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Polymerase Chain Reaction: A Markov Process Approach Mikhail V. Velikanov et al. J. theor. Biol. 1999 Summarized by 임희웅 2003.8.12 Contents Introduction Markov Process Model for Primer Extension Model for Multi-Cycle PCR Runs Numerical Results Discussion Introduction

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polymerase chain reaction a markov process approach

Polymerase Chain Reaction: A Markov Process Approach

Mikhail V. Velikanov et al.

J. theor. Biol. 1999

Summarized by 임희웅

2003.8.12

contents
Contents
  • Introduction
  • Markov Process Model for Primer Extension
  • Model for Multi-Cycle PCR Runs
  • Numerical Results
  • Discussion
introduction
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

l0

l

l+1

L

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
master equation
Master Equation
  • The master equation for the primer extension process
model for multi cycle pcr runs
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
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
Numerical Result
  • Simulation for PCR Runs
slide12
Optimization of PCR Runs

Arrhenius’ law

discussion
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.