A kinetic model of quantitative real-time polymerase chain reaction

Sarika Mehra, Wei Shou Hu

Research output: Contribution to journalArticlepeer-review

40 Scopus citations


Real-time polymerase chain reaction (PCR) is one of the most sensitive and accurate methods for quantifying transcript levels especially for those expressed at low abundance. The selective amplification of target DNA over multiple cycles allows its initial concentration to be determined. The amplification rate is a complex interplay of the operating conditions, initial reactant concentrations, and reaction rate constants. Experimentally, the compounded effect of all factors is quantified in terms of an effective efficiency, which is estimated by curve fitting to the amplification data. We present a comprehensive model of PCR to study the effect of various reactant concentrations on the amplification efficiency. The model is used to calculate the kinetic progression of the target DNA concentration with cycle number under conditions when different species are stoichiometrically or kinetically limiting. The reaction efficiency remains constant for the initial cycles. As the primer concentration becomes limiting, the efficiency is marked by a gradual decrease. This is in contrast to a steep decline under nucleotide limiting conditions. Under some conditions, commonly used experimentally, increasing primer concentration has the adverse effect of reducing the final amplified template concentration. This phenomenon seen at times experimentally is explained by the simulation results under rate limiting enzyme concentrations. Primer dimer formation is shown to significantly affect the reaction rates, effective efficiency, and the estimated initial concentrations. This model, by describing the interplay of the many operating variables, will be a useful tool in designing PCR conditions and evaluating its results.

Original languageEnglish (US)
Pages (from-to)848-860
Number of pages13
JournalBiotechnology and bioengineering
Issue number7
StatePublished - Sep 30 2005


  • Mathematical model
  • Reaction efficiency
  • Real-time polymerase chain reaction


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