BioInformatics - PCR Efficiency in real-time PCR

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.

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.

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%.

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.

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.

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.

A new real-time PCR method to overcome significant quantitative inaccuracy due to slight amplification inhibition.
BMC Bioinformatics 2008, 9:326
Michele Guescini, Davide Sisti, Marco BL Rocchi, Laura Stocchi, Vilberto Stocchi
Background
Real-time PCR analysis is a sensitive DNA quantification technique that has recently gained considerable attention in biotechnology, microbiology and molecular diagnostics. Although, the cycle-threshold (Ct) method is the present “gold standard”, it is far from being a standard assay. Uniform reaction efficiency among samples is the
most important assumption of this method. Nevertheless, some authors have reported that it may not be correct and a slight PCR efficiency decrease of about 4% could result in an error of up to 400% using the Ct method. This reaction efficiency decrease may be caused by inhibiting agents used during nucleic acid extraction or copurified from the biological sample. We propose a new method (Cy0) that does not require the assumption of equal reaction efficiency between unknowns and standard curve.
Results
The Cy0 method is based on the fit of Richards’ equation to real-time PCR data by nonlinear regression in order to obtain the best fit estimators of reaction parameters. Subsequently, these parameters were used to calculate the Cy0 value that minimizes the dependence of its value on PCR kinetic. The Ct, second derivative (Cp), sigmoidal curve fitting method (SCF) and Cy0 methods were compared using two criteria: precision and accuracy. Our results demonstrated that, in optimal amplification conditions, these four methods are equally precise and
accurate. However, when PCR efficiency was slightly decreased, diluting amplification mix quantity or adding a biological inhibitor such as IgG, the SCF, Ct and Cp methods were markedly impaired while the Cy0 method gave significantly more accurate and precise results.
Conclusion
Our results demonstrate that Cy0 represents a significant improvement over the standard methods for obtaining a reliable and precise nucleic acid quantification even in suboptimal amplification conditions overcoming the underestimation caused by the presence of some PCR inhibitors.
Highly accurate sigmoidal fitting of real-time PCR data by introducing a parameter for asymmetry.
Andrej-Nikolai Spiess, Caroline Feig and Christian Ritz
BMC Bioinformatics 2008, 9:221
Background: Fitting four-parameter sigmoidal models is one of the methods established in the analysis of quantitative real-time PCR (qPCR) data. We had observed that these models are not optimal in the fitting outcome due to the inherent constraint of symmetry around the point of inflection. Thus, we found it necessary to employ a mathematical algorithm that circumvents this problem and which utilizes an additional parameter for accommodating asymmetrical structures insigmoidal qPCR data.

Results: The four-parameter models were compared to their five-parameter counterparts by means of nested F-tests based on the residual variance, thus acquiring a statistical measure for higher performance. For nearly all qPCR data we examined, five-parameter models resulted in a significantly better fit. Furthermore, accuracy and precision for the estimation of efficiencies and calculation of quantitative ratios were assessed with four independent dilution datasets and compared to the most commonly used quantification methods. It could be shown that the fiveparameter model exhibits an accuracy and precision more similar to the non-sigmoidal
quantification methods.
Conclusion: The five-parameter sigmoidal models outperform the established four-parameter model with high statistical significance. The estimation of essential PCR parameters such as PCR efficiency, threshold cycles and initial template fluorescence is more robust and has smaller variance. The model is implemented in the qpcR package for the freely available statistical R environment. The package can be downloaded from the author's homepage.
qpcR: an R package for sigmoidal model selection in quantitative real-time polymerase chain reaction analysis.
Christian Ritz and Andrej-Nikolai Spiess
BIOINFORMATICS APPLICATIONS NOTE Vol. 24 no. 13 2008, pages 1549–1551
Summary: The qpcR library is an add-on to the free R statistical environment performing sigmoidal model selection in realtime quantitative polymerase chain reaction (PCR) data analysis. Additionally, the package implements the most commonly used algorithms for real-time PCR data analysis and is capable of extensive statistical comparison for the selection and evaluation of the different models based on several measures of goodness of ﬁt.

Availability: www.dr-spiess.de/qpcR.html.
Supplementary Information: Statistical evaluations of the implemented methods can be found at www.dr-spiess.de under ‘Supplemental Data’.

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