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Amplification efficiency: linking baseline and bias in the analysis of quantitative PCR data.

Ruijter JM, Ramakers C, Hoogaars WM, Karlen Y, Bakker O, van den Hoff MJ, Moorman AF - Nucleic Acids Res. (2009)

Bottom Line: This article shows that baseline estimation errors are directly reflected in the observed PCR efficiency values and are thus propagated exponentially in the estimated starting concentrations as well as 'fold-difference' results.Because of the unknown origin and kinetics of the baseline fluorescence, the fluorescence values monitored in the initial cycles of the PCR reaction cannot be used to estimate a useful baseline value.The variability, as well as the bias, in qPCR results was significantly reduced when the mean of these PCR efficiencies per amplicon was used in the calculation of an estimate of the starting concentration per sample.

View Article: PubMed Central - PubMed

Affiliation: Heart Failure Research Center, Academic Medical Center, University of Amsterdam, The Netherlands. j.m.ruijter@amc.uva.nl

ABSTRACT
Despite the central role of quantitative PCR (qPCR) in the quantification of mRNA transcripts, most analyses of qPCR data are still delegated to the software that comes with the qPCR apparatus. This is especially true for the handling of the fluorescence baseline. This article shows that baseline estimation errors are directly reflected in the observed PCR efficiency values and are thus propagated exponentially in the estimated starting concentrations as well as 'fold-difference' results. Because of the unknown origin and kinetics of the baseline fluorescence, the fluorescence values monitored in the initial cycles of the PCR reaction cannot be used to estimate a useful baseline value. An algorithm that estimates the baseline by reconstructing the log-linear phase downward from the early plateau phase of the PCR reaction was developed and shown to lead to very reproducible PCR efficiency values. PCR efficiency values were determined per sample by fitting a regression line to a subset of data points in the log-linear phase. The variability, as well as the bias, in qPCR results was significantly reduced when the mean of these PCR efficiencies per amplicon was used in the calculation of an estimate of the starting concentration per sample.

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Setting the W-o-L. (A) Flowchart of the algorithm to determine the position of the W-o-L. The search for the optimal W-o-L starts with the upper limit of this window set at the mean fluorescence level found at the maximum of the second derivative (SDM) of the baseline-corrected fluorescence data. After application of this initial window, a loop is started in which the window is systematically lowered by half of the fluorescence increase per cycle. For each window, the coefficient of variation (CV) is calculated from the mean and the standard deviation of the PCR efficiencies. The minimum CV marks the W-o-L in which the PCR efficiencies of the samples show the least variation relative to the mean efficiency. (B) Intermediate results of the W-o-L setting algorithm. The left panel shows the baseline-corrected amplification curves of an example data set and the optimal W-o-L. The mean PCR efficiency and its standard deviation are plotted for each W-o-L (right panel). The smallest CV, and thus the smallest between-sample PCR efficiency variation, marks the optimal W-o-L. Data points at the beginning of the log-linear phase are preferentially present when a positive statistical noise carries them just above baseline. Consequently, in a very low W-o-L those samples behave as if their baseline was under-estimated and they contribute a low efficiency to the mean. This leads to the decrease of the mean efficiency in the lower-than-optimal windows.
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Figure 4: Setting the W-o-L. (A) Flowchart of the algorithm to determine the position of the W-o-L. The search for the optimal W-o-L starts with the upper limit of this window set at the mean fluorescence level found at the maximum of the second derivative (SDM) of the baseline-corrected fluorescence data. After application of this initial window, a loop is started in which the window is systematically lowered by half of the fluorescence increase per cycle. For each window, the coefficient of variation (CV) is calculated from the mean and the standard deviation of the PCR efficiencies. The minimum CV marks the W-o-L in which the PCR efficiencies of the samples show the least variation relative to the mean efficiency. (B) Intermediate results of the W-o-L setting algorithm. The left panel shows the baseline-corrected amplification curves of an example data set and the optimal W-o-L. The mean PCR efficiency and its standard deviation are plotted for each W-o-L (right panel). The smallest CV, and thus the smallest between-sample PCR efficiency variation, marks the optimal W-o-L. Data points at the beginning of the log-linear phase are preferentially present when a positive statistical noise carries them just above baseline. Consequently, in a very low W-o-L those samples behave as if their baseline was under-estimated and they contribute a low efficiency to the mean. This leads to the decrease of the mean efficiency in the lower-than-optimal windows.

Mentions: Based on this consideration, the algorithm to set the W-o-L searches for the window with the least variation between efficiencies. This algorithm is illustrated in Figure 4A. The procedure has to be carried out per amplicon, because the PCR efficiency can differ per primer pair and amplicon sequence. The window with the minimum coefficient of variation of efficiency values is chosen as the optimal W-o-L. No criterion is set on the absolute value of the efficiencies. However, in all datasets, the minimum variance coincides closely with a maximum mean efficiency (Figure 4B, right). When the experimental condition is suspected to influence the PCR efficiency, a W-o-L has to be set per condition and the resulting PCR efficiencies should be compared.Figure 4.


Amplification efficiency: linking baseline and bias in the analysis of quantitative PCR data.

