Living Hardware to Solve the Hamiltonian Path Problem Students: Oyinade Adefuye, Will DeLoache, Jim Dickson, Andrew Martens, Amber Shoecraft, and Mike Waters, Jordan Baumgardner, Tom Crowley, Lane Heard, Nick Morton, Michelle Ritter,

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Transcript Living Hardware to Solve the Hamiltonian Path Problem Students: Oyinade Adefuye, Will DeLoache, Jim Dickson, Andrew Martens, Amber Shoecraft, and Mike Waters, Jordan Baumgardner, Tom Crowley, Lane Heard, Nick Morton, Michelle Ritter,

Living Hardware to Solve the
Hamiltonian Path Problem
Students: Oyinade
Adefuye, Will
DeLoache, Jim
Dickson, Andrew
Martens, Amber
Shoecraft, and Mike
Waters, Jordan
Baumgardner, Tom
Crowley, Lane Heard,
Nick Morton, Michelle
Ritter, Jessica Treece,
Matt Unzicker,
Amanda Valencia
Faculty: Malcolm Campbell, Todd Eckdahl, Karmella
Haynes, Laurie Heyer, Jeff Poet
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
Computation
Computation
http://www.dnamnd.med.usyd.edu.au/
http://www.turbosquid.com
Computational Complexity
• Non-Polynomial (NP)
# of Processors
• No Efficient Algorithms
Cell Division
Flipping DNA with Hin/hixC
Flipping DNA with Hin/hixC
Flipping DNA with Hin/hixC
Using
Hin/hixC
toSolve
Solve
HPP
Using
Hin/hixC to
thethe
HPP
1
4
3
2
5
1 3
4 5
4 3
3 2 1 4 2 4
3 5
4 1
Using
Hin/hixC
toSolve
Solve
HPP
Using
Hin/hixC to
thethe
HPP
1
4
3
2
5
1 3
4 5
4 3
3 2 1 4 2 4
hixC Sites
3 5
4 1
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
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
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.
Predicting Outcomes of
Bacterial Computation
Probability of HPP Solution
Starting Arrangement
4 Nodes & 3 Edges
Number of Flips
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
100000000.00
1
Total # of Positives
# of True Positives ÷
Positives
# of
Total
Total
# of
Positives
10000000.00
1000000.00
100000.00
10000.00
1000.00
100.00
10.00
1.00
4/6
6/9
7/12
7/14
of Nodes / # of Edges
## of
Nodes / # of Edges
0.75
0.5
0.25
0
4/6
6/9
7/12
# of Nodes / # of Edges
7/14
Building a Bacterial Computer
Choosing Graphs
C
A
A
B
B
Graph 1
Graph 2
D
Splitting Reporter Genes
Green Fluorescent Protein
Red Fluorescent Protein
Splitting Reporter Genes
Green Fluorescent Protein
Split by hixC
Red Fluorescent Protein
Split by hixC
HPP Constructs
Graph 0 Construct:
A
AB
B
Graph 1 Constructs:
Graph 0
ABC
C
ACB
A
B
Graph 1
BAC
Graph 2 Construct:
DBA
A
B
Graph 2
D
Measuring Fluorescence
GFP Excitation Spectra for 4 HPP Constructs
(at an Emission Wavelength of 515nm)
450 nm chosen as excitation
wavelength to measure GFP
Measuring Fluorescence
RFP Excitation Spectra for 4 HPP Constructs
(at an Emission Wavelength of 608nm)
560 nm chosen as excitation
wavelength to measure RFP
Normalized Fluorescence Measurements
Construct
Observed Color on UV Green
(450/515)
Box
Red
(560/608)
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
AB (R1-hixC-R2-G1-hixC-G2)
Green
72
18
ABC (R1-hixC-R2-G1-hixC-G2)
Yellow
340
255
ACB (R1-hixC-R2-G1-hixC-R2)
Red
1
143
BAC (R1-hixC-G2)
None
11
3
DBA (R1-hixC-G2)
Hybrid green
15
3
Uncoupled Hin and Reporter Gene Expression
Hin
Cotransformation
Purify
flipped HPP
plasmid
Unflipped
HPP
Flipped
HPP
Cotransformation
T7
RNAP
Observe
colony
fluorescence
Coupled Hin and Reporter Gene Expression
Hin +
Unflipped
HPP
Transformation
Observe
colony
fluorescence
Flipping Detected by Phenotype
ABC
(Yellow)
ACB
(Red)
BAC
(None)
Flipping Detected by Phenotype
ABC
(Yellow)
ACB
(Red)
BAC
(None)
Hin-Mediated
Flipping
ABC Flipping
Yellow
Hin
Yellow, Green, Red, None
ACB Flipping
Red
Hin
Yellow, Green, Red, None
BAC Flipping
None
Hin
Yellow, Green, Red, None
Flipping Detected by PCR
ABC
ACB
BAC
BAC
ABC
ACB
Unflipped Flipped
Flipping Detected by Sequencing
BAC
RFP1
hixC
GFP2
hixC
RFP2
Hin-BAC
RFP1
Conclusions
• Mathematical modeling revealed the feasibility of
our approach to building a bacterial computer
• GFP and RFP were successfully split using hixC
• Added 69 parts to the Registry
•Test constructs were built that encode HPP problems
in bacteria
• Flipping of DNA was shown by PCR and
fluorescence phenotypes
• Our results support the conclusion that our bacterial
computers are working on the HPP and may have
solved it
Pending Experiments
• Obtain complete DNA sequence of solution
• Produce clonal colonies that contain flipped HPP
• Conduct coupled transformations with DBA and
screen for false-positives
• Split 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
Acknowledgements: Thanks to The Duke Endowment, HHMI, NSF DMS 0733955,
Genome Consortium for Active Teaching, Davidson College James G. Martin
Genomics Program, Missouri Western SGA, Foundation, and Summer Research
Institute, and Karen Acker (DC ’07). Team member Oyinade Adefuye is from North
Carolina Central University and Amber Shoecraft is from Johnson C. Smith University.
Extra Slides
Traveling Salesperson Problem
Other Attempts at Gene Splitting
Reporter Gene
Status
Kanamycin Resistance
Failed
Tetracycline Resistance
Failed
Chloramphenicol Resistance
Undetermined
(Issues in building)
Cre Recombinase
Undetermined
(Issues in testing)
True Positives
1
4
3
2
5
Elements in the shaded region can
be arranged in any order.
N edges
Number of True Positives = N! * 2N
Another Gene-Splitting Method
RBS + ATG ------hixC----- 1 bp + Reporter Gene1
Front Half
Back Half
RBS + ATG + 1bp ------hixC----- Reporter Gene2
Front Half
Back Half
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