1. Molecular Evolutionary Computing (MEC) for Maximum Clique Problems March 9, 2004 Biointelligence Laboratory School of Computer Science and Engineering Seoul National University Dong-Yeon Cho (dycho@bi.snu.ac.kr)

2. © 2004 SNU CSE Biointelligence Lab 2 Introduction (1/2) Molecular Evolutionary Computing (MEC)  Previous DNA computing techniques  We have to make all possible solutions but it is so difficult.  Conventional Experiments A few pico mole: 6.02  10 11  Ex) Binary problems (n = 50) 2 50  1.1  10 15  Ex) Combinatorial problems (n = 20) 20!  2.4  10 18  Evolutionary Computation  Evolutionary computing uses the power of natural selection to turn computers into automatic optimization and design tools.  The three mechanisms that drive evolution forward are reproduction, variation (crossover or mutation) and the Darwinian principle of survival of the fittest.

3. © 2004 SNU CSE Biointelligence Lab 3 Introduction (2/2) Previous Work [Wood et al., 2001]  A design for DNA computation of the OneMax problem  One nucleotide for one gene  It is difficult to implement crossover and mutation.  I doubt that this approach can be applied to other problems. Our Approach  Constructive method  Serially assembling the building blocks  Only primitive experiments

4. © 2004 SNU CSE Biointelligence Lab 4 Problem Maximum Clique Problem  Clique  A set of vertices in which every vertex is connected to every other vertices by an edge  Maximum clique problem  Given a graph containing n vertices and m edges, how many vertices are in the larges clique?  Example  (4, 1, 0) → 010011  (5, 4, 3, 2) → 111100 23 1 0 4 5 1 0 4 23 4 5 2 1 0

5. © 2004 SNU CSE Biointelligence Lab 5 Previous Work (1/3) Basic Blocks [Ouyang et al., 1997]  two DNA sections bit’s value bit’s value (V i )V 0 ~V 5 0 bp when V i =1 10 bp when V i =0 position value position value (P i )P 0 ~P 6 20 bp  Longest = 6  10 + 7  20 = 200bp (000000) Shortest = 6  0 + 7  20 = 140bp(111111) dsDNA

6. © 2004 SNU CSE Biointelligence Lab 6 Previous Work (2/3) POA (parallel overlap assembly)  12 oligonucleotides P i V i P i+1 for even i P’ i+1 V’ i P’ i for odd i P 0 V 0 P 1 P 2 V 2 P 3 P 4 V 4 P 5 P’ 2 V’ 1 P’ 1 P’ 4 V’ 3 P’ 3 P’ 6 V’ 5 P’ 5 DNA polymerase + dNTPs

7. © 2004 SNU CSE Biointelligence Lab 7 Previous Work (3/3) Logical Process  Unique restriction enzyme for each V i  Not scalable Unconnected edge 0-2

8. © 2004 SNU CSE Biointelligence Lab 8 Our Approach (1/3) Before POA After POA Before POA After POA

9. © 2004 SNU CSE Biointelligence Lab 9 Our Approach (2/3) Constructive method  Serially assembling the building blocks  Mix and.  Perform POA.  PCR with (P0) and lower primer (P’4).  Gel electrophoresis and extraction.  Mix and, then we can obtain. 0-21-3  = 0-3

10. © 2004 SNU CSE Biointelligence Lab 10 Our Approach (3/3)  Split into 3 tubes.  PCR with different primers.  P 0 V 0 (0) and V’ 5 (0)P’ 6  P 0 V 0 (0) and V’ 5 (1)P’ 6  P 0 V 0 (1) and V’ 5 (0)P’ 6 Final Step  The mixed solution may contains the candidate DNA molecules, that is, the cliques.  The clique of largest size is represented by the shortest length of DNA.  The lowest band is the answer.

11. © 2004 SNU CSE Biointelligence Lab 11 Discussion Advantage  There is no restriction enzymes.  Only primitive experimental steps  POA (similar to PCR), PCR, and Gel electrophoresis  Scalability Disadvantage  Errors in POA step  Serial constructive steps  (n(n-1)/2 – m) m is the number of connected edges in the given graph.