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,
Download ReportTranscript 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,
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 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 Computation Computation http://www.dnamnd.med.usyd.edu.au/ http://www.turbosquid.com Computational Complexity • Non-Polynomial (NP) # of Processors • No Efficient Algorithms Cell Division Flipping DNA with Hin/hixC Flipping DNA with Hin/hixC Flipping DNA with Hin/hixC Using Hin/hixC toSolve Solve HPP Using Hin/hixC to thethe HPP 1 4 3 2 5 1 3 4 5 4 3 3 2 1 4 2 4 3 5 4 1 Using Hin/hixC toSolve Solve HPP Using Hin/hixC to thethe HPP 1 4 3 2 5 1 3 4 5 4 3 3 2 1 4 2 4 hixC Sites 3 5 4 1 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 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 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. Predicting Outcomes of Bacterial Computation Probability of HPP Solution Starting Arrangement 4 Nodes & 3 Edges Number of Flips 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 100000000.00 1 Total # of Positives # of True Positives ÷ Positives # of Total Total # of Positives 10000000.00 1000000.00 100000.00 10000.00 1000.00 100.00 10.00 1.00 4/6 6/9 7/12 7/14 of Nodes / # of Edges ## of Nodes / # of Edges 0.75 0.5 0.25 0 4/6 6/9 7/12 # of Nodes / # of Edges 7/14 Building a Bacterial Computer Choosing Graphs C A A B B Graph 1 Graph 2 D Splitting Reporter Genes Green Fluorescent Protein Red Fluorescent Protein Splitting Reporter Genes Green Fluorescent Protein Split by hixC Red Fluorescent Protein Split by hixC HPP Constructs Graph 0 Construct: A AB B Graph 1 Constructs: Graph 0 ABC C ACB A B Graph 1 BAC Graph 2 Construct: DBA A B Graph 2 D Measuring Fluorescence GFP Excitation Spectra for 4 HPP Constructs (at an Emission Wavelength of 515nm) 450 nm chosen as excitation wavelength to measure GFP Measuring Fluorescence RFP Excitation Spectra for 4 HPP Constructs (at an Emission Wavelength of 608nm) 560 nm chosen as excitation wavelength to measure RFP Normalized Fluorescence Measurements Construct Observed Color on UV Green (450/515) Box Red (560/608) 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 AB (R1-hixC-R2-G1-hixC-G2) Green 72 18 ABC (R1-hixC-R2-G1-hixC-G2) Yellow 340 255 ACB (R1-hixC-R2-G1-hixC-R2) Red 1 143 BAC (R1-hixC-G2) None 11 3 DBA (R1-hixC-G2) Hybrid green 15 3 Uncoupled Hin and Reporter Gene Expression Hin Cotransformation Purify flipped HPP plasmid Unflipped HPP Flipped HPP Cotransformation T7 RNAP Observe colony fluorescence Coupled Hin and Reporter Gene Expression Hin + Unflipped HPP Transformation Observe colony fluorescence Flipping Detected by Phenotype ABC (Yellow) ACB (Red) BAC (None) Flipping Detected by Phenotype ABC (Yellow) ACB (Red) BAC (None) Hin-Mediated Flipping ABC Flipping Yellow Hin Yellow, Green, Red, None ACB Flipping Red Hin Yellow, Green, Red, None BAC Flipping None Hin Yellow, Green, Red, None Flipping Detected by PCR ABC ACB BAC BAC ABC ACB Unflipped Flipped Flipping Detected by Sequencing BAC RFP1 hixC GFP2 hixC RFP2 Hin-BAC RFP1 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 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 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. Extra Slides Traveling Salesperson Problem Other Attempts at Gene Splitting Reporter Gene Status Kanamycin Resistance Failed Tetracycline Resistance Failed Chloramphenicol Resistance Undetermined (Issues in building) Cre Recombinase Undetermined (Issues in testing) True Positives 1 4 3 2 5 Elements in the shaded region can be arranged in any order. N edges Number of True Positives = N! * 2N 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 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