), ATTCG TAAGCCCATTG GGTAACATTCG TAAGC 7

+ Cohesive Ends 8 Depicted by hatted (prime) and un-hatted letter labels Each edge needs a complimenting edge. Chemically this is this different bases pairing. c ĉ. ATTCG TAAGCCCATTG GGTAACATTCG TAAGC c ĉ.

+ Terminology and Definitions A tile is a branched junction molecule with specific half edge orientation and type. 9

+ Problem Statement 10 The goal is to build self assembling DNA Nanostructures within the octet truss using minimal tile types.

+ The Octet Truss 11 Why is the Octet Truss a good construct? What else is it used for? Why do we use it? Source: Wikimedia Commons Distributed under GNU Free Documentation license.

+ Differentiating the Molecular Building Blocks π /3 radians π /2 radians (2 π )/3 radians π radians 12 Categorizations Only four possible angles

13 Graphing Naming Tiles Schlegel diagrams It is very helpful to be able to picture these molecules as one dimensional and 3D dimensional.

+ Orientation The problem of orientation What are equivalent tiles? 14 Tile A Tile D Tile C Tile B c ĉ.

+ Constraints 1. Arms are straight and rigid 2. The positions of the arms are fixed 3. The arms do not bend or twist in order to bond. 4. No molecule has more than 12 arms or less than 2 arms. 5. Final DNA structures must be complete. 6. No design may allow structures smaller than the target structure to form. 15

+ Approach What exists within the octet truss for possible arm configurations? What can we build by just looking at the octet truss? What do we think we can build? What about the Platonic & Archimedean Solids? How can we do this in as few different tile types as possible? 16

+ Constructions Platonic Solids Tetrahedron Octahedron 17 Archimedean Solids Cuboctahedron Truncated Tetrahedron Truncated Octahedron

+ Tetrahedron 18 Source: Wikimedia Commons Distributed under GNU Free Documentation license.

19 Truncated Tetrahedron Source: Wikimedia Commons Distributed under GNU Free Documentation license.

+ Octahedron 20 Source: Wikimedia Commons Distributed under GNU Free Documentation license.

+ Octahedron Construction 21

+ Octahedron Construction 22

+ Octahedron Construction 23

+ Octahedron Construction 24

+ Octahedron Construction 25

26 Truncated Octahedron Source: Wikimedia Commons Distributed under GNU Free Documentation license.

+ Cuboctahedron 27 Source: Wikimedia Commons Distributed under GNU Free Documentation license.

+ Conclusions Development of the Tile Model Constructs Categorization Cohesive Ends Orientation Determined Platonic and Archimedean Solids do fit in Octet Truss. Proof by Tile Model 28

+ Extensions Looking for a better way to talk about orientations of tiles and arms. Model is limited in some respects. Arms are not entirely rigid in reality and this does affect the problem statement. 29

+ Future Problem Statement 30 What we know: We have all the 2 and 3 arm configurations We possibly have all the 4 configurations Need to find all the structures that can be made from one tile type with an even number of arms, and two tile types with an odd number of arms. Hopefully we will be able to find some pattern and be able to create a generalization of rule, but we will need data and examples first.

+ Questions or Answers? 31

32 Acknowledgements

33 References