Determination of PCR Efficiency  (1)
Determination of PCR Efficiency  (main)
Determination of PCR Efficiency  (2)
Determination of PCR Efficiency  (3)
Determination of PCR Efficiency  (4)
Determination of PCR Efficiency  (5)

• Estimation via classical  "calibration dilution curve and slope calculation"
• real-time PCR Standard Curve Slope to Efficiency Calculator (by Stratagene)
• on each individual cDNA (Rasmussen 2001)
• on each individual cDNA (Stahlberg et al. 2003)
• on a mixture of multiple cDNA (cDNA pool, Pfaffl 2001)
• Experimental validation of novel and conventional approaches to quantitative real-time PCR data analysis (Peirson, 2003)
• Mathematics of quantitative kinetic PCR and the application of standard curves (Rutledge & Cote 2003)
• Qiagen Manual: High PCR efficiency enable more accurate quantification in real-time PCR (QNews 2, 2004, page 49)
• Accurate and statistically verified quantification of relative mRNA abundances using SYBR Green I and real-time RT-PCR (Marino et al. 2003)
• Impact of DNA polymerases and their buffer systems on quantitative real-time PCR. (Wolffs et al. 2004)
• Addressing fluorogenic real-time qPCR inhibition using the novel custom Excel file system 'FocusField2- 6Gallupq PCRSet-upTool-001' to attain consistently high fidelity qPCR reactions. (Gallup & Ackermann, 2006)
  

• Estimation via increase in  "absolute fluorescence"
  
• Estimation via increase in "absolute fluorescence" method 1 (linear regression, Pfaffl 2001)
• Estimation via increase in "absolute fluorescence" method 2 (Liu & Saint 2002)
• Estimation via increase in "absolute fluorescence" method 3  (3 data points, Peccoud & Jacob 1998)
• Estimation via increase in "absolute fluorescence" method 4  (window-of-linearity, Ramakers et al. 2003)
• Estimation via increase in "absolute fluorescence" method 5  (Shiao et al. 2003)

• Potential influence of the first PCR cycles in real-time comparative gene quantifications  (Nogva & Rudi, 2004)

• Q-Gene: processing quantitative real-time RT–PCR data  (Perikles Simon, 2003)

• KOD in real-time PCR
• KOD (Kinetic Outlier Detection) in real-time PCR  (Tzachi Bar et al., 2003)
• Kinetics quality assessment for relative quantification by real-time PCR. (Bar T, Muszta A., 2005)

Figure 1: Quantification of purified PCR product of the human HER2/neu gene in the LightCycler Instrument. The reaction was monitored with SYBR Green I. Acquisitions were taken once per cycle after extension.

Figure 2: A standard curve constructed from the data in figure 1. The slope of the line is -1/log (efficiency) giving an efficiency in this case of 1.73. The intercept is the log of the amount of DNA at threshold divided by the log of the efficiency.

A quantitative real-time PCR method for detection of B-Lymphocyte Monoclonality
by comparison of kappa and lambda Immunoglobulin Light Chain Expression.
Anders Ståhlberg, Pierre Åman, Börje Ridell, Petter Mostad, and Mikael Kubista (2003)
Clinical Chemistry 49(1): 51-59

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A new mathematical model for relative quantification in real-time RT-PCR.
       Pfaffl Michael W.  (2001) 
Nucleic Acids Res. 2001 May 1; 29(9): E45-E45.

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Experimental validation of novel and conventional approaches
to quantitative real-time PCR data analysis.

Stuart N. Peirson, Jason N. Butler and Russell G. Foster (2003)

Real-time PCR is being used increasingly as the method of choice for mRNA quantification, allowing rapid analysis of gene expression from low quantities of starting template. Despite a wide range of approaches, the same principles underlie all data analysis, with standard approaches broadly classiffed as either absolute or relative. In this study we use a variety of absolute and relative approaches of data analysis to investigate nocturnal c-fos expression in wild-type and retinally degenerate mice. In addition, we apply a simple algorithm to calculate the amplifcation effciency of every sample from its amplifcation profle. We confrm that nocturnal c-fos expression in the rodent eye originates from the photoreceptor layer, with around a 5-fold reduction in nocturnal c-fos expression in mice lacking rods and cones. Furthermore, we illustrate that differences in the results obtained from absolute and relative approaches are underpinned by differences in the calculated PCR effciency. By calculating the amplifcation effciency from the samples under analysis, comparable results may be obtained without the need for standard curves. We have automated this method to provide a means of streamlining the real-time PCR process, enabling analysis of experimental samples based upon their own reaction kinetics rather than those of artificial standards.

