Heuristic solution to a 10-city asymmetric traveling salesman problem using Probabilistic DNA computing

DNA hybridization was used to make a probabilistic computation to identify the optimal path for a fully connected asymmetric 10 city traveling salesman problem. Answer set formation was achieved using a unique DNA 20mer for each edge capable of hybridizing to half of each neighboring vertex. This allowed the vertex 20mers to be linked in all possible combinations to form paths through the network. Hybridization occurred in the presence of an excess of vertex 20mers, while edge 20mers were added in limiting amounts inversely proportional to the weight of each edge, resulting in the paths with the least cumulative weight being the most abundant. Correct answers, 230bp in length, contained a single copy of each vertex and were purified by PAGE and by successive magnetic bead affinity separations with probes for each vertex. Answer detection was accomplished using LCR of probes complementary to each vertex in a manner that identified the sequential order of vertices in each path by identifying vertex pairs. Optimal answer identification was accomplished using a conventional computer by normalizing the abundance of vertex pairings, and was found to be the same as that calculated by in silico.