Living Hardware to Solve the Hamiltonian Path Problem

1. Living Hardware to Solve the Hamiltonian Path Problem Professors: Dr. Malcolm Campbell and Dr. Laurie Heyer Students: Oyinade Adefuye, Will DeLoache, Jim Dickson, Andrew Martens, Amber Shoecraft, and Mike Waters

2. The Hamiltonian Path Problem

3. Millennium Problem • P=NP? • Brute Force required Computational Complexity Does a Hamiltonian Path exist in this graph?

4. Why Should We Use Bacteria? VS. Adleman LM (1994). Science 266 (11): 1021-1024.

5. Flipping DNA with Hin/hixC

6. Using Hin/hixC to Solve the HPP

7. Using Hin/hixC to Solve the HPP hixC Sites

8. Using Hin/hixC to Solve the HPP

9. Using Hin/hixC to Solve the HPP

10. Using Hin/hixC to Solve the HPP Solved Hamiltonian Path

11. What Genes Can Be Split? GFP before hixC insertion

12. What Genes Can Be Split? GFP displaying hixC insertion point

13. Gene Splitter Software Input Output Generates 4 Primers (optimized for melting temperature). 2. Biobrick ends are added to primers. 3. Frameshift is eliminated. 1. Gene Sequence 2. Where do you want your hixC site? 3. Pick an extra base to avoid a frameshift

14. Gene-Splitter Output Note: Oligos are optimized for melting temperatures.

15. Use GFP to Split RFP Green Fluorescent Protein Red Fluorescent Protein

16. Can We Detect A Solution?

17. True Positives Elements in the shaded region can be arranged in any order. (Edges-Nodes+1) Number of True Positives = (Edges-Nodes+1)! * 2

18. False Positives Extra Edge

19. False Positives PCR Fragment Length PCR Fragment Length

20. Detection of True Positives Total # of Positives # of Nodes / # of Edges # of True Positives ÷ Total # of Positives # of Nodes / # of Edges

21. 9 1 mL of culture = 10 cells . k-1 x ∑ -λ λ e _____ X=0 X! How Many Plasmids Do We Need? k = actual number of occurrences λ= expected number of occurrences λ = m plasmids * # solved permutations of edges ÷ # permutations of edges Cumulative Poisson Distribution: P(# of solutions ≥ k) = 1 -

22. Starting Arrangement 4 Nodes & 3 Edges Probability of HPP Solution Number of Flips

23. Where Are We Now?

24. First Bacterial Computer Starting Arrangement

25. First Bacterial Computer Starting Arrangement Solved Arrangement

26. Future Directions Split additional genes: Make more complex graphs: Solve other problems such as the Traveling Salesperson Problem:

27. Living Hardware to Solve the Hamiltonian Path Problem Collaborators at MWSU: Dr. Todd Eckdahl, Dr. Jeff Poet, Jordan Baumgardner,Tom Crowley, Lane H. Heard, Nickolaus Morton, Michelle Ritter, Jessica Treece, Matthew Unzicker, Amanda Valencia Additional Thanks: Karen Acker, Davidson College ‘07 Support: Davidson College The Duke Endowment HHMI NSF Genome Consortium for Active Teaching James G. Martin Genomics Program

28. Extra Slides

29. Traveling Salesperson Problem

30. Problem: Processivity • The nature of our construct requires a stable transcription mechanism that can read through multiple genes in vivo • Initiation Complex vs. Elongation Complex • Formal manipulation of gene expression (through promoter sequence and availability of accessory proteins) is out of the picture Solution : T7 bacteriophage RNA polymerase • Highly processive single subunit viral polymerase which maintains processivity in vivo and in vitro

31. Path at 3 nodes / 3 edges HP- 1 12 23 1 2 T 3

32. 2 1 T 4 3 Path at 4 nodes / 6 edges HP-1 12 24 43

33. 1 2 5 T 4 3 Path 5 nodes / 8 edges HP -1 12 25 54 43

34. 1 2 6 5 T 4 3 Path 6 nodes / 10 edgesHP-1 12 25 56 64 43

35. 1 2 6 5 T 4 3 7 Path 7 nodes / 12 edgesHP-1 12 25 56 67 74 43

36. More Gene-Splitter Output

37. Promoter Tester RBS:Kan:RBS:Tet:RBS:RFP Tested promoter-promoter tester-pSBIA7 on varying concentration plates • Used Promoter Tester-pSB1A7 and Promoter Tester-pSB1A2 without promoters as control • Further evidence that pSB1A7 isn’t completely insulated

38. Promoters Tested • Selected “strong” promoters that were also repressible from biobrick registry • ompC porin (BBa_R0082) • “Lambda phage”(BBa_R0051) • pLac (BBa_R0010) • Hybrid pLac (BBa_R0011) • None of the promoters “glowed red” • Rus (BBa_J3902) and CMV (BBa_J52034) not the parts that are listed in the registry

39. Splitting Kanamycin Nucleotidyltransferase • Determined hixC site insertion at AA 125 in each monomer subunit • -AA 190 is involved in catalysis • -AA 195 and 208 are involved in Mg2+ binding • -Mutant Enzymes 190, 205, 210 all showed changes in mg+2 binding from the WT • -Substitution of AA 210 (conserved) reduced enzyme activity • -AA 166 serves to catalyze reactions involving ATP • -AA 44 is involved in ATP binding • -AA 60 is involved in orientation of AA 44 and ATP binding • -We did not consider any Amino Acids near the N or C terminus • -Substitution of AA 190 caused 650-fold decrease in enzyme activity • -We did not consider any residues near ß-sheets or ∂-helices close to the active site because hydrogen bonding plays an active role in substrate stabilization and the polarity of our hix site could disrupt the secondary structure and therefore the hydrogen bonding ability of KNTase) • Did not split

40. Plasmid Insulation • “Insulated” plasmid was designed to block read-through transcription • Read-through = transcription without a promoter • Tested a “promoter-tester” construct • RBS:Kan:RBS:Tet:RBS:RFP • Plated on different concentrations of Kan, Tet, and Kan-Tet plates • Growth in pSB1A7 was stunted • No plate exhibited cell growth in uninsulated plasmid and cell death in the insulated plasmid

41. Tetracycline Resistance Protein • Did not split • Transmembrane protein • Structure hasn’t been crystallized • determined by computer modeling • Vital residues for resistance are in transmemebrane domains (efflux function) • HixC inserted a periplasmic domains AA 37/38 and AA 299/300 • Cytoplasmic domains allow for interaction with N and C terminus

42. Splitting Cre Recombinase

43. What Genes Can Be Split? GFP before hixC insertion GFP displaying hixC insertion point

44. Gene Splitter Software