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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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Comparison of the use of individual, common or amplicon-specific PCR efficiencies. (A) PCR efficiency values for ATG5 (gray) and PSMB5 (white) in controls and Huntington patients were based on the individual sample (individual window), a W-o-L for all samples from both amplicons (common window) and a W-o-L set for each of the two amplicons (amplicon window). For each amplicon, the variation in PCR values was highest in individual windows and lowest when a W-o-L per amplicon (F-test, P < 0.001 for both amplicons) was used. The mean efficiency per amplicon did not differ between the three W-o-L settings (one-way ANOVA; P = 0.183 and P = 0.101, respectively) but for all windows the efficiencies of the two amplicons differed significantly (t-test: all P < 0.0001). EC indicates the common PCR efficiency that results when the difference between amplicons is ignored. (B) Starting concentrations (N0 expressed in arbitrary fluorescence units) in brain tissue for both amplicons in Controls and Huntington patients calculated with the individual, common, and amplicon efficiency. There is no significant difference between the variation in N0 values per amplicon and experimental group although the variation is lowest when the common PCR efficiency was used. For both amplicons, the starting concentrations are significantly lower when the results were obtained with a common efficiency (t-test, P ≤ 0.001 for both amplicons and comparisons). The N0 values do not differ when they were obtained with individual or amplicon efficiencies (t-test, P = 0.916 and P = 0.994 for ATG5 and PSMB5, respectively). (C) Frequency distributions of the individual PCR efficiency values determined with a W-o-L per amplicon. The distribution of efficiency values is symmetrical and normally distributed (Shapiro–Wilk test; P = 0.933 and P = 0.478 for ATG5 and PSMB5, respectively). (D) When the gene expression ratio (PSMB5/ATG5) in Controls and Huntington patients is based on the N0 values calculated with the individual or the amplicon efficiency, the average ratios are similar (dotted lines), but the variation in the ratios is significantly reduced when the amplicon efficiencies are used [F-test on log(ratio); P = 0.009]. When the expression ratio is calculated with the common efficiency the average ratio is significantly biased (t-test; P < 0.0001 compared to both the individual and the amplicon efficiency results). This bias results from ignoring the difference between the amplicon efficiencies (Box 1; Equation 7).
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Figure 5: Comparison of the use of individual, common or amplicon-specific PCR efficiencies. (A) PCR efficiency values for ATG5 (gray) and PSMB5 (white) in controls and Huntington patients were based on the individual sample (individual window), a W-o-L for all samples from both amplicons (common window) and a W-o-L set for each of the two amplicons (amplicon window). For each amplicon, the variation in PCR values was highest in individual windows and lowest when a W-o-L per amplicon (F-test, P < 0.001 for both amplicons) was used. The mean efficiency per amplicon did not differ between the three W-o-L settings (one-way ANOVA; P = 0.183 and P = 0.101, respectively) but for all windows the efficiencies of the two amplicons differed significantly (t-test: all P < 0.0001). EC indicates the common PCR efficiency that results when the difference between amplicons is ignored. (B) Starting concentrations (N0 expressed in arbitrary fluorescence units) in brain tissue for both amplicons in Controls and Huntington patients calculated with the individual, common, and amplicon efficiency. There is no significant difference between the variation in N0 values per amplicon and experimental group although the variation is lowest when the common PCR efficiency was used. For both amplicons, the starting concentrations are significantly lower when the results were obtained with a common efficiency (t-test, P ≤ 0.001 for both amplicons and comparisons). The N0 values do not differ when they were obtained with individual or amplicon efficiencies (t-test, P = 0.916 and P = 0.994 for ATG5 and PSMB5, respectively). (C) Frequency distributions of the individual PCR efficiency values determined with a W-o-L per amplicon. The distribution of efficiency values is symmetrical and normally distributed (Shapiro–Wilk test; P = 0.933 and P = 0.478 for ATG5 and PSMB5, respectively). (D) When the gene expression ratio (PSMB5/ATG5) in Controls and Huntington patients is based on the N0 values calculated with the individual or the amplicon efficiency, the average ratios are similar (dotted lines), but the variation in the ratios is significantly reduced when the amplicon efficiencies are used [F-test on log(ratio); P = 0.009]. When the expression ratio is calculated with the common efficiency the average ratio is significantly biased (t-test; P < 0.0001 compared to both the individual and the amplicon efficiency results). This bias results from ignoring the difference between the amplicon efficiencies (Box 1; Equation 7).

Mentions: A dataset of qPCR samples of brain tissue containing Huntington patients and control samples served to study the effect of averaging efficiencies on the variation and the bias of the reported concentrations for two amplicons. Three different window settings were used. We previously proposed to base the W-o-L on the best-fitting straight line though 4–6 data points (15). This setting resulted in highly variable PCR efficiencies (Figure 5A, left). When the W-o-L is set per amplicon, the variability between individual PCR efficiencies is significantly reduced (Figure 5A, right) and neither amplicon showed a difference in PCR efficiencies between Control and Huntington patients (Supplementary Figure S4B). For both amplicons, the frequency distribution of the observed PCR efficiencies is normal and symmetrical around the mean PCR efficiency (Figure 5C). This justifies the use of the mean of these efficiencies as an estimate for the true PCR efficiency per amplicon. For further discussion, the efficiency values were also determined by setting a common window for both amplicons (Figure 5A, middle) and a common (mean) PCR efficiency (EC) was calculated, thus ignoring the amplification difference between amplicons.Figure 5.


