Hamilton Path Problem Catherine Doyle, James Harden, Julia Fearrington

Solving the Hamilton Path Problem Through Golden Gate Shuffling

Golden Gate Shuffling vs. BioBricks Golden Gate Shuffling Pros – Allows us to split at any site with 4 bp in common – Hix sites unnecessary – No scars – Make all the edges possible – Make all possible paths – Feasible Selection processes – Quick1-2 hrs Cons – In vitro – More random assembly Bio Bricks Pros – Can flip single DNA fragment or multiple adjacent fragments – in vivo Cons – Scars – Takes a long time: days – Can only build one edge at a time – Attach each component through ligations – Unintentional recombination

Design 6 Edges 6 Half edges RBS Promoter RBS A1 B1 C1 A2 C2 B2 Promoter B2 RBS A1 Promoter C2 Promoter A2 RBS B1 RBS C1

Controlled Design PCR w/ primers to create 6 half edges Promoter B2 RBS A1 GGS RBS Promoter A1 B2 6X GGS N edges With all different half edges Size Selection Clone and Measure phenotypes Solution(s)

1 st level of Randomness Design PCR w/ primers to create 6 half edges GGS RBS Promoter RBS A1 B1A2 C2 B2 Promoter RBS B1 C1 A2 C2 B2 Clone and PCR Screen for 6 desired edges Promoter RBS A1 B1 C1 A2 B2 C2 GGS N edges Size Selection Clone and Measure Phenotypes Solution(s) GGS N Edges Size Selection Clone and Measure Phenotypes Solution(s) OR Harder Problem Easier Problem

2 nd Level of Randomness Design PCR w/ primers to create 6 half edges GGS N edges Size Selection Clone and Measure Phenotypes Solution(s)

Column Method z z A1 X2 4 4 C1 X2 4 4 B1 X2 4 4 B1 A2 4 4 A1B2 4 4 B1C2 4 4 C1B2 4 4 C1A2 4 4 A1C2 4 4 A1B2 4 4 B1 C2 4 4 C1B2 4 4 C1A2 4 4 A1C2 4 4 B1A Y1A2 4 4 Y1 C2 4 4 Y1B GGS N Edges Clone and measure Phenotypes Solution(s) PCR w/ primers to create all half edges GGS

Conclusions Can use GGS problems with Hin and Hix Probably will use the controlled method first go around and advance to the Column method. Using all 6 edges is not mathematically interesting but is biologically – Will probably not use all 6 edges in experiment