DNA computing on a chip Mitsunori Ogihara and Animesh Ray Nature, 2000 발표자 : 임예니

Idea  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  Report a technique for massively parallel elimination Harness the power of DNA chemistry to solve a particularly difficult problem in mathematical logic (NP problems)  Complexity classes  Whether sequential algorithms can solve all NP problems in polynomial time is still unknown.

Complexity classes  The class P is the set of decision problems that can be solved by a deterministic sequential machine in polynomial time.  The class NP is the set of decision problems that can be solved by a non-deterministic Turing machine in polynomial time.  The NP-complete problems are the most difficult problems in NP. A decision version of a combinatorial optimization problem is proved to belong to the class of NP-complete problems, then the optimization version is NP-hard.

Leonard Adleman  Present a DNA-based polynomial time method for the Hamilton path problem The problem of finding an airline flight path between several cities on a map such that each city is visited only once.

Hamiltonian path problem  Algorithm for directed Hamiltonian path problem Step 1: Generate random paths through the graph Step 2: Keep only those paths that begin with v in and end with v out Step 3: If the graph has n vertices, then keep only those paths that enter exactly n vertices. Step 4: Keep only those paths that enter all of the vertices of the graph at least once. Step 5: If any paths remain, say “Yes”, otherwise, say “No”  In order to achieve the small computation time, Adleman traded space (the amount of DNA needed) for time (the number of biochemical steps to be used).

Hamiltonian path problem  Step 1 Cities on a map, paths between pairs of cities, may be encoded in strands of DNA. Millions of DNA strands, diffusing in a liquid, can self- assemble into all possible flight-path configurations.  Step 2 ~ Step 4 From that configurations, molecular maneuvers can fish out the correct solution. PCR amplification, running on an Agarose gel, magnetic bead separation

Liu  3-SAT Every NP problem can be seen as the search for a solution that simultaneously satisfies a number of logical clauses, each composed of three variables.  (x1 OR x2 OR ^x3) AND (^x4 OR x5 OR ^x6)  Representation The variables in a given 3-SAT formula Binary strings Single-stranded DNA sequence X1 OR x2 OR ^x3 110 CTTCG

Surface-based approach  Watson strands For n variables, there are 2 n unique Watson strands. For small 3-SAT, you need 8 Watson strands.  Crick strand For each Watson strand, there is also a complementary Crick strand created by the base- pairing rule : A-T, C-G.  Goal to identify those strings out of a library of eight that satisfy all the clauses of a particular 3-SAT formula.

Surface-based approach 1. They made 8 Watson strands. 2. They attached the Watson DNA strings corresponding to all candidate solutions on a specially treated gold surface. 3. They added all possible Crick strands that will stick to a Watson string satisfying the first clause. Such pairing creates double- stranded DNA. 4. The remaining single-stranded molecules are destroyed by enzymes.

Surface-based approach 5. The surface is then heated to melt away the complementary strands, washed and a fresh collection of Crick strands is paired with strings satisfying the second clause. 6. The DNA answers are attached randomly to the surface, to read out the answer, the surviving strands first have to be amplified using the polymerase chain reaction (PCR).

Polymerase Chain Reaction (PCR)  A molecular biological method for amplifying (creating multiple copies of) a short, well-defined part of a DNA strand  3 steps Melting : The double-stranded DNA has to be heated to 96°C in order to separate the strands. Annealing : The temperature is lowered so the primers can attach themselves to the single DNA strands. The temperature is usually 5°C below melting temperature of primer. Elongation : The DNA-Polymerase has to fill in the missing strands. It starts at the annealed primer and works its way along the DNA strand.

Polymerase Chain Reaction (PCR)

Computation time  Surface-based approach only 3k+1 steps  for a brute-force evaluation of all 2 n possible answers  where k is the number of clauses  Best computer algorithm 1.33 n steps  where n is the number of variables  3-SAT problem ( k=30, n=50 ) could be solved in approximately 1.6 million steps by an ordinary computer algorithm, but in only 91 steps by surface-based approach.

Issues  Scaling up this technique to solve larger 3-SAT problems is unrealistic.  Issue of correcting errors arising from the inherent sloppiness of DNA chemistry  High cost of tailor-made DNA sequences 50-variable problem will require unique DNA strands.  The exponentially increasing number of DNA molecules needed to compute even small 3-SAT problems A compromise may be achieved by reducing search space through heuristics

The future of technology  The ideal application for DNA computation does not lie in computing large NP problems.  Some day there may be a need for fully organic computing devices implanted within a living body that can integrate signals from several sources and compute a response in terms of an organic molecular delivery device.

References  Q. Liu, L. Wang, A.G. Frutos, A.E. Condon, R.M. Corn, L.M. Smith, “DNA computing on surfaces, “ Nature 403, (2000).  L.M. Adleman, “Molecular Computation of Solutions to Combinatorial Problems, “ Science 266, (1994).  M. Ogihara and A. Ray, “DNA-based parallel computation by counting,” DIMACS Series in Discrete Mathematics and Theoretical Computer Science Volume 48, The American Mathematics Society Press, pages , 1999    