DNA Computer~ 回顧 Leonard M. Adleman之研究

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DNA Computer之優點• Low energy consumption• Less space• Efficient• Accurate• : :

摘要1. Use DNA to solve the “Hamiltonian

Path Problem”2. DNA Computer (a) the unrestricted (DNA) model (b) A sticker Based Model

1. Computing with DNA

1994 Leonard M. Adleman Use DNA to Solve the

“Hamiltonian Path Problem”

Hamiltonian Path Problem

如同“ Traveling Salesman Problem”

A

B

C

DE

F

G

由 A 到 G, 每個城市都要經過 , 只經過一次 , 且只能依照箭頭方向前進

傳統的解題步驟 Step 1: Generate a set of random paths through the graph.Step 2:Check wheather that path starts at the start vertex and

ends with the end vertex. If not,remove that path from the set.

Step 3: Check if that path passes through exactly n vertices. If not,remove that path from the set.

Step 4: For each vertex, check if that path passes through that vertex. If not,remove that path from the set.

Step 5: If the set is not empty,then report that there is a Hamiltonian path. If the set is empty, report that th

ere is no Hamiltonian path.

When the number of cities is increased to 70, the problem becomes too complex for even a supercomputer.

解決方法 :

~ DNA Computation ~

What is DNA

• A : adenine• T : thymine• C : guanine• G : cytosine

Watson-Crick pairing

If a molecule of DNA in solution meets its Watson-Crick complement, then the two strands will anneal---twist around each other to form the famous double helix.

Programming with DNA

為簡化題目 , 此處只考慮四個城市 , 六種航線飛機

start

End

解法 :Step 1

Create a unique DNA sequence for each city A through G. For each path, for example, from A to B, create a linking piece of DNA that matches the last half of A and first half of B

Step 2

Watson-Crick pairing Mix the DNA with flight number and c

omplement DNA with city name in a test tube, with some of these DNA strands sticking together. A chain of these strainds represents a possible answer.

Watson-Crick pairing

Watson-Crick pairing

A B C D

A B

A B C D

A B B C C D

TGAA CGTC AGCC TGAC CCGA TACA GGCTCGTT

GCAG TCGG ACTG GGCT ATGT CCGA

Step 3: polymerase chain reaction

Because it is difficult to “remove” DNA from the solution, the target DNA ( start at A and end at G) was copied over and over again until the test tube contained a lot of it relative to the other random sequences.

Step 4: Gel electrophoresis

Separates DNA by length. 7 “cities” long were separated from

the rest.

Step 5: Purified

例 : 想去掉沒有含 A 的 DNA, 可以利用含有 A城市名的 DNA 將會和 complement A 城市的 DNA 結合 , 其餘不會 .去掉沒經過 A 的

B ： G

-------------------------------------剩下 ABCDEFG 都有經過的

Step 6

All that was left was to sequence the DNA, revealing the path from A to B to C to D to E to F to G.

2. DNA computer

(a) the unrestricted (DNA) model1995

Leonard M. Adleman“ On Constructing A Molecular Computer”

(a) the unrestricted (DNA) model

A (test) tube is a set of molecules of DNA ( i.e. a multi-set of finite strings over the alphabet {A,C,G,T}) , 對於此 test tube T , 有四種 operations:

1. Separate

Give a tube T and a string of symbols S over {A,C,G,T}, produce two tubes:

(1) +(T,S) --> all of the molecules of DNA in T which contain the S

(2) -(T,S) --> all of the molecules of DNA in T which do not contain the S在 molecular biology 技術上 , 可使用 affinity c

olumn 分離。

2. Merge

Give tubes T1,T2, produce (T1,T2) where:(T1,T2)=T1 T2

即將 T1和 T2混在一起 , 成為 (T1,T2)=T1 T2

)2,1( TT

3. Detect

Detect 如果試管內含有任何 DNA molecule, 則為 "yes" 否則為 "no" 。 可用 PCR, 及光譜偵測。

4. Amplify

Give a tube T produce two tubes T’(T) and T”(T) such that T=T’(T)=T”(T).

複製 T’(T),T”(T) 使得 T=T’(T)=T”(T)

Write ‘programs’

For example: 假設 DNA 分子只由 A 構成 ,傳回“ yes”, 否則 , 傳回“ no”• Input (T)• T1=-(T,C) 去掉含有 C 的 DNA 分子• T2=-(T1,G) G• T3=-(T2,T) T• Output( Detect(T3)) ……………..”yes”

2. DNA computer

(b) 1996 S. Roweis, E. Winfree: Computation and Neural Systems Option R. Burgoyne: Department of Biomedical Engineering N. F. Goodman: Department of Biological Science N. V. Chelyapov, P. W. K. Rothemund, L. M. Adleman : Depart

ment of Computer Science

“A Sticker Based Model for DNA Computation”

A Sticker Based Model for DNA Computation

有和 stickers 鍵結者為“ 1”, 沒有為“ 0”

Four principle operations

1. Combination of two sets of strings into one new set

2. Separation of one set of strings into two new sets

3. Setting (turn on) a particular bit in every string of a set

4. Clearing (turn off) a bit in every string of a set

Data Tube

(1) A closed cylinder with a nipple connector in either end that allows fluid to flow in or out.

(2) Near one end on the inside is a permanent membrane which passes solvent but not stickers or memory strands.

Operator Tubes: Separation

(1) Separation operator tube contains many identical copies of one bit’s oligo probe. It is designed so that the probes cannot escape from the tube but unbound memory complexes can.

Operator Tubes: Sticker

(2) A sticker operator tube is identical expect for a permanent filter on its inside which passes stickers but not memory strands.

Operator Tubes: Blank

(3) A blank operator tube is merely empty tube with nipple connectors on each end.

Setup for a generic operation in the stickers machine

The dirty sides of the data tubes are connected to the operator tube; the clean sides of the data tubes are joined by a pump. Solution is cycled through all three tubes. The temperature, salinity, direction and duration of the flow is controlled by the electronic computer.

Combination

To combine two sets of complexes simply select the two data tubes and a blank operator tube. Cycle cold solution towards (say) the first data tube. This catches all the memory complexes in the first data tube. The second data tube and the blank operator are discarded.

Separation

By control the temperature and direction of the flow to separate a set of complexes.

Set Bit Clear Bit

結論Computation with DNA is possible.

Will we succeed in creating molecular computers that can compete with

electronic computers???

Challenges

In biology and chemistry: challenges in understanding cellular and molecular mechanisms and making them available for use.

In computer science and mathematics: challenges in finding appropriate problems and efficient molecular algorithms to solve them.

In physics and engineering: challenges in building large scale, reliable molecular computers.

References

1. Leonard Adleman: Molecular computation of solutions to combinatorial problems. Science, 266:1021-1024. (Nov. 11). 1994.

2. M. Linial, N. Linial, Y. M. D. Lo, K. F. C. Yiu, S. L. Wong, B. Bunow, L. M. Adleman, Science, 268, 5210, 481-484 ,1995.

3. Leonard Adleman: On constructing a molecular computer, DNA Based Computers, Eds. R. Lipton and E. Baum, DIMACS: series in Discrete Mathematics and Theoretical Computer Science, American Mathematical Society. 1-21 ,1996.

4. S. Roweis, E. Winfree, R. Burgoyne, N. V. Chelyapov, N. F. Goodman, P. W. K. Rothemund, L. M. Adleman,”A sticker Based Model for DNA computation”,1996.

5. L. M. Adleman, Science American, Aug. , 34-41 (1998).