1. DNA Solution of the Maximal Clique Problem
Q. Ouyang, P. D. Kaplan, S. Liu, A. Libchaber
발표자 : 김진

2. The Clique Problem Every vertex is connected to every other vertex.
Represented by an N-digit binary number.
1 : a vertex in the clique, 0 : a vertex not in the clique
Complementary graph : containing all edges missing in the original graph
Complementary Graph
111100

3. Algorithm
Transform the complete set of possible cliques into an ensemble of all N-digit binary numbers (complete data pool.)
Find pairs of vertices that are not connected by an edge.
Eliminate numbers containing connections in the complementary graph.
Find the data containing the largest numbers of 1’s.

4. DNA encoding Form : double-stranded DNA (dsDNA).
Each bit in a binary number is represented by two DNA sections
Pi : position, P6 is needed for PCR amplification.
Vi : bit’s value
Length
Pi : 20bp (base pairs)
Vi :0 bp if the value is 1, 10 bp if 0.
Longest DNA(000000) has 200bp, shortest(111111) has 140bp.

5. Constructing the DNA data pool Parallel overlap assembly (POA)
Each oligonucleotide consists of two position and one value
for even i , for odd I
Starts with the 12 oligonucleotides listed in next table.
During each thermal cycle, the position strings annealed to the complementary string of the next oligonucleotide.
After a few thermal cycles, a data pool with all combinations of V0V1V2V3V4V5 was built.

6. Oligonucleotides used to construct the DNA data pool
Value sequences are written with lowercase letters.
Restriction enzyme sites are indicated by underlining.
Each restriction enzymes were applied to cut each values.
Ex) Afl II – V0, Hind III – V1, Spe I – V2, etc.

7. Parallel overlap assembly (POA)

8. Eliminating vertices not in clique
Ex) Eliminate
0-2 connection
Divide the data pool into t0 and t1.
In t0, cut strings containing v0=1
In t1, cut strings containing v2=1
Combine t0, t1.

9. Reading the answer The lowest band is the answer Use molecular cloning
The clique of largest size is represented by the shortest length of DNA.
Use molecular cloning
Insert the DNA of the answer into M13 bacteriophage.
The mutagenized M13 phage DNA was transfected into E. coli bacteria, cloned, and its DNA extracted and sequenced.
The result is the correct answer.

10. Error Handling Production of ssDNA during PCR
This cannot be cut by restriction enzymes
Avoid this error by digesting the ssDNA with S1 nuclease before restriction digestions.
Incomplete cutting by restriction enzymes
Repeating the digestion-PCR process increase the s/n ratio arising from incomplete digestion.
The selected restriction enzymes worked well.

11. Conclusion & Future work
Advantage of DNA computing.
High parallelism.
Size is limited.
27 with picomole, 36 with nanomole chemistry.
New algorithms are needed.
Resembling in vitro evolution.
Initial data pool need not contain every possible final answer.
Rapid and accurate data access are needed.
Current technology are either too slow or too noisy.