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DNA Computing on a Chip Mitsunori Ogihara and Animesh Ray Nature, vol. 403, pp. 143-144 Cho, Dong-Yeon Abstract In a DNA computer The input and output are both strands of DNA. A computer in which the strands are attached to the surface of a chip can now solve difficult problems quite quickly. [Liu et al., 2000] Liu, Q. et al., “DNA computing on a chip,” Nature, vol. 403, pp. 175-179, 2000. Arriving at the truth by elimination Problem classes Polynomial time or P problems O(1), O(n), O(nlogn), O(n2), O(n3), … Non-deterministic polynomial time or NP problems ‘Hard’ NP problems have running times that grow exponentially with the number of the variables. O(2n), O(3n), O(n!) … New technology for massively parallel elimination [Liu et al., 2000] This algorithm harnesses the power of DNA chemistry and biotechnology to solve a particularly difficult problem in mathematical logic. Adleman’s experiments Hamilton path problem Millions of DNA strands, diffusing in a liquid, can self-assemble into all possible path configurations. A judicious series of molecular manoeuvres can fish out the correct solutions. Adleman, combining elegance with brute force, could isolate the one true solution out of many probability. Liu’s experiments Satisfiability Problem Find Boolean values for variables that make the given formula true 3-SAT Problem ( x1 x3 x4 ) ( x4 ) ( x2 x3 ) ( x1 or x2 or x3 ) AND ( x4 or x5 or x6 ) Every NP problems can be ( x1 or x2 or x3 ) AND ( x1 or x2 or x3 ) seen as the search for a solution that simultaneously satisfies a number of logical clauses, each composed of three variables. Procedure Step 1. Attach DNA strings encoding all possible answers to a specially treated gold surface. Step 2. Complementary DNA strands that satisfy the first clauses are added to the solution. The remaining single strands are destroyed by enzymes. The surface is then heated to melt away the complementary strands. This cycle is repeated for each of the remaining clauses. Step 3. The surviving strands first have to be amplified using the PCR. Their identities are then determined by pairing with an ordered array of strings identical to the original set of sequences. O(3k+1) vs. O(1.33n), O(2n) k: the number of clauses n: the number of variables Problems Scaling up this technique to solve larger 3-SAT problems is still unrealistic. Correcting errors arising from the inherent sloppiness of DNA chemistry High cost of tailor-made DNA sequences 50-variable 3-SAT: 1015 unique DNA strands Designing enough unique DNA strands Exponentially increasing number of DNA molecules A compromise may be achieved by reducing the search space through heuristics. Conclusions The ideal application for DNA computation does not lie in computing large NP problems There may be a need for fully organic computing devices implanted within a living body that can integrated signals from several sources and compute a response in terms of an organic molecular-delivery device for a drug or signal.