DNA computing began in 1994 when Leonard Adleman proved thatDNA computing was possible by finding a solution to a real- problem, a Hamiltonian Path Problem, known to us as the Traveling Salesman Problem,with a molecular computer. In theoretical terms, some scientists say the actual beginnings of DNA computation should be attributed to Charles Bennett's work. Adleman, now considered the father of DNA computing, is a professor at the University of Southern California and spawned the field with his paper, "Molecular Computation of Solutions of Combinatorial Problems." Since then, Adleman has demonstrated how the massive parallelism of a trillion DNA strands can simultaneously attack different aspects of a computation to crack even the toughest combinatorial problems.

**Adleman's Traveling Salesman Problem:**

The objective is to find a path from start to end going through all the points only once. This problem is difficult for conventional computers to solve because it is a "non-deterministic polynomial time problem" . These problems, when they involve large numbers, are intractable with conventional computers, but can be solved using massively parallel computers like DNA computers. The Hamiltonian Path problem was chosen by Adleman because it is known problem.

The following algorithm solves the Hamiltonian Path problem:

1.Generate random paths through the graph.

2.Keep only those paths that begin with the start city (A) and conclude with the

end city (G).

3.If the graph has n cities, keep only those paths with n cities. (n=7)

4.Keep only those paths that enter all cities at least once.

5.Any remaining paths are solutions.

The key was using DNA to perform the five steps in the above algorithm. Adleman's first step was to synthesize DNA strands of known sequences, each strand 20 nucleotides long. He represented each of the six vertices of the path by a separate strand, and further represented each edge between two consecutive vertices, such as 1 to 2, by a DNA strand which consisted of the last ten nucleotides of the strand representing vertex 1 plus the first 10 nucleotides of the vertex 2 strand. Then, through the sheer amount of DNA molecules (3x1013 copies for each edge in this experiment!) joining together in all possible combinations, many random paths were generated. Adleman used well-established techniques of molecular biology to weed out the Hamiltonian path, the one that entered all vertices, starting at one and ending at six. After generating the numerous random paths in the first step, he used polymerase chain reaction (PCR) to amplify and keep only the paths that began on vertex 1 and ended at vertex 6. The next two steps kept only those strands that passed through six vertices, entering each vertex at least once. At this point, any paths that remained would code for a Hamiltonian path, thus solving the problem.

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