Living Hardware to Solve the Hamiltonian Path Problem Faculty: Drs. Malcolm Campbell, Laurie Heyer,...

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)

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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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False Positives

PCR Fragment Length

PCR Fragment Length

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0.25

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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

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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

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34

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TT

Path 5 nodes / 8 edges HP -1 12 25 54 43

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34

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TT

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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

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34

1

TT

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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