Mathematics of quantitative kinetic PCR and the application of standard curves

Abstract

Fluorescent monitoring of DNA amplification is the basis of real-time PCR, from which target DNA concentration can be determined from the fractional cycle at which a threshold amount of amplicon DNA is produced. Absolute quantification can be achieved using a standard curve constructed by amplifying known amounts of target DNA. In this study, the mathematics of quantitative PCR are examined in detail, from which several fundamental aspects of the threshold method and the application of standard curves are illustrated. The construction of five replicate standard curves for two pairs of nested primers was used to examine the reproducibility and degree of quantitative variation using SYBER Green I fluorescence. Based upon this analysis the application of a single, well- constructed standard curve could provide an estimated precision of +/-6-21%, depending on the number of cycles required to reach threshold. A simplified method for absolute quantification is also proposed, in which quantitative scale is determined by DNA mass at threshold.

Figure 1

Output of a typical amplification run used for construction of the standard curves in this study. Four replicate amplification reactions were conducted for each concentration of DNA standard, covering six magnitudes of target DNA concentration. (A) Plot of the log of reaction fluorescent versus thermocycle that provides a graphic representation for each amplification reaction, in which the linear region represents the exponential phase of the amplification. Fluorescent threshold provides the reference point from which the threshold cycle (C_t) is calculated. (B) The resulting standard curve generated by plotting the log of target DNA concentration versus threshold cycle. Linear regression analysis is used to determine the slope and intercept, which correspond, respectively, to the amplification efficiency and the number of amplicon molecules at threshold, as described by equation 4.