Thpark DNA Computing

8/3/2019 Thpark DNA Computing

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DNA-Based Computing& Development of

Efficient Operatorsfor Solving Traveling Salesman ProblemTai Hyun ParkTai Hyun Park

School of Chemical EngineeringSchool of Chemical Engineering

Seoul National UniversitySeoul National University


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ContentsContents IntroductionIntroduction

DNA computing for solving traveling salesman problemDNA computing for solving traveling salesman problem

Traveling salesman problem (TSP)

Molecular algorithm for TSP Experimental implementation

Unit operators in DNA computingUnit operators in DNA computing Denaturation temperature gradient polymerase chain reaction

(DTG-PCR)

Initial pool generation using parallel overlap assembly (POA)


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Rise and Growth of DNA ComputingRise and Growth of DNA Computing AdlemanAdlemanss work in 1994work in 1994

Hamiltonian path problem (graph problem, NP problem)

City and road information representation using DNA sequences(indicative information)

Solution-based DNA computing

LiuLius work in 2000s work in 2000 SAT problem

Surface-based DNA computing

BenensonBenensonss work in 2004work in 2004 Application to disease diagnosis and drug (antisense)

administration


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Our Work in DNA Computing EraOur Work in DNA Computing Era Solving traveling salesman problemSolving traveling salesman problem

Graph problem with weighted edges

Representation of numerical information

Expansion to larger problems (in progress)

Development of unit operatorsDevelopment of unit operators

Denaturation temperature gradient PCR (DTG-PCR)

Initial pool generation for TSP using parallel overlap assembly

(POA)

Modeling and simulation of DTG-PCR and POA

New application to medical diagnosisNew application to medical diagnosis

Disease diagnosis model development

Experimental verification (in progress)


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Objective (traveling salesman problem)Objective (traveling salesman problem) Application of DNA computing to mathematicalApplication of DNA computing to mathematical

problemsproblems 7-city traveling salesman problem

Graph problem with weighted edges

Representation of numerical values (weighted edges)Representation of numerical values (weighted edges)

Expansion to practical problemsExpansion to practical problems 26-variable TSP 26 subway stations in Seoul


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Traveling Salesman ProblemTraveling Salesman Problem FindFind

The cheapest way of visiting all the cities and returning to the

starting point

when a number of cities to visit and the traveling cost between

each pair of cities are given.

Previous work for weight (cost) representationPrevious work for weight (cost) representation DNA length

DNA concentration

Our method for weight (cost) representationOur method for weight (cost) representation Thermal stability of DNA duplex

Melting temperature (Tm), GC content


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Target Problem & Encoding MethodTarget Problem & Encoding Method

1

0

3

2 5

6

4

3

5 33

7 11

3

3

9

11

3

3

start & end

city 7-city traveling salesman problem- 7 cities (0 to 6), 23 roads, 5 costs

- optimal path: 01234560

7-city traveling salesman problem

- 7 cities (0 to 6), 23 roads, 5 costs

- optimal path: 01234560

Oligonucleotides & Encoding- cities and costs are 20-base ssDNA

- roads are 40-base ssDNA

- 35 oligonucleotides

(7 cities, 23 roads, 5 costs)

Oligonucleotides & Encoding- cities and costs are 20-base ssDNA

- roads are 40-base ssDNA

- 35 oligonucleotides

(7 cities, 23 roads, 5 costs)

(20 bases) (20bases) (20 bases)

city A cost A to B city B5 3

3 5road A to B

(40 bases)


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Weight (Cost) EncodingWeight (Cost) Encoding

Seoul $ 500 Tokyo $ 200 Sapporo

Road from Seoul to Tokyo Road from Tokyo to Sapporo

20-base ssDNAwith 50% GC

content

20-base ssDNAwith 50% GC

content

20-base ssDNAwith higher GC

content

20-base ssDNAwith higher GC

content

20-base ssDNAwith lower GC

content

20-base ssDNAwith lower GC

content

40-base ssDNAcomplementary

to city and cost sequence

40-base ssDNAcomplementary

to city and cost sequence

More amplification of

DNA strand which has

lower sum of cost

More amplification ofDNA strand which has

lower sum of cost

Separation

and detection

Separation

and detection

DTG-PCR

TGGE

Lower costLower cost

Lower TmLower Tm

NACST/seq


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DenaturationDenaturation Temperature GradientTemperature Gradient

Polymerase Chain Reaction (DTGPolymerase Chain Reaction (DTG--PCR)PCR)

92~95

Denaturation

68~72Extension

(Tm

-5)

Annealing

Cycle

Conventional PCRConventional PCR

Denaturation (Td)

Annealing (Ta)

Extention (Te)

Modification of conventionalModification of conventional

PCR protocolPCR protocol

Variation in Td


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DenaturationDenaturation Temperature GradientTemperature Gradient

Initial denaturationTemperature ~ 70

Final denaturationtemperature~ 94

High Td

Amplification regardless of Tm

Low Td

More amplification of DNA strand

which has lower Tm (lower cost)

Cycle pr ogress

Biased operator:Biased operator: more amplification of DNA strands with lower Tmore amplification of DNA strands with lower Tmm

biased search for lower cost


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Molecular AlgorithmMolecular Algorithm

1

3

(1) Generation of

all random pathsHybridization/ligation

(2) Selection of paths

satisfying TSP conditionsPCR/electrophoresis/affinity

2

(3) More amplificationof the cheapest path

DTG-PCR

4Readout!Sequencing

5

(5) Elution ofthe cheapest path

Gel elution

(4) Separation ofthe cheapest path

TGGE


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Sequence Design for Cities and CostsSequence Design for Cities and Costs

Using NACST/Using NACST/seqseq

NonNon--cross hybridizationcross hybridization

Similar TSimilar Tmm among citiesamong cities

Different TDifferent Tmm among costsamong costs


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Experimental ImplementationExperimental Implementationfor TSP Conditionsfor TSP Conditions

StratingStrating and ending with city 0and ending with city 0

PCR using primers complementary to city 0

Visiting every cityVisiting every city

A series of affinity chromatography

Each affinity column contains ssDNA complementary

to each city.