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)

Comparison of the use of individual, common or amplicon-specific PCR efficiencies. (A) PCR efficiency values for ATG5 (gray) and PSMB5 (white) in controls and Huntington patients were based on the individual sample (individual window), a W-o-L for all samples from both amplicons (common window) and a W-o-L set for each of the two amplicons (amplicon window). For each amplicon, the variation in PCR values was highest in individual windows and lowest when a W-o-L per amplicon (F-test, P < 0.001 for both amplicons) was used. The mean efficiency per amplicon did not differ between the three W-o-L settings (one-way ANOVA; P = 0.183 and P = 0.101, respectively) but for all windows the efficiencies of the two amplicons differed significantly (t-test: all P < 0.0001). EC indicates the common PCR efficiency that results when the difference between amplicons is ignored. (B) Starting concentrations (N0 expressed in arbitrary fluorescence units) in brain tissue for both amplicons in Controls and Huntington patients calculated with the individual, common, and amplicon efficiency. There is no significant difference between the variation in N0 values per amplicon and experimental group although the variation is lowest when the common PCR efficiency was used. For both amplicons, the starting concentrations are significantly lower when the results were obtained with a common efficiency (t-test, P ≤ 0.001 for both amplicons and comparisons). The N0 values do not differ when they were obtained with individual or amplicon efficiencies (t-test, P = 0.916 and P = 0.994 for ATG5 and PSMB5, respectively). (C) Frequency distributions of the individual PCR efficiency values determined with a W-o-L per amplicon. The distribution of efficiency values is symmetrical and normally distributed (Shapiro–Wilk test; P = 0.933 and P = 0.478 for ATG5 and PSMB5, respectively). (D) When the gene expression ratio (PSMB5/ATG5) in Controls and Huntington patients is based on the N0 values calculated with the individual or the amplicon efficiency, the average ratios are similar (dotted lines), but the variation in the ratios is significantly reduced when the amplicon efficiencies are used [F-test on log(ratio); P = 0.009]. When the expression ratio is calculated with the common efficiency the average ratio is significantly biased (t-test; P < 0.0001 compared to both the individual and the amplicon efficiency results). This bias results from ignoring the difference between the amplicon efficiencies (Box 1; Equation 7).
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Figure 5: Comparison of the use of individual, common or amplicon-specific PCR efficiencies. (A) PCR efficiency values for ATG5 (gray) and PSMB5 (white) in controls and Huntington patients were based on the individual sample (individual window), a W-o-L for all samples from both amplicons (common window) and a W-o-L set for each of the two amplicons (amplicon window). For each amplicon, the variation in PCR values was highest in individual windows and lowest when a W-o-L per amplicon (F-test, P < 0.001 for both amplicons) was used. The mean efficiency per amplicon did not differ between the three W-o-L settings (one-way ANOVA; P = 0.183 and P = 0.101, respectively) but for all windows the efficiencies of the two amplicons differed significantly (t-test: all P < 0.0001). EC indicates the common PCR efficiency that results when the difference between amplicons is ignored. (B) Starting concentrations (N0 expressed in arbitrary fluorescence units) in brain tissue for both amplicons in Controls and Huntington patients calculated with the individual, common, and amplicon efficiency. There is no significant difference between the variation in N0 values per amplicon and experimental group although the variation is lowest when the common PCR efficiency was used. For both amplicons, the starting concentrations are significantly lower when the results were obtained with a common efficiency (t-test, P ≤ 0.001 for both amplicons and comparisons). The N0 values do not differ when they were obtained with individual or amplicon efficiencies (t-test, P = 0.916 and P = 0.994 for ATG5 and PSMB5, respectively). (C) Frequency distributions of the individual PCR efficiency values determined with a W-o-L per amplicon. The distribution of efficiency values is symmetrical and normally distributed (Shapiro–Wilk test; P = 0.933 and P = 0.478 for ATG5 and PSMB5, respectively). (D) When the gene expression ratio (PSMB5/ATG5) in Controls and Huntington patients is based on the N0 values calculated with the individual or the amplicon efficiency, the average ratios are similar (dotted lines), but the variation in the ratios is significantly reduced when the amplicon efficiencies are used [F-test on log(ratio); P = 0.009]. When the expression ratio is calculated with the common efficiency the average ratio is significantly biased (t-test; P < 0.0001 compared to both the individual and the amplicon efficiency results). This bias results from ignoring the difference between the amplicon efficiencies (Box 1; Equation 7).
Mentions: A dataset of qPCR samples of brain tissue containing Huntington patients and control samples served to study the effect of averaging efficiencies on the variation and the bias of the reported concentrations for two amplicons. Three different window settings were used. We previously proposed to base the W-o-L on the best-fitting straight line though 4–6 data points (15). This setting resulted in highly variable PCR efficiencies (Figure 5A, left). When the W-o-L is set per amplicon, the variability between individual PCR efficiencies is significantly reduced (Figure 5A, right) and neither amplicon showed a difference in PCR efficiencies between Control and Huntington patients (Supplementary Figure S4B). For both amplicons, the frequency distribution of the observed PCR efficiencies is normal and symmetrical around the mean PCR efficiency (Figure 5C). This justifies the use of the mean of these efficiencies as an estimate for the true PCR efficiency per amplicon. For further discussion, the efficiency values were also determined by setting a common window for both amplicons (Figure 5A, middle) and a common (mean) PCR efficiency (EC) was calculated, thus ignoring the amplification difference between amplicons.Figure 5.

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