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Machine Learning Framework for
DNA Computing
3rd MEC Workshop
2001.11.30
신수용
DNAC vs. Lego

Consider each DNA base as “LEGO block”
 A, C, G, T
DNA Lego
(C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/
DNAC vs. Lego

Solution
 Sequence of blocks
 AACTG
A+A+C +T+ G
 Fixed length

Computing
 Decompose the solution to each block
 Rebuild the solution from those blocks
(C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/
Lego operation

Hybridization
 Combining the lego blocks each other.

Ligation
 Given a lego blocks of length n, append a block to it and make a
lego blocks of length n+1.

Electrophoresis
 Check a lego length.

PCR
 Amply (put into) lego blocks.

Selection
 Extract a lego which we want to do exactly
(C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/
DNAC vs. Lego
Computing Process
(C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/
Search Space

Most machine learning algorithms can be
considered as the process of seeking for the
optimal solution in the huge search space.
Solutio
n
Initial
(C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/
Search Space in DNAC

Do parallel search
Solutio
n
Initial
(C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/
Conventional ML algorithms
vs. DNAC algorithms

For n nodes Graph problems
 Conventional ML algorithms
Search for solution in the ONLY n! space.
 DNAC algorithms (ideally)
Search for solution in the
 We
space.
can provide blocks unlimitedly
(C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/
Conventional ML algorithms
vs. DNAC algorithms
n! space

 n! space
n 1
(C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/
Exhaustive Search
DNA Computing

It is important to limit search space.
 Do not exhaustive search.
 We need more intelligent search process.
 Evolutionary process!
(C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/
Molecular Evolutionary Computing

Combining DNA computing with evolutionary
computation.
 Use huge parallelism of DNA computing and
smart techniques of evolutionary computation.
 We can think that molecular evolutionary computing
as evolutionary computation with unlimited
population size (ideally).
(C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/
MEC

Search  Selection  Search  Selection …
Select proper
search process
(C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/
MEC

Abstract flow
Search
Selection
Solution
(C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/
Theoretical problem in DNAC

Hybridization is not wholly controlled, can we
make a solution exactly?

Case by case approach
(C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/
Theoretical problem in DNAC

Case
Hybridization
prob.
Number of
blocks
Number of
reactions
Search
step
Case1
Constant p
Unlimited
Unlimited
Step by
step
Case2
Decrease
Unlimited
Unlimited
Step by
step
Case3
Decrease
Limited
Limited
Step by
step
case4
Decrease
Limited
Limited
arbitrary
(C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/
Case (Tree view)
Reaction stage
Stage 1
Stage 2
Step 4
AA
Source
(Limited or Unlimited)
A
AT
AG
AC
Step 1, 2, 3
Stage 3
Stage 4
AAT
AAC
......
Hybridization
probability P
(C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/
Case1
 k  1 r
k r


p
(
1

p
)

 
k  r  r  1
 k 1
 
r
 p   (1  p) k r
k  r  r  1
 r  k 1


r
(1  p) k
 p  
k 0  r  1 






Constant hybridization success
ratio, unlimited blocks,
experiments and step by step
search
Select best string at each step
(each depth in tree)
hybridize only selected string for
next step
 r
r
Then the number of experiment X  p  ( p  1) k

 
follows the negative binomial
k 0  k 
distribution
Thus, in this case, DNAC
 p r (1  ( p  1)) r
guarantees the success of
experiments
 p r p r
  r
 r  k  1 
    (1) k 
 
 k
 k 
  
 r

  k
r
 (1  x)     x 


k 0  k  

(C) 2001, SNU Biointelligence
 1Lab, http://bi.snu.ac.kr/
Case 2
CASE 2, 3, 4
CASE 1
Add
existing pool
select
expand
select
(C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/
Case 2, 3, 4

Case2
 Uniform (?)
 Formulation


Case3, 4
Verify solutions
 Probability

sample space ,
event X  
1. P ( X )  0
2. P (  )  1
3. for mutually exclusive X k (k  1,2, )


k 1
k 1
P ( X k )   P ( X k )
Verify assumptions in real life experiments
(C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/