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PCR Modeling

PCR Modeling. 2004.08.31 MEC Lim Hee Woong. Denaturation. dsDNA conc. input. Melting curve of known DNA conc. Temp. input. K eq output. denaturation efficiency. Released ssDNA conc. output. Melting Profile Sigmoid function assumption Parameters T m : Melting temperature

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PCR Modeling

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  1. PCR Modeling 2004.08.31 MEC Lim Hee Woong

  2. Denaturation dsDNA conc. input Melting curve of known DNA conc. Temp. input Keq output denaturation efficiency Released ssDNA conc. output

  3. Melting Profile • Sigmoid function assumption • Parameters • Tm:Melting temperature • : Transition width: begin & end temperature • Cinit: initial dsDNA concentration for melting profile • Measured and fitted by experiment with UV spectrophotometer or real-time PCR machine

  4. Equilibrium Constant Kd from Tm Profile

  5. Denaturation • Cds0: initial dsDNA strand in denature step • Kd(T): equlibrium constant from melting profile

  6. Annealing • 경쟁적인 annealing반응, primer vs. template

  7. 다른 step (denaturation, extension)과는 달리 각 template에 대해forward와 backward를 구분 • 대칭성에 의해 forward와 backward strand의 농도변화는 같다고 가정 • 위의 계산식에 사용되는 Css, 와 Chd 는 forward 혹은 backward의 한쪽 방향 strand에 대한 농도 • 앞의 denaturation step에서 계산된 ssDNA의 농도의 절반 만큼의 농도를 할당하여 계산 수행하고 Annealing이 끝난 후 위 계산 결과에 2를 곱하여 backward/forward의 구분을 없앰 • Rate constant k의 값을 몰라도 그 비율만으로 최종 product의 비율을 계산 가능 • Wetmur (Annu. Rev. Biophys. Bioeng. 1976) • Calculation • Numerical method, Runge-Kutta formulae • Matlab function “ode45” Wetmur (Annu. Rev. Biophys. Bioeng. 1976)

  8. Annealing 2-Temperature Ramping- • Tm,hdDNA<Tm,dsDNA • Pre-annealing takes place before competitive annealing annealing Temperature Pre-annealing Template Tm hdDNA Tm Competitive annealing Time Pre-annealingof template Competitive annealingto form dsDNA and hdDNA

  9. Wetmur (Annu. Rev. Biophys. Bioeng. 1976)

  10. Extension • rt: t 초 후의 reaction rate • ke: extension rate for one polymerase • knu: nucleotide incorporation rate of one polymerase • Ea,t: t초 후에 실제 polymerization에 참가하는 enzyme의 농도 From Hsu et al. BB 1997

  11. 실제 polymerization에 참가하는 enzyme 의 농도 • Active enzyme • Cenz: thermal deactivate되지 않고 남아있는 polymerase 농도 • Cenz를 hetero duplex부분과 template duplex부분의 비율로 나누어 실제 polymerization에 참가하는 enzyme의 비율을 구한다. • 단순히 duplex의 농도만 고려하는 것이 아니라 duplex region의 길이까지도 고려함 • Kainz (BBA 2000) paper 참조 • Calculation • Numerical method, Runge-Kutta formulae • Matlab function “ode45”

  12. Enzyme Deactivation • Hsu et al. (BB, 1997) 논문의 deactivation 식에 temperature ramping을 추가하여 확장 • at: remaining enzyme ratio after t second • considering temperature ramping • T1, T2, ∆t: ∆t초 동안 T1에서 T2로 온도가 변함 • Calculation • Numerical method, Runge-Kutta formulae • Matlab function “ode45” From Hsu et al. BB 1997

  13. Product Flow

  14. Simulation

  15. 9e-012  4.93815e-008

  16. 9e-013  4.28836e-008

  17. 9e-014  3.59484e-008

  18. PCR Plateau? • When varying amounts of a single target are amplified, a constant maximum level of product is obtained. • Coamplification of different concentrations of different targets results in retention of the initial proportions. • Morrison et al. BBA, 1994 Figures from TAKARA

  19. Factors of Plateau? • Reduction in the denaturation efficiency • Utilization of substrates (dNTPs or primers) • Reannealing of specific product at concentrations above 10-8 M • Thermal inactivation or limited concentration of DNA polymerase • Exonuclease activity of Taq polymerase • Inhibition of enzyme activity by increasing pyrophosphate

  20. In Plateau • In plateau • The template concentration reaches constant level (about 10-8 order), even if the order of initial concentration varies. • What occurs at each step in plateau? • Denaturation • Constant denaturation efficiency and ssDNA concentration • ≈ 1, almost perfect denaturation • Not only in plateau • Annealing • Constant annealing efficiency and hdDNA concentration • ≈ 0 or >> 0 ? • Extension • Constant extension efficiency • ≈ 0 or >> 0 ? • Question… • Annealing efficiency and the amount of hdDNA in plateau • Extension efficiency in plateau • What is the major factor for plateau

  21. Other Insignificant Factors • Mis-annealing of primers • Reaction condition change • pH change? • MgCl2 concentration? • DNA contaminants (non-specific products, primer-dimer)

  22. Parameters to Fit • Hybridization rate constant • Extension rate constant • Pre-annealing (?) region

  23. Extension2 • Michaelis-Menten Equation + BB paper

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