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

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          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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          Most cited references 33

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          A new mathematical model for relative quantification in real-time RT-PCR.

           M. Pfaffl (2001)
          Use of the real-time polymerase chain reaction (PCR) to amplify cDNA products reverse transcribed from mRNA is on the way to becoming a routine tool in molecular biology to study low abundance gene expression. Real-time PCR is easy to perform, provides the necessary accuracy and produces reliable as well as rapid quantification results. But accurate quantification of nucleic acids requires a reproducible methodology and an adequate mathematical model for data analysis. This study enters into the particular topics of the relative quantification in real-time RT-PCR of a target gene transcript in comparison to a reference gene transcript. Therefore, a new mathematical model is presented. The relative expression ratio is calculated only from the real-time PCR efficiencies and the crossing point deviation of an unknown sample versus a control. This model needs no calibration curve. Control levels were included in the model to standardise each reaction run with respect to RNA integrity, sample loading and inter-PCR variations. High accuracy and reproducibility (<2.5% variation) were reached in LightCycler PCR using the established mathematical model.
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            Relative expression software tool (REST) for group-wise comparison and statistical analysis of relative expression results in real-time PCR.

             M. Pfaffl (2002)
            Real-time reverse transcription followed by polymerase chain reaction (RT-PCR) is the most suitable method for the detection and quantification of mRNA. It offers high sensitivity, good reproducibility and a wide quantification range. Today, relative expression is increasingly used, where the expression of a target gene is standardised by a non-regulated reference gene. Several mathematical algorithms have been developed to compute an expression ratio, based on real-time PCR efficiency and the crossing point deviation of an unknown sample versus a control. But all published equations and available models for the calculation of relative expression ratio allow only for the determination of a single transcription difference between one control and one sample. Therefore a new software tool was established, named REST (relative expression software tool), which compares two groups, with up to 16 data points in a sample and 16 in a control group, for reference and up to four target genes. The mathematical model used is based on the PCR efficiencies and the mean crossing point deviation between the sample and control group. Subsequently, the expression ratio results of the four investigated transcripts are tested for significance by a randomisation test. Herein, development and application of REST is explained and the usefulness of relative expression in real-time PCR using REST is discussed. The latest software version of REST and examples for the correct use can be downloaded at
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              Assumption-free analysis of quantitative real-time polymerase chain reaction (PCR) data.

              Quantification of mRNAs using real-time polymerase chain reaction (PCR) by monitoring the product formation with the fluorescent dye SYBR Green I is being extensively used in neurosciences, developmental biology, and medical diagnostics. Most PCR data analysis procedures assume that the PCR efficiency for the amplicon of interest is constant or even, in the case of the comparative C(t) method, equal to 2. The latter method already leads to a 4-fold error when the PCR efficiencies vary over just a 0.04 range. PCR efficiencies of amplicons are usually calculated from standard curves based on either known RNA inputs or on dilution series of a reference cDNA sample. In this paper we show that the first approach can lead to PCR efficiencies that vary over a 0.2 range, whereas the second approach may be off by 0.26. Therefore, we propose linear regression on the Log(fluorescence) per cycle number data as an assumption-free method to calculate starting concentrations of mRNAs and PCR efficiencies for each sample. A computer program to perform this calculation is available on request (e-mail:; subject: LinRegPCR).

                Author and article information

                Nucleic Acids Res
                Nucleic Acids Res
                Nucleic Acids Research
                Oxford University Press
                April 2009
                22 February 2009
                22 February 2009
                : 37
                : 6
                : e45
                1Heart Failure Research Center, Academic Medical Center, University of Amsterdam, The Netherlands, 2Department of Neuroscience, Faculty of Mental Health, University of Maastricht, The Netherlands, 3Nestec Ltd, PTC Orbe, Switzerland and 4Department of Endocrinology and Metabolism, Academic Medical Center, University of Amsterdam, The Netherlands
                Author notes
                *To whom correspondence should be addressed. Tel: +30 20 5665386; Fax: +30 20 6976177; Email: j.m.ruijter@

                Present addresses: C. Ramakers, Department of Clinical Chemistry & Hematology, St Elisabeth Hospital, Tilburg, The Netherlands W. M. H. Hoogaars, Department of Human Genetics, Leiden University Medical Center, Leiden, The Netherlands

                © 2009 The Author(s)

                This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License ( which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

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