Ruijter JM, Ramakers C, Hoogaars WM, Karlen Y, Bakker O, van den Hoff MJ, Moorman AF - Nucleic Acids Res. (2009)

Setting the W-o-L. (A) Flowchart of the algorithm to determine the position of the W-o-L. The search for the optimal W-o-L starts with the upper limit of this window set at the mean fluorescence level found at the maximum of the second derivative (SDM) of the baseline-corrected fluorescence data. After application of this initial window, a loop is started in which the window is systematically lowered by half of the fluorescence increase per cycle. For each window, the coefficient of variation (CV) is calculated from the mean and the standard deviation of the PCR efficiencies. The minimum CV marks the W-o-L in which the PCR efficiencies of the samples show the least variation relative to the mean efficiency. (B) Intermediate results of the W-o-L setting algorithm. The left panel shows the baseline-corrected amplification curves of an example data set and the optimal W-o-L. The mean PCR efficiency and its standard deviation are plotted for each W-o-L (right panel). The smallest CV, and thus the smallest between-sample PCR efficiency variation, marks the optimal W-o-L. Data points at the beginning of the log-linear phase are preferentially present when a positive statistical noise carries them just above baseline. Consequently, in a very low W-o-L those samples behave as if their baseline was under-estimated and they contribute a low efficiency to the mean. This leads to the decrease of the mean efficiency in the lower-than-optimal windows.
© Copyright Policy - creative-commons
Related In: Results  -  Collection

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Figure 4: Setting the W-o-L. (A) Flowchart of the algorithm to determine the position of the W-o-L. The search for the optimal W-o-L starts with the upper limit of this window set at the mean fluorescence level found at the maximum of the second derivative (SDM) of the baseline-corrected fluorescence data. After application of this initial window, a loop is started in which the window is systematically lowered by half of the fluorescence increase per cycle. For each window, the coefficient of variation (CV) is calculated from the mean and the standard deviation of the PCR efficiencies. The minimum CV marks the W-o-L in which the PCR efficiencies of the samples show the least variation relative to the mean efficiency. (B) Intermediate results of the W-o-L setting algorithm. The left panel shows the baseline-corrected amplification curves of an example data set and the optimal W-o-L. The mean PCR efficiency and its standard deviation are plotted for each W-o-L (right panel). The smallest CV, and thus the smallest between-sample PCR efficiency variation, marks the optimal W-o-L. Data points at the beginning of the log-linear phase are preferentially present when a positive statistical noise carries them just above baseline. Consequently, in a very low W-o-L those samples behave as if their baseline was under-estimated and they contribute a low efficiency to the mean. This leads to the decrease of the mean efficiency in the lower-than-optimal windows.
Mentions: Based on this consideration, the algorithm to set the W-o-L searches for the window with the least variation between efficiencies. This algorithm is illustrated in Figure 4A. The procedure has to be carried out per amplicon, because the PCR efficiency can differ per primer pair and amplicon sequence. The window with the minimum coefficient of variation of efficiency values is chosen as the optimal W-o-L. No criterion is set on the absolute value of the efficiencies. However, in all datasets, the minimum variance coincides closely with a maximum mean efficiency (Figure 4B, right). When the experimental condition is suspected to influence the PCR efficiency, a W-o-L has to be set per condition and the resulting PCR efficiencies should be compared.Figure 4.

Bottom Line: This article shows that baseline estimation errors are directly reflected in the observed PCR efficiency values and are thus propagated exponentially in the estimated starting concentrations as well as 'fold-difference' results.Because of the unknown origin and kinetics of the baseline fluorescence, the fluorescence values monitored in the initial cycles of the PCR reaction cannot be used to estimate a useful baseline value.The variability, as well as the bias, in qPCR results was significantly reduced when the mean of these PCR efficiencies per amplicon was used in the calculation of an estimate of the starting concentration per sample.

View Article: PubMed Central - PubMed

Affiliation: Heart Failure Research Center, Academic Medical Center, University of Amsterdam, The Netherlands. j.m.ruijter@amc.uva.nl

ABSTRACT
Despite the central role of quantitative PCR (qPCR) in the quantification of mRNA transcripts, most analyses of qPCR data are still delegated to the software that comes with the qPCR apparatus. This is especially true for the handling of the fluorescence baseline. This article shows that baseline estimation errors are directly reflected in the observed PCR efficiency values and are thus propagated exponentially in the estimated starting concentrations as well as 'fold-difference' results. Because of the unknown origin and kinetics of the baseline fluorescence, the fluorescence values monitored in the initial cycles of the PCR reaction cannot be used to estimate a useful baseline value. An algorithm that estimates the baseline by reconstructing the log-linear phase downward from the early plateau phase of the PCR reaction was developed and shown to lead to very reproducible PCR efficiency values. PCR efficiency values were determined per sample by fitting a regression line to a subset of data points in the log-linear phase. The variability, as well as the bias, in qPCR results was significantly reduced when the mean of these PCR efficiencies per amplicon was used in the calculation of an estimate of the starting concentration per sample.

Show MeSH
Related in: MedlinePlus