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

2. The 1 st Year Research - Linear Implementation

3. Proteome Research Lab, http://gene.hanyang.ac.kr Proteome Research Lab, http://gene.hanyang.ac.kr 2003. 3. 27 Theorem Proving using Resolution Refutation Nil, add R as

4. Proteome Research Lab, http://gene.hanyang.ac.kr Proteome Research Lab, http://gene.hanyang.ac.kr 2003. 3. 27 PrimerSequenceLengthModification GC Content ( % ) ST¬Q 5’ - AAG CAG TAG CGA CCA ATT GAC GCA AAT TGA CGT ACG TAC GCT GAA - 3’ 45 merNone46.7 ¬RPQ 5’- CAT ACA ATG AAC GCA GTC AAC GCA AGG CAG TTC AGC GTA CGT ACG - 3’ 45 merNone51.1 ¬P 5’- CTG CCT TGC GTT GAC - 3’ 15 mer 5’-phosphate60.0 R 5’- TGC GTT CAT TGT ATG – 3’ 15 mer 5’-phosphate40.0 ¬S 5’ - TGG TCG CTA CTT –3’ 15 mer 5’-phosphate53.3 ¬T 5’ - TCA ATT TGC GTC AAT-3’ 15 mer 5’-phosphate33.3 The Sequence for Linear Implementation

5. Proteome Research Lab, http://gene.hanyang.ac.kr Proteome Research Lab, http://gene.hanyang.ac.kr 2003. 3. 27 587 540 504 458 434 267 234 213 192 184 124/123 104 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

6. The 2 nd Year Research - Hairpin Implementation

7. Proteome Research Lab, http://gene.hanyang.ac.kr Proteome Research Lab, http://gene.hanyang.ac.kr 2003. 3. 27 Sequence for Hairpin Implementation5mer5mer 6 mer ¬P P ¬Q Q

8. Proteome Research Lab, http://gene.hanyang.ac.kr Proteome Research Lab, http://gene.hanyang.ac.kr 2003. 3. 27 Primer Sequence(5 ’ → 3’) LengthModification GC Content ( % ) P TATTAAGACTTCTTGTAGTCT 21 mer 5 ’ -Phosphate 28.5 Q TCATGTTCCT 10 mer 5 ’ -Phosphate 40.0 ¬P TAATAAGGAA 10 mer 5’-Phosphate20.0 ¬Q CATGA 5 mer 5’-phosphate40.0 ¬R TCATGTTCCT 10 mer 5’-phosphate33.3 The Sequence for Hairpin Implementation

9. Proteome Research Lab, http://gene.hanyang.ac.kr Proteome Research Lab, http://gene.hanyang.ac.kr 2003. 3. 27 The Amplification of Hairpin Molecule Fig 2. The amplification of hairpin molecule in 3% agarose gel electrophoresis 50 bp 25 bp

10. The 3 rd Year Plan - The Pigeon Hole Problem(PHP)

11. Proteome Research Lab, http://gene.hanyang.ac.kr Proteome Research Lab, http://gene.hanyang.ac.kr 2003. 3. 27 The PigeonHole Principle (PHP) (n > m) n If n pigeons fly into m pigeonholes (n > m) n Then at least one hole must contain two or more pigeons.

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

13. Proteome Research Lab, http://gene.hanyang.ac.kr Proteome Research Lab, http://gene.hanyang.ac.kr 2003. 3. 27 A pigeonhole must contain at least two pigeons

14. Proteome Research Lab, http://gene.hanyang.ac.kr Proteome Research Lab, http://gene.hanyang.ac.kr 2003. 3. 27 Pigeonhole Principle (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.

