+ Design Strategies for DNA Nanostructures Part I: Problem Formulation Presented By: Jacob Girard and Mary Spuches, Saint Michael’s College With collaboration from: Thomas Dickerson, Andrew Gilbert, Brian Goodhue, Daniel Koch, Daniel Lewis, and Andrew Parent

+ Outline Background DNA and Nanostructures Terminology Octet Truss Our Geometric model Schlegel Diagram Constructions Coming Attractions Acknowledgments 2 Source: MS Office Clip Art

+ Structure of DNA Sugar, phosphate, nitrogenous base. Complementary base pairing Chemical composition determines structure 3

+ The Chemists Job Build DNA nanostructures Topoisomerases  Cut and mend specific sequences of DNA Ligation  The final binding process 4

+ The Basics Branched Junction Molecule Series of double stranded ends extending from the central vertex Sticky end (cohesive end) A double stranded DNA sequence with a single strand extending longer than the other 5

+ Practical Applications Biochip technology Self assembling DNA nanocapsules for drug delivery Nanoelectronics / htm

+ What is a tile? 7 A tileBranched-Junction Molecule A tile represents a branched junction molecule with specific half edge orientation and type.

+ Complementary bases adhere 8 Denoted by hatted 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.

+ Sticky ends D. Luo, “The road from biology to materials,” Materials Today, 6 (2003), ATTCG TAAGCCCATTG GGTAACATTCG TAAGC 9

+ What are some self-assembled DNA nanostructues? A self-assembled DNA cube and Octahedron 10

+ A pot of tiles 11 Both complete complexes (1) and incomplete complexes (2) can be constructed by the following pot type P with 4 tiles a c s â ĉ ŝ â ĉ s t1t1 t4t4 a c ŝ t3t3 t2t2 t1t1 t2t2 t3t3 ŝ t2t2 ac t1t1

+ Octahedron Construction 12

+ Geometric Constraints Arms are straight and rigid The positions of the arms are fixed Arms are of unit length The arms do not bend or twist in order to bond No molecule has more than 12 arms or less than 2 arms Final DNA structures must be complete No design may allow structures smaller than the target structure to form 13

+ Why the Octet Truss? 14 Source: Wikimedia Commons Distributed under GNU Free Documentation license.

+ Problem Statement 15 The goal is to build self assembling DNA Nanostructures within the octet truss using a minimal number of tile types.

+ Identifying arms at a vertex π /3 radians π /2 radians (2 π )/3 radians π radians 16 Geometric Configuration Only four possible angles

17 Schlegel Diagram of Cuboctahedron Naming Tiles This diagram is easier to draw than the actual geometric arrangement Vertices in the Schlegel diagram correspond to arms

+ Orientation is important The problem of orientation What are equivalent tiles? 18 Tile A Tile D Tile C Tile B c ĉ.

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

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

+ Octahedron 21 Source: Wikimedia Commons Distributed under GNU Free Documentation license.

+ 22 Truncated Octahedron Source: Wikimedia Commons Distributed under GNU Free Documentation license.

+ Cuboctahedron 23 Source: Wikimedia Commons Distributed under GNU Free Documentation license.

+ Coming attractions Determine the graphs within the octet truss that can be self assembled using one or two tile types Determine all possible geometric configurations of n-armed tiles for n from 2 to 12 Then determine all possible sticky end assignments for those tiles From these possibilities determine the complete complexes that can self assemble 24

+ Questions? 25

26 Acknowledgements

27 References