The 3 rd Research on Theorem Proving MEC Meeting Hanyang University Proteome Research Lab 2003. 3. 27 Park, Ji-Yoon

The 3The 3rdrd Research on Research on Theorem ProvingTheorem Proving

MEC Meeting

Hanyang University Proteome Research Lab

2003. 3. 27

Park, Ji-Yoon

The 1The 1stst Year Research Year Research- Linear Implementation- Linear Implementation

2003. 3. 27 2003. 3. 27 Proteome Research Lab, http://gene.hanyang.ac.kr Proteome Research Lab, http://gene.hanyang.ac.kr

Theorem Proving using Resolution Theorem Proving using Resolution Refutation Refutation

NilNil

, add R as, add R as


Primer Sequence Length ModificationGC Content

( % )

ST¬Q5’ - AAG CAG TAG CGA CCA ATT

GAC GCA AAT TGA CGT ACG TAC GCT GAA - 3’

45 mer None 46.7

¬RPQ5’- CAT ACA ATG AAC GCA GTC

AAC GCA AGG CAG TTC AGC GTA CGT ACG - 3’

45 mer None 51.1

¬P 5’- CTG CCT TGC GTT GAC - 3’ 15 mer 5’-phosphate 60.0

R 5’- TGC GTT CAT TGT ATG – 3’ 15 mer 5’-phosphate 40.0

¬S 5’ - TGG TCG CTA CTT –3’ 15 mer 5’-phosphate 53.3

¬T 5’ - TCA ATT TGC GTC AAT-3’ 15 mer 5’-phosphate 33.3

The Sequence for Linear The Sequence for Linear Implementation Implementation


587

540

504

458

434

267

234

213

192

184

124/123

104

89/80

64/57/51/

21/18/11/8

75 bp 75 bp

M 1 2

The Amplification of Linear Molecule

Fig 1. The amplification of linear molecule in 3% agarose gel electrophoresis

Lane 1: PCR product with S and ¬R Lane 2: PCR products with ¬ S and R Lane M is a 25 bp molecular DNA ladder

The 2The 2ndnd Year Research Year Research- Hairpin Implementation- Hairpin Implementation


Sequence for Hairpin Implementation

5mer5mer

5mer5mer

6 mer6 mer

¬P¬P

PP ¬Q¬Q

Q Q

RR

P

Q

S

TP

Q

S

T


Primer Sequence(5’ → 3’) Length ModificationGC Content

( % )

P TATTAAGACTTCTTGTAGTCT 21 mer 5’-Phosphate 28.5

Q TCATGTTCCT 10 mer 5’-Phosphate 40.0

¬P TAATAAGGAA 10 mer 5’-Phosphate 20.0

¬Q CATGA 5 mer 5’-phosphate 40.0

¬R TCATGTTCCT 10 mer 5’-phosphate 33.3

The Sequence for Hairpin Implementation


The Amplification of Hairpin Molecule

Fig 2. The amplification of hairpin molecule in 3%Fig 2. The amplification of hairpin molecule in 3% agarose gel electrophoresis agarose gel electrophoresis

50 bp50 bp

25 bp25 bp

The 3The 3rdrd Year Plan Year Plan- The Pigeon Hole Problem(PHP)- The Pigeon Hole Problem(PHP)


The PigeonHole Principle The PigeonHole Principle (PHP)(PHP)

If n pigeons fly into m pigeonholes ((nn > > mm)) Then at least one hole must contain two or more Then at least one hole must contain two or more

pigeons.pigeons.


PigeonsPigeons

PigeonholesPigeonholes

4

3


A pigeonhole mustA pigeonhole must

contain at least two pigeonscontain at least two pigeons


Pigeonhole Principle Pigeonhole Principle (formally)(formally)

A function from one finite set to a smaller finite set cannot be one-to-one.

There must be at least two elements in the domain that have the same image in the co-domain.


