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Living Hardware to Solve the Hamiltonian Path Problem
Faculty: Drs. Malcolm Campbell, Laurie Heyer, Karmella Haynes
Students: Oyinade Adefuye, Will DeLoache, Jim Dickson, Andrew Martens, Amber Shoecraft, and Mike Waters
Faculty: Drs. Todd Eckdahl, Jeff Poet
Students: Jordan Baumgardner, Tom Crowley, Lane H. Heard, Nickolaus Morton, Michelle Ritter, Jessica Treece, Matthew Unzicker, Amanda Valencia
The Hamiltonian Path Problem
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The Hamiltonian Path Problem
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Advantages of Bacterial Computation
Software Hardware Computation
Advantages of Bacterial Computation
Software Hardware Computation
Computation
http://www.turbosquid.comhttp://www.dnamnd.med.usyd.edu.au/
Advantages of Bacterial Computation
Software Hardware Computation
Computation
Computation
Computational Complexity
• Non-Polynomial (NP)
• No Efficient Algorithms
Computational Complexity
Cell Division
• Non-Polynomial (NP)
• No Efficient Algorithms
Flipping DNA with Hin/hixC
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
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
Solved Hamiltonian Path
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How to Split a Gene
RBSRBS
Promoter
ReporterReporterDetectable Phenotype
How to Split a Gene
RBSRBS
Promoter
ReporterReporter
hixCRBSRBS
Promoter
Repo- Repo- rter
Detectable Phenotype
Detectable Phenotype
?
Gene Splitter Software
Input Output
1. Gene Sequence (cut and paste)
2. Where do you want your hixC site?
3. Pick an extra base to avoid a frameshift.
1. Generates 4 Primers (optimized for Tm).
2. Biobrick ends are added to primers.
3. Frameshift is eliminated.
http://gcat.davidson.edu/iGEM07/genesplitter.html
Gene-Splitter Output
Note: Oligos are optimized for Tm.
Can We Detect A Solution?
Starting ArrangementP
roba
bilit
y of
HP
P S
olut
ion
Number of Flips
4 Nodes & 3 Edges
Elements in the shaded region can be arranged in any order.
True Positives
Number of True Positives = (Edges-(Nodes-1))! * 2(Edges-Nodes+1)
1
3
5
4
2
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?
P(# of solutions ≥ k) =
€
1−e−λ • λ x
x!x=0
k−1
∑
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
Probability of at least k solutions on m plasmids for a 14-edge graph
False Positives
Extra Edge
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3
5
4
2
False Positives
PCR Fragment Length
PCR Fragment Length
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3
5
4
2
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
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
Graph A Constructs:
Graph B Construct:
HPP0
HPP-A0
HPP-A1
HPP-A2
HPP-B1
Positive Control Construct:
Graph B
Graph A
Green Fluorescence
Double FluorescenceHPP0
T7 RNAP
HPP-A0
T7 RNAP
Green Fluorescence
Yellow Fluorescence
Double FluorescenceHPP0
T7 RNAP
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
Hin-Mediated Flipping
HPP-A0
HPP-A1
HPP-A2
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
Support: Davidson College
Missouri Western State University The Duke Endowment
HHMI NSF Genome Consortium for Active Teaching James G. Martin Genomics Program
Thanks to: 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
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
•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
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