Polymerase Chain Reaction:A Markov Process Approach

Mikhail V. Velikanov et al.

J. theor. Biol. 1999

Summarized by 임희웅2003.8.12

Contents Introduction Markov Process Model for Primer

Extension Model for Multi-Cycle PCR Runs Numerical Results Discussion

Introduction A stochastic approach to PCR

Focus on the microscopic nature of amplification process Elementary reaction: binding of dNTP Markov process master equation

Analytical solution for the probability distribution of DNA length

Main qualitative feature Sensitivity of the reaction condition The amplification plateau effect Optimal duration of amplification for each cycle

Markov Process Model for Primer Extension Amplification process as Markov process

Binding of dNTP occurs randomly, with the probability per unit time determined entirely by the present state of the system.

State: length of primer Reaction rate: w = k(t) n

n: total number of dNTP in the current system k(t): the rate coefficient which depends on temperature (time) l + n = l0 + n0 = m0 constant

n0: initial total number of dNTP

l0 l l+1… L…

Master Equation The master equation for the primer

extension process

Analytical Solution

Model for Multi-Cycle PCR Runs Additional feature

Increasing number of DNA molecules Statistical independence of the extension process n0: initial number of dNTPs per template strand

np: the number of primers per template strand

Complementarity Two kinds of strand: +, - Pi

+(l,n): Prob. distribution of + strand in ith cycle

Evolution of Probability Distribution

ηn: duration of the extension phase of each cycle

The distribution for the first cycle Consumed dNTP in first cycle

Numerical Result Simulation for PCR Runs

Optimization of PCR Runs

Arrhenius’ law

Discussion Primary assumption

DNA synthesis occurs independently on each template strand.

Advantage in Markov process approach The model can be solved exactly by analytical means.

simple calculation It accounts for the fluctuations inherent in PCR kinetics

through a description of their natural microscopic source. The model is easy to modify and can be used as the basis

for constructing dedicated algorithms for numerical simulations of PCR.