Living Hardware to Solve the Hamiltonian Path Problem

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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
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The Hamiltonian Path Problem
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The Hamiltonian Path Problem
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Advantages of Bacterial Computation
Software
Hardware
Computation
Computation
Computation
http//www.dnamnd.med.usyd.edu.au/
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Computational Complexity

• Non-Polynomial (NP)

• No Efficient Algorithms

of Processors
Cell Division
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Flipping DNA with Hin/hixC
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Flipping DNA with Hin/hixC
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Flipping DNA with Hin/hixC
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Using Hin/hixC to Solve the HPP
Using Hin/hixC to Solve the HPP
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Using Hin/hixC to Solve the HPP
Using Hin/hixC to Solve the HPP
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hixC Sites
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Using Hin/hixC to Solve the HPP
Using Hin/hixC to Solve the HPP
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Using Hin/hixC to Solve the HPP
Using Hin/hixC to Solve the HPP
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Using Hin/hixC to Solve the HPP
Using Hin/hixC to Solve the HPP
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Using Hin/hixC to Solve the HPP
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Solved Hamiltonian Path
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How to Split a Gene
Reporter
Detectable Phenotype
RBS
Promoter
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Detectable Phenotype
RBS
Repo-
rter
hixC
Promoter
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Gene Splitter Software
http//gcat.davidson.edu/iGEM07/genesplitter.html
Input
Output

• 1. Generates 4 Primers (optimized for
  Tm).
• 2. Biobrick ends are added to primers.
• 3. Frameshift is eliminated.

1. Gene Sequence (cut and paste) 2. Where do
you want your hixC site? 3. Pick an
extra base to avoid a frameshift.
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Gene-Splitter Output
Note Oligos are optimized for Tm.
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Predicting Outcomes of Bacterial Computation
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Starting Arrangement
4 Nodes 3 Edges
Probability of HPP Solution
Number of Flips
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How Many Plasmids Do We Need?
Probability of at least k solutions on m plasmids
for a 14-edge graph
k actual number of occurrences ? expected
number of occurrences
? m plasmids solved permutations of edges
permutations of edges
Cumulative Poisson Distribution
P( of solutions k)
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False Positives
Extra Edge
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False Positives
PCR Fragment Length
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PCR Fragment Length
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Detection of True Positives
Total of Positives
of Nodes / of Edges
of True Positives Total of Positives
of Nodes / of Edges
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Building a Bacterial Computer
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Choosing Graphs
D
A
B
Graph 2
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Splitting Reporter Genes
Green Fluorescent Protein
Red Fluorescent Protein
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Splitting Reporter Genes
Green Fluorescent Protein Split by hixC
Red Fluorescent Protein Split by hixC
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HPP Constructs
Graph 0 Construct
A
AB
B
Graph 0
Graph 1 Constructs
ABC
C
A
ACB
B
Graph 1
BAC
Graph 2 Construct
D
A
B
DBA
Graph 2
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Measuring Fluorescence
GFP Excitation Spectra for 4 HPP Constructs (at
an Emission Wavelength of 515nm)
450 nm chosen as excitation wavelength to measure
GFP
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Measuring Fluorescence
RFP Excitation Spectra for 4 HPP Constructs(at
an Emission Wavelength of 608nm)
560 nm chosen as excitation wavelength to measure
RFP
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Normalized Fluorescence Measurements
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Uncoupled Hin and Reporter Gene Expression
Hin
Purify flipped HPP plasmid
Cotransformation
Unflipped HPP
FlippedHPP
Observe colony fluorescence
Cotransformation
T7 RNAP
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Coupled Hin and Reporter Gene Expression
Observe colony fluorescence
Hin Unflipped HPP
Transformation
T7 RNAP
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Flipping Detected by Phenotype
ABC (Yellow)
ACB (Red)
BAC (None)
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Flipping Detected by Phenotype
ABC (Yellow)
Hin-Mediated Flipping
ACB (Red)
BAC (None)
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ABC Flipping
Yellow
Yellow, Green, Red, None
Hin
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ACB Flipping
Red
Yellow, Green, Red, None
Hin
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BAC Flipping
None
Yellow, Green, Red, None
Hin
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Flipping Detected by PCR
ABC
ACB
BAC
BAC
ABC
ACB
Unflipped
Flipped
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Flipping Detected by Sequencing
BAC
RFP1 hixC
GFP2
Hin-BAC
RFP1 hixC
RFP2
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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

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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

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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.
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Extra Slides
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Traveling Salesperson Problem
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Other Attempts at Gene Splitting
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True Positives
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Elements in the shaded region can be arranged in
any order.
N edges
Number of True Positives N! 2N
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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
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Path at 3 nodes / 3 edges HP- 1 12 23
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Path at 4 nodes / 6 edges HP-1 12 24 43
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Path 5 nodes / 8 edges HP -1 12 25 54 43
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Path 6 nodes / 10 edgesHP-1 12 25 56 64 43
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Path 7 nodes / 12 edgesHP-1 12 25 56 67 74 43