1 Summarized by Ji Youn Lee

2 Model Development

3 Step 1. Melting of DNA The rate of deactivation of the enzyme K d can be expressed in Arrhenius form The thermal deactivation of Taq DNA polymerase enzyme is first order. Thus, substituting alpha=1 and integrating Eq.(1) with respect to time, we obtain;

4 Step 2. Primer Annealing

5 Step 3. Primer Extension/DNA Synthesis Rate of generation of DNA in the first cycle is given by - N: the ratio of concentration of the product DNA at any time t to the initial concentration of the DNA - K1: amplification per unit time per enzyme in the first cycle.

6 As the number of ssDNAs doubles after the melting step in the second cycle, the reaction rate also doubles. So, for the later cycles, where K 0 =Arrhenius constant for the reaction, and E a =energy of activation for synthesis

7 The above rate equations hold if the allotted reaction time is sufficient and the ratio of active enzyme to ssDNA concentration (  ) is >1.0. For all these cycles, the time taken to complete the extension of the primer– template (i.e., rate of extension once the polymerase bind is constant). In this case,  n for the nth cycle is defined as: E 0 : initial concentration of the active enzyme in moles per liter a n : fraction of enzyme activity remaining after n cycles. At the point where  decreases to below 1.0, the exponential accumulation of PCR amplification product is still possible if the allotted reaction time is sufficient. During these cycles, the time taken for the reaction increases from cycle to cycle. Once the time required for the complete reaction exceeds the allotted time, the exponential accumulation of product becomes a limited process, and it has been reported by Saiki et al. (1988) that the product accumulates in a linear rather than an exponential manner. This phenomena can be described mathematically in what follows.

8 Total number of cycle: p n (number of cycle) = 1, 2, 3, …, r-1, r, r+1, …, m-1, m,m+1, …, p-1, p where r th cycle: the primer–template number is higher than the active enzyme number available for reaction Amplification rate in the rth cycle constant change with cycle

9 Results and Discussion

10 Determination of Arrhenius Constants and Activation Energies: Enzyme deactivation T and t 1/2 K d0 and E d Plot ln(K d ) against 1/TCalculate K d Figure 2 K d0 is exceptionally high, because there is a significant change in the half-life of this enzyme within a short temperature range 92°C to 97°C). This might be due to the fact that the bonds which make this enzyme thermostable break within that temperature range, thus the half-life drops sharply.

11 Determination of Arrhenius Constants and Activation Energies: DNA synthesis

12

13 Simulation of Rate Expressions PCR process –Pre-PCR melting step for 1 min. –Step 1. Melting of DNA for 1 min at 94°C. –Step 2. Primer annealing for 1 min at 37°C. –Step 3. Extension (synthesis) of target DNA for 2 min at 72°C. –Template: 500 bp Simulation condition: E 0 /C D0 =4425

14 16 th cycle: deviation between simulated vs theoretical value –From 17 th cycle: linear amplification enzyme and reaction time partial products generation An increase in the extension time or an addition of enzyme Figure 3

15 Taq DNA polymerase deactivation profile –Not much loss in the activity (above 70% remain active) after 25 cycles –In the later phase, deactivation contributes partially to the plateau

16 Figure 4 Comparison with experimental result –500 bp of λ-DNA, C D0 =1 ng per 100 ㎕, E 0 /C D0 = 4425 –The rate of incorporation of nucleotides for λ-DNA ≈ 3000 nucleotides/minute –The simulated trend matches with the experimental results.

17 Effect of Temperature Ramp on Amplification of DNA Amplification change with different temperature ramps –by incorporating the linear temperature ramp equations in the computer program –The amplification remains almost constant above 5°C/s ramp Figure 5

18 Conclusions Guide to different parameters –enzyme deactivation, extension time, initial target DNA concentration, temperature ramp, and cycle number Prediction of the amplification profile Comparison with the experimental results Temperature ramp effect on amplification The understanding of the PCR process Basic framework for total modeling of the PCR process