Cheapest pathCheapest path

DTG-PCR


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Experimental ResultsExperimental Results Random path generation

(by hybridization and ligation)

Selective amplification of paths startingand ending with city 0(by PCR using primers complementary to city 0)

M 1 2 3

M: 50 bp ladderlane 1,2:

after hybridization/ligation

lane 3: mixture of ssDNA

M 1 M 1

300bp


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Separation of paths containingSeparation of paths containing

every cityevery city

(by a series of affinity chromatography)

More amplification of pathsMore amplification of paths

with lower costswith lower costs

(by DTG-PCR)

M 1

MagneticBead

biotin

streptavidin

City 0Cost

City 1Cost

City 2Cost

300bp

(8 cities)


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Separation of the pathSeparation of the pathwith lowest costwith lowest cost(by TGGE)

TGGETGGE(Temperature Gradient(Temperature Gradient

Gel Electrophoresis)Gel Electrophoresis)

T

DNAmolecules

1 2 3

major

band


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ReadoutReadout

(by cloning and sequencing)

TTCTGCGTTGTTTCGGGGTACAGTGGCTCCTCCGTTCCGCCTGCACTGTGGAGAGGTGAGCAGTGGCTCCTCCGTTCCGCGTGGATTCACAAGGCCATCGCAGTGGCTCCTCCGTTCCGCATACGGCGTGGTTTTTCGGGCAGTGGCTCCTCCGTTCCGCAAACGGTCGTAAGTGATGAACAGTGGCTCCTCCGTTCCGCGCACAGTCCACCTGTAGACACAGTGGCTCCTCCGTTCCGCTATGTCCAGCTGTCGCAAAGCAGTGGCTCCTCCGTTCCGCTTCTGCGTTGTTTCGGGGTA

City 0

Cost 3

City 1

Cost 3

City 2

Cost 3

City 3

Cost 3

City 4

Cost 3

City 5

Cost 3

City 6

Cost 3

City 0


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1

2

24

2

32

5

2

4

1

2

2

2

2

17

8 2

3

5

21

1

11

31

1

21

1

22

2

3 4

711

3

2

1 1

4

4

1

Subway routes in SeoulSubway routes in Seoul

Toward Larger ProblemsToward Larger Problems


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Target Problem:Target Problem:2626--City TSPCity TSP

4

12

16

25

18 19924

2

10 17 21

7

8 23

13

14

120

6 3

15

5 11

22

1

2

24

2

32

5

2

4

1

2

2

2

2

17

8 2

3

5

21

1

11

3

1

1

21

1

22

23 4

7

11

3

2

1 1

4

4

1

0

Graph with 26 vertexes (cities) and 92 edges (roads)Vertex: station connected with more than two stationsWeight: number of stations between vertex stations


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Initial Pool Generation with POAInitial Pool Generation with POA

Initial poolInitial pool

A combinatorial library that contains numerical or indicativeinformation

Initial pool generationInitial pool generation

Prerequisite step of most molecular algorithms formathematical problems

Initial pool generation methodsInitial pool generation methods

Hybridization and ligation method Parallel overlap assembly method


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Initial Pool Generation for TSPInitial Pool Generation for TSP:: POA vs. Hybiridzation/Ligation

Oligonucleotides

First cycle extension

Second cycle extension

Repeat of denaturation/annealing

/extension steps

Ligation: ligase

Phosphorylation

Hybridization: slow cooling


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Experimental ResultsExperimental Results

Marker Lane 1 Lane 2 Lane 3

900700

500

300

200

100

Lane M: 50 bp ladder

Lane 1: mixture of ssDNA

Lane 2: hybridization/ligation

Lane 3: POA

900

700

500

300

200

100

M 1 2 3

Quantification by image analysisQuantification by image analysis


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Comparison of Two MethodsComparison of Two Methods

Parallel overlap assembly Viewpoint Hybridization/ligation

Population size is almost

preserved throughout the

process.

Scalability

Economy

Fidelity

Population size decreases as

hybridization proceeds.

No need of 5-phosphorylation 5-phosphorylation is necessary

Less time & reagents consuming More time & reagents consuming

High error rate by non-specific

priming

Low error rate (higher

hybridization specificity)


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SummarySummary

Development of a molecular algorithm for TSP based onDevelopment of a molecular algorithm for TSP based on

the melting temperature differencethe melting temperature difference

Development of DTGDevelopment of DTG--PCR as an efficient operator forPCR as an efficient operator for

the graph problem with weighted edgethe graph problem with weighted edge

Success in solving 7Success in solving 7--city TSPcity TSP

2626--city traveling salesman problemcity traveling salesman problem

POA as an efficient operator for large size TSPPOA as an efficient operator for large size TSP


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AcknowledgmentsAcknowledgments

Prof. ByoungProf. Byoung--Tak ZhangTak Zhang

(School of Computer Science and Engineering, SNU)(School of Computer Science and Engineering, SNU)

JiJi YounYoun LeeLee

(School of Chemical Engineering, SNU)(School of Chemical Engineering, SNU)

SooSoo--Yong Shin (SNU)Yong Shin (SNU)

(School of Computer Science and Engineering, SNU)(School of Computer Science and Engineering, SNU)

The Ministry of Commerce, Industry, and EnergyThe Ministry of Commerce, Industry, and Energy


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Thpark DNA Computing