Finding a Hamiltonian path on a folded DNA

shape

The Mina and Everard Goodman Faculty of Life Sciences , Bar-Ilan University Ramat-Gan

Hanny Seaman

Advisors:Dr. Ido BacheletProf. Ron Unger

2013

Hamiltonian path

147236513245

NP-complete problem!

DNA strands represent vertices and paths of a 7-node graph

Mix in tube – self complementarity Filtration

Adleman’s solution

Folding of DNA to create nanoscale shapes

Terminology:◦ Scaffold◦ Staples

caDNAno

Origami DNA

Representing the graph Example: 4 vertices

0

Representing the graph Example: 4 vertices

0

1

Representing the graph Example: 4 vertices

0

1

2

Representing the graph Example: 4 vertices

0

1

23

Representing the graph Example: 4 vertices

0

1

23

Representing the graph Example: 4 vertices

0

1

23

Representing the graph Example: 4 vertices

0

1

23

Representing the graph Example: 4 vertices

0

1

23

Representing the graph Example: 4 vertices

0

1

23

Representing the graph Example: 4 vertices

0

1

23

Representing the graph Example: 4 vertices

0

1

23

Example: 4 vertices

Start End Sequence Length Color

0[45] 0[26] GGGCGAAAAACCGTCTATCA 20#aaaa00

0[64] 0[46] CGTGGACTCCAACGTCAAA 19#cc0000

1[26] 1[45] TGTTGTTCCAGTTTGGAACA 20#f74308

1[46] 1[64] AGAGTCCACTATTAAAGAA 19#03b6a2

2[45] 2[26] TAGCCCGAGATAGGGTTGAG 20#03b6a2

2[64] 2[46] CCCTTATAAATCAAAAGAA 19#aaaa00

3[26] 3[45] GAAAATCCTGTTTGATGGTG 20#f7931e

3[46] 3[64] GTTCCGAAATCGGCAAAAT 19#007200

Example: 4 vertices

Edges details

Example: 4 vertices

Scaffold details

7 vertices – planning the graph

Calculate the edges and verticessequences

7 vertices – planning the graph

1 2

7

6

5

4

3

Experiments

7 vertices – increase number of vertices

Experiment 1- increase number of vertices

7 vertices – increase number of vertices

1

Experiment 1- increase number of vertices

7 vertices – increase number of vertices

1 2

Experiment 1- increase number of vertices

7 vertices – increase number of vertices

1 2

3

Experiment 1- increase number of vertices

Experiment 1- increase number of vertices

7 vertices – increase number of vertices

1 2

7

6

5

4

3

Experiment 1- increase number of vertices

7 vertices – increase number of vertices

Unfolded segments

Partial fold

Max fold

Experiment 2- Stepwise assembly

1

Experiment 2- Stepwise assembly

1

Experiment 2- Stepwise assembly

1 2

Experiment 2- Stepwise assembly

1 2

5

4

3

Experiment 2- Stepwise assembly

1 2

7

6

5

4

3

Experiment 3- 7 vertices - FACS

1 2

7

6

5

4

3

Experiment 3- 7 vertices - FACS

(1)Beads

(2)Beads

Ver1-marked

(3)Beads

Ver7-marked

(4)BeadsVer1

unmarked Vers 2-6

Ver7-markedAll staples

(5)Beads

Ver1-marked Vers 2-6

Ver7-markedAll staples

FL4-H

Cou

nt

102

103

104

105

106

107

0

682

1364

2046

2728

Cou

nt

0

1364

2728

1364

2728

Cou

nt

1364

2728

Cou

nt

1364

2728

Cou

nt

102

103

104

105

106

107

FL4-H

1364

2728

Cou

nt

Experiment 3- 7 vertices - FACS

Results - Red

(5)(4)(3)(2)(1)

FL1-H

Cou

nt

102

103

104

105

106

107

0

656

1311

1967

2622

Cou

nt

0

1311

2622

1311

2622

Cou

nt

1311

2622

Cou

nt

1311

2622

Cou

nt

102

103

104

105

106

107

FL1-H

1311

2622

Cou

nt

Experiment 3- 7 vertices - FACS

Results - Green(5)(4)(3)(2)(1)

Representing graph using origami DNA

Find if exists a Hamiltonian Path

Summary

Watching folded DNA using AFM Experiments with:

◦ edges including polyT◦ Large number of vertices◦ Graph with several paths – not only Hamiltonian

What’s next?

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