Design of Problem

6 variables, 9 clauses6 variables, 9 clauses

322232122212

312131112111

323122211211

,,

,,

,,

PPPPPP

PPPPPP

PPPPPP


One of Proof Trees

PP1111∨P∨P1212 ~P12∨~P22

P11∨~P22 P21∨P22

P11∨ P21 ~P21∨~P31

P11∨~P31 P31∨P32

P11∨ P32 ~P12∨~P32

P11∨~P12 P11∨P12

P11

~P11∨~P21 P21∨P22

~P11∨ P22~P22∨~P32

~P11∨ ~P32P31∨P32

~P11∨ P31~P11∨~P31

~P11

nnilil

5~10

5~10


Experimental Procedure

The Problem The Problem (6var, 9clau)(6var, 9clau)

Design of Oligo Design of Oligo Sequence Sequence

Exonuclease III Exonuclease III (remove partial (remove partial solution) solution)

Step IStep I

Step IIStep II

Step IIIStep III

Step IVStep IV

Step VStep V

HybridizationHybridization(95°C→16°C (95°C→16°C cooling down) cooling down)

Synthesis & Synthesis & ModificationModification(5’-Phosphate)(5’-Phosphate)

Ligation(T4 DNA

Ligase: 16°C

Step VIStep VI

Step VIIStep VII

Gel Electrophoresis Gel Electrophoresis

Step VIIIStep VIII

The Final The Final SolutionSolution

* * No Self-No Self-HomologyHomology

* No Cross-* No Cross-HomologyHomology

RCA-Based Detection Methods

for Resolution Refutation (In DNA9 Abstract)(In DNA9 Abstract)


Preliminary Results (I)

The electrophoresis of ligation mixture of blunt ends and sticky ends on 3% agarose gel

Lane 1, 2: Ligation product of sticky Lane 1, 2: Ligation product of sticky ends. 100 pmol & 200 pmol, ends. 100 pmol & 200 pmol, respectively.respectively.

Lane 3, 4: Ligation product of blunt Lane 3, 4: Ligation product of blunt ends. 100 pmol & 200 pmol, ends. 100 pmol & 200 pmol, respectively respectively

MM 11 22 33 4


Preliminary Results (II)

The electrophoresis of RCA results in 3% agarose gel

Lane 1, 2; Hybrid mixture of sticky ends Lane 1, 2; Hybrid mixture of sticky ends & blunt ends.& blunt ends.

Lane 3, 4; Ligation product of sticky ends Lane 3, 4; Ligation product of sticky ends & blunt ends.& blunt ends.

Lane 5, 6; RCA product of lane 3, 4 Lane 5, 6; RCA product of lane 3, 4 Lane 7; Exonuclease III digested product Lane 7; Exonuclease III digested product

of lane 3 and lane 4.of lane 3 and lane 4. Lane 8; RCA product of pUC19Lane 8; RCA product of pUC19 Lane M; 25 bp DNA ladder Lane M; 25 bp DNA ladder

MM 11 22 33 44 55 66 77 88 MM


Further Research

DNA9 Paper Sequence Check & Experiment Sequence Check & Experiment

Self-homology Cross-homology Secondary Structure

Paper Submission BiosystemsBiosystems (Now in writing) (Now in writing)

International patent Linear implementationLinear implementation Hairpin implementationHairpin implementation PigeonHole Principle (PHP)PigeonHole Principle (PHP)


Forward Direction

DNA9 Conference Abstract Submission Abstract Submission

(2/15)(2/15) Experimental Work Experimental Work

Journal Version Biochemical Journal Biochemical Journal Biological Computing Biological Computing

6.3736.373

7.6667.666

3.1613.161

4.493 4.493

5.545 5.545

29.491 29.491

36.242 36.242

24.595 24.595

10.89610.896


Expected Result

Fragments of linear DNA migrate through agarose gels with a mobility that is inversely proportional to the log10 of their molecular weight

Circular forms of DNA migrate in agarose distinctly differently from linear DNAs of the same mass.

