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Living Hardware to Solve the
Hamiltonian Path Problem
Faculty: Drs. Malcolm Campbell, Faculty: Drs. Todd Eckdahl, Jeff
Laurie Heyer, Karmella Haynes
Poet
Students: Jordan Baumgardner,
Students: Oyinade Adefuye,
Will DeLoache, Jim Dickson,
Andrew Martens, Amber
Shoecraft, and Mike Waters
Tom Crowley, Lane H. Heard,
Nickolaus Morton, Michelle Ritter,
Jessica Treece, Matthew Unzicker,
Amanda Valencia
The Hamiltonian Path Problem
1
4
3
2
5
The Hamiltonian Path Problem
1
4
3
2
5
Advantages of Bacterial Computation
Software
Hardware
Computation
Advantages of Bacterial Computation
Software
Hardware
Computation
Computation
Advantages of Bacterial Computation
Software
Hardware
Computation
Computation
Computation
http://www.dnamnd.med.usyd.edu.au/
http://www.turbosquid.com
Computational Complexity
• Non-Polynomial (NP)
• No Efficient Algorithms
Computational Complexity
• Non-Polynomial (NP)
• No Efficient Algorithms
Cell Division
Flipping DNA with Hin/hixC
Using
Hin/hixC
toSolve
Solve
HPP
Using
Hin/hixC to
thethe
HPP
1
4
3
2
5
Using
Hin/hixC
toSolve
Solve
HPP
Using
Hin/hixC to
thethe
HPP
1
4
3
2
5
hixC Sites
Using
Hin/hixC
toSolve
Solve
HPP
Using
Hin/hixC to
thethe
HPP
1
4
3
2
5
Using Hin/hixC to Solve the HPP
1
4
3
2
5
Using Hin/hixC to Solve the HPP
1
4
3
2
5
Solved Hamiltonian Path
How to Split a Gene
RBS
Promoter
Reporter
Detectable
Phenotype
How to Split a Gene
RBS
Detectable
Phenotype
Reporter
Promoter
RBS
Promoter
Repo-
rter
hixC
?
Detectable
Phenotype
Gene Splitter Software
http://gcat.davidson.edu/iGEM07/genesplitter.html
Input
1. Gene Sequence
(cut and paste)
2. Where do you want
your hixC site?
3. Pick an extra base to
avoid a frameshift.
Output
1. Generates 4 Primers
(optimized for Tm).
2. Biobrick ends are
added to primers.
3. Frameshift is
eliminated.
Gene-Splitter Output
Note: Oligos are
optimized for Tm.
Can We Detect A Solution?
Probability of HPP Solution
Starting Arrangement
4 Nodes & 3 Edges
Number of Flips
True Positives
1
4
3
2
5
Elements in the shaded region can
be arranged in any order.
(Edges-Nodes+1)
Number of True Positives = (Edges-(Nodes-1))! * 2
How Many Plasmids Do We Need?
Probability of at least k solutions on m plasmids for a 14-edge graph
k=1
5
10
20
m = 10,000,000
.0697
0
0
0
50,000,000
.3032
.00004
0
0
100,000,000
.5145
.0009
0
0
200,000,000
.7643
.0161
.000003
0
500,000,000
.973
.2961
.0041
0
1,000,000,000
.9992
.8466
.1932
.00007
k = actual number of occurrences
λ = expected number of occurrences
λ = m plasmids * # solved permutations of edges ÷ # permutations of edges
Cumulative Poisson Distribution:
e   x
P(# of solutions ≥ k) = 1 
x!
x0
k1
False Positives
Extra Edge
1
4
3
2
5
False Positives
PCR Fragment Length
1
4
3
2
5
PCR Fragment Length
Detection of True Positives
Total # of Positives
1.0E+08
1.0E+07
1.0E+06
1.0E+05
1.0E+04
1.0E+03
1.0E+02
1.0E+01
1.0E+00
6/9
7/12
7/14
# of Nodes / # of Edges
1
Total # of Positives
# of True Positives ÷
4/6
0.75
0.5
0.25
0
4/6
6/9
7/12
# of Nodes / # of Edges
7/14
Building a Bacterial Computer
Splitting Reporter Genes
Green Fluorescent Protein
Red Fluorescent Protein
Splitting Reporter Genes
Green Fluorescent Protein
Red Fluorescent Protein
3-Node Graphs
Graph A
Graph B
HPP Constructs
Positive Control Construct:
HPP0
Graph A Constructs:
HPP-A0
HPP-A1
Graph A
HPP-A2
Graph B Construct:
HPP-B1
Graph B
Double Fluorescence
HPP0
Green Fluorescence
T7 RNAP
Double Fluorescence
HPP0
Green Fluorescence
T7 RNAP
HPP-A0
Yellow Fluorescence
Fluorometer Measurements
GFP Excitation Spectra for 4 HPP Constructs
(at an Emission Wavelength of 515nm)
450 nm chosen as excitation
wavelength to measure GFP
Fluorometer Measurements
RFP Excitation Spectra for 4 HPP Constructs
(at an Emission Wavelength of 608nm)
560 nm chosen as excitation
wavelength to measure RFP
Normalized Fluorometer Measurements
Construct
Fluorescent Color on
UV Box
Green
Red
pLac-RBS-RFP
Red
7
263
pLac-RBS-RFP-RBS-GFP
Red
144
370
pLac-GFP1-hixC-GFP2
Green
136
0
pLac-RBS-RFP1-hixC-RFP2 None
0
147
pLac-RBS-GFP1-hixC-RFP2 None
11
2
pLac-RBS-RFP1-hixC-GFP2 None
13
2
HPP-B0
Green
72
18
HPP-A0
Yellow
340
255
HPP-A1
Red
1
143
HPP-A2
None
11
3
HPP-B1
Hybrid green
15
3
Flipping Detected by Phenotype
HPP-A0
HPP-A1
HPP-A2
Flipping Detected by Phenotype
HPP-A0
HPP-A1
HPP-A2
Hin-Mediated
Flipping
Flipping Detected by PCR
HPP-A0
HPP-A1
HPP-A2
Unflipped Flipped
Pending Experiments
• Test clonal colonies that contain flipped HPP and
have the solution sequenced.
• Perform a false-positive screen for HPP-B1
• Split 2 antibiotic resistance genes using a reading
frame shift just after the RBS
• Solve larger graphs
• Solve the Traveling Salesperson Problem
Living Hardware to Solve the
Hamiltonian Path Problem
Thanks to:
Karen Acker, Davidson College ‘07
Support:
Davidson College
Missouri Western State University
The Duke Endowment
HHMI
NSF
Genome Consortium for Active Teaching
James G. Martin Genomics Program
Extra Slides
Traveling Salesperson Problem
Processivity
Problem:
•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
Path at 3 nodes / 3 edges
HP- 1 12 23
1
2
T
3
Path at 4 nodes / 6 edges
HP-1 12 24 43
1
2
T
4
3
Path 5 nodes / 8 edges
HP -1 12 25 54 43
1
2
5
T
4
3
Path 6 nodes / 10 edges
HP-1 12 25 56 64 43
1
2
6
5
T
4
3
Path 7 nodes / 12 edges
HP-1 12 25 56 67 74 43
1
2
6
5
T
4
7
3
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
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
What Genes Can Be Split?
GFP before hixC insertion
GFP displaying hixC insertion point
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
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
More Gene-Splitter Output
Gene Splitter Software