=>  Download of  DART PCR version 1.0

DART-PCR provides a simple means of analysing real-time PCR data from raw flurescence data. This allows an automatic calculation of amplification kinetics, as well as performing the subsequent calculations for relative quantification and calculation of assay variability. Amplification efficiencies are also tested to dtect anomalus samples within groups (outlayers) and differences between experimatal groups (amplification equivalence).

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 Mathematics of quantitative kinetic PCR and the application of standard curves.
Rutledge RG, Cote C.
Nucleic Acids Res.  2003 Aug 15;31(16):e93

Natural Resources Canada, Canadian Forest Service, Laurentian Forestry Centre,
1055 du P.E.P.S., PO Box 3800, Sainte-Foy, Quebec G1V 4C7, Canada.

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 s determined by DNA mass at threshold.

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Accurate and statistically verified quantification of relative mRNA abundances
using SYBR Green I and real-time RT-PCR.

Marino JH, Cook P, Miller KS.
J Immunol Methods. 2003 Dec;283(1-2):291-306.

Faculty of Biological Sciences, The University of Tulsa, 600 S. College Avenue,
Tulsa, OK 74104-3189, USA.

Among the many methods currently available for quantifying mRNA transcript abundance, reverse transcription- polymerase chain reaction (RT-PCR) has proved to be the most sensitive. Recently, several protocols for real-time relative
RT-PCR using the reporter dye SYBR Green I have appeared in the literature. In these methods, sample and control mRNA abundance is quantified relative to an internal reference RNA whose abundance is known not to change under the differing experimental conditions. We have developed new data analysis procedures for the two most promising of these methodologies and generated data appropriate to assess both the accuracy and precision of the two protocols. We demonstrate that while both methods produce results that are precise when 18S rRNA is used as an internal reference, only one of these methods produces consistently accurate results. We have used this latter system to show that mRNA abundances can be accurately measured and strongly correlate with cell surface protein and carbohydrate expression as assessed by flow cytometry under different conditions of B cell activation.

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Impact of DNA polymerases and their buffer systems on quantitative real-time PCR.

Wolffs P, Grage H, Hagberg O, Radstrom P.
J Clin Microbiol. 2004 Jan;42(1):408-11.



Applied Microbiology, Lund Institute of Technology, Mathematical Statistics,
Lund University, SE-221 00 Lund, Sweden.

An investigation of the influence of five DNA polymerase-buffer systems on real-time PCR showed that the choice of both DNA polymerase and the buffer system affected the amplification efficiency as well as the detection window. The analytical repeatability of the data for different systems changed clearly, leading us to conclude that basing quantitative measurements on single-data-set standard curves can lead to significant errors.

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Addressing fluorogenic real-time qPCR inhibition using the novel custom Excel file system 'FocusField2-6GallupqPCRSet-upTool-001' to attain consistently high fidelity qPCR reactions.

Jack M. Gallup and Mark R. Ackermann

Department of Veterinary Pathology, College of Veterinary Medicine, Iowa State University. Ames, Iowa 50011-1250. USA.

Biol. Proced. Online 2006;8:87-152.

