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

The 1 st Year Research - Linear Implementation

Proteome Research Lab, Proteome Research Lab, Theorem Proving using Resolution Refutation Nil, add R as

Proteome Research Lab, Proteome Research Lab, 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

Proteome Research Lab, Proteome Research Lab, / /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 2 nd Year Research - Hairpin Implementation

Proteome Research Lab, Proteome Research Lab, Sequence for Hairpin Implementation5mer5mer 6 mer ¬P P ¬Q Q

Proteome Research Lab, Proteome Research Lab, 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

Proteome Research Lab, Proteome Research Lab, The Amplification of Hairpin Molecule Fig 2. The amplification of hairpin molecule in 3% agarose gel electrophoresis 50 bp 25 bp

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

Proteome Research Lab, Proteome Research Lab, 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.

Proteome Research Lab, Proteome Research Lab, Pigeons Pigeonholes

Proteome Research Lab, Proteome Research Lab, A pigeonhole must contain at least two pigeons

Proteome Research Lab, Proteome Research Lab, 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.

Proteome Research Lab, Proteome Research Lab, Design of Problem 6 variables, 9 clauses

Proteome Research Lab, Proteome Research Lab, 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

Proteome Research Lab, Proteome Research Lab, 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

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

Proteome Research Lab, Proteome Research Lab, 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

Proteome Research Lab, Proteome Research Lab, 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 M

Proteome Research Lab, Proteome Research Lab, 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)

Proteome Research Lab, Proteome Research Lab, 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

Proteome Research Lab, Proteome Research Lab, 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.

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, (2001)

Proteome Research Lab, Proteome Research Lab,

Proteome Research Lab, Proteome Research Lab, Mathematical Models of Cell Cycle Regulation The Fission Yeast cell cycle Xenopus embryosBudding Yeast Cell Cycle Mammalian cells

Proteome Research Lab, Proteome Research Lab, Regulatory Diagram: the activation of the tumor-suppressor protein p53

Proteome Research Lab, Proteome Research Lab, 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)

Proteome Research Lab, Proteome Research Lab, Modelling the λ-bacteriophage Circuitry

Proteome Research Lab, Proteome Research Lab, 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

Proteome Research Lab, Proteome Research Lab, 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

Proteome Research Lab, Proteome Research Lab,

Proteome Research Lab, Proteome Research Lab,

Proteome Research Lab, Proteome Research Lab, 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 -

Proteome Research Lab, Proteome Research Lab, 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

Proteome Research Lab, Proteome Research Lab, 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)