Effectiveness of DTG-PCR for Biased DNA Algorithms

1. Effectiveness of DTG-PCR for Biased DNA Algorithms Ji Youn Lee

2. Goal of DNA Computing Computer Science Smart DNA word design Physics Mathematics Development of efficient and smart algorithms Development of new biological tools Engineering Chemistry Biology

3. Polymerase Chain Reaction (PCR) • In vitro amplification of nucleic acids • Thermus aquaticus (Taq) DNA polymerase • Consists of three reactions at different temperatures • Denaturation/ annealing/ extension • Cyclic reaction • Essential tool in molecular biology/DNA computing

4. Melting of template DNA Denaturation temp.  92~95℃ Hybridization of primer to template DNA Extension of the primer by a DNA polymerase Extension temp.  68~72℃ Annealing temp.  (Tm-5)℃ TD TA TE Three steps of polymerase chain reaction (PCR)

5. DTG-PCR • Stands for… • Denaturation Temperature Gradient-Polymerase Chain Reaction • Temperature gradient in denaturation reaction with the cycle progress • Selectively more amplify the DNA strands of lower melting temperature

6. Temperature Gradient Encoding • Traveling salesman problem • Weight (real number) representation • Temperature related tools • DTG-PCR • TGGE • The range and limit of DTG-PCR

7. Theoretical Description

8. Necessity of Theoretical Description • Understanding of the reaction mechanism • The groundwork for modeling • For a prediction of experimental result

9. Formal Approaches I • Efficiency-based expression: efficiency of each cycle Anal. Biol. Chem. 214 (1993) pp 582-585 "Quantitative PCR: Theoretical considerations with practical implications"

10. Formal Approaches II • Enzymological considerations J. theor. Biol. 184 (1997) pp 433-440 "Enzymological Considerations for a Theoretical Description of the Quantitative Competitive Polymerase Chain Reaction"

16. Formal Approaches III • Probabilistic consideration • Markov process model for primer extension J. theor. Biol. 201 (1999) pp 239-249 "Polymerase Chain Reaction: A Morkov Process Approach"

17. Rate or Efficiency of the PCR • Influenced by the factors… • Concentrations of template DNA, DNA polymerase, dNTPs, MgCl2 and primers • Denaturation, annealing and extension temperatures • Time and number of cycles • Ramping rates (of the machine) • The presence of contaminating DNA and inhibitors in the sample • Etc…  Appropriate assumptions are necessary!!

18. Causes of Plateau • Increase of template • Decrease of the ratio of enzyme to template • Renaturation between templates • Inactivation of polymerase • Binding or extension efficiency • Exhaustion of dNTPs, primers • Efficient concentrations

19. Basic Assumptions • Discrete reactions • One reaction in one step • Optimized reaction condition • Optimized annealing temperature • Optimized buffer concentration • Plentiful reaction time • No existence of intermediate molecules of insufficient length (assumption of complete extension)

20. Optimization Conditions • MgCl2 concentration: 3.0~6.0 mM • dNTP concentration: 200~600 mM each • Taq DNA polymerase: 1.25~4.5 U/50 ml reaction • Primer concentration: 100~500 nM • An symmetric primer concentration • Probe or dye concentration

21. Notation Summary Nds number of double-stranded DNA or template Nss number of single-stranded DNA or template eds molar extinction coefficient of double-stranded DNA ess molar extinction coefficient of single-stranded DNA Np number of primer Nhd number of heteroduplex molecule Q number of polymerase Q’ effective number of polymeraes Ncomplex number of heteroduplex combined with polymerase NdNTP number of dNTPs Nextended(i) number of extended heteroduplex by i mer Ncomplex’ number of fully extended molecule combined with polymerase

22. Denaturation Step • Dissociation of Watson-Crick complement • Can be considered the reverse compliment to denaturating • Denaturation efficiency calculation Two possible approaches • Melting curve-based approach • Kinetics-based approach

23. Melting Curve-Based Approach

24. Melting Curve • Measure with UV spectrophotometer or real-time PCR machine • Sigmoid function • Parameters • Melting temperature • Transition width: begin & end temperature 1 ssDNA fraction 0 temperature

25. Melting Temperature, Tm • The Tm is the temperature at which half the DNA is present in a single-stranded (denatured) form. • Primarily influenced by four parameters • Temperature • pH • Concentration of monovalent cations • Presence of organic solvents

