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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.
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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 • Every NP problems can be 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.