Whilst the term kinetic PCR was originally used for what is now more commonly referred to as real-time PCR (Higuchi et al., 1993; Higuchi and Watson, 1999), it has come to be used to describe those approaches to qPCR where the reaction efficiency is derived from the kinetics of the samples under analysis. A number of approaches to kinetic PCR have been proposed (Liu and Saint, 2002a; Liu and Saint, 2002b; Tichopad et al., 2002; Ramakers et al., 2003, Peirson et al., 2003), though the main consideration of such approaches here is that they enable E to be derived without the use of additional standards. At their simplest form, kinetic approaches involve calculating the slope of an amplification plot to determine E (Figure 6.3A).
The region of the amplification plot used for kinetic analysis presents a similar problem to threshold setting. If the region used is too low then E will be inaccurate due to background noise, and too high, then E will be too low as the reaction will be approaching a plateau (Kainz et al., 2000). This raises the concern of selecting an 'optimum threshold' for both kinetic analysis and threshold setting, which is a trade-off between background noise and plateau effects (Peirson et al., 2003). Changing the placement of a threshold will therefore affect the R0 value obtained. The nature of these inaccuracies is dependent upon the data under analysis. Analysis of the c-fos data presented in Peirson et al. (2003) suggests that a two-fold change in the threshold only alters the R0 value by less than 2% of its midpoint value, a five-fold change in threshold yields around a 6% change, and a ten-fold change in threshold results in a change of around 18%. In all cases, lowering the threshold created a larger deviation in R0 value than increasing it, illustrating that the placement of a threshold too close to background noise may introduce considerable errors when evaluating expression levels by qPCR. This possible source of assay noise also suggests that platforms with a narrow fluorescent signal range between background noise and reaction plateau may be more prone to errors introduced due to threshold placement.
An advantage of kinetic approaches is that the individual E values may be used as a criterion for outlier detection and sample exclusion. As the raw data from qPCR is in the form of Ct values, even a small amount of noise associated with these measurements may result in the introduction of large systematic errors. Bar et al., (2003) suggested the use of kinetic outlier detection (KOD) to circumvent this problem, whereby aberrant kinetics may be detected based upon deviations of E from a training set (Figure 6.3B).
Problems with kinetic approaches include that such approaches may only be possible on certain platforms where there is a wide fluorescent signal range between background noise and reaction plateau. If this signal range is low, limits are imposed on the amount of data available for kinetic analysis, and such analysis may be inaccurate. Similarly, inappropriate background subtraction may affect the slope of amplification plots, with over-subtraction creating artificially high values for E (Bar et al., 2003).
0 10 20 30 40 Cycle
0 10 20 30 40 Cycle
1 2 3 4 5 6 7 8 910111213141516 Sample
Kinetic qPCR. A. Use of linear regression to determine slope of amplification plot. Slope was determined in the region indicated by the filled circles, providing a slope of 0.277. Amplification efficiency (E) = 1 00277 = 0.893. B. Amplification efficiency (E) determined from the kinetics of 16 ocular samples (circles), with kinetic outlier detection limits indicated by horizontal lines. Sample 5 demonstrated abnormally low E, and was therefore excluded from further analysis.
Kinetic approaches appear to offer the promise of correcting each sample for slight differences in their individual amplification rates. However, this is unfortunately a false hope, as any calculation of E from raw data, like any measurement, is only an estimate, limited by the precision of the measuring device. Due to the technical noise present within the raw data, data preprocessing as well as the algorithm used, E will vary, and based upon the sum of errors from multiple sources, theoretically should conform to a normal distribution. As shown in eq. 2, the efficiency correction is applied as an exponent, and therefore even small differences in E will produce enormous differences in R0. For example, a 1% difference in the efficiency used will produce around a 13% difference in R0 after 26 cycles, whereas a 5% difference will produce nearly a two-fold change (Freeman et al., 1999). As such, the optimum approach is to use the mean efficiency (ideally after KOD), which if based on repeated measures, should provide an accurate estimate of E.
Consideration of this problem also suggests that the main source of inter-assay variability in any form of qPCR is due to the method used to calculate E between experiments. A standard curve run on multiple consecutive days will never provide exactly the same E, due to the presence of cumulative small errors in, for example, spectrophotometry, pipetting and fluorescent measurement. Once again, barring dramatic outliers, such errors would be expected to result in values of E that conform to a normal distribution.
The kinetic approach described above, based on use of the R0 method is automated in DART-PCR, an Excel®-based worksheet for qPCR data analysis. This is available as supplementary data from Peirson et al., (2003), or freely available on request.
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