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Living Hardware to Solve the Hamiltonian Path Problem Faculty: Drs. Malcolm Campbell, Faculty: Drs. Todd Eckdahl, Jeff Laurie Heyer, Karmella Haynes Poet Students: Jordan Baumgardner, Students: Oyinade Adefuye, Will DeLoache, Jim Dickson, Andrew Martens, Amber Shoecraft, and Mike Waters Tom Crowley, Lane H. Heard, Nickolaus Morton, Michelle Ritter, Jessica Treece, Matthew Unzicker, Amanda Valencia 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 Advantages of Bacterial Computation Software Hardware Computation Computation 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) • No Efficient Algorithms Computational Complexity • Non-Polynomial (NP) • No Efficient Algorithms Cell Division Flipping DNA with Hin/hixC 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 hixC Sites 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 Promoter Reporter Detectable Phenotype 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. Can We Detect A Solution? Probability of HPP Solution Starting Arrangement 4 Nodes & 3 Edges Number of Flips True Positives 1 4 3 2 5 Elements in the shaded region can be arranged in any order. (Edges-Nodes+1) Number of True Positives = (Edges-(Nodes-1))! * 2 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! x0 k1 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 Total # of Positives 1.0E+08 1.0E+07 1.0E+06 1.0E+05 1.0E+04 1.0E+03 1.0E+02 1.0E+01 1.0E+00 6/9 7/12 7/14 # of Nodes / # of Edges 1 Total # of Positives # of True Positives ÷ 4/6 0.75 0.5 0.25 0 4/6 6/9 7/12 # of Nodes / # of Edges 7/14 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 Positive Control Construct: HPP0 Graph A Constructs: HPP-A0 HPP-A1 Graph A HPP-A2 Graph B Construct: HPP-B1 Graph B Double Fluorescence HPP0 Green Fluorescence T7 RNAP Double Fluorescence HPP0 Green Fluorescence T7 RNAP HPP-A0 Yellow Fluorescence 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 HPP-A0 HPP-A1 HPP-A2 Hin-Mediated Flipping 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 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 Extra Slides Traveling Salesperson Problem 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 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 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 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 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 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