Computational Studies of Gene Regulatory Networks:

In Numero Molecular BiologyIn Numero Molecular Biology

MEC Meeting

Hanyang University Proteome Research Lab

Park, Ji-Yoon

Jeff Hasty, David McMillen, Farren Isaacs & James J. Collins

Nature Reviews Genetics 2, 268-279 (2001)



Mathematical Models of Cell Cycle Mathematical Models of Cell Cycle RegulationRegulation

The Fission Yeast cell cycle

Xenopus embryosBudding Yeast Cell Cycle

Mammalian cells


Regulatory Diagram: Regulatory Diagram: the activation of the tumor-suppressor protein p53the activation of the tumor-suppressor protein p53


Modelling Methods Modelling Methods

‘Logical’ or ‘Binary’ approach (; 2 States ON or OFF) Traditional method Relatively easy to implement, simplify the examination of large sets of

genes Impossible to include many of the details of cellular biology (disadvantage)

‘Chemical kinetics’ or ‘Rate-equation’ approach The dynamics → Rate of production & decay of protein Ordinary differential equation Mathematical analysis & computational simulation

‘Stochastic kinetics’ approach (;Probabilistic; governed by chance) Complete & Detailed system Simulation of chemical reaction

(protein-DNA binding, transcription, translation)


Modelling the Modelling the λλ-bacteriophage Circuitry-bacteriophage Circuitry


Negatively Regulated Synthetic Gene NetworkNegatively Regulated Synthetic Gene Network - Toggle switch, Repressilator, Autorepressor- Toggle switch, Repressilator, Autorepressor

a) a) toggle switchtoggle switch - 2 repressor gene & 2 co-repressive promoter

b) Repressilator - 3 gene repressive network by three strong constitutive promoter

c) Atutorepressor - single-gene negative-feedback network


Graphical Toggle Switch EquationGraphical Toggle Switch Equation & &

Dynamic Co-Repressive Network Dynamic Co-Repressive Network

a) Analysis of a bistable toggle network with equal promoter strenth driving the expression of lac I and cI

b) Experimental bistability of a genetic toggle switch in E. coli




The Methods The Methods

Numerics Numerics - All theoretical curves were calculated numerically from equation

Plasmid constructionPlasmid construction - Restriction enzymes, vector

Strains, growth conditions and chemicalsStrains, growth conditions and chemicals - host strain(E.coli) - antibiotics - inducer

Assay of gene expressionAssay of gene expression -


TermTerm

OperatorOperator A A region of DNAregion of DNA that interacts with a repressor protein to control the that interacts with a repressor protein to control the

expression of a gene or group of genes expression of a gene or group of genes

RepressorRepressor The protein that binds to the regulatory sequence or operator for a gene, The protein that binds to the regulatory sequence or operator for a gene,

blocking its transcription blocking its transcription

RepressorRepressor The protein that binds to the regulatory sequence or operator for a gene, The protein that binds to the regulatory sequence or operator for a gene,

blocking its transcription blocking its transcription


Concluding Remarks Concluding Remarks

The modeling gene regulatory networkThe modeling gene regulatory network Rely on characterization of the behavior of small subsystems Formation of hypothesis about how these subsystems interconnect Mathematical model & experimentation

The synthetic network The synthetic network Experimental behavior is consistent with predictions (in numero modelling) Theoretical model (design criteria)

Strong constitutive promoter Effective transcriptional repression Cooperative protein interaction & Similar protein degradation rate

Nearyly 30 years since the pineering theoretical work on the synthetic genetic networkNearyly 30 years since the pineering theoretical work on the synthetic genetic network Using living microorganism → Engineered gene circuit ( Real DNA Computing) Using living microorganism → Engineered gene circuit ( Real DNA Computing)

Documents

The 3 rd Research on Theorem Proving MEC Meeting Hanyang University Proteome Research Lab 2003. 3. 27 Park, Ji-Yoon