Figure 1:    Plot of fluorescence observations from LightCycler (Roche Diagnostics). Forty observations give a sigmoid trajectory that can be described by full data fit (four parametric logistic model). Ground phase can be well linearly regressed (inlay). Following data of n > 7 are considered exponentially behaved and can be fitted by exponential model. Various model fits are designated in legend within figure. FDM and SDM denote position of first and second derivative maximum within full data fit.


Figure 2:    Flowchart of statistical estimation of the exponential phase beginning based on inspection of externally studentised residuals.  

ERRATUM  download PDF   tichopad-et-al-nar-2003-figure-2.pdf

ERRATUM  download PDF   tichopad-2003-erratum.pdf

Inhibition of real-time RT–PCR quantification due to tissue-specific contaminants

Ales Tichopad, Andrea Didier, Michael W. Pfaffl (2004)  
Molecular and Cellular Probes (18): 45-50

Real-time reverse transcription–polymerase chain reaction (RT–PCR) is currently considered the most sensitive method to study low abundance gene expression. Since comparison of gene expression levels in various tissues is often the purpose of an experiment, we studied a tissue-linked effect on nucleic acid amplification. Based on the raw data generated by a LightCycler instrument, we propose a descriptive mathematical model of PCR amplification. This model allowed us to study amplification kinetics of four common housekeeping genes in total RNA samples derived from various bovine tissues. We observed that unknown tissue-specific factors can influence amplification kinetics but this affect can be ameliorated, in part, by appropriate primer selection.

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Locked nucleic acid (LNA) single nucleotide polymorphism (SNP) genotype analysis
and validation using real-time PCR.

Johnson MP, Haupt LM, Griffiths LR.

Nucleic Acids Res. 2004 Mar 26;32(6):e55. 



Genomics Research Centre, School of Health Science, Griffith University Gold
Coast, PMB 50, Gold Coast Mail Centre, QLD 9726, Australia.

With an increased emphasis on genotyping of single nucleotide polymorphisms (SNPs) in disease association studies, the genotyping platform of choice is constantly evolving. In addition, the development of more specific SNP assays and appropriate genotype validation applications is becoming increasingly critical to elucidate ambiguous genotypes. In this study, we have used SNP specific Locked Nucleic Acid (LNA) hybridization probes on a real-time PCR platform to genotype an association cohort and propose three criteria to address ambiguous genotypes. Based on the kinetic properties of PCR amplification, the three criteria address PCR amplification efficiency, the net fluorescent difference between maximal and minimal fluorescent signals and the beginning of the exponential growth phase of the reaction. Initially observed SNP allelic discrimination curves were confirmed by DNA sequencing (n = 50) and application of our three genotype criteria corroborated both sequencing and observed real-time PCR results. In addition, the tested Caucasian association cohort was in Hardy-Weinberg equilibrium and observed allele frequencies were very similar to two independently tested Caucasian association cohorts for the same tested SNP. We present here a novel approach to effectively determine ambiguous genotypes generated from a real-time PCR platform. Application of our three novel criteria provides an easy to use semi-automated genotype confirmation protocol.

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Sigmoidal curve-fitting redefines quantitative real-time PCR with the
prospective of developing automated high-throughput applications.

Rutledge RG.
Nucleic Acids Res. 2004 32(22): e178.



Natural Resources Canada, 1055 du P.E.P.S, Sainte-Foy, Quebec, Canada G1V 4C7.

Quantitative real-time PCR has revolutionized many aspects of genetic research, biomedical diagnostics and pathogen detection. Nevertheless, the full potential of this technology has yet to be realized, primarily due to the limitations of the threshold-based methodologies that are currently used for quantitative analysis. Prone to errors caused by variations in reaction preparation and amplification conditions, these approaches necessitate construction of standard curves for each target sequence, significantly limiting the development of high-throughput applications that demand substantive levels of reliability and automation. In this study, an alternative approach based upon fitting of fluorescence data to a four-parametric sigmoid function is shown to dramatically increase both the utility and reliability of quantitative real-time PCR. By mathematically modeling individual amplification reactions, quantification can be achieved without the use of standard curves and without prior knowledge of amplification efficiency. Combined with provision of quantitative scale via optical calibration, sigmoidal curve-fitting could confer the capability for fully automated quantification of nucleic acids with unparalleled accuracy and reliability.

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Improved real-time RT-PCR method for high-throughput measurements using second
derivative calculation and double correction.

Van Luu-The, Paquet N, Calvo E, Cumps J.
Biotechniques. 2005 Feb;38(2):287-93.



Molecular Endocrinology and Oncology Research Center, Laval University, Quebec, Canada.

Quantification of mRNA expression levels using real-time reverse transcription PCR (RT-PCR) is increasingly used to validate results of DNA microarrays or GeneChips. It requires an improved method that is more robust and more suitable for high-throughput measurements. In this report, we compare a user non-influent, second derivative method with that of a user influent, fit point method that is widely used in the literature. We also describe the advantage of using a double correction: one correction using the expression levels of a housekeeping gene of an experiment as an internal standard and a second using reference expression levels of the same housekeeping gene in the tissue or cells. The first correction permits one to decrease errors due to sample preparation and handling, while the second correction permits one to avoid the variation of the results with the variability of housekeeping in each tissue, especially in experiments using various treatments. The data indicate that the real-time PCR method is highly efficient with an efficiency coefficient close to the theoretical value of two. The results also show that the second derivative method is more accurate than the fit point method in quantifying low gene expression levels. Using triplicate experiments, we show that measurement variations using our method are low with a mean of variation coefficients of <1%.

