Abstract

Quantitative PCR as a Discrete Dynamical System

Steven Smith, Professor, City of Hope Beckman Research Institute

The quantitative polymerase chain reaction (qPCR) can be viewed as a discrete dynamical system. The reaction rate at each cycle during the evolution of the system is given by the Michaelis-Menten equation evaluated at the substrate concentration available at each cycle. The system is described by a 1st order non-linear recurrence-relation. Although the recurrence relation has no closed form solution it can form the basis of a least-squares algorithm that provides an accurate fit of the data over its full range. In addition to the quantification of the initial target-concentration, this approach allows for the determination of Michaelis-Menten constants for the DNA polymerases used in PCR amplification. Moreover, the approach permits a comparison of the influence of factors like, duplex re-annealing, thermal loss of DNA polymerase and the reduction in single-strand availability associated with the potential for non-B structure formation on the dynamics of the reaction.