15. Proteome Research Lab, http://gene.hanyang.ac.kr Proteome Research Lab, http://gene.hanyang.ac.kr 2003. 3. 27 Design of Problem 6 variables, 9 clauses

16. Proteome Research Lab, http://gene.hanyang.ac.kr Proteome Research Lab, http://gene.hanyang.ac.kr 2003. 3. 27 One of Proof Trees P 11 ∨ P 12 ~P 12 ∨ ~P 22 P 11 ∨ ~P 22 P 21 ∨ P 22 P 11 ∨ P 21 ~P 21 ∨ ~P 31 P 11 ∨ ~P 31 P 31 ∨ P 32 P 11 ∨ P 32 ~P 12 ∨ ~P 32 P 11 ∨ ~P 12 P 11 ∨ P 12 P 11 ~P 11 ∨ ~P 21 P 21 ∨ P 22 ~P 11 ∨ P 22 ~P 22 ∨ ~P 32 ~P 11 ∨ ~P 32 P 31 ∨ P 32 ~P 11 ∨ P 31 ~P 11 ∨ ~P 31 ~P 11 nil 5~10

17. Proteome Research Lab, http://gene.hanyang.ac.kr Proteome Research Lab, http://gene.hanyang.ac.kr 2003. 3. 27 Experimental Procedure The Problem (6var, 9clau) Design of Oligo Sequence Exonuclease III (remove partial solution) Step I Step II Step III Step IV Step V Hybridization (95°C→16°C cooling down) Synthesis & Modification (5’-Phosphate) Ligation (T4 DNA Ligase: 16°C Step VI Step VII Gel Electrophoresis Step VIII The Final Solution * No Self-Homology * No Cross-Homology

18. (In DNA9 Abstract) RCA-Based Detection Methods for Resolution Refutation (In DNA9 Abstract)

19. Proteome Research Lab, http://gene.hanyang.ac.kr Proteome Research Lab, http://gene.hanyang.ac.kr 2003. 3. 27 Preliminary Results (I) n n The electrophoresis of ligation mixture of blunt ends and sticky ends on 3% agarose gel n Lane 1, 2: Ligation product of sticky ends. 100 pmol & 200 pmol, respectively. n Lane 3, 4: Ligation product of blunt ends. 100 pmol & 200 pmol, respectively M1 23 4

20. Proteome Research Lab, http://gene.hanyang.ac.kr Proteome Research Lab, http://gene.hanyang.ac.kr 2003. 3. 27 Preliminary Results (II) n n The electrophoresis of RCA results in 3% agarose gel n Lane 1, 2; Hybrid mixture of sticky ends & blunt ends. n Lane 3, 4; Ligation product of sticky ends & blunt ends. n Lane 5, 6; RCA product of lane 3, 4 n Lane 7; Exonuclease III digested product of lane 3 and lane 4. n Lane 8; RCA product of pUC19 n Lane M; 25 bp DNA ladder M 12345678M

21. Proteome Research Lab, http://gene.hanyang.ac.kr Proteome Research Lab, http://gene.hanyang.ac.kr 2003. 3. 27 Further Research n DNA9 Paper n Sequence Check & Experiment n Self-homology n Cross-homology n Secondary Structure n Paper Submission n Biosystems (Now in writing) n International patent n Linear implementation n Hairpin implementation n PigeonHole Principle (PHP)

22. Proteome Research Lab, http://gene.hanyang.ac.kr Proteome Research Lab, http://gene.hanyang.ac.kr 2003. 3. 27 Forward Direction n DNA9 Conference n Abstract Submission (2/15) n Experimental Work n Journal Version n Biochemical Journal n Biological Computing n Biological Computing 6.373 7.666 3.161 4.493 5.54529.49136.242 24.595 10.896

23. Proteome Research Lab, http://gene.hanyang.ac.kr Proteome Research Lab, http://gene.hanyang.ac.kr 2003. 3. 27 Expected Result n n Fragments of linear DNA migrate through agarose gels with a mobility that is inversely proportional to the log 10 of their molecular weight n n Circular forms of DNA migrate in agarose distinctly differently from linear DNAs of the same mass.