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Gene expression of HIF-1 α and XRCC4 measured in human samples by real-time RT-PCR
using the sigmoidal curve-fitting method.

Hao Qiu, Karine Durand, Hélène Rabinovitch-Chable, Michel Rigaud, Virgile Gazaille,
Pierre Clavère, and Franck G. Sturtz
BioTechniques 42:355-362 (March 2007)

Quantitative reverse transcription PCR (RT-PCR) has become an important tool for studying functional gene expression. However, the most often used cycle threshold (CT)-based method, primarily related to the required amplification efficiency determination via serial dilution, can call into question the level of quantitative reliability and accuracy that can be achieved, in addition to the impracticalities inherent to CT-based methodologies. In this study, an alternative method, named the sigmoidal curve-fitting (SCF) method, was compared with the classic CT method for two target genes (XRCC4 and HIF-1α) and a reference gene (HPRT). The PCR conditions were optimized for each gene on a LightCycler® apparatus. Fluorescence data were fitted to a four-parametric sigmoidal function, and the initial messenger RNA (mRNA) copy number was determined by a theoretical fluorescence (F0) value calculated from each fitting curve. The relative expression of the target gene versus that of the reference gene was calculated using an equation based upon these F0 values. The results show that the F0 value had a good linearity with the initial number of target genes between 107 and 101 copies. The reproducibility tests showed that the variations of initial target quantity were well reflected by F0 values. Relative expression of target gene calculated by the SCF method and by the CT method showed similar results. In our hands, the SCF method gave reliable results and a more precise error description of quantitative RT-PCR.

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Model based analysis of real-time PCR data from DNA binding dye protocols.

Alvarez MJ, Vila-Ortiz GJ, Salibe MC, Podhajcer OL, Pitossi FJ.

Gentron Research Unit, Arenales Piso, Buenos Aires C1061AAO, Argentina.

BMC Bioinformatics. 2007 8:85.

BACKGROUND: Reverse transcription followed by real-time PCR is widely used for quantification of specific mRNA, and with the use of double-stranded DNA binding dyes it is becoming a standard for microarray data validation. Despite the kinetic information generated by real-time PCR, most popular analysis methods assume constant amplification efficiency among samples, introducing strong biases when amplification efficiencies are not the same.
RESULTS: We present here a new mathematical model based on the classic exponential description of the PCR, but modeling amplification efficiency as a sigmoidal function of the product yield. The model was validated with experimental results and used for the development of a new method for real-time PCR data analysis. This model based method for real-time PCR data analysis showed the best accuracy and precision compared with previous methods when used for quantification of in-silico generated and experimental real-time PCR results. Moreover, the method is suitable for the analyses of samples with similar or dissimilar amplification efficiency.
CONCLUSION: The presented method showed the best accuracy and precision. Moreover, it does not depend on calibration curves, making it ideal for fully automated high-throughput applications.

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A kinetic-based sigmoidal model for the polymerase chain reaction and its application to high-capacity absolute quantitative real-time PCR
Robert G Rutledge & Donald Stewart

BMC Biotechnology 2008, Published: 8 May 2008

Background:  Based upon defining a common reference point, current real-time quantitative PCR technologies compare relative differences in amplification profile position. As such, absolute quantification requires construction of target-specific standard curves that are highly resource intensive and prone to introducing quantitative errors. Sigmoidal modeling using nonlinear regression has previously demonstrated that absolute quantification can be accomplished without standard curves; however, quantitative errors caused by distortions within the plateau phase have impeded effective implementation of this alternative approach.
Results:  Recognition that amplification rate is linearly correlated to amplicon quantity led to the derivation of two sigmoid functions that allow target quantification via linear regression analysis. In addition to circumventing quantitative errors produced by plateau distortions, this approach allows the amplification efficiency within individual amplification reactions to be determined. Absolute quantification is accomplished by first converting individual fluorescence readings into target quantity expressed in fluorescence units, followed by conversion into the number of target molecules via optical calibration. Founded upon expressing reaction fluorescence in relation to amplicon DNA mass, a seminal element of this study was to implement optical calibration using lambda gDNA as a universal quantitative standard. Not only does this eliminate the need to prepare target-specific quantitative standards, it relegates establishment of quantitative scale to a single, highly defined entity. The quantitative competency of this approach was assessed by exploiting "limiting dilution assay" for absolute quantification, which provided an independent gold standard from which to verify quantitative accuracy. This yielded substantive corroborating evidence that absolute accuracies of +/-25% can be routinely achieved. Comparison with the LinReg and Miner automated qPCR data processing packages further demonstrated the superior performance of this kinetic-based methodology.
Conclusions:  Called "linear regression of efficiency" or LRE, this novel kinetic approach confers the ability to conduct high-capacity absolute quantification with unprecedented quality control capabilities. The computational simplicity and recursive nature of LRE quantification also makes it amenable to software implementation, as demonstrated by a prototypic Java program that automates data analysis. This in turn introduces the prospect of conducting absolute quantification with little additional effort beyond that required for the preparation of the amplification reactions.

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The E-Method: a highly accurate technique for gene-expression analysis

Gudrun Tellmann
Nature, Application Note, July 2006

Roche Applied Science has repeatedly set standards for high-speed real-time PCR systems. The newLightCycler® 480 System offers different methods of data analysis for relative quantification of geneexpressionbehavior. Whereas the ∆∆CT Method provides fast, easy analysis of gene expression, the E-Method from Roche Applied Science can produce more accurate relative quantification data bycompensating for differences in target and reference-gene amplification efficiency, either within anexperiment or between experiments.

LC 480 System - Innovative solutions for relative quantification