The purpose of this manuscript is to discuss fluorogenic real-time quantitative polymerase chain reaction (qPCR) inhibition and to introduce/define a novel Microsoft Excel-based file system which provides a way to detect and avoid inhibition, and enables investigators to consistently design dynamically-sound, truly LOG-linear qPCR reactions very quickly. The qPCR problems this invention solves are universal to all qPCR reactions, and it performs all necessary qPCR set-up calculations in about 52 seconds (using a pentium 4 processor) for up to seven qPCR targets and seventy-two samples at a time – calculations that commonly take capable investigators days to finish. We have named this custom Excel-based file system "FocusField2- 6GallupqPCRSet-upTool-001" (FF2-6-001 qPCR set-up tool), and are in the process of transforming it into professional qPCR set-up software to be made available in 2007. The current prototype is already fully functional.

Download Excel file

Quantitative applications of the Polymerase Chain Reaction (PCR), also known as Quantitative-PCR (Q-PCR) are intended either to determine the number of copies of a given nucleic acid sequence, or more generally, to determine the relative abundance of two sequences. Current methods to determine exact numbers of molecules overcome the determination of the amplification rate by assuming identical amplification rates for a target DNA sequence and a standard of known quantity introduced into the experiment design, so that only the ratio of amplified products need be determined. Violations of the hypothesis of identical amplification rates for two sequences will result in a systematic bias in the experiment results that underestimates or overestimates the initial copy numbers. Acquisition of kinetic PCR data was pioneered by Higuchi et al. (Higuchi et al., 1993; Higuchi et al., 1992) and commercial instruments have been available since early 1996. Kinetic data provide a new way to determine the amplification rate, and we can foresee that their availability will rekindle interest in the algorithms used to compute the initial quantities of DNA sequences. Analysis of kinetic PCR patterns will soon make its way into the family of recipes that have been in use for some years in this field. This chapter provides evidence that a statistical analysis of the amplification rate is critical to ensuring a reliable estimate of the initial copy number.

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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.

 
Figure:
Illustration of the linear regression calculations implemented in a Microsoft Excelw spreadsheet for determining starting concentrations and PCR efficiencies per sample.

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A new reverse transcription-polymerase chain reaction method for accurate quantification

Yih-Horng Shiao
BMC Biotechnology (2003)

Background: Reverse transcription-polymerase chain reaction (RT-PCR) is a very sensitive technique to measure and to compare mRNA levels among samples. However, it is extremely difficult to maintain linearity across the entire procedure, especially at the step of PCR amplification. Specific genes have been used as baseline controls to be co-amplified with target genes to normalize the amplification efficiency, but development or selection of reliable controls itself has created a new challenge.
Results: Here, we describe a new quantitative RT-PCR to compare two mRNA samples directly without the requirement of synthetic control DNAs for reference. First, chimeric RT primers carrying gene-specific and universal PCR priming sequences with or without a linker for size distinction were utilized to generate cDNAs. The size-different cDNAs were then combined in a single reaction for PCR amplification using the same primer set. The two amplified products were resolved and detected with gel electrophoresis and fluorescence imaging. Relative abundance of the two products was obtained after a baseline correction.
Conclusion: This methodology is simple and accurate as indicated by equal amplification efficiency throughout PCR cycling. It is also easily implemented for many existing protocols. In addition, parameters affecting RT linearity are characterized in this report.

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Potential influence of the first PCR cycles in real-time comparative gene quantifications.

Nogva HK, Rudi K.
Biotechniques. 2004 Aug;37(2):246-8, 250-3. 



Norwegian Food Research Institute, AS, Norway.

There is an underlying assumption in real-time PCR that the amplification efficiency is equal from the first cycles until a signal can be detected. In this study, we evaluated this assumption by analyzing genes with known gene copy number using real-time PCR comparative gene quantifications. Listeria monocytogenes has six 23S rRNA gene copies and one copy of the hlyA gene. We determined 23S rRNA gene copy numbers between 0.9 and 1.6 relative to hlyA when applying the comparative gene quantification approach. This paper focuses on the first cycles of PCR to explain the difference between known and determined gene copy numbers. Both theoretical and experimental evaluations were done. There are three different products (types 1-3) dominating in the first cycles. Type 1 is the original target, type 2 are undefined long products, while type 3 are products that accumulate during PCR. We evaluated the effects of type 1 and 2 products during the first cycles by cutting the target DNA with a restriction enzyme that cuts outside the boundaries of the PCR products. The digestion resulted in a presumed increased amplification efficiency for type 1 and 2 products. Differences in the amplification efficiencies between type 1, 2, and 3 products may explain part of the error in the gene copy number determinations using real-time PCR comparative gene quantifications. Future applications of real-time PCR quantifications should account for the effect of the first few PCR cycles on the conclusions drawn.