24. In Numero Molecular Biology Computational Studies of Gene Regulatory Networks: In 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)

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

26. Proteome Research Lab, http://gene.hanyang.ac.kr Proteome Research Lab, http://gene.hanyang.ac.kr 2003. 3. 27 Mathematical Models of Cell Cycle Regulation The Fission Yeast cell cycle Xenopus embryosBudding Yeast Cell Cycle Mammalian cells

27. Proteome Research Lab, http://gene.hanyang.ac.kr Proteome Research Lab, http://gene.hanyang.ac.kr 2003. 3. 27 Regulatory Diagram: the activation of the tumor-suppressor protein p53

28. Proteome Research Lab, http://gene.hanyang.ac.kr Proteome Research Lab, http://gene.hanyang.ac.kr 2003. 3. 27 Modelling Methods n ‘Logical’ or ‘Binary’ approach (; 2 States ON or OFF) n n Traditional method n n Relatively easy to implement, simplify the examination of large sets of genes n n Impossible to include many of the details of cellular biology (disadvantage) n ‘Chemical kinetics’ or ‘Rate-equation’ approach n n The dynamics → Rate of production & decay of protein n n Ordinary differential equation n n Mathematical analysis & computational simulation n ‘Stochastic kinetics’ approach (;Probabilistic; governed by chance) n n Complete & Detailed system n n Simulation of chemical reaction (protein-DNA binding, transcription, translation)

29. Proteome Research Lab, http://gene.hanyang.ac.kr Proteome Research Lab, http://gene.hanyang.ac.kr 2003. 3. 27 Modelling the λ-bacteriophage Circuitry

30. Proteome Research Lab, http://gene.hanyang.ac.kr Proteome Research Lab, http://gene.hanyang.ac.kr 2003. 3. 27 Negatively Regulated Synthetic Gene Network - Toggle switch, Repressilator, Autorepressor n a) toggle switch n a) toggle switch - 2 repressor gene & 2 co-repressive promoter n n b) Repressilator - 3 gene repressive network by three strong constitutive promoter n n c) Atutorepressor - single-gene negative-feedback network

31. Proteome Research Lab, http://gene.hanyang.ac.kr Proteome Research Lab, http://gene.hanyang.ac.kr 2003. 3. 27 Graphical Toggle Switch Equation & Dynamic Co-Repressive Network n a) Analysis of a bistable toggle network with equal promoter strenth driving the expression of lac I and cI n b) Experimental bistability of a genetic toggle switch in E. coli

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

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

34. Proteome Research Lab, http://gene.hanyang.ac.kr Proteome Research Lab, http://gene.hanyang.ac.kr 2003. 3. 27 The Methods n Numerics n Numerics - All theoretical curves were calculated numerically from equation n Plasmid construction - Restriction enzymes, vector n Strains, growth conditions and chemicals n Strains, growth conditions and chemicals - host strain(E.coli) - antibiotics - inducer n Assay of gene expression -

35. Proteome Research Lab, http://gene.hanyang.ac.kr Proteome Research Lab, http://gene.hanyang.ac.kr 2003. 3. 27 Term n Operator n A region of DNA that interacts with a repressor protein to control the expression of a gene or group of genes n Repressor n The protein that binds to the regulatory sequence or operator for a gene, blocking its transcription n Repressor n The protein that binds to the regulatory sequence or operator for a gene, blocking its transcription

36. Proteome Research Lab, http://gene.hanyang.ac.kr Proteome Research Lab, http://gene.hanyang.ac.kr 2003. 3. 27 Concluding Remarks The modeling gene regulatory network The modeling gene regulatory network n n Rely on characterization of the behavior of small subsystems n n Formation of hypothesis about how these subsystems interconnect n n Mathematical model & experimentation The synthetic network The synthetic network n n Experimental behavior is consistent with predictions (in numero modelling) n n Theoretical model (design criteria) n Strong constitutive promoter n Effective transcriptional repression n Cooperative protein interaction & Similar protein degradation rate n Nearyly 30 years since the pineering theoretical work on the synthetic genetic network n Using living microorganism → Engineered gene circuit ( Real DNA Computing)