1. DNA Computing on a Chip Mitsunori Ogihara and Animesh Ray Nature, vol. 403, pp. 143-144 Cho, Dong-Yeon

2. 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.

3. Arriving at the truth by elimination Problem classes  Polynomial time or P problems  O(1), O(n), O(nlogn), O(n 2 ), O(n 3 ), …  Non-deterministic polynomial time or NP problems  ‘Hard’ NP problems have running times that grow exponentially with the number of the variables.  O(2 n ), O(3 n ), 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.

4. 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.

5. 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.

6. 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.

7. 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(1.33 n ), O(2 n )  k: the number of clauses  n: the number of variables

8. 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: 10 15 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.

9. 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.