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Q-Gene: processing quantitative real-time RT–PCR data

Perikles Simon
Section for Neurobiology of the Eye, University Eye Hospital Tuebingen, Calwerstr. 7/1, 72076 Tuebingen, Germany

Paper:       Online Presentation. 

=> Download - qGENE Software

Summary
Q-Gene is an application for the processing of quantitative real-time RT–PCR data. It offers the user the possibility to freely choose between two principally different procedures to calculate normalized gene expressions as either means of Normalized Expressions or Mean Normalized Expressions. In this contribution it will be shown that the calculation of Mean Normalized Expressions has to be used for processing simplex PCR data, while multiplex PCR data should preferably be processed by calculating Normalized Expressions. The two procedures, which are currently in widespread use and regarded as more or less equivalent alternatives, should therefore specifically be applied according to the quantification procedure used.

Kinetic Outlier Detection (KOD) in real-time PCR

Tzachi Bar, Anders Stahlberg, Anders Muszta and Mikael Kubista
NAR Vol 31 (17):  e105


1Department of Chemistry and Bioscience, Chalmers University of Technology, Medicinargatan 7B,
405 30 Gothenburg, Sweden, 2Department of Mathematical Statistics, Eklandagatan 86, 412 96, Gothenburg,
Sweden and 3TATAA Biocenter, Medicinargatan 7B, 405 30 Gothenburg, Sweden

Real-time PCR is becoming the method of choice for precise quantification of minute amounts of nucleic acids. For proper comparison of samples, almost all quantification methods assume similar PCR effciencies in the exponential phase of the reaction. However, inhibition of PCR is common when working with biological samples and may invalidate the assumed similarity of PCR effiencies. Here we present a statistical method, Kinetic Outlier Detection (KOD), to detect samples with dissimilar effiiencies. KOD is based on a comparison of PCR effciency, estimated from the amplifiation curve of a test sample, with the mean PCR effiency of samples in a training set. KOD is demonstrated and validated on samples with the same initial number of template molecules, where PCR is inhibited to various degrees by elevated concentrations of dNTP; and in detection of cDNA samples with an aberrant ratio of two genes. Translating the dissimilarity in efficiency to quantity, KOD identifies outliers that differ by 1.3±1.9-fold in their quantity from normal samples with a P-value of 0.05. This precision is higher than the minimal 2-fold difference in number of DNA molecules that real-time PCR usually aims to detect. Thus, KOD may be a useful tool for outlier detection in real-time PCR.

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Kinetics quality assessment for relative quantification by real-time PCR.

Bar T, Muszta A.
Biotechniques. 2005 Sep;39(3): 333-338
Chalmers University of Technology, Gothenburg, Sweden.

For proper relative quantification by real-time PCR, compared samples should have similar PCR efficiencies. To test this prerequisite, we developed two quality tests: (i) adjustment of a test for kinetic outlier detection (KOD) to relative quantification; and (ii) comparison of the efficiency variance of test samples with the efficiency variance of samples with highly reproducible quantification. The tests were applied on relative quantification of two genes in 30 sets of 5 replicate samples (same treatment, different animals). Ten low-quality sets and 28 outliers were identified. The low-quality sets showed higher coefficient of variation (cv)% of DNA quantities in replicate experiments than high-quality sets (63% versus 26%; P = 0.001) and contained a higher proportion of outlying quantities (35% versus 5.9%; P = 0.001) when individual samples were detected by adjusted KOD. Outlier detection with adjusted KOD reduced the false detection of outliers by 2/3 compared with the previous, nonadjusted version of KOD (20% versus 5.9%; P = 0.001). We conclude that the presented tests can be used to assign technical reasons to outlying observations.