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Finding a Hamiltonian path on a folded DNA shape

Finding a Hamiltonian path on a folded DNA shape. Hanny Seaman Advisors: Dr. Ido Bachelet Prof. Ron Unger 2013. The Mina and Everard Goodman Faculty of Life Sciences , Bar- Ilan University Ramat- Gan. Hamiltonian path. 1 3245. 1 472365. NP-complete problem!.

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Finding a Hamiltonian path on a folded DNA shape

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  1. Finding a Hamiltonian path on a folded DNA shape Hanny Seaman Advisors: Dr. IdoBachelet Prof. Ron Unger 2013 The Mina and Everard Goodman Faculty of Life Sciences, Bar-IlanUniversity Ramat-Gan

  2. Hamiltonian path 13245 1472365 NP-complete problem!

  3. Adleman’s solution • DNA strands represent vertices and paths of a 7-node graph • Mix in tube – self complementarity • Filtration

  4. Origami DNA • Folding of DNA to create nanoscale shapes • Terminology: • Scaffold • Staples • caDNAno

  5. Representing the graph • Example: 4 vertices 0

  6. Representing the graph • Example: 4 vertices 0 1

  7. Representing the graph • Example: 4 vertices 0 1 2

  8. Representing the graph • Example: 4 vertices 0 1 3 2

  9. Representing the graph • Example: 4 vertices 0 1 3 2

  10. Representing the graph • Example: 4 vertices 0 1 3 2

  11. Representing the graph • Example: 4 vertices 0 1 3 2

  12. Representing the graph • Example: 4 vertices 0 1 3 2

  13. Representing the graph • Example: 4 vertices 0 1 3 2

  14. Representing the graph • Example: 4 vertices 0 1 3 2

  15. Representing the graph • Example: 4 vertices 0 1 3 2

  16. Example: 4 vertices

  17. Example: 4 verticesEdges details

  18. Example: 4 verticesScaffold details

  19. 7 vertices – planning the graph Calculate the edges and vertices sequences

  20. 7 vertices – planning the graph 1 2 3 7 6 4 5

  21. Experiments

  22. Experiment 1- increase number of vertices 7 vertices – increase number of vertices

  23. Experiment 1- increase number of vertices 1 7 vertices – increase number of vertices

  24. Experiment 1- increase number of vertices 1 2 7 vertices – increase number of vertices

  25. Experiment 1- increase number of vertices 1 2 3 7 vertices – increase number of vertices

  26. Experiment 1- increase number of vertices 1 2 3 7 6 4 5 7 vertices – increase number of vertices

  27. Experiment 1- increase number of vertices Max fold Partial fold Unfolded segments 7 vertices – increase number of vertices

  28. Experiment 2- Stepwise assembly 1

  29. Experiment 2- Stepwise assembly 1

  30. Experiment 2- Stepwise assembly 1 2

  31. Experiment 2- Stepwise assembly 1 2 3 4 5

  32. Experiment 2- Stepwise assembly 1 2 3 7 6 4 5

  33. Experiment 3- 7 vertices - FACS 1 2 3 7 6 4 5

  34. Experiment 3- 7 vertices - FACS (1) Beads (2) Beads Ver1-marked (3) Beads Ver7-marked (4) Beads Ver1 unmarked Vers 2-6 Ver7-marked All staples (5) Beads Ver1-marked Vers 2-6 Ver7-marked All staples

  35. Experiment 3- 7 vertices - FACSResults - Red (5) (4) (3) (2) (1)

  36. Experiment 3- 7 vertices - FACSResults - Green (5) (4) (3) (2) (1)

  37. Summary • Representing graph using origami DNA • Find if exists a Hamiltonian Path

  38. What’s next? • Watching folded DNA using AFM • Experiments with: • edges including polyT • Large number of vertices • Graph with several paths – not only Hamiltonian

  39. תודות • לד"ר עידו בצלת ולפרופ' רון אונגר על ההנחייה והליווי לאורך כל הפרוייקט. • לכל חברי המעבדה על העזרה. • תודה על ההקשבה! 

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