26. Typical Melting Profile of DNA Duplex transition width OD or Dissociated Fraction Denatured Inflection point Native Tm Temperature

27. An Example of Fitted Melting Curve

28. Hyperchromic Effect • Calculation of the ssDNA fraction from the optical density and extinction coefficients ()

29. Denaturation Efficiency, hd • Denaturation efficiency can be calculated from the melting curve.

30. Annealing Step • Hybridization of single-stranded DNA template and primer • Factors • Single-stranded DNA template concentration • Primer concentration  Cp/Css (r) and Css

31. Can Be Considered as … • Competition between… • Renaturation of Watson strand and Crick strand • Hybridization of single-stranded DNA template and primer

32. vs Competition between ka and kd-1

33. Denaturation of dsDNA to ssDNA Formation rate of ssDNA Temperature dependency of reaction constant Arrhenius equation

35. An Example of Kinetic Data I Biochemistry 32 (1993) pp 3095-3104 “ Sensitive fluorescence-based thermodynamics and kinetic measurements of DNA hybridization in solution”

36. An Example of Kinetic Data II Proc. Natl. Acad. Sci. USA 95 (1998) pp 1460-1465 “A unified view of polymer, dumbbell, and oligonucleotide DNA nearest-neighbor thermodynamics”

37. NACST/seq Calculation of DH and DS from NN data Data from papers of Santa Lucia Calculation of equilibrium constant Calculation of ssDNA concentration

38. Extension Step • Divided into three reactions (1) Binding of polymerase to the heteroduplex (2) Successive incorporation of dNTPs by polymerase (3) Detachment of polymerase from fully extended DNA

40. Assumptions in Extension Step  1), 3) are dependent on the binding and release activity of polymerase • 2) is dependent on the incorporation activity of polymerase • Assumption • Binding efficiency and detachment efficiency is unity • Therefore, the efficiency of the extension reaction only rely on the dNTP incorporation rate. • The incorporation rate of each dNTPs is same.

41. Factors Affecting the Extension Efficiency • Polymerase activity • Heteroduplex concentration

42. Detailed Extension Reaction • Kinetic mechanism of polymerase action RDS dNTP Dn E’∙Dn∙dNTP E∙Dn E∙Dn∙dNTP k±2 k±3 k±1 E k±4 k±7 k±6 E’∙Dn+1∙PPi Dn+1 E∙Dn+1∙PPi E∙Dn+1 k±5 PPi

43. Parameter Value Kd1 5 nM Binding of template with polymerase Kd2 5 mM dNTP incorporation to form a ternary complex K4 2.5 Chemical catalysis Kd6 100 μM Release of PPi k3 50 sec-1 Conformational change of polymerase k-3 0.5 sec-1 k4 1000 sec-1 Chemical catalysis k-4 400 sec-1 k5 15 sec-1 Second conformational change k-5 15 sec-1 k7 0.06 sec-1 Dissociation of polymerase k-7 1.2107 M-1 sec-1

44. Enzyme Inactivation • Causes • Enzyme aggregation, or enzyme heterogeneity, or formation of partially deactivated forms of the enzyme • Thermal inactivation • Reversible vs irreversible • Due either • to the loss of the native conformation (without rupture or formation of covalent bonds) • or to chemical modification of functional groups of the active site

45. Models of Enzyme Inactivation • First-order model • Bi-exponential models • Isozyme model • Lumry-Eyring model

46. Kinetics of Enzyme Inactivation • Common assumptions; • Assume that thermal inactivation mechanisms involve a single active enzyme form, i.e., the native one. • Assume 1st order kinetics with respect to the native enzyme concentration. • An exponential activity decay is predicted • However, there are exceptions… Due to the occurrence of multiple active forms

47. Irreversible reaction • Involve only two different enzyme forms: native (active) and denatured

48. When assumed 1st order kinetics Real experimental results log (activity) log (activity) time time

49. An Example of the Half Life I • Half life of TaKaRa Taq Polymerase Temperature Half life 97.5℃ 7 min 95℃ 35 min 95℃ (+10% glycerol) > 60 min 95℃ (+5% glycerol) 40 min 92.5℃ > 130 min

50. An Example of the Half Life II • Pierce Taq at 95℃ = 2.5 hours (150 min) • Therefore, if we assume the half life of polymerase is 200 min… • The decay rate constant is about 610-5 s-1