Living Hardware to Solve the Hamiltonian Path Problem

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Living Hardware to Solve the Hamiltonian Path
Problem
Faculty Drs. Malcolm Campbell, Laurie Heyer,
Karmella Haynes
Faculty Drs. Todd Eckdahl, Jeff Poet
Students Jordan Baumgardner, Tom Crowley, Lane
H. Heard, Nickolaus Morton, Michelle Ritter,
Jessica Treece, Matthew Unzicker, Amanda Valencia
Students Oyinade Adefuye, Will DeLoache, Jim
Dickson, Andrew Martens, Amber Shoecraft, and
Mike Waters
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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
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Advantages of Bacterial Computation
Software
Hardware
Computation
Computation
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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

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Computational Complexity

• Non-Polynomial (NP)

• No Efficient Algorithms

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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
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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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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

• 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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Can We Detect A Solution?
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Starting Arrangement
4 Nodes 3 Edges
Probability of HPP Solution
Number of Flips
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True Positives
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Elements in the shaded region can be arranged in
any order.
(Edges-Nodes1)
Number of True Positives (Edges-(Nodes-1))! 2
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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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Splitting Reporter Genes
Green Fluorescent Protein
Red Fluorescent Protein
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Splitting Reporter Genes
Green Fluorescent Protein
Red Fluorescent Protein
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3-Node Graphs
Graph A
Graph B
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HPP Constructs
Positive Control Construct
HPP0
Graph A Constructs
HPP-A0
HPP-A1
Graph A
HPP-A2
Graph B Construct
HPP-B1
Graph B
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Double Fluorescence
HPP0
Green Fluorescence
T7 RNAP
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Double Fluorescence
HPP0
Green Fluorescence
T7 RNAP
T7 RNAP
HPP-A0
Yellow Fluorescence
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Fluorometer Measurements
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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Fluorometer Measurements
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 Fluorometer Measurements
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Flipping Detected by Phenotype
HPP-A0
HPP-A1
HPP-A2
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Flipping Detected by Phenotype
HPP-A0
Hin-Mediated Flipping
HPP-A1
HPP-A2
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Flipping Detected by PCR
HPP-A0
HPP-A1
HPP-A2
Unflipped
Flipped
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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

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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
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Extra Slides
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Traveling Salesperson Problem
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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

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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
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Promoter Tester

• RBSKanRBSTetRBSRFP
• Tested promoter-promoter tester-pSBIA7 on varying
  concentration plates

• Used Promoter Tester-pSB1A7 and Promoter
  Tester-pSB1A2 without promoters as control
• Further evidence that pSB1A7 isnt completely
  insulated

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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

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Plasmid Insulation

• Insulated plasmid was designed to block
  read-through transcription
• Read-through transcription without a promoter
• Tested a promoter-tester construct
• RBSKanRBSTetRBSRFP
• 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

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What Genes Can Be Split?
GFP before hixC insertion
GFP displaying hixC insertion point
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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 mg2 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)

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Tetracycline Resistance Protein

• Did not split
• Transmembrane protein
• Structure hasnt 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

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Splitting Cre Recombinase
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More Gene-Splitter Output
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Gene Splitter Software