1. PCR Modeling
MEC
Lim Hee Woong

2. Denaturation dsDNA conc. input Melting curve of known DNA conc. Temp.
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. Wetmur (Annu. Rev. Biophys. Bioeng. 1976)
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”

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

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

10. Extension rt: t 초 후의 reaction rate
From Hsu et al.
BB 1997
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

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 From Hsu et al. BB 1997
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”

13. Product Flow

14. Simulation

15. 9e-012  e-008

16. 9e-013  e-008

17. 9e-014  e-008

18. PCR Plateau? Figures from TAKARA
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

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 What occurs at each step in plateau? Question…
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
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