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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
The Hamiltonian Path Problem
• Millennium Problem • P=NP?• Brute Force required
Does a Hamiltonian Path exist in this graph?
Computational Complexity
Why Should We Use Bacteria?
Adleman LM (1994). Science 266 (11): 1021-1024.
VS.
Flipping DNA with Hin/hixC
Using Hin/hixC to Solve the HPP
Using Hin/hixC to Solve the HPP
hixC Sites
Using Hin/hixC to Solve the HPP
Using Hin/hixC to Solve the HPP
Using Hin/hixC to Solve the HPP
Solved Hamiltonian Path
What Genes Can Be Split?
GFP before hixC insertion
What Genes Can Be Split?
GFP displaying hixC insertion point
Gene Splitter Software
Input Output
1. Gene Sequence
2. Where do you want your hixC site?
3. Pick an extra base to avoid a frameshift
1. Generates 4 Primers (optimized for melting temperature).
2. Biobrick ends are added to primers.
3. Frameshift is eliminated.
Gene-Splitter Output
Note: Oligos are optimized for melting temperatures.
Use GFP to Split RFP
Green Fluorescent Protein Red Fluorescent Protein
Can We Detect A Solution?
Elements in the shaded region can be arranged in any order.
True Positives
Number of True Positives = (Edges-Nodes+1)! * 2(Edges-Nodes+1)
False Positives
Extra Edge
False Positives
PCR Fragment Length
PCR Fragment Length
0
0.25
0.5
0.75
1
4/6 6/9 7/12 7/14
1.0E+00
1.0E+01
1.0E+02
1.0E+03
1.0E+04
1.0E+05
1.0E+06
1.0E+07
1.0E+08
4/6 6/9 7/12 7/14
Detection of True Positives
Tot
al #
of P
ositi
ves
# of
Tru
e P
ositi
ves
÷
Tot
al #
of P
ositi
ves
# of Nodes / # of Edges
# of Nodes / # of Edges
k = actual number of occurrences
λ = expected number of occurrences
λ = m plasmids * # solved permutations of edges ÷ # permutations of edges
Cumulative Poisson Distribution:
How Many Plasmids Do We Need?
1 mL of culture = 10 cells 9
P(# of solutions ≥ k) = 1 - ∑k-1
X=0
_____e-λ λX!
x.
Starting ArrangementP
roba
bilit
y of
HP
P S
olut
ion
Number of Flips
4 Nodes & 3 Edges
Where Are We Now?
First Bacterial Computer
Starting Arrangement
First Bacterial Computer
Starting Arrangement
Solved Arrangement
Future Directions
Split additional genes:
Solve other problems such as the Traveling Salesperson Problem:
Make more complex graphs:
Living Hardware to Solve the Hamiltonian Path Problem
Collaborators at MWSU:
Support: Davidson College The Duke Endowment
HHMI NSF Genome Consortium for Active Teaching James G. Martin Genomics Program
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
Extra Slides
Traveling Salesperson 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
Problem:
Solution : T7 bacteriophage RNA polymerase
• Highly processive single subunit viral polymerase which maintains processivity in vivo and in vitro
Path at 3 nodes / 3 edges HP- 1 12 23
1 2
3TT
Path at 4 nodes / 6 edges HP-1 12 24 43
2
34
1
TT
Path 5 nodes / 8 edges HP -1 12 25 54 43
2
34
1
TT
5
Path 6 nodes / 10 edgesHP-1 12 25 56 64 43
2
34
1
TT
56
Path 7 nodes / 12 edgesHP-1 12 25 56 67 74 43
2
34
1
TT
56
7
More Gene-Splitter Output
Promoter Tester
• RBS:Kan:RBS:Tet:RBS:RFP• Tested promoter-promoter tester-pSBIA7 on varying concentration plates
Kanamycin Tet Kan-Tet
50 50 50 / 50
75 75 75 / 75
100 100 100 / 100
125 125 125 / 125
•Used Promoter Tester-pSB1A7 and Promoter Tester-pSB1A2 without promoters as control
•Further evidence that pSB1A7 isn’t completely insulated
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
•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
Splitting Kanamycin Nucleotidyltransferase
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
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
Splitting Cre Recombinase
What Genes Can Be Split?
GFP before hixC insertion GFP displaying hixC insertion point
Gene Splitter Software
